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Dozensonline > The Universal Unit System > The Universal Unit System and its notaions 
Posted by: Takashi Jul 4 2010, 12:10 PM 
Hello, dozenal people. The Universal Unit System is a dozenal unit system proposed in the paper http://dozenal.com. The Universal Unit System uses "the light speed in vacuum","the quantum of action" and "the Boltzmann constant" as the definition constants. These constants are made to become integer powers of 12 of the amount of unit quantities strictly. The Universal Unit System can approximate "the Rydberg constant", "the Bohr radius", "the unified atomic mass unit", "ideal gas constant" and "half the value of the Planck length" in the error about or under 2 pergross of integer powers of 12 of the amount of unit quantities. The Universal Unit System can approximate many other physical constants.  the fine structure constant  electron charge  electron mass  molar volume of ideal gas in the standard atmospheric pressure and the ice melting point  blackbody radiation in the ice melting point  density of water  surface tension of water  the half of specific heat of water  the twice of StephanBoltzmann constant etc. The unit quantities and constant expressions are shown in the table retrievable at http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls. See also http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=9 Please give your opinions about the Universal Unit System and its notation. 
Posted by: Takashi Jul 4 2010, 12:11 PM  
# This is a comment to http://z13.invisionfree.com/DozensOnline/index.php?showtopic=137&st=32 In the paper http://dozenal.com, I proposed Variation 1 and Variation 2A. Variation 2B was proposed in the Dozens Online. After discussion, I newly discovered Variation 2C. When thinking about the situation that the only requirement is the following statement: "The calendar time, which is less than 0.390625 second, shoud be expressed using 0.390625 second as a unit." I think that the system naturally generated may be:  If the unit 'hour' is esteemed, the variation 2A.  If the unit 'hour' is disregarded, the variation 2C. I think that Variation 2C is the best of these variations now.  The influence of Connection Range to human activity is less than Variation 1.  Number of units that the ratio doesn't become the integer multiples of 12(*) is less than that of Variation 2A and 2B. See also http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=5 Please give your opinions.  Variation 1 : This variation is corresponding to the Calendar 1 described in §D.1.1 of http://dozenal.com. Variation 2A : This variation is corresponding to the Calendar 2 described in §D.1.2 of http://dozenal.com. Variation 2B : This variation is proposed by Mr. icarus in the article http://z13.invisionfree.com/DozensOnline/index.php?showtopic=137&st=30. Variation 2C : A new variation [doHTML]

Posted by: Takashi Jul 8 2010, 09:48 AM 
The following descriptions are ideas for discussion about prefix notations of the Universal Unit System.  The symbol of the unit of the Universal Unit System is a symbol that adds the suffix to the symbol of the corresponding SI unit. Because the Universal Unit System is designed that the ratios of some fundamental physical constants and the corresponding unit quantities become integer powers of 12.^8(*), we cannot adopt SI prefixes out of range between 1/12.^3 and 12.^3. * See the last paragraph of §3.3 of the paper http://dozenal.com. [doHTML] ** 'septi' (SEventh Power of Two Inversed) is only for the earth local extension. *** Greek prefix is used to distinguish from 'septi'. SI units are combined only with the decimal figures, and units of the Universal Unit System are combined only with dozenal figures. Therefore, if prefix 'milli' is used with dozenal figures or units, 'milli' expresses 1/12.^3. [doHTML] The part enclosed with '()' can be omitted.  The aboveproposed is an explanation of the prefixes put on the unit. As for how to count the pure numbers, I propose base twelve http://en.wikipedia.org/wiki/yllion replacing 10/ten/hundred with 12/dozen/gross. 
Posted by: Takashi Jul 8 2010, 10:58 AM 
There is such an idea that refers to the paper: H. C. Churchman Doremic System of Measures and Weights in the Duodecimal Bulletin 81;(97.) http://www.dozenal.org/archive/DuodecimalBulletinIssue402web.pdf . [doHTML] * 'si' is not used. 
Posted by: Takashi Jul 10 2010, 06:09 PM 
If the variation 2C is selected, the earth local extension for the Universal Unit System may become a following system: [doHTML]***** A mil(li day) is equal to H. C. Churchman's 'moment'. 
Posted by: Takashi Jul 11 2010, 01:18 AM 
The variations are due to the following intention. [The Variation 2A] 1 day = 2 * 10; hours = (2 * 10;) * (8 * 8) octal minutes (1 day = 2 * 12. hours = (2 * 12.) * (8 * 8) octal minutes) This is a variation that the near unit is used for the present calendar time system as much as possible for quantity. An octal minute is equal to 10;^(1) (12.^(1)) clock, an 'hour' is the same as the present calendar time system and a 'minute' is only 9 pergross(6 and quarter %) smaller than the present calendar time system. [The Variation 2B] 1 day = 2 * 8 octal hours = (2 * 8) * (8 * 10;) octal minutes (1 day = 2 * 8 octal hours = (2 * 8) * (8 * 12.) octal minutes) This is a variation that values the interchangeability of an analog clock. The scale of an analog clock is changed from 110;(112.) into 18, and the speed of the minute hand is adjusted to 2/3. An 'hour' is 1 and half times greater than the variation 2A and a 'minute' is the same as the variation 2A. [The Variation 2C'] 1 day = 10;^3 milli days = 10;^3 * 2^7 septi milli days (1 day = 12.^3 milli days = 12.^3 * 2^7 septi milli days) This is a variation that is intended to maximize the range expressed by multiples of integer powers of twelve of a day. 1; septi milli day is equal to 10;^(2)(12.^(2)) octal minute of the variation 2A and 2B. The ratio of (1; milli day)^(1) and (1; octal minute)^(1) is 9/8, that is, the Major 2nd of just intonation. According to the TitiusBode law, the orbital semimajor axis of planets can be approximated by (3 * 2^N + 4) * c_0 * milli days, where c_0 is the speed of light in vacuum and N=infinity,0,1,2,4,5,6. [doHTML] where Txyz = 2^(x)*10;^(y)*50;^(z) day (= 2^(x)*12.^(y)*60.^(z) day) The ratio of the same column units indicated in boldface cannot be approximated by integer powers of their base number. 
Posted by: Takashi Jul 11 2010, 07:32 AM 
[doHTML]The units of this system are listed in the following table. [doHTML] The physical, material and astronomical constants expressed by means of this system are presented in the following table. [doHTML] See a sheet 'Clock_by_Rydberg' in http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls .  [EDIT] The unit of thermodynamic temperature has been changed. The new unit is one10000;th of the old unit. Quantities are updated using http://physics.nist.gov/cuu/Constants/index.html [EDIT 20120203] The power prefixes are revised. 
Posted by: Takashi Jul 11 2010, 11:44 AM 
The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit) become a following system: [doHTML] [EDIT] The unit of thermodynamic temperature has been changed. The new unit is one10000;th of the old unit. Quantities are updated using http://physics.nist.gov/cuu/Constants/index.html 
Posted by: Takashi Jul 12 2010, 10:52 PM 
The comparison of time units of the Universal Unit Systems [doHTML] 
Posted by: Takashi Jul 13 2010, 01:06 PM 
The point at issue is as follows: Q1> Which Universal Unit System should be selected? ( See http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=8 ) 1. Type I : the Universal System of Units Standard 2. Type II : the Universal Unit System with the GCD Unit 3. Type III : the Harmonized Universal Unit System (with the GCD Unit) 4. Other system Q2> Which calendar time hierachy should be selected? ( See http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=1 ) 1. Variation 1 2. Variation 2A 3. Variation 2B 4. Variation 2C 5. Other variation Q3> Whether is the unit of calendar time and physical time assumed to be another dimension or not? ( See note *** of http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=4 ) 1. assumed to be another dimension 2. assumed to be same dimension Q4> Are the cosmic/atomic prefixes acceptable as prefixes of powers of base number? ( See http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=2 ) 1. acceptable 2. traditional prefixes are better than the cosmic/atomic prefixes 3. Other idea The answer of the paper http://dozenal.com was [Q11, Q21 or 2, Q31, Q4"don't care"]. If this is not acceptable from the viewpoint of human activity, I propose another answer [Q13, Q24, Q31, Q41]. Please show your opinions. 
Posted by: Shaun Jul 14 2010, 08:55 AM 
This, I find, is all going over my head. I still think the hour should be kept. 
Posted by: Takashi Jul 14 2010, 03:17 PM  
The unit of calendar time is the most conservative. French Revolution failed to change the unit of calendar time, too.  If the frequency of the situation in which one hour is divided into three and the situation in which one 'minute' is divided into three are compared, it seems that there are a lot of formers. See also http://z13.invisionfree.com/DozensOnline/index.php?showtopic=26&st=25 and http://z13.invisionfree.com/DozensOnline/index.php?showtopic=26&st=30 . This presumption indicates another variation 2D. [doHTML] The variation 2C' and 2D don't contradict each other. The variation 2C' doesn't need to know whether the unit 'hour' is used or not. '10;hour clock', '20;hour clock', and '1000;mil clock' can coexist as a difference of mere calendar time notations. 
Posted by: Takashi Jul 18 2010, 07:36 AM 
The Universal Unit System uses not pi radian but 2 pi radian as a plain angle unit. This is necesary in order to guarantee the consistency of plane and solid angle. See §3.2.2 of http://dozenal.com . Non coherent supplementary constants (powers of radian) [doHTML] 
Posted by: The Mighty Dozen Jul 18 2010, 03:28 PM  
I don't know if I can back this up with an argument, but I feel as tho perhaps the hour would be the most difficult to get rid of out if it, the minute, and the second. I feel like, for example, if we had 72 or 100 or 64 or whatever seconds to a minute, and that number minutes to the hour, so long as the hour as it is was kept, I don't foresee massive problems. 
Posted by: Takashi Jul 22 2010, 01:54 PM 
Shaun and Bryan, thank you for your opinions. The following calendar time notations can coexist: '10;hour clock' notation > (AMPM)H:MM:SS;ss.. , where 0<= H <10; & 0<= MM < 60; '20;hour clock' notation > HH:MM:SS;ss.. , where 0<= HH <20; & 0<= MM < 60; '1000;mil clock' notation > MMM:SS;ss.. , where 0<= MMM < 1000; Therefore, I think that there is no massive problems, too. [doHTML] 
Posted by: Takashi Jul 22 2010, 01:55 PM 
The symbols of the Universal Unit System are brought together in the quartets. Therefoe, they can be arranged as follows: [doHTML] 
Posted by: icarus Jul 25 2010, 01:40 AM 
This is a response to the alysdexia post in the Number Bases:The Resource Thread. If you've got a fancy system, show me (Missouri motto). The diacriticals and doodads over letters in your post make me suspicious. I used my oldest computer to look, so that it didn't spam out and destroy the good stuff (it didn't, no spam). Your links point to google searches that are posts on some boards that talk about a material hardness scale and such, hmm. (I heard about the Moh scale in school and thought it was strange they used fingernails and diamonds, carborundum as "anchor points", seemed mighty arbitrary for science. Maybe I'm dreamin') I don't need to defend Suga (I might admire the Hagia Sophia, but if you want to burn Istanbul that's the Turks' problem...) if you've got something better, show it. I'm interested. It's easy to tear something down but not so easy to build something. Da Vinci beats Godzilla in my book. You don't like radians, ok (neither do i unless ... I am finding an arc length with s = r * theta, then radians are mighty friendly!). You think there are better fundamentals, what are they? I admire polychora and geometry of higher space, but most folks don't walk around conceptualizing the E8 or the 24cell as a solution to anything everyday or earthly. (although they are wonderfully symmetrical). The problem with higher space is there's too many degrees of freedom. time is length, true, but if man is the measure of all things then that ain't gonna fly in peoria. I do agree man should be the measure. We should find something rational to hang our rulers on, however (am i wrong?). There doesn't seem anything clean cut. non integral bases are about as far from the argument to use man as the measure as considering the di(dimension minus one)angles (analogous to the dihedral angles) as alternatives to the radian. So one side it appears you want tangible, social bases for measure, but then you want advanced considerations for measure. hmm. This is why I use: feet and inches. (and pica). And pounds. And seconds, hours, days, etc. Ok a mishmosh. I manage the twitter account (um not that well. Not exactly prancing round town tweeting my breakfast lunch and brunch) if it loads Suga's page that's because he managed to snag dozenal dot com and we've got dozenal dot org and like a silly human I wrote the former accidentally. apologies my friend. 
Posted by: Ruthe Jul 27 2010, 08:31 PM  
And he measured the wall thereof, an hundred and forty and four cubits, according to the measure of a man, that is, of the angel. Revelation 21,17 While this is just a curious coincidence, I do also believe that measures should be based on man, simply because measures are nothing but a comparison with sizes a man is fully familiar with and used in dealing with his workmates and traders. But they should also be rationalized and based on a single number base, and as we all know, twelve is the most advantageous. Perhaps Jaweh knew something of mathematics! 
Posted by: Cymbyz Jul 28 2010, 02:16 AM 
You can be certain that, whenever you see a dozen or multiples thereof in the Bible, the numbers connote Divine perfection. When you see a mixture of numberbases (e.g., the 120 who were in the upper room at Pentecost in Acts 2), you are seeing a symbol of synergy between God (base 12) and Man (base 10). 
Posted by: Shaun Jul 28 2010, 04:21 PM 
and there's also the "tenheaded beast", isn't there? 
Posted by: Cymbyz Jul 28 2010, 05:37 PM 
Yes. Actually, all sorts of numerological what'sits in the Bible, a minefield to trip up the ardent literalistor even the amateur "decoder." 
Posted by: Takashi Aug 2 2010, 03:34 AM  
I am the same opinion. Better unit systems are welcome. The Universal Unit System is opened for proposals. Within the range where the consistency is not ruined, I want to take better proposals. I wanted to accept better proposals concerning the unit of time. This is the reason that I opened this thread. To maintain the consistency when one item is reviewed, various spreads are generated. Therefore, the variation has increased. I want to arrange the increasing variations and to consolidate them.
I think that we should define phrase 'based on' more strictly to proceed to a discussion. Because this is not a topic limited to the Universal Unit System, my interpretation is written http://s13.invisionfree.com/DozensOnline/index.php?showtopic=361&st=7. I want to discuss topics about requirement for general unit system http://s13.invisionfree.com/DozensOnline/index.php?showtopic=361&st=0, and discuss topics only concerning about the Universal Unit System here. 
Posted by: Takashi Aug 2 2010, 03:35 AM 
The angle is a good example what consideration being done for the consistency. I think that nonrational units (rad,sr) and rational units (Ω1=2pi rad,Ω2=4pi sr) are both necessary. The typical example is shown in Appendix B of http://dozenal.com. Nonrational unit and rational unit are not coherent each other. Therefore, it is necessary to give an independent dimension for angle to use it in one unit system. Unit system users always conscious about which unit is used now. It was necessary to assemble the solid angle with the plane angle in order to avoid unbounded increase in units when considering highdimensional hyperspheres in general. 
Posted by: Takashi Aug 10 2010, 09:24 AM 
This is comment to http://s13.invisionfree.com/DozensOnline/index.php?showtopic=374&st=0 1. h vs ħ http://en.wikipedia.org/wiki/Planck_constant h appears only in shape 'h ν', where ν is frequency. On the other hand, ħ appears directly in the http://en.wikipedia.org/wiki/Canonical_commutation_relation, [X,P] = XP  PX = i ħ, that is basic related to the uncertainty principle. Therefore usage of ħ is not limited to the cycle phenomenon, and ħ is used widely. So I decided that it was more effective to express not h but ħ by the integer power of twelve multiples of unit quantity. See Appendix A Eq.(30) of http://dozenal.com. 2. The characteristic impedance of vacuum The characteristic impedance of vacuum is 29.9792458 Ω/ sr = 376.730 313 461 Ω/ Ω_{2}. Therefore the dimension of electric charge is not dimension of sqrt(energy * time / The characteristic impedance of vacuum). If 376.730 313 461 Ω is used as a unit of impedance, the coefficient of Coulomb force equation contains a facter 1/4pi. The Universal Unit Systsm is devised to enjoy the advantage of the rationalized unit system without remaining the factor 1/4pi. See Appendix B of http://dozenal.com. 
Posted by: Takashi Aug 11 2010, 02:37 AM 
'Harmonized' means that human activity and fundamental physical constant are harmonized. There is a word 'harmonic' that matches 'cosmic' and 'atomic' to the rhyme. Is it natural for native speakers to use 'harmonic' instead of 'harmonized'? 
Posted by: dgoodmaniii Aug 11 2010, 05:40 PM 
Well, at least Takahashi's given us the first real competition against TGM for a coherent dozenal system of units. I think you used LaTeX to produce the paper? Have you seen the dozenal package for producing real dozenal characters rather than the makeshift "A" and "B"? Also, your section on the advantages of the dozenal system was brilliant. I, for one, had never noticed these characteristics of dozenal factorials before; testing them with dozdc it sticks out most obviously, but I never would have noticed had you not pointed it out. Still, I have to ask: why marry the unit system to physical constants that are really quite far removed from the daily quantities that normal people have to deal with? The speed of light in a vacuum, for example; for most purposes that most people encounter, the speed of light might as well be instantaneous. It's certainly not a speed that anyone ever regularly observes or can easily relate to, since it's incredibly fast. And are you familiar with some research and theories indicating that http://en.wikipedia.org/wiki/Variable_speed_of_light? I'm also not sure I understand your explanation of choosing the exponents for determining your base units. You explain it on page 13. Doesn't this meant that there's no 1:1 correspondence between units? Won't that make it unnecessarily difficult for users to combine and separate different unit types in calculations? All in all, the systems strikes me as too abstract. In contrast, the customary and Imperial systems, and the better TGM, is very concrete. This is what I consider one of TGM's greatest strengths: it bases its system on quantities that are realities of our daily lives and with which we daily interact. It's also got a 1:1 correspondence between unit types, which I think is important. By the way, why is the summary of units on page 15 in decimal? It appears to be, at least. 
Posted by: Takashi Aug 14 2010, 07:53 AM 
dgoodmaniii, thank you for your opinion.  I wrote "For putting these coincidences to use, the duodecimal system is the only choice." in Chapter 2 "Why the duodecimal system?" in the paper http://dozenal.com . We can make the standard gravitational accelaration the accelaration unit regardless of decimal unit system or duodecimal unit system. The density of water, the meridian length of the earth, too. On the other hand, the unit system that can use the coincidences of the fundamental constants is only the Universal Unit System that adopted duodecimal system. All decimal unit systems cannot use the coincidences of the fundamental constants. It is only the Universal Unit System that can answer the decimal people's question why must be duodecimal unit system.  There was an arrangement of discussion that we should distinguish conceptual origin of the unit and definition of the unit. I want to replace 'conceptual origin' with 'human scale'. 1. The unit quantity should be human scale. (See also http://s13.invisionfree.com/DozensOnline/index.php?showtopic=361&st=7) 2. The unit defintion should guarantee commonness and reproducibility as much as possible in large range. (See the 2nd paragraph of Chapter 1 of the paper http://dozenal.com .) It is the best choice to use the fundamental constants for the unit definitions for Item 2. Especially, the speed of light in vacuum and the quantum of action are vary common and stable in the largest range in current physics paradigm. At the viewpoint of definition, all proposed unit systems such as SI, imperial, TGM use the speed of light in vacuum. SI : meter = (second/299792458.) * c_0, imperial : foot = 0.3048 meter = (0.3048 second/299792458.) * c_0, TGM : Graft = Tim/*4XE49923; * c_0, where c_0 is the speed of light in vacuum. The fundamental constants themselves and Item 1 don't need to relate. The coincidences of the fundamental constants originally contain factors of integer powers of twelve. (See Section 2.1 of the paper http://dozenal.com ). Therefore, it is natural that the units are defined as integer powers of twelve multiple of the fundamental constants.  I discussed about coherent unit system in Appendix A.3 of the paper http://dozenal.com . The concept of unit coherence is important, but not absolute. A day is noncoherent unit for allmost all proposed unit systems such as SI, TGM, and the Universal Unit System. But we cannot prohibit using a day as a unit. Either radian or degree cannot be prohibited, too. I think that we would rather control than prohibit noncoherent units. It only has to clarify the rule of the usage. In this viewpoint the 1st sentence of Chapter 1 of the paper http://dozenal.com is important.  A unit of measure is "a quantity that is used as the basis for expressing a given quantity,  and is of the same type as the quantity that is to be expressed". I learned this perception through the Japanese translated version of M.L. McGlashan's "Physicochemical Quantities and Units(2nd Edition)"  The Royal Institute of Chemistry(1971).  About factorials see also http://z13.invisionfree.com/DozensOnline/index.php?showtopic=92&st=10. 
Posted by: dgoodmaniii Aug 15 2010, 06:23 AM  
I don't know about that; there are lots of arguments for using the dozenal system for units, many of which are much more convincing than coincidences in fundamental constants in terms of daily applicability. Even the fundamental constant coincidences, while extremely interesting (and I'm glad you uncovered them, as I'd never seen them before), are only approximate, if I'm reading your paper right. Is it more convincing to say, "A dozenal unit system is better because of these relationships between constants which you rarely encounter," or, "A dozenal unit system is better because you can easily get exactly one third of a unit without repeating fractional parts?"
I agree, and it's an important distinction.
Agreed.
Here's where I start to wonder. First, our measurements for these things are constantly getting more refined; will you redefine your humanscale units to match up with these newer, more specifically measured fundamental constants? The difference will, of course, be minute, but it's a valid question. Second, what if these refinements render the coincidences in fundamental constants less coincidental? Finally, why is using these values any more common or reproducible? If SI gets along well enough by defining a meter as the distance travelled by light in a totally arbitrarilychosen period of time (picked really to closely correspond to the length of a platinum bar sitting in a vault somewhere in Paris), does using a fundamental constant really lend any additional stability? Terrible as SI is in its principles and decimal base, it's certainly stable within the limits of even the most fastidious practitioners.
I understand that. But how do you decide which integer power of the dozen to use for the humanscale unit? Is it an arbitrary choice based on the one that comes out approximately the right dimension, in your opinion? Or is there some system to it? The paper didn't make that clear, at least to me.
Agreed. Noncoherent units don't bother me much, as long as the system itself is coherent. But I do find that a 1:1 correspondence of basic units is extremely helpful, and without this I think it's hard to say a system is coherent. As I understand it, you've got 1:1 correspondence with your fundamental constants, but not with the humanscale units, which are set by more or less arbitrary (by which I mean only "chosen without systematic justification; it's not meant as pejorative) integer exponents on those fundamental constants. But it's the humanscale units that will be used the vast majority of the time. So while there's a 1:1 correspondence in the fundamental, base units, there is no such correspondence in the humanscale units. Is this correct? 
Posted by: Takashi Aug 22 2010, 02:24 AM  
dgoodmaniii, Thank you for agreeing to a lot of points.
There is no possibility from the viewpoint of 'reproducibility'. Each fundamental constants used for the definition in the Universal Unit System is, not a measured quantity, but a quantity which measures another quantities of the same dimention with enough reproducibility. But, of course, there is always a possibility from the viewpoint of 'commonness' when a new paradigm shift outside expectation happens. A coming expected paradigm shift changes the conceptual position of the gravitational constant. There is no influence because I have dealt with this by considering in Appendix C of http://dozenal.com .
Fundamental constants that relate to nature scale are shown Table 1. Human scale and cosmic/atomic scale are mainly connected through factor 12.^8. This is important for human recognition to nature scale. Moreover, the units should be human scale as the pivot that connects cosmic scale with atomic scale. [doHTML]
It is not 1:1 correspondence. The number of fundamental constants is more than the number of dimensions of the unit. Therefore, the relation shown in a dimensionless ratio comes out between fundamental constants. See 2.1 of http://dozenal.com and Table 1. Because the consideration of coherency of the unit is described in Appendix A.3 of http://dozenal.com, I don't repeat it. If you worry about coherency, you can limit the units used only to the 16. coherent units of http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15.  base units that are natural units  base units that are not natural units  derived units of dynamical quantities  derived units of electro magnetic quantities This is one of the variations of the Universal Unit System, too. 
Posted by: dgoodmaniii Aug 23 2010, 02:05 PM  
Well, it would be silly not to agree when you're right, which of course you often are.
Right. But when they refine the velocity of light by another few akis (to use TGM nomenclature), this will slightly but truly alter the dimensions that you measure via the velocity of light. (Or rather, more accurately, the accuracy of the dimensions measured with the velocity of light will correspondingly increase, altering however slightly your practical values.) Do you incorporate these into your system or not? Also, wouldn't the truth of http://en.wikipedia.org/wiki/Physical_constant#How_constant_are_the_physical_constants.3F wreak considerable havoc with this system?
Right, I know where they're listed, but they seemed arbitrary; that is, not chosen systematically, but more because they simply produce humansized units that seemed right to you. Am I correct? (Multiples here in decimal, since the entire basic unit table is in decimal.) For example, your distance is 12^8, but your time and energy are 12^16, and your temperature is 12^4. Mass is 12^32, and field strength is 12^8. All of these, minus the outlier of temperature being 12^4, are multiples of 8, it's true; but how did you choose these particular multiples of 8 for these particular units? Was it systematic, or was it arbitrary (in other words, based on your opinion of what would yield easy humansized units)?
I thought it wasn't 1:1, and I think that's a problem. Not having a 1:1 correspondence compels mankind to an eternity of miscalculated exponents and other basic calculation errors for no good reason. TGM is a model here, in my opinion. Once the basic unit, the Tim, is selected, every other unit flows from there with an easy, 1:1 correspondence. So once we have the Tim, we can easily measure the unit of acceleration (1 Gee = 1 unit per Tim per Tim), which yields us the unit of velocity (1 unit per Tim) and length (1 Grafut), and so on. Note that this is *not* an objection to your having noncoherent units in your system; as I said before, I don't really have a problem with that. Human needs are many and varied, and it's impossible for any system to anticipate convenient units for every single one of them. TGM, for example, embraces noncoherent units, such as the tumblol (about halfway between an imperial and a customary pint, equal to 3 _2Vm (three duniVolms), a convenient size for a mug of beer. They are given, as Pendlebury says, on a "take or leave basis." New ones can easily be developed as needed. But that doesn't change the fact that the basic units of the system are all related to one another on a 1:1 basis. It's not the coherency of units actually used that's the problem; it's that there doesn't seem to be coherency in the units underlying them. To elucidate: my theory is that, were TGM to become the common system, most of the time scientists would be using TGM units. The hoi polloi (like myself) would often also use some of these noncoherent derived units, like the tumblol and the galvol. But there's still a set of units available for easy use that are coherent; that is, that have a 1:1 correspondence and are systematically derived from very accurately measured base unit(s). These kind of correspondence greatly facilitates calculations. Your system appears to have no such coherency. Rather, there are multiple base units from which different dimensions are derived, and those base units only correspond to one another approximately by multiples of the dozen. You derive humanscaled units from these base units in a nonsystematic manner. Is that correct? Please note that I'm not trying to be belligerent here; I'm just trying to make sure I understand your system correctly. I had trouble following some of the paper and I want to ensure that I've got the system correct before I form a definite opinion about it. 
Posted by: Takashi Aug 28 2010, 01:32 AM  
dgoodmaniii, Thank you for your comments.
The small change of the gravitational constant doesn't influence the definition of the Universal Unit System as commented http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=28 time. However, it is necessary to delete Plank length from last paragraph of Chapter 1 of http://dozenal.com if there is too big change that corresponds to paradigm shift. The change of the fine structure constant revises the ratio of the elementary electric charge and the unit of electrical charge. But the quantity of unit of electrical charge doesn't change.
I think that the improvement of the measurement precision of space and time indirectly leads to the revision of a dimensionless constant like the fine structure constant. In the paradigm of present physics, time and space are combined into the single spacetime continuum. The conversion coefficient of the space metric and time metric of the spacetime continuum is called 'the speed of light in vacuum'. Therefore, there is no influence on the structure of the Universal Unit System as long as the paradigm shift that urges the revolution of recognition of spacetime continuum doesn't happen.
There is finally very little arbitrariness though it was based on human scale which has arbitrariness. The decision details are explained at the last paragraph of 3.3 of http://dozenal.com.  the speed of light in vacuum : 12^P times velocity unit  elementary electric charge : 12^Q times charge unit  unified atomic mass unit : 12^R times mass unit In the above relations, I selected the factor so that the greatest common divisor of P, Q, and R becomes the maximum. The relation between the quantum of action and the elementary electric charge limits arbitrariness. Equation (11) at 2.1.3 of http://dozenal.com is an important scale factor that means the ratio of typical nuclear energy and chemical energy. This ratio contains factor 12^8, too. When the numbers other than 8 (including 0) are chosen, The structure of http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=28 cannot be made. The unit of thermodynamic temperature was changed along with the introducing of http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=7. The new unit is one10000;th of the old unit.
The quoted topic and the topic of the relation between the units and the fundamental constants are another topics. There is only one 'base' unit for coherency corresponding to each dimension. These base units assemble 'derived' units by using coherency. There are 8 base units as shown in http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15:  base units that are natural units  base units that are not natural units (# It means that 'defining constants' are not 'base' units.) There are 8 named derived units in addition to the abovementioned.  derived units of dynamical quantities  derived units of electro magnetic quantities These derived units are automatically coherent according to the definition of word 'derived'. All coherent named units are covered by these. 
Posted by: Takashi Sep 4 2010, 10:24 AM  
I quote http://dozenal.com as a supplementation. Reproducibility Each fundamental constant used for the definition in the Universal Unit System is, not a measured quantity, but a quantity which measures another quantities of the same dimention. Therefore we will find the improvement of reproducibility by reviewing dimensionless ratios descrived in Chapter 2.1 of http://dozenal.com. The definition of the Universal Unit System is
We have already acquired reproducibility enough to guarantee that these approximations are possible. Therefore, it will not result in the revision of the definition even if reproducibility will improve in the future. Appendix E of http://dozenal.com is for reference only. Table of constants is not part of the Universal System of Units Standard. Commonness I descrived the concept of 'paradigm shift' in the paragraph
The great transformation of concept ruins commonness of the corresponding definition constant. Such paradigm shift has the possibility of resulting in the revision of the definition of the Universal Unit System. 
Posted by: Takashi Sep 6 2010, 09:29 AM  
If there is no comment, I will change 'harmonized' to 'harmonic'. 
Posted by: Takashi Sep 20 2010, 02:27 AM 
This is a supplementation about the arbitrariness of the decision of the integer power of twelve for base units. (the last paragraph of 3.3 of http://dozenal.com) (1) the speed of light in vacuum : 12.^P * velocity unit (2) elementary electric charge : 12.^Q * charge unit (3) unified atomic mass unit : 12.^R * mass unit if we put P=n,Q=2n, and R=3n based on the nature of the quantities, then length unit = 12.^(16. + 2n) * universal meter time unit = 12.^(24. + 3n) * universal second mass unit = 12.^(24. + 3n) * universal gram It is only case n=8 that all units become human scale. There is arbitrariness that originates in the definition of human scale. Then, I shelve human scale once, and pay attention to other constants. (4) Typical nuclear energy : 1 * 12.^8 * typical chemical energy (+) _(+) descrived by Equation (11) at 2.1.3 of http://dozenal.com. (5) Age of the universe : 6 * 12.^(+40.  3n) * time unit (6) Planck time : 2 * 12.^(16.  3n) * time unit The ratio of (5) and (6) is 3 * 12.^(7*8) regardless of the value of n. In order to use these all relations (1)(6), n should be an integer multiple of 8: length unit = 12.^(16.*x) * universal meter time unit = 12.^(24.*x) * universal second mass unit = 12.^(24.*x) * universal gram It is only the decision to adopt human scale that we need to determine the quantities of the base units. 
Posted by: LukeJr Mar 10 2011, 02:19 AM 
I can't comprehend this unit specification at all. Can someone put it in simple terms, perhaps similar to Nystrom's Tonal unit definitions? 1. What are the names of the basic units for measurement, weights, temperatures, etc, and what are their imperial/metric equivalents? Why were these values chosen? 2. What are the prefixes/suffixes used to denote larger or smaller amounts of these units? For example, SI has mega, kilo, hecto, deca, centi, milli, micro, nano, while Tonal has bong, mill, san, ton. 
Posted by: Takashi Mar 12 2011, 01:22 AM  
LukeJr, I thank for your having been interested in the Universal Unit System.
See chapter 2.1 and appendix D.1 of http://dozenal.com .
See the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=6 of this thread and 'Clock_by_Rydberg' sheet of http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls .
See the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15 of this thread . As commented in the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=32 of this thread, I changed the word 'hermonized' to 'hermonic' in order to match end rhyme with 'atomic' and 'cosmic'. Please substitute 'hermonized' into 'hermonic' in the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=6 and http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15 of this thread. 
Posted by: LukeJr Mar 12 2011, 01:50 AM  
I guess there are good reasons? I can't really make any sense out of this site.
I'm afraid this still seems too complicated. How many SI or (even better) US/imperial units are each of the new ones?
The first through third exponents seem sensible enough, but then it jumps immediately to 8th exponent? How would one handle 1,000,000 units of whatever? And since cosmic/atomic lack abbreviations(?), one has to write out the full word? What is larger/smaller than cosmic/atomic? After all, a cosmic byte (no new data unit?) would only be equivalent to 430 MB... 
Posted by: Takashi Mar 21 2011, 10:59 AM  
See the last paragraph of chapter 3.3 of http://dozenal.com/ and http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=30,http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=33 of this thread .
See the second table of http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=6 of this thread and prefix column of 'Clock_by_Rydberg' sheet of http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls .
See chapter 4 and the last 2 paragraphs of chapter 3.5 of http://dozenal.com/ .
There are not abbreviations, but http://www.asahinet.or.jp/~dd6tsg/univunite/prefixsample.jpg. I am making a summary now. 
Posted by: Takashi Apr 1 2011, 11:23 AM 
The more a quantity leaves human scale, the less the use frequency of the quantity expression becomes. It is natural that the length of expression is in inverse proportion to frequency for which the corresponding concept is used. Therefore, I think that the abbreviation of 'atomic' and 'cosmic' is unnecessary. Rather I want to express 'dodeci meter' and 'octal century' by shorter words. I want suggestion of native speakers. 
Posted by: LukeJr Apr 1 2011, 02:03 PM 
Please explain how one would easily write 1,000,000,000,000,000; bytes, or even 1,000,000,000,000. 
Posted by: Takashi Apr 2 2011, 10:34 PM 
LukeJr, You can derive the expressions easily if you read the documents which I referred in an article http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=37 of this thread. Please answer by yourself. 
Posted by: Takashi Apr 5 2011, 10:11 PM  
'octal century' = 64 year  half of the Least Common Multiple (LCM) of the length of a day and a tropical year  two times human generation approximately Is there a word to apply to them? The word that an initial is H or S is better. 'dodeci meter' = 2.27 cm  The unit corresponding to inch Probably high use frequency. 
Posted by: Takashi May 13 2011, 01:45 AM 
I refined the table of http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15 of this thread. Please show http://www.asahinet.or.jp/~dd6tsg/univunite/units.pdf and http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf .  <edited May 29 2011, 02:00 PM > tables.pdf has been added. <edited June 5 2011, 05:00 AM > tables.pdf is updated using http://physics.nist.gov/cuu/Constants/index.html 
Posted by: Takashi May 21 2011, 09:49 AM  
Does the word 'Span' apply to the above unit? Is it too abstract when we omit 'life' of 'life Span'? 
Posted by: Takashi Jun 14 2011, 12:46 PM 
LukeJr, I reflected discussions of this thread and revised documents of http://dozenal.com. Please read revised document retrievable at http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf 
Posted by: Takashi Jun 15 2011, 01:43 PM 
How do the constants and the units that the TGM system uses for definitions turn out in the Universal Unit System? I made the following list. [doHTML]The numerical value of above list is all decimal and the factors of powers of twelve are ignored. 
Posted by: Takashi Jun 24 2011, 09:17 AM  
I tried to summarize the policy of the Universal Unit System naming rule. 1.Policy of the naming of the unit terms
2.Policy of the symbol definition

Posted by: Takashi Jun 27 2011, 02:53 PM 
This is a follow up article of http://z13.invisionfree.com/DozensOnline/index.php?showtopic=411&st=3 The mass of nucleon of aluminium is approximately equal to one triatomic universal gram(1 g_{3u}). The mass of nucleon of iron (=The lightest nucleon) is approximately equal to one triatomic harmonic gram(1 g_{3h}). The mass density of H_{2}O is approximately 109; g_{h}/m_{h}^{3} (water:109; g_{h}/m_{h}^{3}, ice:E8; g_{h}/m_{h}^{3}) The molar mass of H_{2}O is approximately 16; g_{h}/mol_{u} Therefore, The molar density of H_{2}O is approximately (109; g_{h}/m_{h}^{3}) / (16; g_{h}/mol_{u}) = 8;6 mol_{u}/m_{h}^{3} It means that the molar density of H_{2}O is approximately 8;6 H_{2}O / m_{h}^{3} = 1;09 H_{2}O / (m_{h}/2)^{3} In other words, a cube of one side of half atomic meter(= 6 times Bohr radius) includes about one H_{2}O molecule.  (1/2) m_{h} * (1/2) m_{h} * (3/4) m_{h} is equal to one U.S. liquid gallon. 
Posted by: Takashi Jul 10 2011, 06:18 AM 
I put http://hosi.org/cgibin/conv.cgi to a Web server. It is not yet tested enough.  [Edit] New physical quantities are supported. A configuration page is added. The collective conversion to plural units is implemented. The Tonal System is added. Mixed radix format for date and time is supported. 
Posted by: icarus Jul 10 2011, 11:51 AM 
Takashi, it's a little technical but works nicely! 
Posted by: Takashi Jul 11 2011, 04:10 PM  
Please point out refinements. 
Posted by: Takashi Jul 19 2011, 12:35 PM 
http://hosi.org/cgibin/conv.cgi has been revised. The followings are some conversion samples.  http://hosi.org/cgibin/conv.cgi?c=Config  http://hosi.org/cgibin/conv.cgi?d=Length&tu=1&c=Convert  http://hosi.org/cgibin/conv.cgi?d=Date&fq=20110719&fu=1&tu=2&c=Convert  http://hosi.org/cgibin/conv.cgi?&d=Time&fq=15:15:25&fu=8&tu=7&c=Convert  http://hosi.org/cgibin/conv.cgi?&d=Time&fq=365.2421875&fu=10&tu=1&tm=on&c=Convert  http://hosi.org/cgibin/conv.cgi?m=0020&d=Sound&fq=90.0000000&fu=5&tu=4&fl=4&tl=6&c=Convert 
Posted by: Takashi Jul 29 2011, 04:04 AM 
Mr. Pendlebury's Brite scale (the last page of the http://www.dozenalsociety.org.uk/pdfs/TGMbooklet.pdf) seems to harmonize with the Universal Unit System. [doHTML] The photon scale is based on the fact that a 540MHz photon's energy is approximately 1 biatomic Joule. 
Posted by: Takashi Sep 19 2011, 06:12 AM 
There are some reasons why the Universal Unit System assumes not 12^12 but 12^8 a prefix interval. (1) 12^8 is led naturally by relations between fundamental constants as I explained http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=30. Mass and amount of substance are three dimensional quantities. Therefore, an atomic scale mass unit should be triple atomic quantity of human scale mass unit, and an atomic scale amount of substance unit should be triple atomic quantity of human scale amount of substance unit. An atomic scale mass unit has to be an atomic mass unit, and an atomic scale amount of substance unit has to be reciprocal Avogadro constant. These relations require that an atomic factor cannot help becoming not 12^12 but 12^8. (2) 12^4 is a upper limit as for the ratio of quantities that a human being can feel intuitionally. The human being can grasp numbers only countable in a work day or a night intuitively. (Example: step counts per day, number of sheep to count at a night) We cannot but grasp the further numbers logarithmically. Therefore I gave quantities to become the base points and designed to express all quantities between the upper and lower 12^4 of these base points. The interval between these base points becomes bigger, the expression becomes more intuitive. This is because situation using the same base point becomes frequent. We come to recognize these base points as XX scale. (such as cosmic scale, atomic scale, ..) Example: It is easy to recognize the relations of atomic km and atomic dm if used to harmonic km and harmonic dm. However, we cannot adopt 12^12 as the base point interval because 12^6 exceeds the limit that we can grasp intuitively. (3) 12^8 and http://en.wikipedia.org/wiki/Knuth_yllion have high affinity.  http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf 2.2.2 explains derived units with special names and symbols. Without the special reason including the influence on health of the human body, The SI did not give new special names to derived units. It is expensive to add new words to common vocabulary. Because the new words disturb the spread, I designed the Universal Unit System to add new words as few as possible. In addition, I reused the words that there had been already in common vocabulary based on the commonality of the meaning. (such as 1000ness) But I designed the prefix system so that slight difference in expression did not bring big difference in content. Therefore, I adopted entirely different words in 12^3 and 12^3. Unfortunately because there is no single word with 10000ness except 'myriad' in common vocabulary, I cannot give single word expressions to 12^4 and 12^4. Expression of 12^4 is longer than expression of 12^8. This is a left problem.  First Paragraphs are edited 20111127 
Posted by: Takashi Nov 6 2011, 10:04 PM 
I intend to use http://en.wikipedia.org/wiki/Knuth_yllion to express pure numbers with the universal unit system. The table shown below explains how the myriad system will be modified for duodecimal system. [doHTML] We find "centy" and "milly" in the last part of this table. It means that we give "centy" a meaning of 12^{2} and "milly" a meaning of 12^{3}. If we adopt these words, 12^{2} will have two different expressions with "centy" and "centi" in same duodecimal context, because "centi" is used for power prefix. 12^{3}, too. This is not desirable. So, I revised power prefixes to accord with the myriad system. http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf ( http://dozenal.com/ ) 
Posted by: Kodegadulo Nov 6 2011, 11:09 PM 
Is there any difference in pronunciation between, for instance, "million" and "myllion"? 
Posted by: Takashi Nov 7 2011, 12:22 PM 
Please click the table shown above. 
Posted by: Takashi Nov 7 2011, 12:23 PM 
The SI units definition will be changed. There does not seem to be the influence on the Universal Unit System. http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf takes note of the intention of the International Committee for Weights and Measures to propose a revision of the SI as follows: • the International System of Units, the SI, will be the system of units in which: • the ground state hyperfine splitting frequency of the caesium 133 atom ąË(^{133}Cs)_{hfs} is exactly 9 192 631 770 hertz, • the speed of light in vacuum c is exactly 299 792 458 metre per second, • the Planck constant h is exactly 6.626 06X ~10^{34} joule second, • the elementary charge e is exactly 1.602 17X ~10^{19} coulomb, • the Boltzmann constant k is exactly 1.380 6X ~10^{23} joule per kelvin, • the Avogadro constant N_{A} is exactly 6.022 14X ~10^{23} reciprocal mole, • the luminous efficacy K_{cd} of monochromatic radiation of frequency 540 ~10^{12} Hz is exactly 683 lumen per watt, <snip> (ii) the symbol X in this Draft Resolution represents one or more additional digits to be added to the numerical values of h, e, k, and N_{A}, using values based on the most recent CODATA adjustment 
Posted by: Kodegadulo Nov 7 2011, 02:04 PM  
When I click on it, my Webroot security software blocks it as a suspicious site. However, I just noticed the caption at the bottom of the image indicating that the "y" has a long /aɪ/ sound rather than a short /ɪ/ sound. This is odd, because if the myllion system is based on myriad /'mɪ.rɪ.əd/ the "y" in the latter has a short /ɪ/ sound. 
Posted by: Kodegadulo Nov 7 2011, 02:10 PM  
What symbol did you mean to write there? 
Posted by: Takashi Nov 8 2011, 03:48 AM 
y seems to be pronounced like mile to distinguish y from i in verbal communication. Please see http://www.google.co.jp/search?hl=ja&q=myllion+pronounce&nfpr=1. Anyway I am thankful if you suggest better pure number name system or unit prefix system, which can be used with http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf of http://dozenal.com/ and, which adapts to the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=46 and http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=53. 
Posted by: Takashi Nov 8 2011, 03:50 AM 
The time unit 'second' will not be changed. ąË(^{133}Cs)_{hfs} means 'the ground state hyperfine splitting frequency of the caesium 133 atom'. 
Posted by: Kodegadulo Nov 8 2011, 05:12 AM  
I understand what (^{133}Cs)_{hfs} means. But there are what seem to be garbage characters just before that:  script f  cent mark  script f  capital E umlaut It seems obvious you didn't intend those characters. I have seen my own posts get corrupted with similar characters when I use special symbols sometimes. So once again, what was the actual symbol you meant there? 
Posted by: Takashi Nov 8 2011, 09:39 AM 
Please see page.2 of http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf 
Posted by: Kodegadulo Nov 8 2011, 12:07 PM  
So then it's captialdelta nu: Δν 
Posted by: Takashi Nov 13 2011, 08:06 AM 
The attention point of agreed revision is that an elementary electric charge becomes the definition constant.  the elementary charge e is exactly 1.602 17X x 10^{19} coulomb This means that the permittivity of vacuum turns into measured quantity. The fine structure constant and the permittivity of vacuum become to link strictly each other. The electromagnetic interaction observed at the macroscopic distance is the renormalized result of interaction between naked electric charge effect and quantum vacuum effect. The fine structure constant may fluctuate by the change of the quantum vacuum in terms of time. Strictly speaking, the following 1) is different from 2) as a concept each other. 1) The quantity of cahrge causing the electromagnetic interaction 2) The number of charges as the quantity of preservation of the quantum mechanics The old definition uses 1), and the new definition uses 2). For example, the quantity which we use for design of motor is 1) but 2). In my opinion, the old definition is more appropriate and we should have treated 2) as kind of 'amount of substance'. # The SI notes "when the mole is used, the elementary entities must be specified and may be # atoms, molecules, ions, electrons, other particles, or specified groups of such particles." 
Posted by: Takashi Nov 17 2011, 01:38 PM 
I minimized the kind of words which have to be added to common vocabulary. The added words are listed in the following table: [doHTML] 
Posted by: Takashi Nov 27 2011, 06:24 AM 
1) In English common vocabulary, the words to express digits are the following 9 or 10 words: 'zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine' On the other hand, the words for positional representation are the following 5 words within daily used range from 1 to 10^12: 'ten', 'hundred', 'thousand', 'million', 'billion' There are more former kinds than latter kinds. Such a phenomenon is not limited to only English. This is a result optimized by the following policies after longtime real use:  Relatively important concepts are discriminated from each other more finely and named more finely.  Relatively non important concepts are discriminated from each other more coarsely and named more coarsely. 2) In English common vocabulary, the words for positional representation of duodecimal numbering system already exist: dozen : 12 gross : 12^2 great gross : 12^3 and some dictionaries describe great gross as dozen gross. It means that we can already express pure numbers smaller than 12^4 using duodecimal numbering system.  The duodecimal myriad system is almost only numbering system which is comprised of a simple rule to satisfy policies 1), and which is connectable to system 2) at the lower limit. I think that it is not accidental but Dr. Knuth's design that the myriad system satisfies polies 1). People (including myself thirty years ago) who assign single word for 12^11 are rare and special people feeling importance of the same degree in 11 and 12^11. Such a feeling is a feeling only for the people who have a special interest in numbers and quantities. There is not the situation using the big number such as 12^11 for daily use if we use appropriate units. I think that this feeling is far apart from the feeling of common people. 
Posted by: icarus Nov 27 2011, 12:50 PM 
On page 87 of Dr. Anton Glaser's History of Binary and Other Nondecimal Numeration, Hermann Hankel is described as having evaluated number bases for their economy of concepts in 1874. He considered the number of concepts required to express a given number up to a certain power of the base, and decided base four was the most economical. This seems a silly and unimportant measure of "best base" because humanity assigns hundreds of concepts even to relatively inconsequential notions such as popular culture and fantasy. Surely, being spare with counting concepts is simply being intellectually miserly. This might not have much to do with Takashi's post, but that is what I am left thinking about with the first part of the most recent post. The concepts you are describing are names for "numeral" and "rank", according to my recollection of Karl Menninger's Number Words and Number Symbols. He describes numeral and rank at great length across cultures (but mostly across European cultures). Georges Ifrah also has a book but I've read a lot of discrediting for it. Perhaps only some parts of it are not solid. He too compares numeral and rank (doesn't use those terms necessarily) across cultures. Truly English does have an inchoate system of duodecimal nomenclature, and Knuth's extension and several others that are related do well in connecting the lower range to upper ranges that become necessary for nomenclature in a system of measure that has a full range of concepts. The great thing about accessing this lowerrange extant duodecimal nomenclature is that we engage an alreadyintelligible nomenclature and minimize what people need to know to use duodecimal numeration in everyday life. Other naming schemes may be more attractive, but most people are already equipped to understand duodecimal numbers up to just under the duodecimal 4th power. This represents the predominance of everyday use for most people. (Technical people easily exceed that). We can say there were four dozen six (or four and a half dozen) at last week's parish breakfast, rather than "about fifty" or "fiftyfour". We can say Saturn has five dozen one moons, or Chicago is one gross ten dozen nine miles from St. Louis. English has more or less common words for some uncials: one sixth, one quarter, one third, one half, two thirds, three quarters, five sixths, and well understood words for divisors of the gross: one eighth, one sixteenth, etc. It needs help below the radix point as well as above the 4th power. The significance of the eleventh power of any number (except perhaps those divisible by eleven) would seem rather low. Eleven is the fifth prime. From observations of the "real world", elevenness seems pretty rarely encountered. Because the naming convention for powers of the base often are modular, beginning with names for the lowest powers that are used everyday, we tend not to have singleword names for the eleventh power. There will be x names, with x being a small integer easily retained in memory. So we might have three, four, or six names. This isn't true in other cultures, perhaps only a western manifestation. Then compounds can be used to produce names for larger numbers. Pendlebury and Kodegadulo both have produced names for rank that operate like a second set of numeral names. This is effective because we then have standard nomenclature for a relatively large range of number. In English, we have standard names up to the hundred million, then differences arise at "billionmilliard", and in the American lexicon, the common person can understand up to "hundred trillion" even if the person might not grasp the correct magnitude of the number (most would think "very very big number" if presented by such). "Quadrillion" isn't yet a concept in the common vocabulary (believe me, the American government is working on it! We don't yet have debt that large!) when we need access to large ranks and want a short word that can be "prefixed" we turn to kilo/mega/giga/tera/peta, with the latter two not quite as well known. Most people haven't heard of exa and above. 
Posted by: m1n1f1g Nov 27 2011, 09:12 PM 
The great benefit of the Pendleburystyle rank names is that they are very easy to use. Just count the digits, take away one and turn that number into the corresponding name. This is easier than long scale, where division by six is needed, as well as short scale, which requires researching to be sure of large numbers  unless you are willing to sound like Brian Cox, for which division by nine is needed. The myriad scale is similarly hard to use as the long or Cox scales. It requires a knowledge of binary powers that we are not easily familiar with. Is 28′ = 2^{5} or 2^{6}? As a programmer, I've bothered learning them, but a lot of people haven't. It's a reasonable and logical suggestion, but so is binary. Also, the myriad system suffers from the short scale problem: "byllion" is not 'bi'anything. 
Posted by: Takashi Dec 3 2011, 11:15 PM 
For putting coincidence of fundamental physical constants to use, the duodecimal number system is the only choice. I do not know any other proposal except the Universal Unit System which can uniquely specify duodecimal number system. An approach such as follows may be good to have common 'decimal' people accept duodecimal number system.  http://en.wikipedia.org/wiki/Planck_units is a natural unit system to consider to be G=c_{0}=ħ=k_{B}=Z_{P}=1. We exchange G with 35G and can constitute a Universal Unit System which defines 35G, c_{0}, ħ, k_{B} and Z_{P} as units for each dimension. We call this variaton of the Universal Unit System 'http://www.asahinet.or.jp/~dd6tsg/univunite/gravitic.pdf'. When we use the gravitic Universal Unit System, the gravitational equation is expressed by the following formula: [doHTML] The values of constants in this unit system become like the following list. [doHTML] If the universe will be over in the time of the 12^{56} units, it is beautiful, but probably will not become so.  Of course the gravitic Universal Unit System is not a practical unit system because precision of G is insufficient. Therefore, the gravitic Universal Unit System does not take the position of the harmonic Universal Unit System.  See also http://en.wikipedia.org/wiki/Talk:Planck_units#Other_possible_normalizations 
Posted by: Takashi Dec 4 2011, 02:03 AM 
uncia: Google finds about 234,000 results for "great gross", about 1,110,000 results for "uncia". How common is the word 'uncia'? Because I'm not native English speaker, I do not know well. I didn't choose 'uncia' as 12ness word in http://www.asahinet.or.jp/~dd6tsg/univunite/myriadd.pdf because I want to make an initial of 12ness word 'd'. hundred trillion: Hundred trillion is nearly equal to dozen myriadd myllion. With the small number like this, common people will not be conscious of the binariness of the myriad system. Units of the gravitic Universal Unit System are examples of non appropriate units. In this case we will be conscious of octalness of the myriad system in scientific field. The exponential notation of the Bohr radius will be '1;00*M^{2@6}' gravitic meter and read 'one point zero zero times myllion to the power two point six gravitic meter'. (';' is duodecimal radix point and '@' is octal radix point.) 
Posted by: Leopold Plumtree Dec 4 2011, 06:29 AM  
It's not very common at all. Other than on the internet, I don't think I've ever encountered anyone using it. I doubt more than a tiny minority realize (or care) it's the etymological origin of inch and ounce. 
Posted by: m1n1f1g Dec 4 2011, 09:10 AM 
"uncia uncia" is the scientific name for the snow leopard, so that might add to the popularity. I have only heard of the word "uncia" on this board; it is certainly not a common word. 
Posted by: dgoodmaniii Dec 4 2011, 01:27 PM  
I agree that "uncia" is quite rare, but "great gross" is rarer. I've at least used "uncia" when studying Latin; I'd never heard anyone use "great gross" until I became a dozenalist, and even dozenalists don't commonly use it. 
Posted by: Kodegadulo Dec 4 2011, 04:07 PM  
It's precisely because uncia is a Latin word, and not an English one, that it makes such a good dozenalmetric prefix, as the centerpiece of http://z13.invisionfree.com/DozensOnline/index.php?showtopic=463&view=findpost&p=4133414. People have come to expect metriclike prefixes to be Greek or Latin based, given their experience with the SI prefixes. But for a possible dozenal English 1000⁞, take a look at http://z13.invisionfree.com/DozensOnline/index.php?showtopic=506&view=findpost&p=4138747 I just made. 
Posted by: Takashi Dec 10 2011, 02:39 AM 
Thank you for all comments. I want the candidate of prefix for 12^{1} to meet the following conditions: 1. The initial character of the candidate is 'd'. 2. The meaning of the candidate has 12ness. 3. The candidate is an English word derived from Latin. uncia: 1. Initial 'u' is confused with 'µ'. The abbreviation of 'pound' is 'lb' which is derived from Roman libra. Generally, is the mismatch of the abbreviation and the spelling permitted? 2. OK. 3. 'uncia' seems to be a Latin word rather than an English word. dozen: 1. OK. 2. OK. 3. 'dozen' is not a word derived from Latin. I could not find any word which satisfies all conditions. At the present I choose 'dozen' rather than 'uncia'. 
Posted by: Takashi Dec 10 2011, 03:15 AM 
If the Newtonian constant of gravitation is according to http://www.vmigip.com/Law_of_Gravitation_in_11_Dimensions.pdf, the Planck force(F_{P}) and energy momentum tensor(T_{ik}) are as follows: [doHTML] where, μ is the proton and electron mass ratio 1.0626*12^{3}. See also http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf about the other constants. μ^{9}/α^{11} = 1.0011*12^{49} !! In the gravitic Universal Unit System, it means that [doHTML] is almost exactly 1/12. [doHTML] shows that the gravitic Universal Unit System approximates this ratio as 35. 
Posted by: icarus Dec 10 2011, 11:26 AM  
The word "dozen" comes to English from French "douzaine", which is derived from the French number "douze" = 12. This must be derived from the Latin "duodecim" = 12. So perhaps English "dozen" is indirectly Latin. 
Posted by: Takashi Dec 10 2011, 11:46 AM 
Thank you icarus. After all 'dozen' is OK. 
Posted by: Takashi Dec 10 2011, 11:49 AM 
I describe how to use symbols with the Universal Unit Systems. [doHTML] Whether context is decimal or duodecimal is indicated by radix point or unit kind. SI units are combined only with the decimal figures (indicated by a periodg.h as radix point), and units of the Universal Unit Systems are combined only with duodecimal figures (indicated by a semicolong;h as radix point). '.' and ',' exchange their roles each other in some countries. Therefore any digit group separator should not be used without radix point. 
Posted by: uaxuctum Dec 10 2011, 04:46 PM  
That word myllion is a completely uninspired, laughable proposal. If it hadn't happened to have been uttered by a renowned IT scientist, I doubt anybody would have taken it seriously. Choosing a differentlyspelled (*) but homophonous word in an attempt to differentiate meaning must be the pinnacle of absurdity (iff vs. if is another such absurdity). Trying to introduce a phonetic distinction afterthefact where there was not meant to be one (and where it cannot be one in other languages without the "long I" vs. "short I" particularity of English) is a poor amendment of a poor idea. Million is an augmentative (suffix on(e)) derived from mille (Latin and Italian for "thousand"); i.e., it literally means "a big thousand", and this is plain obvious to speakers of Romance languages (though it seems not so much so to Englishspeakers like Mr. Knuth). The sane analogous derivative from myriad is something along the lines of myriadon or (simplified) myrion. (As a side note, milliard is, of course, also a derivative from mille, in this case using a pejorative suffix ard of Germanic origin, thus meaning something like "a d*mned [big] thousand". The analogous form from myriad would be myriadard or (simplified) myriard.) (*) Differently spelled in some languages with an archaicizing, etymologizing spelling such as English. But such a fancy spelling is not readily transferrable into many others such as Spanish in which million and myllion are to be rendered exactly the same (millón) in both spelling and pronunciation. 
Posted by: Kodegadulo Dec 10 2011, 05:08 PM 
You might want to consider using http://z13.invisionfree.com/DozensOnline/index.php?showtopic=463&view=findpost&p=4133414 with UUS. It provides a set of dozenal metric prefixes firmly grounded on classical Greek and Latin roots and even features the Latin uncia, with its ancient meaning of "one twelfth", as a deliberate accident. Although it has been presented as a substitute for Pendlebury's prefix system, for use with his TGM units, it's not at all limited to that; it is suitable for use with any metrological system. By the way, SDN was designed to ensure all the prefixes are pronounced distinctly from each other and to be distinct from any previouslyexisting numeric combination forms. 
Posted by: Takashi Dec 10 2011, 11:55 PM 
I think that the Universal Unit System is not my porposal but public proposal, and the essential part of the system is not unit naming, number counting and prefix system but its unit quantities. So, it is available that the Universal Unit System combines with another unit naming, number counting and prefix system, such as SDN or Mr. Pendlebury's system. 
Posted by: Takashi Dec 10 2011, 11:57 PM  
How we do not change system is more important than how we change system.  Strong limitation results unique solution  Learn from the optimization of the present system  Easy to be accepted Better proposals are welcomed. 
Posted by: Takashi Dec 11 2011, 03:23 AM 
A proposal such as follows is possible when we refer to the SDN. (See also http://en.wikipedia.org/wiki/Number_prefix . ) number counting: 12^{4}  semillion 12^{8}  unillion 12^{16}  dullion # Latin cardinal 12^{32}  terllion # Latin multiple Because we have nothing to do with daily life upper 10^{15}, it will not be necessary to distinguish duodecimal context from decimal context after this. prefix: 12^{1}  uncia 12^{2}  ducia 12^{3}  tercia There are three problems.  'uncia' is not popular.  Initial letters are different from SI's.  The correspondency between 12^{1}12^{3} and 12^{1}12^{3} fails. 
Posted by: Takashi Dec 18 2011, 06:38 AM  
It is not suitable. For example, five hundred thousand meters and five handred kilometers are the same length. However, most people will choose the expression of five handred (500) kilometers.
People choose a unit to become the range that they can express quantities with a recognizable number intuitively. We can express all distance on the earth with a recognizable number intuitively if we choose kilometer as a length unit. When the forms of prefixes are similar to cardinal numbers, we cannot make use of this advantage.
The forms of important prefixes should be totally different from cardinal numbers and each other. The current metric system uses the following terms:[doHTML] Terms in the upper rows are more important. In the same rows, more leftsided terms are more important. When we emphasize the words which have totally different forms each other, we can understand that the current metric system is optimized well. 
Posted by: Takashi Dec 18 2011, 08:55 AM 
Google finds about 59,400,000 results for "myriad", about 47,300 results for "one myriad". It seems that "myriad" is not used for number counting in daily use. If this is true, we can indicate duodecimal context without omitting "one" by combining it with "myriad" (not "myriadd"). There are fewer changes: [doHTML] 
Posted by: m1n1f1g Dec 18 2011, 11:00 AM  
That's a different discussion, I would post it on something SDNrelated. The SDN, as well as the myriad system, are as suitable for UUS as they are for TGM. If you believe that the SDN is unsuitable for the UUS, it is also unsuitable for TGM. Your criticism reflects this. I would write a counterargument, but this is not the place for it. 
Posted by: Takashi Dec 18 2011, 12:23 PM  
Yes. I think the SDN and the TGM prefix system are not suitable for the TGM unit system. Please link the place if you write a counterargument. 
Posted by: m1n1f1g Dec 18 2011, 05:00 PM 
Probably, http://z13.invisionfree.com/DozensOnline/index.php?showtopic=463&view=findpost&p=4135557 is the best post on the topic, especially that last, wide table. In short, only a few cardinal numbers need to be the same as the prefixes, and the choice is based on digit grouping. Using a similar example to you, 500′ ^{3}m_{h} (written in a UUSmeetsTGM style) would be said as "five gross harmonic triquametres". 5000′ ^{3}m_{h}, on the other hand, would probably spill over to be "five harmonic hexuametres". Surely that's still satisfactory. Besides, it gives the sense of a "higher magnitude". Well, it looks like I've written the argument here! 
Posted by: dgoodmaniii Dec 18 2011, 07:48 PM  
In my experience, people don't think of a "myriad" as meaning a particular number. It's a bit like "zillion" in that it's used to mean "I'm not really sure precisely how many, but it's a whole lot." I think it would be quite difficult to get people accustomed to using "myriad" to mean a particular number instead of "tons and tons." 
Posted by: Kodegadulo Dec 18 2011, 07:58 PM  
This may be a rule you have specified for your UUS system, and it may be convenient if this condition were met within a given native language, but I dispute that this is any sort of universal requirement that must apply to all usages of metricstyle systems in all human languages.
You incorrectly describe micro and nano as being of Latin origin. They actually come from Greek. The Greek word μικρός (micrós) means "small"; νάνος (nános) means "dwarf". More importantly, and with all due respect, this whole table exhibits a curious and unnecessary Anglocentrism. This is odd coming from someone whose first language is not English. I can cite at least one language, in current use, in which the SI/metric prefixes (or rather, their translations) violate this rule of yours. That language is, in fact, Modern Greek: [doHTML] Except for minor differences in declension, native Greek and Greek metric use precisely the same words. So what makes this rule so important? 
Posted by: dgoodmaniii Dec 18 2011, 07:58 PM  
Despite all the hoopla with people saying, "Metric is easier; just move the decimal point!", I don't think most people really understand exponents. That's why we see things like "0.053 kilometers" on science shows; because they were using kilometers before so they use them again, even though "53 meters" is a much easier thing to say there, and doesn't confuse the issue at all. (I've noticed this happen even when they're not trying to compare scales with something in kilometers, when it's even less justifiable.) That's also why certain SI prefixes, like "hecta" and "deka," or even "deci," are practically never used, even though sometimes they're almost certainly the best choice (human height, for example, should be given in decimeters; but for some reason it's always given in centimeters): because while people understand it when they sit down and think about it, they don't really intuitively grasp the concept of exponentiation, or how to manipulate exponents. Having a consistent set of exponential prefixes, like SDN or Pendlebury, will make it much easier for people to internalize exponentiation. Having done this, fiddling with exponents won't be the exclusive domain of geeks and mathematicians (am I redundant?) anymore; it will be something that people do as it's convenient. This is another benefit that SDN would produce. 
Posted by: Kodegadulo Dec 19 2011, 08:53 PM  
The only condition that I see as necessary is 2. I see no rational purpose in conditions 1 and 3. Condition 1 is a crippling restriction that eliminates 25· out of 26· letters in the English language. Why do you require that? Wouldn't it be better to use any letter other than "d" so that the dozenalmetric prefix for 12·^{1} is distinguished from 10·^{1} (deci)? Wouldn't that avoid confusion? Condition 3 seems like an oxymoron to me: Isn't the whole point that converting to the dozenal system requires us to invent new words that do not already exist in English? Doesn't the "myriad/myllion" system invent an entire bestiary of new words that did not already exist in English?
Of course not! Why would you expect to? Since we need to enhance English anyway, what is wrong with borrowing words such as "uncia" from Latin? Why do you require an "English word derived from Latin"? That description implies that sometime in the past a Latin word was incorporated into English and became accepted as an English word. But again, the whole point is we don't already have enough such words to express dozenal numbers. So why do you think it unsuitable to use exactly the same mechanism today, to do a fresh borrowing from Latin and accept a new word into English? And why only Latin? Wouldn't Greek borrowings be acceptable as well?
So what? It is not necessary to use "u" as a metriclike prefix abbreviation for "uncia". Pendlebury's system of numeric subscripts/superscripts is adequate: harmonic unciameter = _{1}m_{h}. unciaGrafut = _{1}Gf. Besides, nobody should be using "u" as an abbreviation for "micro" anyway. With today's fonts, it should be easy enough to write an actual Greek mu "”"  as you yourself did!  or use the alternative "mc" (e.g. microgram = mcg).
But "dozen" does not mean 12·^{1}, it means 12·^{1}. I suppose you must mean "one dozenth". But how would we use that as a metriclike prefix? Would _{1}m_{h} be a "harmonic dozenthmeter"? 
Posted by: dgoodmaniii Dec 19 2011, 09:58 PM  
I agree with most of your posting, but I did pause a bit at this. Using "u" for "”" is a pretty common practice whenever we're limited by sevenbit characters, which is actually still surprisingly often. I know tgmconv using "u" as the abbreviation for "micro," and I think it's a legitimate way to keep it monoliteral (onelettered; that's a word I just made up, out of mixed LatinGreek borrowings!) while still differentiated from "milli." I don't think that creates any confusion, though; the "u" would only mean "micro" when attached to metric units, not when attached to the units of a dozenal system, where "micro" (decimal 10^{6}) is meaningful but frightfully inconvenient. So while I agree with you that the confusion between "u" and "”" should not be a concern, I disagree that "u" isn't a perfectly fine substitute for "”" when the occasion calls for it. That is, though, the problem with alphabetic prefixes for what's essentially a numeric issue, as you also pointed out: it's introducing a new complication where none is necessary. Why do we need "milli" and friends when we're doing mathematics and not talking about it? What's wrong with just using the exponent, which is what we're talking about anyway, and which bears no potential for ambiguity? The raised and lowered exponents aren't just adequate; they're far superior. 
Posted by: Kodegadulo Dec 19 2011, 11:25 PM  
Agreed. Although with a caveat: The capability to superscript/subscript may not be available in every environment. This should be accommodated with some workaround (just as you accommodate 7bit ASCII environments by substituting "u" for "”"), but I'm not entirely satisfied with the notations I've seen for that. I don't think it will work for instance to substitute 1^Gf for ^{1}Gf (unquaGrafut), since the caret ^ is usually interpreted as a power operator with the term on the right as the exponent, not the term on the left. Perhaps the letter "q" should be used instead, as an abbreviation for SDN's positive power marker "qua". This would yield unquaGrafut = ^{1}Gf = 1qGf. And "c" could stand for SDN's negative power marker "cia". This would yield unciaGrafut = _{1}Gf = 1cGf. Getting back to UUS: Takashi, please reconsider the requirements you have selected for a dozenal counting and/or prefix system. You seem to be under the impression that dozenal counting and/or prefixes must immitate the structure of nativelanguage decimal counting and/or the decimalmetric prefix system. But I see no a priori reason for this. Decimal counting and decimal metric prefixes embody a number of unnecessary flaws and complexities, that they acquired simply because of the fact that they were not constructed rationally (or constructed based on flawed rationales). Why should we slavishly mimic these flaws and complexities in devising a dozenalmetric prefix system? We have to create something new anyway, why not start fresh? Why not, as dgiii points out, make dozenalmetric prefixes more directly represent what we are trying to express with them: that they are powers of 12· raised to specific exponents? Why not directly represent those exponents as words? (Those words can be derived from Latin and Greek.) And why not distinguish the whole prefix as being a power of twelve, by giving it a distinctive marking syllable? This is the rationale behind SDN. This rationale yields a powerful and extensible yet simple system that makes it easier to express and comprehend orders of magnitude. 
Posted by: m1n1f1g Dec 20 2011, 12:02 PM  
That's a good idea, put it on the SDN thread. 
Posted by: Takashi Dec 23 2011, 12:00 AM 
It seems that people in this forum don't discuss about system for common people but discuss about intellectual game. Let's write it once again: How we do not change system is more important than how we change system.  Strong limitation results unique solution.  Learn from the optimization of the present system.  Easy to be accepted (for common people). 
Posted by: Takashi Dec 23 2011, 12:01 AM 
[doHTML] The ratio 8:9 corresponds to the major tone of the just intonation. This is the origin of the name of the Harmonic Universal Unit System. 4:9 = (2:3)^{2}. The ratio 2:3 corresponds to the perfect five of the just intonation.  [Edit] nautical league is added. 
Posted by: m1n1f1g Dec 23 2011, 12:51 AM  
I'm starting to see good sense in using the UUS for quite a lot of scientific purposes. It can be defined consistently and well. The TGM suffers from the silly "ten times the polar diameter of the Earth" definition for the Grafut. However, incorporating G can make TGM very helpful in terrestrial situations. I shall think more about it. 
Posted by: icarus Dec 23 2011, 01:30 AM 
Takashi & m1n1f1g, the very existence of UUS is the only reason I haven't invented a system of my own, and why any other system proposal (to me) is nearly trivial. Now my problem is the profusion of flavors of UUS (or what seems to be a profusion of flavors). The profusion of flavors is confusing, and I am not comfortable with overmuch change in a system I think is well conceived in the first place. If I were to invent a system (and I think I did using codata in the 90s) it would be based on fundamental constants just as UUS). The great thing about Takashi's work is how it situates the selection of duodecimal numeration based on the near coincidences of fundamental and mathematical constants with simple powers and multiples of the dozen. Having read this, I fell in love. What powerful rationale! I think kode's SDN is likewise well thought out, and should UUS use SDN, it would be an even stronger concept. This is a case of "do indeed cross the streams" (sorry takashi, Ghostbusters reference!) Now the obstacle is using the system. My daily work has me laying out digital models of the built environment. I am working in two locations. I use the following modules: 4 inches (8 inches / 2) horizontal and 8/3 inches (8 inches / 3) vertical. These are American common masonry modules. My work is rapid and effective, based on the modules that the world (where I work) uses. So how do I rectify this with a system based on fundamental constants? Note that I'd have this problem with grafeet. Now, back to my 4" x 8/3" virtual world...One project due 4, the other 6 January...gotta step on the gas... 
Posted by: dgoodmaniii Dec 23 2011, 01:17 PM  
Takashi, you really should be able to defend your opinions without insulting those of others. Just because Kode doesn't agree with your criteria doesn't mean that he's an elitist playing intellectual games.
That's not the definition of the Grafut; the Grafut is the distance gained by an object accelerating by a standard gravity per Tim squared. The ten times the polar diameter of the Earth is just how we select what the standard gravity will be, within the narrow limits permitted by the variation of gravity on the Earth's surface. Really, this refinement is moot, because the Grafut's been standardized by the speed of light anyway. I've always liked UUS for the way it reveals the dozenal harmonies of the fundamental constants. I've never liked it like TGM, though, for actual use in the majority of situations. 
Posted by: bluzarro Dec 23 2011, 02:13 PM  
I agree with you on the beauty of dozenal relations in UUS. It sounds to me like you might have some anecdotal experience to share? If so, I would like to hear your comparisons between the two majority metrics on this board. Perhaps a new post. There has got to be a more dozenal name for "metrics"... must ponder. 
Posted by: Kodegadulo Dec 23 2011, 06:35 PM  
I am new to UUS, and honestly haven't digested it enough to be able to form a fair opinion about it one way or another. I think I understand the principles Takashi is attempting to satisfy. The question is whether his work actually satisfies those principles. Thus I have asked questions of Takashi, to see if he can elaborate on it in depth. But he has been at it a long time (30 years?), so perhaps he is just tired of defending his ideas. The table of dozenal coincidences certainly are intriguing. However, given the factorability of the number twelve it's not hard to find useful coincidences, no matter what basis you start with. Indeed, TGM exploits such useful coincidences: For instance, the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=463&view=findpost&p=4135674 are remarkably close to Imperial and US volume units. At this point, my reaction to UUS is much like my reaction has been to TGM at times: I am not compelled by the surface aspect it presents. The "myriad" system leaves me nonplussed. Examples such as "decy" meaning 12[dohtml]^{1} and "septi" meaning 2^{7} just strike me as ridiculous, especially if these are supposed to appeal to the "common man" as somehow "familiar" and "intuitive". A "universal meter" and "harmonic meter" that are both closer to a customary foot than to an SI meter, seem misplaced. But I recognize that these are superficial considerations. UUS's foundation on universal constants is what's essential. It may be possible to clothe UUS with a different surface without disturbing the essence. But Takashi appears to have rejected this suggestion out of hand. 
Posted by: dgoodmaniii Dec 24 2011, 04:21 PM  
Anecdotally, I've found TGM to be incredibly convenient and useful in actual use, and I think the fact that the original TGM booklet, along with my updated version, are littered with useful coincidences and nearcorrespondences to both imperial/customary and SI metric measures shows this. As for UUS, I've expressed my concerns about it on this board many times, most of which have been met with insistence that I've never read the UUS booklet. However, mostly my objections are thus: 1.) It's too abstract. It's great to be based on universal constants, but it's not something that people can really get behind. I don't know about you, but I just don't have any visceral, everyday relation to the gravitational constant. I do, on the other hand, have a very intimate relation to the actual, normal pull of gravity. I think that this basis in everyday, humanscaled realities makes TGM more intuitively useful, and more related to the experience of everyday, common people, than UUS. That, in my opinion, is what's wrong with all the "abstract" metric systems, including SI. A datum like the circumference of the earth is an abstract concept that doesn't relate much, if at all, to the daily experiences of mankind. Things like the mass and density of our most common and important liquid, the pressure of the atmosphere around us, the pull of gravity at the earth's surface, are quite contrarily constantly present and felt phenomena that every human being experiences and closely knows. 2.) The universal constants probably aren't. CODATA has updated their values of these constants many times since UUS was first derived, and most likely will again. TGM has most of these constants as auxiliary units, and thus can absorb the changes in these things without any change in its core units. Not so with UUS, where changing the value of a constant changes the whole basis of the system. Also, Dirac's "changing constants" theory is starting to look more and more like it's probably true, at least in part. The LHC has been challenging so many of our fundamental assumptions about the nature of the universeincluding whether constants like the fine structure constant and the speed of light are really the hardandfast values that we've thought they werethat basing a metric system on those constants seems premature to me. Rather like the original French metric system, trying to base itself on the circumference of the earth when it really wasn't possible to accurately measure that circumference. In sum, while UUS has the potential to be quite useful scientifically, I think it's much too abstract to be useful otherwise; while TGM is concrete enough to be useful to the average man, but still consistent and rigorous enough to be useful scientifically. The best of both worlds. I think, and have always thought, that UUS is a fascinating exploration of the coincidences of dozenalism in the relations of the universal constants. The fact that I don't like it as a metric system doesn't detract from that. 
Posted by: Dan Dec 24 2011, 05:53 PM  
I think the intent of the metric system was to have a decimalized nautical mile. Instead of 1 nautical mile = 1/60 of a degree, you'd have 1 km = 1/100 of a gradian. But the gradian never gained the popularity that the degree did. 
Posted by: m1n1f1g Dec 24 2011, 10:41 PM 
Not that I'm arguing one way or another, but TGM is not exempt from constant changes. It still has a "speed of light" definition, as do most systems. But of course the UUS uses more constants, so is more likely to change. 
Posted by: Takashi Dec 24 2011, 11:28 PM 
Because I do not catch up with an English argument, it seems to be made late comments. I upload what I wrote first of all.  There are four indications that comment need. <y is silly as English.> It seems to remain in stupidity of the degree that a famous scholar can suggest the system. <Only English is considered.> It is only U.K. and U.S. that Dozenal Socity exists. The most important point is success in English language. Other languages can handle new words as words of foreign origin. <We design a system for all people.> probably, it differs from the purpose and becomes the system designed for nobody. For example, (to have been already pointed out;) such as follows have problems. '5 gross trina meters' is 12^{6} times of '5 gross trini meters'. The system producing such a difference by one vowel is very inconvenient in practical use. We can express '5 gross trina meters' with '5 dozen quedra meters'. This flexibility causes confusion of the communication. The interval of big prefixes must be sparse. (I think that the use of the prefixes in the range of 12^{3}..12^{3} should be limited.) The convenience of the sender of the information is made much of, and the convenience of the addressee of the information is considered to be contempt adversely. The mertic system designers considered the balance of the convenience of addressees and senders, and designed the metric system so that problems such as the above do not happen. It is important to learn experience of the metric system. (The metric system is designed for all people, too.) <It is convenient when we make acceleration of gravity of the earth a unit.> The experience of my trial and error shows the following simple fact: The acceleration of gravity of the earth is too big for the unit system of the human scale. Please see also error column of http://www.asahinet.or.jp/~dd6tsg/univunite/harmonic.pdf.  I do not think that my suggestion is the best. It is an alternative suggestion that I want. (Especialy to 12^{1} prefix) 
Posted by: Takashi Dec 24 2011, 11:32 PM 
Because I do not catch up with an English argument, it seems to be made late comments. I upload what I wrote first of all.  There are four indications that comment need. <y is silly as English.> It seems to remain in stupidity of the degree that a famous scholar can suggest the system. <Only English is considered.> It is only U.K. and U.S. that Dozenal Socity exists. The most important point is success in English language. Other languages can handle new words as words of foreign origin. <We design a system for all people.> Probably, it differs from the purpose and becomes the system designed for nobody. For example, (to have been already pointed out;) such as follows have problems. '5 gross trina meters' is 12^{6} times of '5 gross trini meters'. The system producing such a difference by one vowel is very inconvenient in practical use. We can express '5 gross trina meters' with '5 dozen quedra meters'. This flexibility causes confusion of the communication. The interval of big prefixes must be sparse. (I think that the use of the prefixes in the range of 12^{3}..12^{3} should be limited.) The convenience of the sender of the information is made much of, and the convenience of the addressee of the information is considered to be contempt adversely. The mertic system designers considered the balance of the convenience of addressees and senders, and designed the metric system so that problems such as the above do not happen. It is important to learn experience of the metric system. (The metric system is designed for all people, too.) <It is convenient when we make acceleration of gravity of the earth a unit.> The experience of my trial and error shows the following simple fact: The acceleration of gravity of the earth is too big for the unit system of the human scale. Please see also error column of http://www.asahinet.or.jp/~dd6tsg/univunite/harmonic.pdf.  I do not think that my suggestion is the best. It is an alternative suggestion that I want. (Especialy to 12^{1} prefix) 
Posted by: Kodegadulo Dec 25 2011, 02:52 AM  
This kind of argument is a wellknown rhetorical fallacy called "appeal to authority." "Scholar" is too broad a term. Donald Knuth is a brilliant scholar of computer science. But that does not guarantee he is a brilliant scholar of linguistics. The "myllion" system is a very lame idea. In English, the letter "y" is often pronounced exactly like "i" in the same contexts. When an Englishspeaker sees "myllion" for the first time, the natural tendency is to assume it is pronounced exactly like "million", just with an odd, nonstandard spelling. One must be told to violate one's natural tendency, and force oneself to pronounce it with the long "i" sound instead. The result is awkward, and frankly sounds silly (at least, to me).
Haven't we heard from someone in Latin America talking about Spanishlanguage dozenalism? I myself am an advocate for dozenalism in Esperanto, of all things! ;)
A better solution would be to create a system of prefixes derived from Latin/Greek, achieving the same level of "seriousness" as the metric prefixes (but not necessarily exactly imitating them!) This is the intent of SDN. Even if we initially focus on creating English versions of these prefixes, the assumption is that any other language could derive its own versions from the same Latin/Greek roots, adapting them to its own morphology.
I agree with this  but you are talking about Pendlebury's prefix system. I (and others) have made this criticism even stronger than you have made it: Not only does Pendlebury make the only difference between the positive and negative powers a single vowel, but that vowel appears in a nonstressed syllable, which in English tends to be pronounced as a schwa sound (/[dohtml]/) no matter what the vowel is. You must exert an unnatural effort to force one of the prefixes to have a different pronunciation. SDN was designed so that it would not suffer this deficiency. In fact, this problem with Pendlebury's prefixes was the initial motivation for developing SDN! In SDN, the equivalent example would be: 5 gross triquameters is 10[dohtml]^{6} times 5 gross triciameters These prefixes bear quite distinct differences in consonant sounds, not affected by whether the syllables are stressed or not.
You appear to adhere to the philosophy: "Anything that is not mandatory must be forbidden." And the converse: "Anything not forbidden is mandatory." Just because we are given the ability to do something does not mean that we are required to do it! If, in the interest of clarity of communication, you wish to limit yourself to use only every third power prefix, and to advocate that others limit themselves to those as well, that is perfectly acceptable. But even if we limit ourselves to every third power, what is wrong with naming those powers by their exponents? Why not give those powers names that essentially mean "thirdpower", "sixthpower", "ninthpower", "twelfthpower", etc.? (I.e. "triqua", "hexqua", "ennqua", "unnilqua", etc.). What is the purpose behind exponents (or rather, logarithms) in mathematics? Isn't it that they make it easier to deal with orders of magnitude, by transforming them into simple integers? Wouldn't it be easier for someone to produce the name for a large order of magnitude, if all they need to know is the number of zeroes following the one, and simply express that number as part of the name? How does something like the "myriad/myllion" system make it easier to deal with large orders of magnitude? Doesn't it, in fact, make large orders of magnitude very complex and unwieldy, because of all the levels of nesting? Now, suppose someone disagreed that 3 is the best number to use for grouping dozenal digits. What if they had a strong preference for 4 instead? SDN allows for this. Such people can limit their communications to using every fourth power of twelve: e.g. "quadqua", "octua", "unnilqua", "unquadqua", etc.) But it is easy to translate between the 4digit convention and the 3digit convention: Almost as easy as saying 4 = 3+1. "quadqua" = "triqua" * 10[dohtml]
None of the arguments that I've been presenting in this thread are intended to disparage or show contempt to anyone. I don't think I've expressed them in a way that even implies any disrespect to anyone.
I totally disagree with this! Right now, I will express my utter contempt and disrespect for certain people: the designers of the metric system! And I'm not even going to imply my contempt, I'm going to state it directly: They were radical overintellectual Frenchrevolutionary paperpushers and bureaucrats without a shred of common sense, who completely disregarded every practical experience with actual daytoday measurement during their era. The system they constructed was not designed to be useful and convenient for the common man, but to be useful and convenient for paperpushers and bureaucrats like themselves! And, in order to shove their system down the throats of the common man, they needed to exert the full force of law, with the threat of the guillotine to back them up! I mean, they're the same "geniuses" who tried to foist decimal clocks on the world! That being said, I do not wish you to think that I mean you any disrespect because you have a higher opinion of the metric founders than I do. But I believe you are mistaken about them, and should reconsider.
What do you judge this on? The use of the TGM Gee unit for acceleration leads to a Vlos unit for velocity that fits most humanscale speeds within 1 or 2 digits. It also leads to a Gravfoot unit for length that is quite close to a customary foot. The cubic Gravfoot, or Volm, is somewhat large compared to a gallon or a liter, but within 1 to 3 digits to the right of the dozenal point we get quite convenient units: The unciaVolm is right between an Imperial and U.S. halfgallon. The triciaVolm is almost exactly a tablespoon. The use of the density of water and the Volm leads to a Maz unit for mass that is somewhat large compared to a pound or a kilogram. However, masses humans encounter daytoday fit within 1 to 3 digits to the left or right of the dozenal point. A quarter Maz is very close to a British stone. A stone is also a largish unit yet the British don't seem to have any trouble using it. Most importantly, the use of the Gee for unit acceleration makes it trivial to convert between mass and weight (at least, within the Earthlocal environment).
So, why not take a look at SDN, where the exponent is expressed directly with a Latin or Greek root? For example, 10[dohtml]^{1} = uncia, where un = one, cia = negative power. 
Posted by: dgoodmaniii Dec 25 2011, 05:56 AM  
I must admit this threw me, as well. The only unit that seems a bit large is the Maz, and even there its dozenal subdivisions are quite convenient humanly speaking. Others are welldocumented enough that they need not be repeated here. 
Posted by: icarus Dec 25 2011, 09:04 PM  
Ah the gradian, where 30 degrees, one half of the equilateral angle, is 33.3333333333333 . here the metric wonks weren't simply fighting tradition, as metric is a modernist idea; they were at odds with geometry! Here decimal extremists (as my buddy kode and I both take the French revolutionary thinkers that produced the systeme internationale, like many forms of modernism a harsh abstraction of the world based on limited human knowledge at a small instant of history) slammed into the wall, along with decimal time. Dividing the day into ten hours is just silly. Now before we go too darn far, I used to punch in and get decimal hours to the nearest tenth: "8.1 hours" at my teenage job. I always thought about that weird way of recording time. Turns out that the original system neatly accommodates silly overdecimalism: 8.1 hours is exactly 8:06 minutes. So the elder system, "flawed" because it isn't entirely decimal, can represent anything the new system presents to the nearest tenth as an integral number of minutes. But the new shiny modernist system can't precisely and succinctly render 8:20 or 8:10. We're stuck with 8.3 or 8.2 instead. Of course at $3.35 an hour, it doesn't much matter now does it? All this said, I think those involved at crafting the Jules Vernian attempt at a metric system did their best. It's just that there was a better way, and they even knew it! I blame LaGrange. Where they truly presented plans that were truly cumbersome, those plans never made it. That is why they had to eat the second as a unit of time, and why gradians succumbed, and radians are used. But the average bloke in the field doesn't care about the relationship of angle to circumference (unless involved with circles); so we have degrees as a strong, non canonical unit. "Park at a 45 degree angle" the sign says at the local park, not "park at a quarterpi radian angle". What do you suppose we'd get if the sign said the latter? The aluminum curtain wall catalog I looked at on Thursday says "135degree extrusion" and not "3/4pi radian extrusion", though here if they used tau and said "3/8round extrusion" architects may more intuitively picture the item. So clearly implementation of the metric system has a scientific and a common use. Science uses radians and steradians; the average person uses degrees and doesn't know and normally won't understand what a steradian is or why one would ever need to use it. I think there can be a scientific UUS with the CODATAbased units, and a commonuse system with units for everyday use. (same is true with TGM, though many of these units are already humanscale). So now I am going to make the equivalent of 8 inches my basis, have it cover an average size worksite, and use ;6 unit horizontally, ;4 vertically. 
Posted by: m1n1f1g Dec 26 2011, 03:17 PM  
I sort of see what you mean, that the Tim is rather short, but for us down here on Earth, it is very useful. Water is also rather dense, but it should help us to realise how much so if we have it in our unit system. Most liquids are roughly the same density as water, so it makes it really easy to convert volume into mass. Their inconvenient sizes happen to give great benefits to the common man. 
Posted by: dgoodmaniii Dec 26 2011, 04:22 PM  
The Tim's a bit short, but since the fiveminute block is an exact multiple, and we wind up with interim multiples at very convenient sizes, I don't think this is a problem; indeed, as m1n1f1g notes, it's very useful, particularly since it makes other units, like the Grafut, the Vlos, and the Gee such convenient sizes. The only real inconvenience from this I can see is the Maz; but again, it's not *that* big, and its twelfth is quite convenient for daily purposes, only about twice the size of a kilogram, and about four and a quarter the size of a pound. E.g., a fifth of an unciaMaz is about a pound, and half an unciaMaz is about a kilogram. Personally, buying a fifth of an unciaMaz of apples doesn't seem any more inconvenient to me than buying a pound of apples; though I'd expect them to be sold in sixths, rather than fifths, making a bit over a 3/4 of a pound each. (I suppose metric people, used to buying in kilograms, would prefer half unciaMaz to sixths; or do you all buy in halfkilograms?) Either way, there are plenty of easy and convenient humanscaled sizes from the Maz. I'm not sure why you'd say density was a bit high; the Denz is virtually identical to the g/cm^{3}, after all. (Or kg/dm^{3}.) It's certainly high when compared to that of the gases, but not when compared to liquid and solid elements. In any case, water being the most common liquid in our lives by far, it seems like the only reasonable choice for a basis for density anyway. 
Posted by: Takashi Dec 29 2011, 02:26 AM 
< y > I intend that the Latin and Greek numeral last vowel of which is changed into 'y' shows duodecimal system context. I feel this rule same kind of operation as making 'unqua' from 'uncia'. Originally the prefix consonant of 'quinque' was 'p' as well as Greek. It was dragged in 'q' behind. However, nobody will say Romans to be silly. Do you feel the nuance of the dialect? like..  The rain in Spain falls mainly on the plain.  I go to the lake today. (to die?!...) < metric system founders > I don't have a higher opinion to metric system founders. Their porposal includes both the success and the failure. As icarus pointed it out, the decimal time unit system was refused. But the other system was accepted widely. It is this fact that is important. The maintenance policy of current metric system is rational policy supported by the experience of over 200 years. Please read the http://www.bipm.org/en/si/si_brochure/general.html, http://dozenal.com/ and a book which http://www.amazon.com/dp/B001PK7DPE. < the decimal time unit system > The reason why the decimal time unit system was refused is not a problem only for its articulacy. Calendar time units are the most conservative units. Easiness of the conversion between both is necessary for the shifts from the old system to the new system.  What time of the new system is 5 o'clock of the old system?  What time of the old system is 3 o'clock of the new system? Without computers, nobody can answer these questions. Probably I think that the system shift that any (equal or greater than ten minutes order) conversion needs is impossible. There is difference in the degree, but the TGM has the same problem, too. 
Posted by: Takashi Dec 29 2011, 02:28 AM 
In current proposal, 'milly' means that: (adjective) : 12^{3} (noun) : 50 seconds # Abbreviation of 'milly day' Thus, the follows are natural, too. 'dour' means that: (adjective) : 12^{1} (noun) : 2 hours # Abbreviation of 'dour day' 1. The initial character of the candidate is 'd'. 2. The meaning of the candidate has 12^{1}ness. 3. The DSA uses 'dour' as a doublehour meaning. 
Posted by: Takashi Jan 2 2012, 12:34 AM  
The TGM system seems to be suitable for scientific and technological use rather than for daily use.
It is necessary that the unit system to use by daily life expresses amount to grasp intuitionally. On the other hand, we do not mind the unit system to use in science and technology if we can express amount logarithmically. I take up follows as an example of daily expression. [A] A soccer game consists of two halves of forty five minutes. (decimal expression) [B] A soccer game consists of two halves of four dozen six millies. (the Universal Unit System) [C] A soccer game consists of two halves of nine trinaTim. (the TGM system) 'nine trina' means 9×12^{3}. This is an exponential notation. Because the TGM uses the same words for number counting and unit prefix, we are forced to logarithmically grasp a number which is in the range recognizable intuitively.  The difference between expression of [A](45.) and [B](46;) is up to less than two minutes at degree of additinal time. In contrast, [C] is the expression that is totally different in the order of ten minutes. Calendar time units are the most conservative units. I think it is impossible that the daily use system shift between calendar time systems whose expresion for the order of ten minutes is totally different. 
Posted by: Takashi Jan 2 2012, 01:41 AM 
To give a concept a name is to hide the structure of the concept in a black box. When we want to prevent us from being conscious of the structure of a concept by communication, we name the concept. Unit prefixes are this example. On the contrary, we must not name a concept when we use the structure of the concept by communication. The naming policy for derived units is this example. 
Posted by: dgoodmaniii Jan 2 2012, 02:12 AM  
[D] A soccer game consists of two halves of 0;9 hours. (TGM) [E] A soccer game consists of two halves of nine blocks (nine unciaHour). (TGM) [F] A soccer game consists of two halves of nine dozen tocks (nine dozen biciaHour). (TGM) That's the thing about TGM; it's easily adaptable, do the rational procession of prefixes and the convenient sizes of its primary units, to use in this way. Whatever multiple of the base unit, or indeed of auxiliary units (as here, with its use of hours, unciaHours (which we've nicknamed "blocks"), and biciaHours (which we've nicknamed "tocks")), is most convenient can be easily used. 
Posted by: Kodegadulo Jan 2 2012, 03:08 AM 
[G] A soccer game consists of two halves, each lasting three quarters (3/4) of an Hour. [H] A soccer game consists of two halves, each lasting 3 quadrantaHours [using SDN divisor prefix]. [I] A soccer game consists of two halves, each lasting 3 quadrantaquadquaTim [using SDN divisor and power prefixes with TGM unit]. [J] A soccer game consists of two halves, each lasting 1 trinaquadrantaHour [using SDN multiplier and divisor prefixes]. [K] A soccer game consists of two halves, each 1 trinaquadrantaquadquaTim [using SDN multiplier, divisor, and power prefixes, with TGM unit. Use whichever combination suits you. (Caveat: The divisor form derived from the multiplier form with nta modifier is currently just a proposal. It might be replaced with something else if someone can devise a compelling alternative.) 
Posted by: Shaun Jan 2 2012, 12:16 PM 
I'll stick to "threequarters", thank you. 
Posted by: dgoodmaniii Jan 2 2012, 04:13 PM  
Works great! It's funny how when we're thinking up all the different ways to express a given quantity I miss the most obvious. "0;9 hours" comes close, but "three quarters" is so much more intuitive and easier I wonder why I skipped it. Fortunately Kode got it for [G]. 
Posted by: Takashi Jan 3 2012, 12:02 AM  
Recently I added the fourth notation to http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf. The added notation is usable for shift from the o'clock system to the do'clock system. 24. o'clock notation  15:15. 20; o'clock notation  13:16; 10; dour notation  threequarter(46;) to 8^{th} dour [EDIT] [doHTML] 
Posted by: Takashi Jan 6 2012, 09:49 PM 
[doHTML] The ratio 8:9 corresponds to the major tone of the just intonation. This is the origin of the name of the Harmonic Universal Unit System. 4:9 = (2:3)^{2}. The ratio 2:3 corresponds to the perfect five of the just intonation.  [20120129, 20120204] Some ratios are added. [20120412] second > nic 
Posted by: Takashi Mar 10 2012, 07:12 AM 
A nautical mile is the meridian arc length corresponding to one arc minute. 1 sub circle = 12^{4} circle = 25/24 arc minute. Therefore, 1 meridian sub circle = 25/24 nautical mile, where meridian = total meridian length of the Earth / 2π radian as defined in the Earth local extention. http://hosi.org/cgibin/conv.cgi?m=0000&d=0&fq=2.0000000&frq=12&fe=1&fu=12&tu=29&fp=4&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert 
Posted by: Takashi Mar 20 2012, 06:17 AM 
Any prefix of the Universal Unit System without unit part is treated as a noun form. The noun form means the abbreviation of the corresponding plain angle unit prefixed to one circle. This rule prevents that the noun form is treated as any unit other than unit of plain angle. 
Posted by: Takashi Mar 21 2012, 12:33 PM 
http://www.asahinet.or.jp/~dd6tsg/univunite/e23.pdf is the reason why the Universal Unit System uses the characteristic impedance of vacuum for derivation of electric magnetic units. Please see Appendix B of http://dozenal.com . [EDIT] Units with special names and symbols should be comprised of six quartets. Therefore, the characteristic impedance of vacuum must be a natural base unit. 
Posted by: Takashi Apr 5 2012, 07:18 AM 
The natural time scale can be expressed using powers of twelve in the following figure: [doHTML] 
Posted by: Takashi Apr 26 2012, 04:47 AM 
* Definition category (1) conceptual definition Definition that prescribes the rough quantity of the units to constitute a unit system conceptually [SI]: A rotation period of the Earth, the full length of the meridian of the Earth, mass of the water of the unit volume, etc. [The Universal Unit System]: Speed of light in a vacuum, size of a typical atom(Bohr radius), mass of a typical atom(carbon twelve), etc. (2) strict definition Definition that corresponds strictly to the theoretical equations that a unit system is based on [SI]: Definition of the electric current based on the force between the electric current in two wires. [The Universal Unit System]: the Rydberg constant The relation between the Rydberg constant, the Bohr radius, electron mass and the Bohr magneton can be defined strictly if the fine strucrue constant is strictly determined. We can exclude quantities, which need measurement, except the fine structure constant from some theoretical equations if we use the Rydberg constant for strict definition. (3) practical definition Definition in use that secures stability and reproducibility of the unit In many cases, we just use a strict definition as a practical definition, but there are exceptions, too. [SI]: Quantum standards Volt  based on the Josephson constant Ohm  based on the von Klitzing constant These quantum standards become strict definition, when SI uses the elementary charge as the definition of electrical charge by future revision. [The Universal Unit System]: To express a physical time unit in SI seconds is equivalent to using frequency of cesium as practical definition.  * Usage situation (1) daily use Calendar time, length, mass, temperature, area, volume, and plane angle Units and prefixes which are in human scale (2) scientific use All units and prefixes (3) common use All daily use and important scientific use including physical time and electromagnetic units 
Posted by: Takashi Apr 26 2012, 04:54 AM 
We can summarize the element of the Universal Unit System for common use. All these are comprised of quartets.  * General rules (1) Special names Special names same as corresponding SI units prefixed with 'universal' or 'harmonic' are used. 'universal' is used for units of erectrical charge and amount of substance, which don' t depend on length unit definition. 'harmonic' is used for the other units. Don' t use special names and symbols of the SI that is not listed in http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf. (2) Number counting http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf is used for pure number counting. The change for original myriad system is following four point. (i) (change) ten > dozen When 'dozen' is followed by a number from 'one' to 'eleven', 'zen' may not be pronounced. (ii) (change) hundred > gross (iii) (insert as 10.) xeny (iv) (insert as 11.) elfy (3) Power prefixes Power prefixes in the range 12^±3 corresponding SI prefixes duodecimalized by rule (2) are used. 12^±1 does not really have situation to use. (4) Plane angle A prefix with no corresponding unit is treated as a noun form, which means the abbreviation of the corresponding plain angle unit prefixed to one circle. This rule prevents that the noun form is treated as any unit other than unit of plain angle. The calendar time is, in a word, the rotation angle of mean sun (i.e. the rotation angle of the Earth derived by using the direction of the sun as a coordinate origin). So, the dimension of calendar time is treated as plane angle.  * Special definition and exception of general rules (1) The most frequently used units and important unit as a base point of unit deriving have special names, which express duodecimal context by a single word. harmon(m_{h}), nic(s_{h}), looloh(g_{h}), nohm(Ω_{n}) (2) Units to just use a name for of geometric figure square(m_{h}^{2}), cube(m_{h}^{3}), circle/cycle(Ω_{1}), sphere/turn(Ω_{2})  circle, sphere : mainly used under one unit range  cycle, turn : mainly used over one unit range (3) The power prefixes that the Universal Unit System set originally atomic(12^{8}), sub(12^{4}), super(12^{4}), cosmic(12^{8}) (4) The components of the Earth local extension that the Universal Unit System set originally sep(2^{7}), dour(12^{1}), span(64year), deg S(12^{4}K_{h}) Italic components are out of daily use. 
Posted by: Takashi May 11 2012, 01:29 AM  
Why 12^{8} was chosen as a power prefix interval for the Universal Unit System. 1) Affinity with physical constants ( Table 4 in http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf ) The power prefix of atomic scale for the onedimensional quantity is 'atomic'. The power prefix of atomic scale for the threedimensional quantity is 'tryatomic'. 2) Quantity expression consisting of pure number and unit quantity = pure number × base base = prefix × coherent unit  It is undesirable that there is any case that we cannot grasp the ratio of a quantity and its corresponding base intuitively if a power prefix interval is too large. (12^{12} for example) It means that unfortunately we cannot choose 12 as the radix of the exponential expression.  On the contrary, we can grasp the ratio of a quantity and its corresponding base intuitively using non unique pure numbers if a power prefix interval is too small. (12^{1} for example) This is undesirable because it is equivalent to the situation that plural size units are used for in the same context. 12^{8} was chosen as the power prefix interval to meet these limitation condition of both sides. 

Posted by: Takashi May 17 2012, 12:06 AM 
We cannot design any system that is free from 'impedance mismatch'. Moreover, the amount of 'impedance mismatch' is conserved quantity. Therefore, how to handle 'impedance mismatch' is the chance for designer to show what designer can do. http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf p.2 >When trying to construct a coherent unit system, however, it is not possible to use >all of the fundamental physical constants in the definitions of units. p.4 >For human activities on Earth, year and day cannot be ignored as calendar time units. >However, the ratio of year and day is not simple. >Therefore, any calendar time unit system must be a mixed radix system. The 'impedance mismatch' should be placed out of the range used in both daily life and scientific situation as much as possible. For a case of calendar time, the 'impedance mismatch' appears as radix discontinuity. The Universal Unit System with the Earth local extension places this discontinuity between daily use range and scientific use range. ('TGM in daily use' places this discontinuity between day and halfday.) 12^{8} power prefix is required from both physical constants' affinity and a model of human recognition. Its 'impedance mismatch' with the duodecimal system is placed in the domain of 12^{64}. This is out of range used in both daily life and scientific situation. To express whole range pure numbers by exponential expression will sacrifice the recognition efficiency of small pure numbers that are used in daily life for those of huge numbers that are not used throughout our lifetime. 
Posted by: Takashi Jun 23 2012, 09:50 PM 
I think that we can define 'definition categories' as follows: (1) conceptual definition Definition that prescribes the rough quantity of the units to constitute a unit system conceptually [The Universal Unit System]:  2E;(35.) times Newtonian gravitational constant  speed of light in a vacuum  quantum of action  Boltzmann constant  Planck impedance (2) strict definition Definition that corresponds strictly to the theoretical equations that a unit system is based on [The Universal Unit System]:  100,1700; cycle over Redberg constant  10;^{8} times speed of light in a vacuum  10;^{+26;} times quantum of action  10;^{+20;} times Boltzmann constant  Planck impedance 1,0017;(20,755.) that is a multiple of 2E;(35.) is chosen to make the coefficient of the following approximation's denominator 1. [doHTML] (The factor 1,0017;97(±1;2E) is derived from the Newtonian gravitational constant and its standard deviation. Because divisibility with 2E;(35.) is important, 1,0017;(20,755.) will not be revised even if the standard deviation will become smaller and the difference become beyond one standard deviation in the future.) 
Posted by: Takashi Jul 5 2012, 04:34 AM 
The Harmonic Universal Unit System with the Earth local extension: From a viewpoint of common user 0. Pure number counting 'duodecimal myriad system' is used. Duodecimal figures are indicated by a semicolon ';' as the duodecimal radix point. dozen  10;(12.) gross  100;(144.) myriad  10;^{4}(12.^{4}) myllion  10;^{8}(12.^{8}) 'dozen gross', 'great gross', and 'grand gross' are all available as an equivalent expression of 10;^{3}(1728.). Future daily users may decide whether they use single word 'grand' as 10;^{3}(1728.) or not. The numerical expression less than one follows the existing those expression of each language. 1. Core units The core units used most frequently have special names peculiar to the Universal Unit System. If it is not scientific or technical use, the understanding of the strict definition of these units is unnecessary. (In each following item, I commented on the comparison with the definition of the metric system.) In daily use, one or two digits precision is enough for mental calculation. On the other hand, in scientific and technical use, ratios that are not one are necessary for these calculations in not only the Universal Unit System but also SI. Length: harmon [hm]  http://hosi.org/cgibin/conv.cgi?m=0080&d=0&fq=1.0000000&frq=12&fe=0&fu=0&tu=1&fp=0&tp=3&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert, http://hosi.org/cgibin/conv.cgi?m=0080&d=0&fq=1.0000000&frq=12&fe=0&fu=0&tu=24&fp=0&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert This is slightly shorter than 1/1000,0000; of the quadrant meridian length of the Earth(=279.136507 mm, difference 2.5%). Physical time: nic [nc]  http://hosi.org/cgibin/conv.cgi?m=0080&d=2&fq=1.0000000&frq=12&fe=0&fu=0&tu=1&fp=0&tp=3&fm=off&fr=12&tr=10&fl=0&tl=0&c=Convert This is almost 1/1000; of the difference of the length of one Julian year and one mean tropical year.(difference 0.14% at the beginning of year 1900) (In the period from 1956 through 1967, the definition of the SI second based on the length of one mean tropical year at the beginning of year 1900.) 100,000. seconds(difference 2.8%), 10,0000; nics(almost exact), and 1â days are nearly equal. Mass: looloh [ll]  http://hosi.org/cgibin/conv.cgi?m=0080&d=3&fq=1.0000000&frq=12&fe=0&fu=0&tu=1&fp=0&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert, http://hosi.org/cgibin/conv.cgi?m=0080&d=3&fq=1.0000000&frq=12&fe=0&fu=0&tu=9&fp=0&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert This is slightly lighter than 1/100; of the mass of water in one cubic harmon capacity.(difference 6.4%) On the other hand, this is slightly heavier than 1/100; of the mass of ice in the same capacity.(difference 2.4%) 'looloh gee' will be used to express weight in daily use.(gee = 5;6 hm/nc^{2}) Conversion from gee to hm/nc^{2} is not necessary in daily use. On the other hand, in scientific and technical use, gee should be treated as a variable because the acceleration of gravity varies at each place. Temperature: degree S [Â°S]  http://hosi.org/cgibin/conv.cgi?m=0090&d=1&fq=1.0000000&frq=12&fe=0&fu=4&tu=1&fp=0&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert, http://hosi.org/cgibin/conv.cgi?m=0090&d=1&fq=1.0000000&frq=12&fe=0&fu=0&tu=7&fp=4&tp=0&fm=off&tm=off&fr=12&tr=10&fl=0&tl=0&c=Convert Temperature goes up 2 Â°S when we give water of one looloh energy of 1,0000; units. 100.Â°C corresponds to 100;Â°S. (The boiling point of water) 37.Â°C corresponds to 78;Â°S. (Human body temperature) 14.Â°C corresponds to 61;Â°S. (Mean temperature of the whole Earth) Â°C = 1E;/17; Ă Â°S  62;4 Â°S = 17;/1E; Ă Â°C + 51;5 Boldfaced differences show us that the Universal Unit System is a kind of duodecimalized metric system.(*) 2. Calendar time units The Earth local extension expresses calendar time by its plain angle of mean solar direction using binaryduodecimal mixed radix system. sep  25./64.(=0.390625) seconds milly  50. seconds (=128. seps) dour  2. hours (=100; millies) day  24. hours (=10; dours) span  64. years (=10,0362,8000; seps) 'minute' and 'second' are replaced by 'milly' and 'sep'. We can use 'year', 'month', and 'hour' like before. 3. Geometrical and mathematical units Geometrical unit names are associated with the name of the corresponding figures. Area: square [sq]  741.757241 cm^{2} Volume: cube [cb]  20.2019221 dm^{3} Plain angle: cycle  360. degrees (This is mainly used for plain angle more than 360. degrees.) Information: Byte  8 log_{e}2 We can use 'dour', 'centy' and 'milly' as plain angle units because their dimension is plain angle. dour  30. degrees centy  2.5 degrees milly  0.2083.. degrees (1 degree equals 4.8 millies) 4. Power prefixes for units atomic  10;^{8} sub [s]  10;^{4} super [S]  10;^{+4} cosmic  10;^{+8} sub cube [scb]  0.974244cm^{3} super harmon [Shm]  3.50919 miles (2 super harmons nearly equal 7 miles) super looloh [Sll]  2.73361191 tons 5. The other units and prefixes The other units and prefixes defined in http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf are mainly used for scientific and technological use. 6. Out of the Universal Unit System The units out of the Universal Unit System exist, too. These units will be used together with the Harmonic System in daily life. Currency unit: mon  100; times least valued currency unit for each country(or economic group) This is named for 'harhttp://en.wikipedia.org/wiki/Japanese_mon_(currency)ic'. Its value is distinguished by attaching the name of country after 'mon'. 'centy mon' means the least valued currency unit. Length:  10;^{1} harmon (=22.6960172 mm) Each language may assign one word special name to 10;^{1} harmon.(for example: 'uncia') Length: league  10;^{+4} harmon (=5.64749534 km) Speed: atol  1; harmon / nic(=2.50999719 km/h)  (*)[Addition] >Boldfaced differences show us that the Universal Unit System is a kind of duodecimalized metric system. The decimal meter was defined as 1/10,000,000. of the quadrant meridian length of the Earth. So, the duodecimal meter can be defined as 1/1000,0000; of the quadrant meridian length of the Earth. 1000,0000; duodecimal meters = 10,000,000. decimal meters As same way, the duodecimal second and kilo gram can be defined as follows: 10,0000; duodecimal seconds = 100,000. decimal seconds duodecimal kilo gram / cubic duodecimal meter = decimal kilo gram / cubic decimal deci meter These equations derive following units: duodecimal meter = 0.2790816 m duodecimal second = 0.4018776 s duodecimal kilo gram = 21.736711 kg (=144. Ă 150.9494 g) If we use ice in substitution of water as definition constant of duodecimal kilo gram, the last relation varies as follows: duodecimal kilo gram = 19.928775 kg (=144. Ă 138.3643 g) Difference between these units and the Universal Unit System is less than 3%. 
Posted by: Takashi Jul 8 2012, 12:23 PM 
I copy the following table which I wrote in other thread to this thread. [doHTML] 
Posted by: Takashi Aug 25 2013, 05:39 AM 
The unit name of 'logalithm of an integer' has been revised from 'Bel' to 'figure'. The prefix for 10; has been named 'dirac'. http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf http://www.asahinet.or.jp/~dd6tsg/univunite/units.pdf ( http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf ) 
Posted by: Takashi Oct 26 2013, 11:38 AM 
http://dozenal.wikia.com/wiki/The_Harmonic_System has been created. 
Posted by: wendy.krieger Oct 27 2013, 09:18 AM 
I had a chance to view the 'revised.pdf' over the last few days. The system described therein seems to replicate much of the wreckage found in the SI. I thought there was too many base mass units in it. The rydberg constant depends on the electron mass, but we see also the dalton (unified mass unit), and the gravitational constant creeping in. The dalton is a 'speckle constant', there are lots of different values to pick from: five have been used historically. It's a measure of convenience, rather than a constant. The value of G is very poorly known. GM for the earth is fairly well known, well enough to get to the moon, but this is known far better than G or M. The reason i selected the electron mass and its finestructurethouansd multiple, is because there is only one electronmass, and the size of the resulting mole is a pleasingly small number (ie 10.3). Let's start with 'rationalisation'. In SI, the measure \(\Omega_2\) appears three times (gravity, electricity, light), and is treated in three different ways (unrationalised, rationalised, and dimensioned). This system replicates the first two, in the same manner. It should be noted that rationalisation comes as a result of Maxwell's equations, where the constant connecting charge/flux is the the whole sphere, rather than the radian. Heaviside showed as long ago as 1895 that if a field travels at a finite speed, then it acquires magneticlike properties. see eg http://en.wikipedia.org/wiki/Gravitoelectromagnetism Oleg Jefimenko has written several books on this subject. Suppose then that gravity has maxwelllike equations, then the next likely step is to rationalise it. This means, zb \(F = GMm/4\pi r^2\). Have a look at KU and KO, which are unrationalised and rationalised systems based on atomic constants. The tables (esp the second halves of them), closely follow the CODATA format, with additional historical quantities that have since been dropped reinstated. For example, the franklin is actually set a C/29.9792458 in SI, to allow 'in e.s.u.' to be treated in SI. http://z13.invisionfree.com/DozensOnline/index.php?showtopic=872 For the greatest part, most of the values fall at \( n \pi \) or \(n\), for n=1, 2, 4. There's one '\(6\pi\)' in there, or 137.036 divided by these numbers. The base units are taken as 'electron charge', 'electron mass', 'speed of light', and 'fine structure hundred' (ie \(1/\alpha\), 'the impedence of space' (376.730 ohms), and 'the linkage of space' (ie 1 C / Amperesecond). The rationalisation changes angleunits and their derivitives. So things like wavelengths, rydberg constants, planck constants, bohr radius, have varying units as one rationalises. One in effect rationalises by changing 1 F/m to 1 F/(4\pi m). 
Posted by: Takashi Oct 27 2013, 11:51 AM 
I am glad to have comment after a long interval. >I had a chance to view the 'revised.pdf' Probably you had better read Appendix B and A of http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf rather than 'revised.pdf'. The biggest reason why I do not make the unit system rational forcibly is that http://www.asahinet.or.jp/~dd6tsg/univunite/e23.pdf has good overall prospect for unit systems. The definition of the Universal Unit System is"the unit system that is constructed by using the duodecimal number system and the speed of light in vacuum, the quantum of action, and the Boltzmann constant as the defining constants in such a way that these constants become strict multiples of integer powers of twelve of the unit quantities, and the Rydberg constant, the unified atomic mass unit, the Bohr radius, and half the value of the Planck length can be approximated by multiples of integer powers of twelve of the unit quantities". Unfortunately, the electron mass is out of range which meets the definition mentioned above, it cannot be adopted as a unit constant. 
Posted by: wendy.krieger Oct 28 2013, 08:59 AM 
Thanks. I downloaded the pdf and read most of it, including appendix B. However, the bulk of this post regards appendix B and its figure 1. I've given latexbibliography at the end of this post. The introduction of measures representing 'rationalisation' is not something that one is likely to see in texts on electromagnetism. It only appears when you start to compare systems. For example, Lorentz:1915 "The theory of electrons" introduces the HLU with a passing remark (like: let's use a different system of units). The authoritive account on bringing all electricity and magnetism is by Leo Young (Young:1969), which proposes no fewer than six base units. The basic dimensions follows what's in appendix B, but the presentation is different. Young starts off with Maxwell's equations, with six constants, and reduces these down to SI and two extra measures (S and U). If you have a reliable sorce of SI and CGS equations, you can introduce S and U into the SI, where you want a \( 4\pi \) and \( 1/c \) to appear. S then corresponds largely to your \( \Omega_2 \). U is passingly mentioned, but does not appear as a dimension. U appears in equations that have both electric and magnetic quantities. When one supposes that 'I' (electric current) is reckoned as a magnetic effect, then with \( I = (Q/t) U \), then U represents a 'turn'. In gaussian units, I is in biots, and Q in franklins, then U would represent a curl of "c turns". Another equation containing U is \( \epsilon \mu c^2 U^2 = 1 \). This allows for example, hlu and cgs to set \( \epsilon = \mu = 1 \), and let U appear as an interscalar. In your figure '1', we see that the middle top and bottom entries \( \rho \) and \( j \) are actually incorrect. Instead, these ought be \( \sigma \) or \( P \), at the top, and \( i = \lambda I \) or \( M \) at the bottom. The correction at the top sets P (density of electric dipole = charge displaced by a field), directly opposite D (displacement or electric flux density). Likewise, the bottom measures directly connect a surface current i with the field H directly above it. When Young's six dimensions are applied, the row 'time' is replace by 't/U' (seconds per turn: Q gives by division, ampereturns per second). The vertical columns become ZU (impedence * turn), and S. If you now put arrows out to the left of \( \Phi \) you end up with where 'magnetic charge' would appear. This was the first model of magnetism. The value of the arrows is the same between \( Q \) and \( \Psi \). When you have all six units (L, M, T, Q, S and U), and equations to match, then it is possible to write a set of equations which, by letting Q, S and U adopt different values, give anywhere between 3 and 6 dimensions. The appendix i am putting into the cof document develops this theory somewhat. The 'great confusion' one reads about is not in the original theory, but the use of faulty dimensional analysis in places where it is not appropriate. In short, trying to pretend that everything is an SIlike system. It isn't. One can, for example, pretend that gaussian is a mix of e.s.u and e.m.u, and use these systems to make the gaussian units. Likewise an unrationalised system can be made into a mix of rationalised units. One then constitutes the gaussian system as a mix of various 'prefix' and 'suffix' systems. The prefix handles the 'c' or U factor, the suffix handles the 'S'. When one aplies Young's dimensions to figure1, and eliminate L and T then the top two rows correspond to M/QU, Q, QS, and the bottom two rows to M/Q, QU, and QUS. When M is held constant, one has by merging S and U into Q, four different systems: EI: Q (Q, \( \sigma\), M/Q: ( V, E) MI QU ( I, i, M) M/QU (B, A, \( \Phi \) ) EY QS ( \(\Psi\), D ) , M/QS MY QSU (U, H), M/QSU (p = magnetic charge). However, not every quantity belongs to one of these systems. For example, ratios between different systems can give rise to different systems. ER QQS/M ( \(\epsilon\) ) MR M/QQUUS ( \(\mu\) ) Quantities do not have dimensions: it lies further up, at 'scales'. One can easily show this, by taking an equation like \( F = c Qq / 4\pi r^2 \), and saying that in fpsc units, this defines the 'verber'. Even though the dimensions are wrong, it works as an equation in numbers, and one soon gets ` 1 C = 94.55 vb `. When a unit is something that matches a number, then the bulk of different systems in table '3' in appendix B disappear. Simply defining an ohm or \( \mu = 10^{7}\) or volts, does not constitute a new system, no more than changing from density to mass changes MKS. (the original kg was defined by a volume and density). Since dimensional analysis (DA) requires a stable body of equations, for which it is an algebraic reduction of the nonnumber bits, then simply changing the body of equations can disrupt the DA. An other thing is that in older use, one can have several different scales per dimension. One either divides these into separate quantities, or create different systems to handle them. The esu and emu are in part this, (each with U=1), while in practice, one could have units of both systems, writing, eg 'e' and 'e/c' for the electron charge in esu and emu. Likewise, the gravitational units (psi of pressure, pound of force), is usually presented as comming from the 'footslugsecond', because the DA theory can not cope with having multiple scales (and an interscalar), in quantities. That is, you can't have force with dimensions \(M\) and \(ML/T^2\). One of the principles behind TGM, for example, is to make the interscalar into unity. @book{Lorentz:1915, Author={H. A. Lorentz}, Title={The Theory of Electrons: and Its Applications to the Phenomena of Light and Radiant Heat (Dover Books on Physics)}, Publisher={Dover Publications}, Year={2011}, ISBN={0486495582} } @book{Young:1969, author={Leo Young}, title={System of Units in Electricity and Magnetism}, year={1969}, publisher={Oliver \& Boyd}, address={Edinburgh} } 
Posted by: Takashi Nov 2 2013, 12:29 AM 
The Universal Unit System intends to make use of coincidences described in Table 4 of http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf. We have to adopt a duodecimal system to take advantage of these coincidences. Therefore, I have established the definition of the Universal Unit System as follows: The definition of the Universal Unit System is that "the unit system that is constructed by using the duodecimal number system and the speed of light in vacuum, the quantum of action, and the Boltzmann constant as the defining constants in such a way that these constants become strict multiples of integer powers of twelve of the unit quantities, and the Rydberg constant, the unified atomic mass unit, the Bohr radius, and half the value of the Planck length can be approximated by multiples of integer powers of twelve of the unit quantities".  In the Universal Unit System, the speed of light in vacuum, the quantum of action, and the Boltzmann constant must be strict multiples of integer powers of twelve of the unit quantities.  On the other hand, it is all right that the expressions of the Rydberg constant, the unified atomic mass unit, the Bohr radius, and half the value of the Planck length are approximate. The definition of the atomic mass unit has vagueness, so it is not suitable for the definition of unit systems. This is a reason why the atomic mass unit is classified in the second category. However, the expression of the atomic mass unit has to fall within the range which permits that the Avogadro constant becomes 100;^{10;} per universal mole. Because any unit system which assumes an electron mass as the base unit of mass does not meet the condition mentioned above, such a unit system is not the Universal Unit System. We had better argue about such a unit system in http://z13.invisionfree.com/DozensOnline/index.php?showtopic=872s.  A unit of measure is "a quantity that is used as the basis for expressing a given quantity and is of the same type as the quantity that is to be expressed". An advantage of the unit system, like coherent unit system, which derives any unit by multiplication and division of base units is that the value and name of derived units are decided automatically. Each name corresponds to its specific concept. An important point of http://www.asahinet.or.jp/~dd6tsg/univunite/e23.pdf is that "the concepts that are to be distinguished are arranged so that their dimensions are all mutually different". This characteristic is lost when we reduce the number of base units. For another example, the Universal Unit System recommends that we use the gravitational radius (half the Schwarzschild radius) rather than mass directly to represent the mass of a celestial body. However, to reduce the number of base units is similar to the situation that we express like not "the gravitational radius of the Sun is 1.5 km" but "the mass of the Sun is 1.5 km". (Of course, the statement "the mass of the Sun is 1.5 km" is consistent when we redefine and use the concept "mass" as "mass * c_{0}^{2}/ Planck force".)  It seems that 'U' of Leo Young's system does not correspond to 'Î©_{n}'. So, generally speaking that Leo Young's system and Appendix B of the http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf of http://dozenal.com are merely different. (The charge densities should have used different symbols for Figure 1(charge/length^{2}) and corresponding expressions(charge/length^{3}).) We had better evaluate the quality of unit system by its consistency and convenience. As wendy.krieger pointed it out, the solid angle is treated in SI as follows:  electromagnetism : rationalized  gravity : nonrationalized  light : dimensioned For unit system consistency, these cases should be same handlings. So, the following two equation's right side coefficients should be the same. [doHTML] 
Posted by: wendy.krieger Nov 2 2013, 08:12 AM 
Nothing in your system corresponds to Leo Young's U, since LY uses a sixdimensional scheme, and you use only five. So, for example, the gaussian system and the HLU system are coherent to LY's theory. I use a threedimensional 'nameinterscalar', where if S is an interscalar, and X is a unit in some quantity, then the same name can be used at XS. For example, in Leo Young's theory I is in 'ampere', and IU is a magnetic potential measured in ampereturns. But because i hold the turn to be a namecarrying interscalar, these map to the same measure. Your \( \Omega_n \) in LY's theory carries the dimensions of \( ML^2/TQ^2SU\), in my revised version (where i have \( \beta = 1/S = 1/\Omega_2, \eta = 1/\Omega_n, \kappa = 1/U \), then the dimensions are more symmetrically arranged over the eight base vectors (E, H, D, B, and K, M, K, J), the second being 1/S of the first, and K, J are measured in C/m^2 and Wb/m^2. I don't know fourvectors, so what i think is your gravity equation is a mystery to me. 
Posted by: wendy.krieger Dec 27 2013, 09:02 AM 
Myriad just means 'many', as well as 1,0000. I use the series 'hundred', 'thousand' , 'cention', and 'million' for my first four powers of twelfty, but like all numbers >10, they are read as columnholders. Cention cent = hundred, ion = big, so million, milli = thousand, ion = big, one sees ion in bunion, medalion, etc. Thousand means 'strong hundred', the thu stem is seen in thuringa (strong people: German provence). What i noticed, is when you have numbers like 7,60.00.00.00, which is seven million, sixty hundred thousand, the 'hundredthousand' section was happening often enough to need a name, so i settled for seven million sixty cention, longcount. Of course, it is probably necessary to fake a parahistorical PIE root for 10, 11, and follow the soundlaws. You solve the problem in many languages at once, and get what sounds natural. Currently the stem for 10 is something like *mdl or *ml, but i will have to get my IE book out to round it out. Ten is < tehund = two hands, so if you figure out how to count to 12 on both hands (eg the spaces between the fingers, and outside too), you can legitimately call 3*4=ten. tig ( ME ty) is apparently related to tehun, but i should have to compare it. 
Posted by: Takashi Jan 2 2014, 01:16 AM  
Happy new year
Yes, therefore we cannot omit 'one' of expression 'one myriad'. I think that the following policy is applicable to not only unit naming but also numerical expression.
As for huge numbers, use frequency decreases exponentially. It is a systematicness than brevity to be important to such a numerical expression. I think that it is proper to use 'y' for the duodecimal myriad system at this point of view.
I recommend that we use the digit group separators as follows in the duodecimal myriad system:

Posted by: wendy.krieger Jan 2 2014, 02:04 AM 
For dozenal, it would be better to write , at the twelves, and . at either 3 or 4. So, eg 1844.6744,0737.0955.1616; or 18.446.744,073.709.551.616;, it is easier to count the 12's and units in either case, and one can accomidate the 1000 or 10000 divisions. 
Posted by: Takashi Jun 19 2014, 10:28 AM 
The duodecimal myriad system for the Universal Unit System was revised. quadryllion > myllillion http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf was revised mainly, and http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf and http://www.asahinet.or.jp/~dd6tsg/univunite/units.pdf were affected, too. 
Posted by: Takashi Jul 12 2014, 11:43 AM 
The following is the URL of the list of articles that summarized the point at issue in Japanese.(Two years ago) http://suchowan.at.webry.info/201208/article_20.html (> http://www.excitewebtl.jp/world/english/web/?wb_url=http%3a%2f%2fsuchowan%2eat%2ewebry%2einfo%2f201208%2farticle_20%2ehtml&wb_lp=JAEN) I link the URL from this thread for reference. 
Posted by: PiotrGrochowski Jul 15 2014, 11:01 AM 
What is the universal unit system?. 
Posted by: icarus Jul 15 2014, 11:59 AM 
Piotr, read the OP, please. 
Posted by: PiotrGrochowski Jul 15 2014, 12:01 PM  
What is op?. 
Posted by: PiotrGrochowski Jul 15 2014, 12:06 PM  
PĆEASE BAN ICARUS! 
Posted by: Takashi Aug 8 2014, 03:29 AM 
The source code of unit converter 'a converter' has been released today on the GitHub ( https://github.com/suchowan/a_converter ). The links of the Universal Unit System resources at the present: _homepage___ : http://dozenal.com/ _blog________ : http://suchowan.at.webry.info/201208/article_20.html (> http://www.excitewebtl.jp/world/english/web/?wb_url=http%3a%2f%2fsuchowan%2eat%2ewebry%2einfo%2f201208%2farticle_20%2ehtml&wb_lp=JAEN) _abstract_____ : http://dozenal.wikia.com/wiki/The_Harmonic_System _definition____ : http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf _background__ : http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf _converter____ : http://hosi.org/cgibin/conv.cgi?m=1080 _(GitHub)_____: https://github.com/suchowan/a_converter _spreadsheet__: http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls _myriad system: http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf _planck unit___: http://en.wikipedia.org/wiki/Talk:Planck_units/Archive_3#Other_possible_normalizations 
Posted by: Takashi Oct 4 2014, 04:27 AM 
I found an interesting commentary. Why TGM isnât Based on âFundamental Constantsâ http://gorpub.freeshell.org/dozenal/blosxom.cgi/fund_const.html The reasons are: 1. Accuracy of our Measures 2. Scaling the Constants 3. Selecting Appropriate Constants 1. Accuracy of our Measures (a) The fundamental constants' values are not stable, and (b) their significant digit are insufficient. Problem (a) is the problem of basic understanding about the fundamental constants. For example, the numerical value that expressed Rydberg constant in International System of Units when we look from the viewpoint of God is the stable constant value. The reason why the recommended values in CODATA change at every revision is not the change of fundamental constants' quantities. This is the problem by the system of measurement rather than the problem by the fundamental constants. The description such as "Takashi Suga's Universal Unit System, based on CODATA" in https://twitter.com/dozenal/status/240516766416125952 is incorrect. Even if numerical values of CODATA's fundamental constants change so much, the Universal Unit System is not influenced. Problem (b) is the problem of technical measurement accuracy. This problem is becoming a thing of the past. According to http://www.bipm.org/utils/common/pdf/24_CGPM_Convocation_Draft_Resolution_A.pdf, the units of SI will be defined based on the fundamental constants from the next revision. 2. Scaling the Constants Scaling factor of the Universal Unit System is 10;^{8} rather than 10;. (http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf p.13, the last paragraph of section 3.3) Therefore, the arbitrariness does not remain when we adopt the requirement that the scale of the units should be human scale. The scale of units is decided uniquely. It is an important characteristic of the Harmonic System to be human scale. 3. Selecting Appropriate Constants According to Table 2 of http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf, the ratios of many fundamental constants(almost all important fundamental constants except the Newtonian constant of gravitation) and the corresponding units of the Universal Unit System become approximately: 2^{n} â 12^{m}, where n is 0,Â±1 and m is some integer. There is not the large difference in the unit systems that, as a result, are derived even if we select any these fundamental constants for the definition of the unit. 
Posted by: Silvano Oct 7 2014, 01:51 AM  
In fact, that's the case. The first definition of the meter was the 10millionth of the quarter of Earth's polar circumference. This quarter is 100 gradians. One hundredth of a gradian is one tenthousandth of this quarter, i.e. one thousand meters. 
Posted by: Kodegadulo Oct 7 2014, 10:18 AM  
The gradian was never viable, because of decimal's lack of divisibility by 3. As already noted, it's just ridiculous to have to resort to repeating decimals d66.6666... and d33.3333.... to represent such important angles as the equilateral triangle interior angle and its complement, just so the right angle can be d100. But any division involving dozens works. Using various http://z13.invisionfree.com/DozensOnline/index.php?showtopic=661&view=findpost&p=22022153 as angle units, these same angles can be: [dohtml] Had the French Revolutionary metricists gone with Laplace's advice and adopted a duodecimal system, then they might have discovered a quadciaturn along the Earth's circumference would have made a longishbutgood nautical mile: [dohtml] Moreover, the septciaturn would have made a longishbutgood yard (or shortishbutgood ell), and the octciaturn would have made a shortishbutgood hand measure (leading to a volume very close to a quart). Or they could have started with the quadrant: [dohtml] The quadciaquadrant as a nautical "mile" would have been a bit short, but the septciaquadrant would have made a shortishbutgood foot, and the octciaquadrant a shortishbutgood inch. (Actually, the triciaquadrant wouldn't have made a bad league.) 
Posted by: Silvano Oct 7 2014, 11:39 AM  
The problem is that a dozenal unit system is not coherent with a decimal number system. We strive here to the same coherence, but within a dozenal system. 
Posted by: Kodegadulo Oct 7 2014, 03:37 PM  
Yes of course, the presumption is that they would also have had to impose a shift to dozenal numeration, and force the population to be, er, reeducated. Or maybe educated in the first place. In that era the peasants were mostly illiterate and innumerate anyway, so it may not have been any worse than being told to throw out all their old weights and measures. The merchant bourgeoise might have supported the shift, perhaps even with enthusiasm, given the utility of selling wares by the dozen and the gross. 
Posted by: Silvano Oct 7 2014, 03:58 PM 
I have read in this forum that the doubledozenal hour system is so ingrained in our culture it is impossible to change, even for a twelvedouraday system, and was even impossible to change during the French Revolution. Do you really think a decree could have then changed the way people had counted for millenia? Decimal counting dates back to ProtoIndoEuropean... 
Posted by: dgoodmaniii Oct 7 2014, 05:19 PM  
<historicalpedantry> Moderns like to imagine filthy peasants knowing nothing until the shining light of the modern public school system shed its benevolent rays upon the world, but the vision isn't really accurate. Literacy in prerevolutionary France was actually quite a lot higher than most people think. Simon Schama writes about research showing that in Paris literacy levels in 1789 (decimal) varied heavily by class and location, but were almost always above half. In the Rue StDenis, a district of lowerclass craftsman, literacy was above 80.%. In 1780., over a third of wills in the Third Estate included books, despite these being enormously expensive. It's hard to imagine illiterate peasants spending the equivalent of weeks of labor on books. So while literacy was certainly much lower than it is today, it was hardly a rare thing among the lower classes. Also, innumeracy is hard to imagine in lower classes, except possibly those so poor that they had to pay their taxes in labor. The monetary system was poundsshillingspence; even for the peasant, who dealt mostly with sous, it would be hard to get around without knowing at least twelves arithmetic. Also, a working farmer needs a lot of numbers and the arithmetic to go with them. He wouldn't have known about logarithms and trigonometry, but to call him innumerate probably isn't fair. </historicalpedantry> <regularpedantry> But the Revolution...well, revolutionized the way everyone, peasants included, dealt with the most common numbers in their lives: namely, money and measures. They went from poundsshillingspence to francs and centimes; they went from a myriad of varying traditional metric systems to a single, very decimalized one. While the resistance of time and angle is a testament to the power of highly divisible numbers, it's an isolated outlier in the grand scheme of things. Uprooting peoples' habits to that degree isn't far behind changing the way they count, as well. Particularly if they hadn't changed the old money system, the merchants would have been very much in favor; and since they had the money, that would have been a powerful force. </regularpedantry> <shamelessselfpromotion> I've opined on a general outline for laws which would encourage, though not compel, adoption of dozenal counting and measures: http://gorpub.freeshell.org/dozenal/blosxom.cgi/bill.html It's simplified, of course, but the general outline isn't out of the question for a sufficiently motivated legislator and populace. </shamelessselfpromotion> 
Posted by: wendy.krieger Oct 8 2014, 11:35 AM 
Well, the english used a different counting system until the 1300's, so i don't know where ye get this 'millenia' stuff from. <honest_plan target=USoA> One might note that eight ounces of drinking chocolate, strategily placed around random places in say, washington dc, (eg the canteen at the congress), might induce enough senators to vote on a proposition to convert the US to something more congenial to twelfty, like base 120. The easiest way to start is with money. That's the easy bit. You get rid of those dollar beads they have over there, and introduce something like a shilling of 12 pence. A shield would be then 120 shillings, and so forth. Weights and measures would follow. It would take a little while to do this, but i suppose you could give it a fortnight or two. Education was always going to be the tricky part, because most of the schools are in 'school districts'. You would have to find someone over there who understands how they work. I talk to a number of teachers over there, and it is more confusing than it is here. You could always get religion on the side. That's how decimals won in england, and why the metrics were hampered (ungodly revolutionists: they want to take our christmas and our pound). </honest_plan> 
Posted by: Silvano Oct 8 2014, 12:33 PM  
English is an IndoEuropean language, and all IE languages have the same counting system (something with more emphasis on twenties, but that's all). However, if you have info about something else, I'd gladly have a look at it. 
Posted by: Kodegadulo Oct 8 2014, 04:04 PM  
Maybe Wendy is referring to the notations used for numbers, rather than the words. Hindu/Arabic numbers and the placevalue system are still relatively recent; it's surprising how long the old Roman numeral system persisted. Or she might be referring to her contention that "hundred" historically meant her beloved d120, and only later came to mean d100. (But it's often hard to tell what Wendy is talking about.) English does have the word "score" meaning d20, but it doesn't seem to be very dominant in the English number system. I thought it was French that was more mired in twenties. French doesn't even have a distinct word for "seventy", it comes out more like "sixtyten". But English of course does also have distinct words for z10 and z100: "dozen" and "gross". In Old Germanic "mass" even meant z1000. "Eleven" and "twelve" have their own unique etymology, distinct from that of the other "teens". So at least the Germanic side of English has had some affinity for duodecimal. But yes, as a general rule, most human languages, not just the IE family, have a predominantly decimal number system. Languages with completely dozenal numbering are very rare. 
Posted by: Silvano Oct 8 2014, 04:20 PM  
The language I know that relies most on twenties in Danish. Dozen and gross are originally French words. 
Posted by: Kodegadulo Oct 8 2014, 08:00 PM  
Oh yeah, you're right. douzaine snd grosse. It was eleven and twelve that came from Old Germanic (ainlif and twalif, cognate with German elf and zwoelf). Although dozen also appears to have a cognate in German: Dutzend. Or was that a borrowing? German also has the word Gros, with about the same meanings as the English "gross", except apparently not "twelve dozen". 
Posted by: Silvano Oct 8 2014, 08:21 PM  
The German groĂ comes from an ancient Germanic word, apparently cognate with the Latin grossus/crassus, as well as with the English great (as the Dutch groot). Couldn't find the etymology of Dutzend, but I believe a borrowing from French/Latin is quite possible. FYI, the French word douzaine comes frome douze, twelve, and aine (from Latin anus, as in Canadian), suffix we find in many numberderived words, as huitaine, quinzaine (in fact seven and fourteen days), semaine, dizaine, vingtaine, trentaine, quarantaine (also means quarantine), cinquantaine, soixantaine, centaine (and some others as jokes). They mean a group of such number or, for decades, the ten years of age beginning at this age. 
Posted by: Takashi Oct 9 2014, 12:00 AM 
It is not necessary to abolish the unit 'hour' even if we introduce the Universal Unit System. Because the relation '1 hour = 60. minutes (decimal)' only is merely moved for '1 hour = 60; millies (duodecimal)', as described in section 2.2 of http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf . We can leave to future generations the decision of whether we continue using the unit 'hour' or not. 
Posted by: dgoodmaniii Oct 9 2014, 01:04 AM  
Indeed, it's exactly like "sixtyten": soisantedix. You then proceed soisanteonce, soisantedouze, and so forth, up to soisantedixneuf, literally "sixtytennine." The next number is quatrevingt, "four twenties." And our "ninetynine" is quatrevingtdixneuf, literally "four twenties ten nine"! This is limited largely to France and Quebec, though; as I understand it, even Belgium doesn't have this system, instead having "septante", "octante," and some form for "ninety." 
Posted by: Silvano Oct 9 2014, 01:47 AM  
To be more precise: It's soixantedix, soixanteonze, soixantetreize... soixantedixneuf, quatrevingts, quatrevingtun, quatrevingtdeux... quatrevingtdix, quatrevingtonze... quatrevingtdixneuf. (Louis IX founded in 1260 a hospital named HĂŽpital des QuinzeVingts, with place for 300 people.) In Switzerland, Belgium and DR Congo, they say septante and nonante. In Switzerland, they say huitante. It seems that octante has disappeared. In Danish... 10 : ti 20 : tyve 30 : tredive 40 : fyrre 50 : halvtreds (halfthird, that is two and a half [twenties]) 60 : tres (three [twenties]) 70 : halvfjerds 80 : firs 90 : halvfems 
Posted by: Takashi Oct 11 2014, 01:22 AM 
The basic requirements for number counting and prefix system are follows: 1) Sparseness of new vocabulary (>http://translate.weblio.jp/web/english?lp=JE&url=http%3A%2F%2Fsuchowan.at.webry.info%2F201207%2Farticle_5.html&rdt=tl&sentenceStyle=spoken) 2) Do not convert 2 and 3 into 100 and 1000 in the domain of daily use. (>http://translate.weblio.jp/web/english?lp=JE&url=http%3A%2F%2Fsuchowan.at.webry.info%2F201207%2Farticle_3.html&rdt=tl&sentenceStyle=spoken) Unfortunately SDN does not satisfy these requirements. Do not mind even if a huge number and minute numerical expression are complicated. It is natural that a complicated concept is expressed by complicated expression. There is exponentially few opportunity to use those numbers. It is a problem to become the system against these requirements as the result of taking account of these numbers. A point of the word 'milly' is to replace a part of the word (which has not threeness but thousandness) in 'y'(which expresses dozenal context). It is this structure to be important. I am not particular about the concrete expression of the pattern to express dozenal context. I welcome constructive suggestion of English native speakers.  # The comment of the origin of this reply seemed to be deleted. 
Posted by: Takashi Oct 11 2014, 01:52 AM 
For the reference of the recent arguments http://www.sf.airnet.ne.jp/~ts/language/number.html 
Posted by: Takashi Oct 20 2014, 10:21 AM 
conv.cgi has become able to handle IDUS's units. http://hosi.org/cgibin/conv.cgi?m=10080 
Posted by: Silvano Oct 20 2014, 11:26 AM  
Good news! 
Posted by: m1n1f1g Oct 27 2014, 02:30 PM  
I don't see why these are crucial, or even helpful. Sparseness can be achieved simply by not using certain prefixes (which seems to be common practice), and not basing the morpheme for 10^2 on 2 requires a nonregular system. The regular SDN system can be made nonregular by adhoc addition of prefixes. SDN's denseness gives the advantage of flexibility. NoĂ¶ne needs to use both âtriquaâ and âquadquaâ in the same context, but they can choose which one they are going to use. 
Posted by: Takashi Nov 1 2014, 10:11 AM  
I think the flexibility is not an advantage. I quote the comment that I wrote in http://z13.invisionfree.com/DozensOnline/ar/t594.htm before.

Posted by: Kodegadulo Nov 2 2014, 11:27 AM  
Takashi, merely stating general principles does not prove that the particular system you have come up with necessarily is the ideal embodiment of those principles. We may already agree with many of your general principles  while at the same time espousing other principles that we also find important. Different goals can rise to importance in different contexts. We may disagree on whether what you have offered actually meets all the principles that we do share with you, and may point out how it overlooks other principles that are important to us. You have a tendency to express your principles and your goals as if they are "universal" and inviolable  to the point that it sounds like dogma. But from my own perspective they appear to be a matter of your personal taste. It is perfectly fine to create something that appeals to your personal taste, and it is perfectly fine to offer rationalizations and explanations for why you think it is a good thing, and offer it up to the rest of the community to see who else it might appeal to. But unless you can prove your assertions with actual empirical science that has been thoroughly examined and analyzed by the community, we must respectfully say that they are only your personal opinions, and we might disagree with you. We may respect your choices and tastes as being important to you, without necessarily sharing them with you. It would be dishonorable to accuse others in this forum, who have demonstrated a great degree of thought and consideration about many subjects, of being "unconscious", without at the same time demonstrating that one has made the same effort to raise one's own consciousness of the issues they have raised as well. 
Posted by: Silvano Nov 5 2014, 09:55 PM  
IMHO, ordinary people don't care at all how units are defined. They just want to use pratical and simple units, that don't vary from city to city, as feet and pounds used to. 
Posted by: Takashi Nov 14 2014, 12:49 AM 
In the design of the unit system, it depends on each designer what kind of requirement are emphasised or disrespected. These requirements are often incompatible with each other. So, the unit system which everybody satisfies does not exist. Probably, the difference of the main viewpoints from other people is the three following points: (1) Communication model that was presented in the previous article (2) Evaluating SI more affirmatively than other people (3) Regarding the Imperial unit system as one of the unit systems that are ethnic SI reflects longtime practice and attaches importance to the reliable and ambiguityfree communication rather than efficiency. It is result of this thought that SI inhibits multiprefix and peculiar name without special reason. (1) is not my personal dogma but natural thought based on SI's longtime practice. It is strange why this community is not going to absorb experience of SI. I felt the discussion http://z13.invisionfree.com/DozensOnline/ar/t1118.htm misdirected. Although there is descriptions that double with the article in the past, my opinion at present is put summarized as the following. "The quantity which is not 1 although it is close to 1" "The quantity which is not 1 although it is close to 1" must be treated as a variable. Multiplication and division are necessary to deal with it.  Technical use The convenience of "the quantity which is not 1 although it is close to 1" is low at the view point of the technical use. Not a human being but a computer performs multiplication and division process. If a value is not 1, whether it is close to 1 or not will not care about the computer.  Daily use The convenience of "the quantity which is not 1 although it is close to 1" is high at the view point of the daily use. This is because human comes to be able to grasp the amount by the mental arithmetic calculation. However, there are few people who daily do the multiplication and division of the number of two digits or more by mental arithmetic. In other word, the mental arithmetic with daily use convenience is one figure of significant digit at most. So, the convenience does not improve if the amount is close to 1 more than one figure of significant digit. In addition, figure shifts and the multiplication and division by 2 would also be within the mental arithmetic.  Because the gravitational acceleration and density of water are not constant, when we use them as the definition, we will adopt the representative values for the definition. An actual value for practical situation has deviation with representative value. It means that the actual value should be treated as "the quantity which is not 1 although it is close to 1" mentioned above. If an another unit system with another convenience derives the representative values which are also easy for the mental arithmetic by chance, it is advisable to adopt the unit system. It is disadvantageous to adopt the amount about which it does not care over one significant digit for the definition. Unit that got used The convenience of a unit that got used is low if we shift from decimal system to duodecimal system. Although a matter of course, even if we adopt the unit X that got used with decimal context:  12 times X differs from 10 times X.  144 times X differs from 100 times X. Conversion is necessary after all. (1) decimal system > duodecimal system (2) X > Y (Y / X is not 1 although is close to 1) (1) is much higher barriers than (2). It does not seem with rational that the person who accepted change from familiar decimal system to unfamiliar duodecimal system refuses the unit Y. The argument seems to be not realistic whether a unit system comes to be accepted for nondozenelists if the amount of its units are tuned finely. "Analogy" and "Homology" It is advisable that the scale of a unit is a scale convenient for human to use it. However, because the room for the subjectivity is large, a constructive discussion of convenient for human(human scale) is difficult. When the amount of human scale is presumed referring to the units widely used among the world, it is necessary to take care about the difference between 'analogy' and 'homology'. Analogy  the resemblance of the unit value is caused by a limit by the human scale. Homology  the resemblance of the the unit value depends on the origin being common. Concerning about units with 'analogy' and units with 'homology', the treatment differs at the time of the unit system change. If units of a certain magnitude, which have been used in various places, are derived from a common origin, we count them as one kind. It might be able to be presumed that there is "common condition"( convenience for human ) there if the units of the similar size are seen in various places though these origins are different. The change from a unit with 'analogy' to a different unit outside the human scale range continues having a difficulty forever. The change from a unit with 'homology' to a different unit within the human scale does not have any problem if used enough. If there is a similar unit among the totally different cultural countries, we can regard it with 'analogy'. In this case we can consider that the unit amount to be within human scale. If there is no similar unit among the totally different cultural countries, we can regard it with 'homology'. In this case we can consider the limitation by the human scale is weaker. Length: The range around 24cm  35cm is regarded as human scale. Mass: It is regarded as homology not analogy that units similar to pound are distributed. The limit by the human scale may be weaker. However, probably Maz is too heavy and out of human scale range. Almost of all the unit systems that are derived using the density of water for the definition are the same. Pysical time: I thing that the combination with human scale of length and physical time corresponds to human walking speed. Probably Tim is too short and out of human scale range. Almost of all the unit systems that are derived using the gravitational acceleration for the definition are the same. We can not insist on the validity of the shift from decimal system to duodecimal system if we regard 'homology' as most important.  There is no relation whether or not the Universal Unit System is suitable for daily use and whether or not the deriving method is abstract. I think that the Universal Unit System is suitable for daily use rather than the TGM system. This is because the universal unit system is the unit system that is human scale (except thermodynamic temperature) whereas the TGM system is not the unit system that is human scale. If there is a person who feels that the TGM system is more suitable for daily use, it is because the person is accustomed to the Imperial unit system. I cannot agree with the selection of the unit system by the custom to the unit system if it is required to use it forever. In accordance with the opportunity to change, we should shift to the unit system with higher convenience. Merit of unit system coherency The advantage of coherent unit systems is that the quantity and name of each dimension unit is derived automatically. Derived units should not be named peculiarly without special reason. Derived units with peculiar name should be only a small number of units of the starting point of derivation. (Not until eliminating the established existing name.) It is optional for the sender of information which derived name or peculiar name to use. It is flexibility for the sender. However, it is mandatory for the addressee of information to know both derived name and peculiar name. It is inconvenient that units of all dimensions have both derived name and peculiar name. 
Posted by: wendy.krieger Nov 14 2014, 10:13 AM 
Coherent Units Units are coherent to a theory. A system of units is coherent to a body of equations. However, the theory of 'quantity analysis' can perfectly handle unmatched units. A unit can be thought of as an 'algebraic blob', like 1 (mile) = 1 (5280 ft). As long as you set the equation up so the units cancel out, it is possible to use any combination of units. My 'DD' system was designed so that when one does calculations with a range of common units, the numbers in the brackets generally cancel out, and you are left with a simple calculation. Here is power (hp) = force (tons) * speed (mph), used to calculate power used by applying a force at a speed (like a railway engine). imperial: p (550 ft lb/s ) = f (2240 lb) * v (5280 ft/3600 s) => p = 448/75 fv metric: p (75 kg m/s) = f (1000 kg) * v (1000 m /3600 s) => p = fv / 0.27 dd: (in z) p (140 ft lb/s ) = f (1000 lb) * v (4000 ft / 10000 s) => p = 3 fv Since ordinary people are using things like mph or km/h rather than the coherent fps or SI unit, and talking in horsepower rather than watts, and a power in weight, rather than newtons or poundals, the above calculation is a valid argument. You can have multiple coherent units on the same quantity. For example, there are several scales for energy, and even three different pressure scales are still to be found. thermal energy: M ĂŸj : fps BTU = lb.Â°Fj ; cgs calorie = g Â°Cj ; MKS Calorie kg Â°Cj gravitational: Mg L : fps duty = ft.lbf ; cgs cmpond = gf cm; MKS mkp = kgf m "energy": LÂČM/TÂČ: fps footpoundal ; cgs erg; MKS joule mass: Mg TÂČ/L : fps: slug: cgs glug; MKS hyl or TME Saying something like 'the cgs unit of energy is ...' is rather pointless, because there are several different scales of energy, and the conversion like 1 calorie = 4186.8E7 ergs is dimensionally 1 cal = j ergs, where the specific heat of water is j ergs/g.Â°C, is a dimensioned quantity with a pure number. Base Units The number of base units is arbitary, but SI is oversupplied here, and undersupplied there. In any case, the legal implementation of the base units does not necessarily mean that it's the best to calculate with: LengthMassTime is a carryover of national weights and measures (footpoundgallon), rather than a new system to simplify calculations. In the SI, the mole is a base unit. Everyone else has this as a derived unit with the dimensions of Mn. The natural constant is M/Mn = u, the 'dalton' or umu. You look up tables to derive the weight of reagents in daltons, and then divide this into the actual weight to get a 'number of molecules' as a weight. Water is 18u, so a pound of water gives 1 lb / 18 u = 1/18 lbmole of water. In short, the gmole is a derived unit, but in SI, it is a base unit, because they use kg with gmole, and have an artificial constant 1 kg / mole = 1000 daltons. The basic theory of electricity coherent to all systems requires six base units: that is, six measures that are not defined in the theory. CGS defines three of these, and SI defines four. I'm pretty sure that UUS has five, but i have to do a complete analysis of it: it has some rather strange notions. The extra two are a factor of \(4 \pi\) that varies between SI and CGS, and a factor of \( \kappa \) that is 1 in SI, but c in CGS (and HLU) eg \(\epsilon\mu c^2=\kappa^2\). Keeping both of these in the theory helps when one sifts through the midling gravity (gravitomagnetism, weak field linear approximation of GRT, etc), where \( \kappa = 1 \mbox{ or } 2\). "The quantity which is not 1 although it is close to 1" Although it is useful to treat something like gravity as a variable, and distinguish between M and Mg, for many purposes it is better to fold these onto one scale, M. An example is 'axleloads'. People are not going to do something like multiply 3.5 tons by 9.8 N/kg to get 34.3 kN, to decide whether it's safe to cross. Axleloads, even though a force, ought be expressed as a mass as F/g. Setting g=1 means that you can have a unit 'ton', and then have an exact force 'tonleo' and a forcetogravity 'tonforce'. For practical purposes, a tonleo = tonforce = ton, and one does not have to convert anything. Quoting a bridge axleload at 5 tons, is not the breaking point of the bridge, but what you are willing to let cross it. Likewise, a 'cup of water' = 250 g, directly converts a spiglitre = kilogram, even if this is not an exact measure, it is faster to measure out a weight by the cup than to set up the scales. This is the reason behind the spig as a base unit. The systems that have the spig and leo, falling inside the specific gravity of water, and a notional gravity of the earth, can only produce usable units if the units are small. In the design of COF, i read this. In this sense, it's not so much the large numbers that come out of it, but the numbers mean the same thing. For example, the horsepower is 2D5, ie 200,000;. The dimensionnumber of power is 7, so the corresponding size of the tgm unit is 6^7 = 116,000; which is more than what a man can exert. If all the common units are selected to be nice round numbers of COF, then the actual calculations are not that hard. Unit that got used The question here is to think whether the unit is a midling unit, or the bottom scratch on the scale, and whether a bigger unit is the 'real' unit in question. Consider temperature. The degrees are the tiny little scales on the thermometer. Farhenheit divided Romer's degrees into four smaller ones, because his thermometer could read smaller units, and thus to avoid fractions, one uses a bigger number of smaller degrees. Fahrenheit's scale went from 'reproducable cold' to some sort of 'body heat', so that 0100 covers the 'habitable scale'. The scales based around icepoint and boiling point do so because these are fairly easy to reproduce, and of the accuracy of the instrument. There's nothing magic about these points. If you look in an atlas, you may come across maps with isotherms or equal temperatures on them. The fahrenheit scale has a dotted line between the 30F and 40F, for 32F (ice point). What this all tells us, is that it's best to put 'humancold' at some 0 figure, and 'humanhot' at 100, and have icepoint on some 10. If you can squeeze absolute zero into the scale, all good and well, but no loss otherwise. COF and TIOF and TGM derive their temperature unit from the specific heat, but use a large number to represent thermometer units. The 100 K range between ip and bp is in COF units, z18E 0000; in TIOF, zd101,00,00: units. Raising water by a degree corresponds to lifting it against gravity by something like 400 metres. The COF scale is pretty close to 100 F = 100 degF, and aligning 40 F = 32 degF (at 1/3), pretty much replicates the largescale fahrenheit with a smaller degree. When you are free to pick the size of the degree, you can note that if bp = 1, then absolute zero = 2.7316, which is near enough to 41/15. Since you can't really use bpip as a unit, you can do zp (abs zero) = 0, ip (ice point) = 410 (350), bp = boiling point = 560 (480), The human cold (300) is then 33.333 C and human hot (400) is +46.666 C gives a nice range, with an absolute scale. When 300 = 3.00: it's gorems, twelftywise, when 300 = 300; it's rankines, dozenally. 
Posted by: wendy.krieger Nov 16 2014, 07:49 AM 
I had a fairly critical look at the UUS, largely to see where it fits in with other systems in my catalogue. There are some curious things in it. It is rather strange why he opts to set a time length as a base unit, and derive the velocity, (which is c/D8 ), rather than the other way around. The mole is an interesting story. The only reason it's a base unit is that SI does not derive it like everyone else does. The actual base unit is a 'dalton' or amu. The size of N_A is then 1 M = N_A daltons, giving a number Mn. You weigh your reagents in ordinary units like lbs or kgs, and divide this weight by the atomic weight in daltons to get 'zillions of molecules'. It's the zillions, not the grams that the chemical equation matches. Here we have the zillion set to 1D24, and a new weight derived from this. It's not that one disects the zillion, it's just more convenient to avoid the 1D24, and use the elsewhere derived weight. The actual unit of weight (m), is derived from a different value: one has by the radiation law, \(L= 12^{38} \hbar/M c\) one finds the mass whose radianlength is 1/(rydberg wave constant), and heads from there, The electrical units in size, follow the UES rule NU. The unitnames have been mapped onto the intersection with NI, with the sr given the role of shifting the \( 4\pi \). The names are mostly points with SI names, except for gauss, oersted and gram. So the unit for H in cgsm is oersted, but in UUS is oerstedsr (Osr). The equations in the appendix B3 represent NU forms where there is \( \Omega_2 \) where a \( 4\pi \) might be, this is given this value. While gravity could do with a similar treatment, this isn't done. Instead, the main novelty here is that a length is derived from mass by L = GM/c^2, and this length is used in place of either GM or GM/c^2. It's useful to note that the geometric scale of gravity (curvature, black holes), are multiples of this. It follows SI too closely, and SI, by way of an implementation based on cost, rather than good design, is severely broken, and some of these breakages show here. 
Posted by: Kodegadulo Nov 16 2014, 10:48 PM  
I probably do not understand Takashi very well at all. Much of the meaning he is trying to convey seems to be lost in translation from his native Japanese. This problem may be insurmountable. But from what I can understand, it appears that he considers SI, its ideas, its conventions, its style, to be the default baseline of what people are most familiar with and therefore what needs to be preserved for greatest understanding. For instance, the way SI's prefix system mimics natural language seems to be a good thing to him, while I view that same fact as being a chief flaw of SI. Natural language develops by accident, and the accidental features of natural languages often cause blindspots in people's thinking. Instead of copying every feature of natural language, we should critically evaluate their utility to the problem at hand, and if necessary break free of their limitations by deliberately using a different structure. This can expand the mind and create a better understanding of the scientific principles underlying the nomenclature. Takashi complains that SDN confuses, for instance, "thousandness" with "threeness". But to do science at many scales, it is necessary to master the concept of orders of magnitude, and how they are arranged into a logarithmic sequence based on their exponents in some base, be it ten or twelve or something else. Being able to express and comprehend a quantity in "scientific notation" is an important skill. Being able to comprehend the differences in the scale of different quantities at different orders of magnitude, is also an important skill. SI's prefixes seem exactly the opposite of what is needed in this case: They are nonsense syllables that completely obscure the actual order of magnitude, i.e., the value of the exponent of the power that they attempt to express. What is needed is something that directly expresses those exponents. SI also is limiting to the mind, because it singles out every third power, for no particularly good reason, but simply because that's what natural language does. This discourages people from selecting the optimal power for any given situation, and instead encourages them to look at the nearest third power. Rather than thinking in terms of a single base for the logarithmic scale, people must contend with two: Base ten for actual scientific notation, and base "thousand"  poorly and obscurely expressed  in SI's prefixes. We should not repeat this mistake when designing a prefix system for dozenal metrologies. We each of us have various things we are conservative about, while at the same time proposing radical change for other things. I have my own things that I believe should not be redesigned (such as the punctuation used in mathematical expression, and the rules for how they fit into ordinary prose text) while urging change elsewhere. I just disagree with Takashi about which features fall into which category. 
Posted by: wendy.krieger Nov 17 2014, 01:45 AM 
SI is as much a wreckage of use as imperial, just that the wreckage is in a different place. You think: what does CGS have that makes it better for cosmology, and why is this sudden interest in the HLU. (In takashi's system, it has \( \Omega_2=1\), but the rest as gaussian.) The room one has in a new system is to bring in new ideas into the core. Moreover, SI reflects a different level of thinking to the base metrology. SDN labels its prefixes by columnnumber, so that '3' represents column 3. To put this sort of number beside a real '3', you need to invoke a secondnumber series. Writing something lke three trimetre would be as confusing to a program as writing three mitsumetre is to us, even though mitsu is japanese for 'three'. The dms system uses raised roman numerals, like 3iii = 3'". I probably have no issues with the thousandbase, because the tenbase can get a little tedious. However the metrics never scaled their prefixes right, so you a prefix for every thousand rather than a doubleprefix, like Â”Â” and mÂ”, the older forms for p and n respectively. The use of prefixes can get confusing if one couples a unit to a function, eg millimetre squared and milli(metre squared) are diferent things. It's more so with 'metrecandle' = lux vs cmcandle = 10,000 lux. SI prefixes are simply incollapsed danish number names: atto = 18, femto = 15, zetto = 7, yotta = 8, etc. I disagree with your comments on punctuation etc, since this stiffles anything better coming along. It is rather like telling the french that we already have words for these things, and that different arithmetic forms have different needs. Like TGM and SI, UUS does things that i would not do, but one has to think that this is the result of other people's perceptions, and they did it for a varied reasons. It is therefore useful to understand these reasons. 
Posted by: Kodegadulo Nov 17 2014, 02:42 AM 
There are really two goals to achieve with power prefixes: 1. Represent the exponent of the power in a clear, direct, and simple way. SI prefixes utterly fail at this, because of the adhoc names and the mapping to thousandbase. So do naturallanguage "million" systems, whether short or long scale, because of the mapping to thousandbase or millionbase. The myllion system Takashi favors inherits the problems of natural language and compounds them by introducing recursive complexity. The "ordinal/cardinal" system Wendy described succeeds because it is quite direct. Pendlebury's original prefixes were direct but a bit strange and therefore not very clear; the indistinctness of the a vs i did not help. SDN is direct, clearly distinguishes positive qua from negative cia, and respects the original forms of Classical roots, so it maintains familiarity, and therefore succeeds. 2. Clearly distinguish mantissadigits from powerexponents; mark the latter sufficiently to avoid confusing them with the former. The "ordinalcardinal" system fails at this because both wind up using the same words from the same language; there is no marking at all. Pendlebury and SDN succeed because both rely on expressing mantissa in English but power in Classical language,with a mild mutation in SDN, but extreme mutation in Pendlebury. Allowing multiplier and power prefixes together in SDN may or may not succeed. This may be a matter of opinion: Is there sufficient marking on the power prefixes? This is why I have proposed Revised SDN, with more emphatic marking of power digits. Using even a foreign language for the power prefixes ("mitsulengthel") might succeed if the learningcurve is not too hard. 
Posted by: m1n1f1g Nov 18 2014, 08:11 PM  
Surely that's half a point in favour of including such constants in the unit system. 1 is still the easiest number to multiply and divide by mentally, beating even 2, 10, 1/1000 &c. Changing magnitudes is not completely trivial in daily use. 
Posted by: Silvano Nov 18 2014, 08:44 PM  
But Takashi's harmonic system doesn't do that. 
Posted by: Takashi Nov 25 2014, 02:28 AM  
Are the most important difference between the revised SDN and the original SDN definition of the initials? Which document should I refer to the definition of the revised SDN from? The duodecimal myriad system for the Universal Unit System was revised in the article: http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=146 [Jun 19 2014, 10:28 AM], and this change affected the first figure in the article: http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=87 [Dec 18 2011, 08:55 AM]. 
Sorry, I feel that Wendy is particular about the point which is not so important. It is not essential what is chosen as a basic unit, as long as the equivalent nature of the unit system is guaranteed. The choice of basic units in the Universal Unit System is the result of arranging the portion of upper part of p.13 of http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf simply. Like derived units with peculiar name, convenient units are chosen as base units as the starting point of derivation. 
Posted by: Kodegadulo Nov 25 2014, 02:46 AM 
I have given up on the experiment to revise SDN. The potential errors of beginners will just need to be a risk. Just go with the http://z13.invisionfree.com/DozensOnline/index.php?showtopic=463 at the top of the original thread. 
Posted by: Takashi Mar 31 2015, 09:58 AM 
I'm sorry not to be able to write here because I have been busy with other matter ( http://hosi.org ). I think the SDN to be one of reasonable systems under the following limitation. 1. It's used for the use of science and technology field. 2. Maximize convenience of sender of information. However, the system that we propose should suit the usage both in daily life and in the science and technology field. Qualitative difference in both is how to recognize when we hear and read. We analyze a word of the science and technology field in a decided rule and recognize it. However, on the other hand, we recognize a word in daily life with pattern matching. Please see http://justriddlesandmore.com/Cambridge.html . We can confirm that we recognize a word by a pattern matching without reading the letters of the word by one character. The clue is word's head sound/character, foot sound/character, and its length. As for 'bicia' and 'biqua' all the these are same, although the quantity even 4 figure differs. It's inconvenient that both of them coexist in the same context. In the International System of Units(SI), 'hecto' is a Greek origin, and 'centi' is a Latin origin. Both the word form is quite different. As for real life the everyday usage is main. Therefore the consideration to the everyday usage is more important for the system that we propose. It is necessary, to give priority to the convenience of recognition by the pattern matching, and to prevent word form of terms frequently used from being similar as much as possible. The SI meets this requirement, but the SDN does not meet this requirement. Communication is consists only equipped with both the sender and recipient of information. Bbroadcast is often made presentday information. When aiming at specific information, the number of the recipients becomes quite a lot more than the number of the senders. Therefore, the convenience that we should maximize is convenience of the recipients of the information not the convenience of the sender of the information. The SI maximum notes "Certainty and misunderstanding prevention" as seen in the following quotation examples. I think that this is the result of considering the recipients' convenience than the sender of the information. When we assign prefixes to all figures equally, two or more kinds of expressions combined with everyday word, such as dozen and gross, will arise to the same quantity. It's a mistake to evaluate this situation from the view point of the sender of information "it's flexible". We should evaluate from the view point of the recipient of information and make it a problem that it will be easy to produce misunderstanding if many expressions of the same quantity exist. Even if anyone works as a sender as for the same information in the same context, it should become the same expression. It is an ideal that any quantity is expressed with "a number of daily use X prefix X unit" uniquely. In above situation, it is qualitatively the same as the existence of two or more units that a lot of expressions of the same amount exist. There is no worth to unify the units. Even the SI assigned prefixes to all figures at first. However, after the late 19th century, it switched to a method to assign every three figures. There is an aggressive reason to attempt the convenience of the recipients of the information as well as the negative reason that the etymology which should be made a source is limited. Unit power prefixes must be sparse to avoid using them in the same context. It is important to analyze natural languages and existing unit system including the SI without prejudice. Of course current dozenal myriad system is not a best. From the point of view of this article, it is welcome if you can do suggestion to be improved more. <Supplements> I assume the border of the every day use and the science and technology use to be 10;^4 . I think that it's no problem that similar forms of another words appear in different contexts each other. See also http://suchowan.at.webry.info/theme/c16d13ae17.html , especially 2012 July articles. 
Posted by: Takashi Mar 31 2015, 09:58 AM 
The followings are quotation of the associated part of the SI definition document. http://www.bipm.org/utils/common/pdf/si_brochure_8.pdf  1.1 Quantities and units (p.103) In order to establish a system of units, such as the International System of Units, the SI, it is necessary first to establish a system of quantities, including a set of equations defining the relations between those quantities. This is necessary because the equations between the quantities determine the equations relating the units, as described below.  2.2.2 Units with special names and symbols; units that incorporate special names and symbols (p.117) Among these names and symbols the last four entries in Table 3 are of particular note since they were adopted by the 15th CGPM (1975, Resolutions 8 and 9; CR, 105 and Metrologia, 1975, 11, 180), the 16th CGPM (1979, Resolution 5; CR, 100 and Metrologia, 1980, 16, 56) and the 21st CGPM (1999, Resolution 12; CR, 334335 and Metrologia, 2000, 37, 95) specifically with a view to safeguarding human health.  3.1 SI prefixes (p.122) Compound prefix symbols, that is, prefix symbols formed by the juxtaposition of two or more prefix symbols, are not permitted. This rule also applies to compound prefix names.  5.1 Unit symbols (p.130) A prefix is never used in isolation, and compound prefixes are never used.  5.3.1 Value and numerical value of a quantity, and the use of quantity calculus (p.132) Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra. This procedure is described as the use of quantity calculus, or the algebra of quantities. For example, the equation T = 293 K may equally be written T/K = 293. It is often convenient to write the quotient of a quantity and a unit in this way for the heading of a column in a table, so that the entries in the table are all simply numbers. 
Posted by: Takashi Mar 31 2015, 09:59 AM 
Please see http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&view=findpost&p=22128654 and http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf . The dozenal myriad system is comprised of the 'second sequence' coming from classical language, too. 1: m (role of 'un') 2: b (role of 'bi') 3: mib (role of 'tri') 4: tr (role of: 'quad') 5: mitr (role of 'pent') 6: bitr (role of 'hex') 7: mibitr (role of 'sept') dozenal context mark: y 0: lli (role of 'nil') positive power: on (role of 'qua') negative power: no (role of 'cia') The characteristic is following:  Its radix is octal. Therefore, each digit of dozenal myriad system('second sequence') and octal exponential notation('first sequence') of myllion correspond mutually. (Please see http://z13.invisionfree.com/DozensOnline/index.php?showtopic=594&view=findpost&p=22006945 .)  For pattern matching optimization and sparseness in everyday life discussed in previous articles, another expressions are used in the range 12^012^7. As for second sequence 57, it is most important that the rule is clear because almost they are not used. Moreover it is preferred that length of these words is varied. 
Posted by: Kodegadulo Apr 1 2015, 01:05 AM  
Note that this was a study of English language reading comprehension. Modern English is a language that has relatively few inflections. The predecessor languages it evolved from were much more highly inflected, such that many closelyrelated shades of meaning differed only by the nature of a final ending of a word. ProtoIndoEuropean was a highly inflected language indeed, but there has been a steady erosion of inflection over the millenniums since then, and in Modern English most of that has disappeared. English words now tend to be more concise than their ancestors, with both the start and end of words tending to be parts of the original "roots" of their ancient inflected forms. So this phenomenon of English words remaining understandable even when their letters are jumbled, so long as their first and last letters remain anchored in the same positions, might only work in such a language. Has such a study been attempted with other languages, such as Spanish, Italian, Greek, Russian, etc., which still retain much of the ancient inflected character of IndoEuropean? Would, say, a noun in Spanish still be recognizable if only its first letter and its final vowel (which usually just indicates its gender) remained in place, but the final consonant of its root was in a random spot  or does that final root consonant also need to stay in place too, in order to get the same effect that this study found for English? Until such matters are studied in much greater detail, across a broad spectrum of languages, it is hard to make sweeping generalizations about human nature based on such a small sample. Human psychology is a very complicated thing, and it is not amenable to the same reductionist techniques that can be applied to sciences such as physics. Meanwhile, there are still numerous languages that are still highly inflected, and their speakers have absolutely no trouble distinguishing shades of meaning based solely on a difference of endings. In my second language Greek, one can say (I will transliterate this into Latin alphabet): [dohtml] *"Man" in the sense of "human being", without the genderspecificity of the English word "man". That's the declension of a noun. As complex as that seems, it's nothing compared to how ancient Greek nouns were declined. Conjugation of verbs is an even more complex affair, e.g.: [dohtml] I assure you, Greek speakers have absolutely no trouble forming and hearing these slightly different words and instantly understanding the fine gradations of meaning. But that is what they are used to. Speakers of English have a harder time learning such languages as second languages, because their own language does not inflect words nearly as much, so their brains are not as trained to process inflection. Yet English does retain some rudimentary forms of inflection: [dohtml] So here we have words for cardinal numbers, slightly altered by a systematic ending, to give them different meanings as ordinal or reciprocal numbers.
It is not advisable to make sweeping general statements about language based on the dubious choices of the French Metricists. They were not linguistic experts, by any stretch of the imagination. There is no general trend, in English or any language, that absolutely requires that cardinals, ordinals, and reciprocals be completely different words. There are special cases such as "one" vs. "first", and "two" versus "second" versus "half". But those are exceptions, or irregularities, not general rules. English speakers have absolutely no problem distinguishing something that weighs "one million pounds" versus something that weighs "one millionth of a pound", even though these are just slightly different words. So why should there be any trouble distinguishing something that weighs "one hexqua pounds" versus something that weighs "one hexcia of a pound"? 
Posted by: Stella of the Sapphire Apr 5 2015, 04:03 AM 
If as Takashi says, the convenience of recievers is at least as important as that of the sender(s), then a system that clearly marks every power of twelve with distinct numeral roots like the Standard Dozenal Nomenclature (SDN) devised by Kodegadulo is preferable to analogues of Knuth's myllion system that Takashi advocates here. With the SDN a reader can see plainly and clearly that 'hexqua' means twelve ('qua') to the sixth ('hex') power, and 'hexcia' onetwelfth ('cia') to the sixth power and even 'untriqua' as twelve to the dozen('un')andthird('tri') power, right? Something like 'bitryon' (23'positive exponent'?) or 'bitryno' (23'negative exponent') or 'myllimbitrion' (What the hell???) is sure to leave a typical reader in confusion, and surely would look up the guide too many times before finally memorizing this insane system! (see http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf for source of the 'myllion' system referenced here) 
Posted by: Takashi Apr 13 2015, 09:58 AM 
The examples of Kodegadulo do not become the counterexample. It is bacause that most examples are the example by which the difference in the length of the word contributes to their pattern match. The fact that the effectiveness of pattern match does not change when we write Japanese that is an entirely different language with Kana character. I think that it is probably involved in the universal human cognitive style. Stella of the Sapphire, please see http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf . Another expressions are used in the range 12^012^7 for pattern matching optimization and sparseness as described in my previous article. 'bitryon' > gross myriad 'myllimbitrion'(if it means 12^{15}) > migross myriad myllion 'myllion to the power of one two point three'(M^{12@3}) > migross byllion myllillion (migross:3, byllion:2, myllillion:1) 
Posted by: wendy.krieger Apr 14 2015, 12:16 PM 
SI's denial of multiple prefixes, is a reaction against the use of prefixes such as Â”Â”F. The use of multiple prefixes does not cloud the issue, no more than saying 'hundred thousand' does. The reality is that there really isn't a demand for large numbers, except for the money market. The use of `billion' to mean variously 1e9 and 1e12 bears witness to this. But if you really do need large (or small) numbers, there is always the method of `of the order of' or `of the "Nth twelftyband" or the 'twelftydole', which represents positive and negative powers of twelfty. There is no simple expression for fractions in common speech, and here i have been considering naming the negative powers of twelfty too, such as prat (1/120), and thusforth. The romans used weights here, supposing a pound to be a unit. Thus 1/120 is a penny, and 1/14400 is a grain, so 1/9 is thirteen pennies forty grains. A carat, as 1/24, comes from 1/24 of a solidus or roman shilling, or a metkal (the arabic coin that copies it), that saying 22 carat gold, is 22 solidus in the metkal. A carat was formerly divided into four grains (the metric carat of 200 mg is divided into four metric grains of 50 mg, 25 such carats makes 1/5 metric oz of 25 g, which is the weight to two dimes (6d) or the US 'nickel' (3d). 
Posted by: m1n1f1g Apr 16 2015, 12:20 AM  
It's not clear to me how to construct this experiment in Japanese. Even in text with katakana words, there aren't usually enough characters in a word to jumble them up to any great extent. And if there are katakana words, well, we can tell from context what phrase looks like ă±âŠăžă»ăŠâŠăŁ. So please explain, preferably with some evidence that the experiment has been done. The on/no distinction seems to be the result of overfitting to the study. Having said that, it looks rather dubious, by those standards, when written in katakana (ăȘăł and ă end with similarlooking strokes). Even more dubious is the use of the repeated infix âlliâ. We can surely agree that distinguishing words solely on a repeated infix is the worst possible way to do so, from a readability perspective. For some confusing word middles, see: âthoughâ/âthroughâ/âthoroughâ. Repeated infixes are so confusing in speech that I can't imagine them occurring naturally, so I don't have an example. But, as Wendy seems to point out, none of this matters. In all situations, we can assume either context or carefulness. If we have context, we're not going to make multipleorderofmagnitude misreadings without checking. Context is the thing that allows us to interpret the jumbled word âwhotuitâ and to distinguish âmyllionâ from âmyllillionâ. 
Posted by: wendy.krieger Apr 16 2015, 12:11 PM 
The word purple comes from purpur. Repeated syllables can get broken, and sounds can mutate under the presence of other ones (like got you > gotcha). This is something one has to watch in conlanguages. In any case, if a unit does not exist in the right area, people will invent them separately. Measurement dictionaries are full of them: Angstrong, xunit, janksky, siriusweit, light year. parsec, lambda (1e9 litre), micron, debye, darcy, horsepower, it goes on and on. 
Posted by: Takashi May 2 2015, 04:38 AM  
When arguing in http://z13.invisionfree.com/DozensOnline/index.php?showtopic=594 before, my opinion could not be readily understood. However this time, it seems that other people write what I want to insist on.  Very large numbers such as myllillion are actually used hardly because of their largeness. Therefore, it is not so important to ask whether 'lli' is convenient as a morpheme. The important point is the structure rather than the morpheme (*). The purpose of the revision in this time is to correspond 2nd sequence and 1st sequence with a simple rule. 1st sequence : 'myllion to the power of one two point three'(M^{12@3}) 2nd sequence : migross byllion myllillion (migross:3, byllion:2, myllillion:1) (Isaac Asimov's idea named 'Tformation' is helpful.)  The example which assumes '(i)no' and 'on' as pair suffix really exists like 'neutrino' <> 'neutron'. However, 'no' does not conflict with 'on' in daily life because 'on' is not used in the daily life range 12^0  12^7 (*).  In order to introduce an actually required new unit, the prefix which the common frame provides beforehand should be sparse. When the common frame is not sparse, the new unit coexists with the already existing prefix. If there is flexibility of the choice coexisting on the sender side, for the receiver side, it will become rather obstructive. The coexistence of 'pico' and 'micro micro' is similar. The stance of SI about special names is helpful.
 (*) Of course, I welcome suggestions for relatively better morphemes. 
Posted by: Takashi May 24 2015, 05:55 AM 
Calendars in the appendix D of http://dozenal.com/ were discussed in the mailing list CalndrL. If you are interested, please see http://calndrl.10958.n7.nabble.com/JitterofRETakashiSugasCalendarstp15807.html . 
Posted by: Takashi Jun 29 2015, 09:19 AM 
Fundamental physical constants from NIST are revised. ( http://physics.nist.gov/cuu/Constants/index.html ) I revised documents affected by this CODATA revision. Please visit the top left corner of http://dozenal.com . Units converter for UUS, TGM and etc. is also revised. http://hosi.org/cgibin/conv.cgi?m=01000 
Posted by: icarus Jul 2 2015, 03:23 PM 
This is always what I loved about UUS: its basis on fundamental constants. Because of this, however, it needs "recalibration" once in a while. I guess NISTCODATA is to icarus as sevensegmentpetrolstationnumerals are to many other people. 
Posted by: wendy.krieger Jul 3 2015, 01:51 AM 
When the imperial and metric systems were defined on separate standards, then the metreininches ratio depended on the comparison of two different standards, thus. The survey feet come from an era when the ellipsoid of the earth was first measured exactly. Clarke even goes as far as giving a true metre based on his ellipsoid. Kater 1818 1 metre = 39.37079 inches Clarke 1866 1 metre = 39.370432 inches (Survey foot in AUS and RSA) Indian legal 1 metre = 39.370142 inches (Survey foot in India, &c) US legal 1866 1 metre = 39.3700 inches (Suvey foot in US) Beniot 1898 1 metre = 39.370113 Seera and Jolly 1933 1 metre = 39.370147 inches International agreement 1 metre = 39.37007974 All of these represet exeriments that were used to define the inch/metre ratio. There were others that never made it (Rogers 1834 39.37027). One should note that temperature affects the size of things, and the 1911 Encyclopedia notes that a brass metre, of perfect legal exactitude, will, by expanding from 32 F to 62 F, will become a greater number of inches, thus a brass metre becomes 39.382 inches, and this is its true commercial equilivant. The effects are slight, but note that there is the "Enfield inch", used in gun manufacturer, which gives something much closer to 39.382 inches than any of the legal ratios. The CODATA tables, especially for the electron, can be made into a coherent measurement system, with a wonky base (137.036). What we're seeing is that the metric and atomic scales are being djusted in the same way as the foot and metre above. 
Posted by: Takashi Nov 14 2016, 06:02 AM 
myllion  12^{8} byllion  12^{16}  v not: tryllion  12^{24} but: tryllion  12^{32} It will be easy to be misunderstood if 'tr' is used. So, http://www.asahinet.or.jp/~dd6tsg/univunite/myriad.pdf and http://www.asahinet.or.jp/~dd6tsg/univunite/tables.pdf are slightly revised. The pure number counting uses the following series which is only in Latin: bi(2), ter(3) The prefixes to atomic and cosmic use the following Greek series: di(2), tri(3), tetra(4), ... http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf and http://hosi.org:8080/cgibin/conv.cgi?m=01000 have been afected. Online converter URL is http://hosi.org:8080/cgibin/conv.cgi?m=01000 . The port number '8080' is required. 
Posted by: Takashi Nov 15 2016, 08:46 AM 
The UUS is NOT based on CODATA. For example, units of length, time, and mass can be strictly expressed as follows using fundamental physical constants. hm  length : 100,1700; Ω_{1} / R_{∞} nc  time : 10;^{+8} hm / c_{0} ll  looloh : 10;^{+32;} ħ / (c_{0} hm) These expressions have nothing to do with CODATA. The same applies to the other units. The reason for referring to CODATA in http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf etc. is because CODATA describes the relationship between fundamental physical constants and the SI units. Updating the numerical value of CODATA is not a problem of the UUS, it is a matter of the SI unit system. 
Posted by: Takashi Dec 2 2016, 09:25 AM 
[doHTML] It is said that there is a difference of 40 figures between electromagnetic force and gravity. Let  M = 12.^{8} , then  cosmic : M^{+1} ,  atomic : M^{1} . The difference between them becomes M^{2} .  (1)  Elementary charge : M^{2} universal Coulomb  Atomic mass unit : M^{3} looloh The difference between them becomes M . Since this difference exists at both ends, the contribution becomes M^{2} .  (2)  Mass ratio of nucleon and electron : 12.^{3} Since this difference exists at both ends, the contribution becomes 12.^{6} = M / 12.^{2} .  (3) Since both ends of the gravity diagram are 7 x 5 instead of 1 x 1,  7 x 5 = 35. ≒ 12.^{2} / 4  (4) By multiplying (1)(2)(3) and (4) will result in  M^{5} / 4 . Sure it is almost 40 figures. Thus, in the UUS this ratio can be approximated by mental arithmetic. 
Posted by: wendy.krieger Dec 2 2016, 10:58 AM 
The exact values of the values in CODATA are given http://z13.invisionfree.com/DozensOnline/index.php?showtopic=872 In essence, it's based on the electron in the ideal Bohr atom. But unlike conventional approaches, I derive the base from the constants as well. The values are given in decimal, but the units are given in K n SIunit, actually means 137^n of the KO or KU unit that matches it. In practice, 137 is a standin for the 'fine structure hundred' (137.035999056), and different units (like m vs cm) are known to different precisions. The CODATA is then the conversion from this system into SI. When I generate the CODATA data for different systems, i pick the most exact values and derive a system from that. As to gravity, I start with constants near 1, and (1) \( F = M m / 4\pi c_0 a^2 r^2 \) where a ~ 1. (2) \( F = Z_0c_0 Q q / 4\pi r^2 \) where Z_0 ~ 1 If instead of mapping c onto 1, one maps it onto 12^8 for example, then one has L = 12^8 T, and energy = 12^16 mass. Since (1) and (2) above give mass and charge in terms of length and time, you get, where v = L/T = 12^8. cT = T cosmological time (say, one second) cL = v.T cQ = v^3 T cM = v^4 T G ~ 1 You get something very close to the atomic scale, by supposing aT = atomic time &c This comes from the observation that c/ aT = v.T = v cT aL = v.L = v2. cT aQ = v^2 L = v5. cT aM = v^3 M = v7 cT Unlike the usual exponents of a base, v is actually a negativepower, like 12^8. The size of the universe is of the order of T/v^2, and T/v is the order of a century. Unlike Dirac (the large number hypothesis), i don't attatch the age of the universe to any exact point here, instead, suppose that these are some kind of numerical incidence of cosmological consequence. The last two digits in my current dimension numbers derive from the tens as the cosmological scale, and the units as the atomic scale. So eg charge is 132, the first is cQ = v^3 Q, Q = v^2 aT. It's pretty useful. The current system puts the base at A1 (ie the fine structure constant), the electron mass at A30, and the electron charge at A20. The speed of light is A4, and the radius of the electron as A10. The gravitational radius is then about M/L, for the elctron, A10, which gives electron*electron = A20 ~ 10^40. Planck scale, for L, M, T and Q is then A19.5, the planck constant itself is A39. 
Posted by: Kodegadulo Dec 2 2016, 11:21 AM  
You define your UUS units in terms of natural constants. So, technically speaking, the "definition" of your units never changes. But if we get revised values for those natural constants, based on more and more accurate measurements, then the actual values of your units need to change accordingly, if they are to keep with their definitions. But how are we to know exactly how "big" those values are, if we cannot measure them against some kind of stable reference standard? SI units are are not defined in terms natural constants that get revised. They are relatively arbitrary standards, but at least the values for those standards are stable. CODATA is reporting revised values for natural constants, using SI units, but that doesn't matter. Any system with stable standards could be used to report the revised values. We could convert those to TGM, or Primel, or anything else. We could measure them in multiples or fractions of wavelengths of emissions from a specific isotope, and multiples or fractions of oscillation periods of a particular isotope, values we know with extreme accuracy. It doesn't matter. The natural constants you are depending on do not all have perfectly stable values yet. But that is not simply an artifact of how SI defines its units. That is just a fact of life at this point in history. However, the values we do have at this point are probably accurate enough that it won't really matter for most practical purposes. 
Posted by: Takashi Dec 2 2016, 02:38 PM 
It is already decided that the definition of the SI unit system should be replaced with the definition using the fundamental physical constants in the next revision. That is, the SI unit system comes closer to the UUS. As a result, there will be no gap left except units for physical time and electric charge. Since their precisions are at least 10 digits, practical problems do not remain. 
Posted by: Kodegadulo Dec 2 2016, 03:06 PM 
Right, but I would make a distinction to say that SI's units are not "based" on natural units. The notional basis of the SI units are still the quadrant of the Earth, the mean solar day, the density of water, the difference between water"s melting and boiling points, etc. They are simply planning to use natural units as a way to precisely and reproducibly "specify" the SI units. Presumably scientists anywhere in the universe can reproduce the natural constants and then multiply by the correct factors to reproduce the SI units. But your UUS units _are_ based on natural units. 
Posted by: Takashi Dec 2 2016, 09:59 PM 
Right, the UUS units are based on not CODATA but natural constants. 
Posted by: Takashi Dec 2 2016, 10:38 PM 
It may be better to identify the following rather than 'based on': (http://dozenal.wikia.com/wiki/The_Harmonic_System )  Conceptual design  Strict definition  Common usage image(?) From the last point of view, I want the following facts to be known more. (http://z13.invisionfree.com/DozensOnline/index.php?showtopic=1550&st=43 )  The quadrant meridian length of the Earth : almost strictly equal to 10. ^ 7 SI meters and roughly(=2.5% difference) equal to 12. ^ 7 times length unit  9 / 8 days : roughly(=2.8% difference) equal to 10. ^ 5 SI seconds and almost strictly equal to 12. ^ 5 times physical time unit  The density of ice < 12. ^ 2 times density unit < the density of water  When heat of unit energy is added to water of unit mass, the temperature rises twice the unit temperature. 
Posted by: Kodegadulo Dec 2 2016, 10:42 PM 
Yes... but we only know how big those natural constants are, to whatever degree scientists have been able to measure them so far. When they do so, they report the data in SI units. It does not mean your units are based on SI, but we only know how big your units actually are to the extent that we can relate them to accurate data. 
Posted by: Takashi Jan 18 2017, 10:01 AM 
I think that the following three points should be commented on the article http://z13.invisionfree.com/DozensOnline/index.php?showtopic=1569&view=findpost&p=40003531. 1. I wrote to http://www.asahinet.or.jp/~dd6tsg/univunite/Errata.html quite a while ago, http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf p.23 B.4 Figure 1 and the expressions of B.3 are quoted from different manuscripts. For this reason the symbols of both do not correspond. Currently the most reliable description is http://www.asahinet.or.jp/~dd6tsg/univunite/revised.pdf p.13. 2. I put a translation of the excerpt of the textbook which became the original story of http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf Appendix B.4 as http://www.asahinet.or.jp/~dd6tsg/univunite/electromagnetism.pdf. (Since this textbook adopts the MKS rationalized unit system, the solid angle is dimensionless.) 3. As can be seen from http://www.asahinet.or.jp/~dd6tsg/univunite/univunite.pdf Appendix B and http://www.asahinet.or.jp/~dd6tsg/univunite/electromagnetism.pdf, we can construct a mathematically and physically consistent system with the dimension of 'turn' as the solid angle. This does not immediately deny the existence of a mathematically and physically consistent system with the dimension of 'turn' as the plane angle. However, I do not know how to make it possible to withstand the discussion on http://www.asahinet.or.jp/~dd6tsg/univunite/electromagnetism.pdf pp.810, while setting the dimension of 'turn' as a plane angle. 
Posted by: wendy.krieger Jan 19 2017, 08:42 AM 
The idea of turns and loops, arises from Maxwell's notion that magnetism is a vortex in a fluid. The other model of magnetism is the WeberLorentz model that it is due to a moving charge. The equations look like this. (1) \( \vec D = Q\vec s \qquad \vec H = Qv \times\vec s\) (2) \(\vec F = Q\vec E \qquad \vec F = Qv \times \vec B\) (3) \( E = zcD \quad = \quad zH = cB \) While Weber constructed magnetism as an extension of electrics, Lorentz deals with 'electrons' (ie charged particles'), where the 'current' is actually a stream of charged particles. The sum \(F = F_e+F_m\) is the lorentzforce, and the extra equality in (3) is what is required to keep photons as single entities across the boundary condition. The idea of circulation (turns) is due to Maxwell's notion that the EM field exists in a compressionless viscousless fluid (where we get Maxwell's equations from). None the same, circulation has been quite clearly demonstrated in transformers. 
Posted by: wendy.krieger Jan 19 2017, 09:59 AM 
The issues discussed on page 810 of your PDF has little to do with turns. The point O in the diagram on page 6, sees the two loops as magnetic dipoles, rather than current loops. That it sees m=IA and m'=IA', so positioned that m/r^2 = m'/r'^2. In any case, that I is not seen means this is not connected to the solid angle. The vector area A does not change when the surface changes. It is a geometric trick, that relies on volume not changing with coordinate, and that volume is the moment of surface. (1) \( V = \int x \cdot dS\quad \) volume = sum of coordinate dot surface normal. (2) \( \int dS = 0 \quad \) volume does not depend on coordinate, has zero sum We now suppose that the loop L is part of a solid bounded by two shells S and S+. Since S + S+ = 0, we can keep S and replace S+ with any other surface that is bounded by S. Ampere Current A current as Q/T, can be read as a linear density (1/L) of individual moving charges (QL/T). This reduces the current to a stream of several different things. In a coil, the current goes around and around many times, but the magnetic field is being produced by n different instances of Qv. If the coil is a 1000 qv's we would find that the flux is due to #16, and #1016, and #2016, and #3016 etc, rather than several instances of current. In the diagram on page 10, we see the doublecrossing is due to two instances of qv crossing the plane formed by the loop. So the point P is actually 'hearing' the current from two different points. The idea of 'ampere current' is magnetically defined by m='I'A, would be equal to the 'electric current', only if all the parts of 'I' were collected. But in a coil, we hear different instances of qv, that what would be spread over 50 metres is wrapped into 1 dm. We here it 500 times not from one lot of qv, but 500 separate instances of qv. When turns matter Dimensionally, turns have been connected when an electric current is coiled to an amperecurrent, or magneticflux is coiled into faradayflux. Since without the turn concept, it is not possible to define electrics from magnetics, the turn is used to allow separate electrical and magnetic systems to be part of a common system. The idea is to measure a charge electrostatically, and then measure the time it takes for this charge to discharge, measuring the current in magnetics. This experiment has been repeated many times (speed of light by emu/esu), and is one of the key parts involved in showing that light is an electromagnetic effect. Dimensionally, it is easy to find. For electric quantities, one supposes that I is unchanged, or replace IT with Q. For magnetic quantities, one replaces I with IU. In equations with both electric and magnetic quantities, the values of U will not be balanced, and the CGS form is found by balancing out U with U = 1/c [which is the size of 1 turn in c curls]. \[ \nabla \times \overset{U}{H} = \tau D + J \qquad \nabla \times \overset{U}{H} = \overset{U}{U}\tau D + \overset{U}{U}J \qquad \nabla \times {H} = \frac 1c\tau D + \frac 1c J\] Note here the dimensional analysis goes term over term, that is, + and  are treated as equals. It's like "metres = metres + metres". 
Posted by: Kodegadulo Jan 19 2017, 06:30 PM  
This is so garbled. \(d\mathbf{S}\) is a differential of a vector area. The integral of this over some surface \(S\) is not a volume and is not zero. It is simply the total area of the surface, i.e. \(\displaystyle\iint_S d\mathbf{S} = S\). Really now, this is pretty elementary calculus. 
Posted by: wendy.krieger Jan 20 2017, 12:52 AM 
Theęe vectors, hun. Not scalars. (1) is the moment of outvector, (2) is the sum of outvectors. 