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Takashi 
Posted: Jul 4 2010, 12:10 PM

Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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/i...wtopic=371&st=9 Please give your opinions about the Universal Unit System and its notation. 
Takashi 
Posted: Jul 4 2010, 12:11 PM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
# This is a comment to http://z13.invisionfree.com/DozensOnline/i...topic=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/i...wtopic=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/i...topic=137&st=30. Variation 2C : A new variation


Takashi 
Posted: Jul 8 2010, 09:48 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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. prefix example
** '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. unit example
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 myriad system replacing 10/ten/hundred with 12/dozen/gross. 

Takashi 
Posted: Jul 8 2010, 10:58 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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/DuodecimalB...ssue402web.pdf . prefix example
* 'si' is not used. 

Takashi 
Posted: Jul 10 2010, 06:09 PM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
If the variation 2C is selected, the earth local extension for the Universal Unit System
may become a following system: The earth local extension for the Universal Unit System with the GCD unit
* The suffix E is used for the Earth characteristics as a celestial body. g_{E} is defined that the gravitational radius of the Earth is expressed as g_{E} * (m_{E} * rad / c_{0})^{2}. See §C.1 of http://dozenal.com . ** See §A.3.1 of http://dozenal.com . *** It seems that the dimension of the quantity of a day can be plane angle rather than physical time. The calendar time is, in a word, the rotation angle of the earth derived by using the direction of the sun as a coordinate origin. See Seaman,Rob (April 2003). "Proposal to Upgrade UTC" retrievable at http://iraf.noao.edu/~seaman/leap/ . **** the units suffixed e is units of the Universal Unit System with the GCD unit [calendar time unit s_{e} = 2^{7}10;^{3} day( correspondent to 0.390625 s)]. See a sheet 'Clock' in http://www.asahinet.or.jp/~dd6tsg/univunite/condensed.xls . [Variation 2C'] over range  : powers of 10;  octal century +   2^6  year 1;003628*10;^9  1;003628*3^6/2  day   10;^3  md [mil(li day)] *****   2^7 smd [septi m(illi day)]+  : powers of 10;  under range***** A mil(li day) is equal to H. C. Churchman's 'moment'. 

Takashi 
Posted: Jul 11 2010, 01:18 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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.
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. 

Takashi 
Posted: Jul 11 2010, 07:32 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
The Harmonic Universal Unit System is a Universal Unit System (with the GCD Unit) which uses 1001700;/R_{∞} as a length unit. A letter 'h', which means 'human' or 'harmonic universal', is suffixed to the corresponding SI unit symbols to use in place of the new symbols required by the Harmonic Universal Unit System (with the GCD Unit). For example, the length unit is m_{h} and called 'harmonic universal meter', and the time unit is s_{h} and called 'harmonic universal second'.The units of this system are listed in the following table.
The physical, material and astronomical constants expressed by means of this system are presented in the following table.
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 CODATA(2010) [EDIT 20120203] The power prefixes are revised. 

Takashi 
Posted: Jul 11 2010, 11:44 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit) become a following system:
The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit)
* 1; Ω_{1} m_{E} = 40,007,860. m (called 'Earth meridian circle': the total meridian length of the Earth) 1; rad m_{E} = 6,367,449. m (called 'Earth meridian radian': the radius length of the Earth) 0;0001 Ω_{1} m_{E} = 1,929.391 m (called 'Earth meridian semiatomic circle': dozenal nautical mile) ** 0.0 °S_{h} is corresponding to 118,2356; K_{h}(definition) 0.0 °C is corresponding to 51;5 °S_{h} 14.0 °C is corresponding to 61;0 °S_{h} 37.0 °C is corresponding to 78;0 °S_{h} 100.0 °C is corresponding to 100;0 °S_{h} [EDIT] The unit of thermodynamic temperature has been changed. The new unit is one10000;th of the old unit. Quantities are updated using CODATA(2010) 

Takashi 
Posted: Jul 12 2010, 10:52 PM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
The comparison of time units of the Universal Unit Systems


Takashi 
Posted: Jul 13 2010, 01:06 PM

Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
The point at issue is as follows:
Q1> Which Universal Unit System should be selected? ( See http://z13.invisionfree.com/DozensOnline/i...wtopic=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/i...wtopic=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/i...wtopic=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/i...wtopic=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. 
Shaun 
Posted: Jul 14 2010, 08:55 AM

Dozens Disciple Group: Admin Posts: 1,116 Member No.: 3 Joined: 2August 05 
This, I find, is all going over my head.
I still think the hour should be kept. 
Takashi 
Posted: Jul 14 2010, 03:17 PM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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/i...wtopic=26&st=25 and http://z13.invisionfree.com/DozensOnline/i...wtopic=26&st=30 . This presumption indicates another variation 2D. [Variation 2A'] [Variation 2D] over range over range   : powers of 10; : powers of 10;   octal century + octal century +   2^6   2^6  year  year 1;003628*10;^9  1;003628*3^6/2 1;003628*10;^9  1;003628*3^6/2  day  day+   20;   20;  hour  10;^3 hour   2^6   60;  octal minute  md [mil(li day)]   10;^2   2^7 smd [septi m(illi day)]+ smd [septi m(illi day)]+   : powers of 10; : powers of 10;   under range under range 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. 

Takashi 
Posted: Jul 18 2010, 07:36 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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)


The Mighty Dozen 
Posted: Jul 18 2010, 03:28 PM


Administrator Group: Admin Posts: 571 Member No.: 1 Joined: 2August 05 
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. 

Takashi 
Posted: Jul 22 2010, 01:54 PM

Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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. [Variation 2D'] over range  : powers of 10;  octal century +   2^6  year 1;003628*10;^9  1;003628*3^6/2  day+    2   halfday(AM/PM)  10;^3  10;   hour   60;  md [mil(li day)]   2^7 smd [septi m(illi day)]+  : powers of 10;  under range 
Takashi 
Posted: Jul 22 2010, 01:55 PM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
The symbols of the Universal Unit System are brought together in the quartets.
Therefoe, they can be arranged as follows:


icarus 
Posted: Jul 25 2010, 01:40 AM

Dozens Demigod Group: Admin Posts: 1,913 Member No.: 50 Joined: 11April 06 
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. 
Ruthe 
Posted: Jul 27 2010, 08:31 PM


Regular Group: Members Posts: 361 Member No.: 47 Joined: 27February 06 
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! 

Cymbyz 
Posted: Jul 28 2010, 02:16 AM

Casual Member Group: Members Posts: 40 Member No.: 27 Joined: 8September 05 
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).

Shaun 
Posted: Jul 28 2010, 04:21 PM

Dozens Disciple Group: Admin Posts: 1,116 Member No.: 3 Joined: 2August 05 
and there's also the "tenheaded beast", isn't there?

Cymbyz 
Posted: Jul 28 2010, 05:37 PM

Casual Member Group: Members Posts: 40 Member No.: 27 Joined: 8September 05 
Yes. Actually, all sorts of numerological what'sits in the Bible, a minefield to trip up the ardent literalistor even the amateur "decoder."

Takashi 
Posted: Aug 2 2010, 03:34 AM


Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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 here. I want to discuss topics about requirement for general unit system there, and discuss topics only concerning about the Universal Unit System here. 

Takashi 
Posted: Aug 2 2010, 03:35 AM

Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
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. 
Takashi 
Posted: Aug 10 2010, 09:24 AM

Regular Group: Members Posts: 186 Member No.: 571 Joined: 12April 10 
This is comment to the post
1. h vs ħ The Plank constant h appears only in shape 'h ν', where ν is frequency. On the other hand, ħ appears directly in the 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. 
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