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 The Universal Unit System and its notaions, The Universal Unit System
Silvano
Posted: Oct 9 2014, 01:47 AM


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QUOTE (dgoodmaniii @ Oct 8 2014, 09:04 PM)
QUOTE (Kodegadulo @ Oct 8 2014, 04:04 PM)
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 "sixty-ten".

Indeed, it's exactly like "sixty-ten": soisante-dix. You then proceed soisante-once, soisante-douze, and so forth, up to soisante-dix-neuf, literally "sixty-ten-nine." The next number is quatre-vingt, "four twenties." And our "ninety-nine" is quatre-vingt-dix-neuf, 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."

To be more precise:
It's soixante-dix, soixante-onze, soixante-treize... soixante-dix-neuf,
quatre-vingts, quatre-vingt-un, quatre-vingt-deux...
quatre-vingt-dix, quatre-vingt-onze... quatre-vingt-dix-neuf.

(Louis IX founded in 1260 a hospital named Hôpital des Quinze-Vingts, 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 (half-third, that is two and a half [twenties])
60 : tres (three [twenties])
70 : halvfjerds
80 : firs
90 : halvfems
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Takashi
Posted: Oct 11 2014, 01:22 AM


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The basic requirements for number counting and prefix system are follows:

1) Sparseness of new vocabulary (->sorry, machine translation of a blog article)
2) Do not convert 2 and 3 into 100 and 1000 in the domain of daily use. (->sorry, machine translation of a blog article)

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 three-ness but thousand-ness) 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.
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Takashi
Posted: Oct 11 2014, 01:52 AM


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For the reference of the recent arguments

http://www.sf.airnet.ne.jp/~ts/language/number.html
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Takashi
Posted: Oct 20 2014, 10:21 AM


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conv.cgi has become able to handle IDUS's units.

http://hosi.org/cgi-bin/conv.cgi?m=10080
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Silvano
Posted: Oct 20 2014, 11:26 AM


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QUOTE (Takashi @ Oct 20 2014, 06:21 AM)
conv.cgi has become able to handle IDUS's units.

Good news!
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m1n1f1g
Posted: Oct 27 2014, 02:30 PM


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QUOTE (Takashi @ Oct 11 2014, 02:22 AM)
1) Sparseness of new vocabulary (->sorry, machine translation of a blog article)
2) Do not convert 2 and 3 into 100 and 1000 in the domain of daily use. (->sorry, machine translation of a blog article)

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 non-regular system. The regular SDN system can be made non-regular by ad-hoc addition of prefixes.

SDN's denseness gives the advantage of flexibility. Noöne needs to use both “triqua” and “quadqua” in the same context, but they can choose which one they are going to use.
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Takashi
Posted: Nov 1 2014, 10:11 AM


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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.

QUOTE (Takashi @ April 22, 2012 01:58 AM)
Because a unit system is a tool to communicate information, it is necessary
to design both convenience of senders and addressees of the information.

Because the number of senders and addressees of information is one-to-many
correspondence in most cases, the convenience of the addressees is more
important than those of the senders.

Even if anyone works as a sender as for the same information in the same context,
it should become the same expression.

However, proposers of unit system are apt to assume the convenience of the sender
the policy of their design.

This is often unconsciousness.
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Kodegadulo
Posted: Nov 2 2014, 11:27 AM


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QUOTE (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.

QUOTE (Takashi @  April 22, 2012 01:58 AM)
Because a unit system is a tool to communicate information, it is necessary
to design both convenience of senders and addressees of the information.

Because the number of senders and addressees of information is one-to-many
correspondence in most cases, the convenience of the addressees is more
important than those of the senders.

Even if anyone works as a sender as for the same information in the same context,
it should become the same expression.

However, proposers of unit system are apt to assume the convenience of the sender
the policy of their design.

This is often unconsciousness.

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.
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Silvano
Posted: Nov 5 2014, 09:55 PM


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QUOTE (dgoodmaniii @ Dec 24 2011, 11:21 AM)
[ I think that this basis in everyday, human-scaled 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.

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.
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Takashi
Posted: Nov 14 2014, 12:49 AM


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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 ambiguity-free communication rather than efficiency.
It is result of this thought that SI inhibits multi-prefix 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 non-dozenelists 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.
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wendy.krieger
Posted: Nov 14 2014, 10:13 AM


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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 þj : fps BTU = lb.°Fj ; cgs calorie = g °Cj ; MKS Calorie kg °Cj
gravitational: Mg L : fps duty = ft.lbf ; cgs cm-pond = gf cm; MKS m-kp = kgf m
"energy": L²M/T²: fps foot-poundal ; cgs erg; MKS joule

mass: Mg T²/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.°C, is a dimensioned quantity with a pure number.

Base Units

The number of base units is arbitary, but SI is over-supplied 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: Length-Mass-Time is a carry-over of national weights and measures (foot-pound-gallon), 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 lb-mole of water.

In short, the g-mole is a derived unit, but in SI, it is a base unit, because they use kg with g-mole, 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 'axle-loads'. 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. Axle-loads, 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 'ton-leo' and a force-to-gravity 'ton-force'. For practical purposes, a ton-leo = ton-force = ton, and one does not have to convert anything. Quoting a bridge axle-load 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 spig-litre = 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 dimension-number 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 0-100 covers the 'habitable scale'. The scales based around ice-point 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 'human-cold' at some 0 figure, and 'human-hot' at 100, and have ice-point 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, z|18E 0000; in TIOF, zd|101,00,00: 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 large-scale 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 bp-ip 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.
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wendy.krieger
Posted: Nov 16 2014, 07:49 AM


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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 radian-length is 1/(rydberg wave constant), and heads from there,

The electrical units in size, follow the UES rule NU.

The unit-names 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 oersted-sr (O-sr). 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.
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Kodegadulo
Posted: Nov 16 2014, 10:48 PM


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QUOTE (wendy.krieger @ Nov 16 2014, 07:49 AM)
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.

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 blind-spots 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.
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wendy.krieger
Posted: Nov 17 2014, 01:45 AM


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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. More-over, SI reflects a different level of thinking to the base metrology.

SDN labels its prefixes by column-number, so that '3' represents column 3. To put this sort of number beside a real '3', you need to invoke a second-number series. Writing something lke three tri-metre would be as confusing to a program as writing three mitsu-metre 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 thousand-base, because the ten-base can get a little tedious. However the metrics never scaled their prefixes right, so you a prefix for every thousand rather than a double-prefix, like µµ and mµ, 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 'metre-candle' = lux vs cm-candle = 10,000 lux.

SI prefixes are simply in-collapsed 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.
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Kodegadulo
Posted: Nov 17 2014, 02:42 AM


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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 ad-hoc names and the mapping to thousand-base. So do natural-language "million" systems, whether short or long scale, because of the mapping to thousand-base or million-base. 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 mantissa-digits from power-exponents; mark the latter sufficiently to avoid confusing them with the former. The "ordinal-cardinal" 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 ("mitsu-lengthel") might succeed if the learning-curve is not too hard.
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m1n1f1g
Posted: Nov 18 2014, 08:11 PM


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QUOTE (Takashi @ Nov 14 2014, 01:49 AM)
"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.

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.
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Silvano
Posted: Nov 18 2014, 08:44 PM


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QUOTE (m1n1f1g @ Nov 18 2014, 03:11 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.

But Takashi's harmonic system doesn't do that.
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Takashi
Posted: Nov 25 2014, 02:28 AM


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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/i...opic=371&st=146 [Jun 19 2014, 10:28 AM],

and this change affected the first figure in the article:
http://z13.invisionfree.com/DozensOnline/i...topic=371&st=87 [Dec 18 2011, 08:55 AM].
-------

QUOTE (=wendy.krieger @ Nov 16 2014, 07:49 AM)
It is rather strange why he opts to set a time length as a base unit

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 revised.pdf simply.
Like derived units with peculiar name, convenient units are chosen as base units as the starting point of derivation.
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Kodegadulo
Posted: Nov 25 2014, 02:46 AM


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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 original description at the top of the original thread.
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Takashi
Posted: Mar 31 2015, 09:58 AM


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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 present-day 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.
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Takashi
Posted: Mar 31 2015, 09:58 AM


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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, 334-335
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.
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Takashi
Posted: Mar 31 2015, 09:59 AM


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Please see http://z13.invisionfree.com/DozensOnline/i...post&p=22128654
and http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/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/i...post&p=22006945 .)

- For pattern matching optimization and sparseness in everyday life discussed in previous articles,
another expressions are used in the range 12^0-12^7.

As for second sequence 5-7, 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.
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Kodegadulo
Posted: Apr 1 2015, 01:05 AM


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QUOTE (Takashi @ Mar 31 2015, 09:58 AM)
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.

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 closely-related shades of meaning differed only by the nature of a final ending of a word. Proto-Indo-European 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 Indo-European? 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):
o ánthropos = the man* [singular, nominative case, subject of a sentence].
ton ánthropo = the man [singular, accusative case, object of a verb or preposition].
tu anthrópu = of the man / to the man [singular, genitive or dative case, possession or indirect object]
ó ánthrope = O man [singular, vocative case, addressing someone spoken to]
i anthrópi = the men [plural, nominative case, subject of a sentence].
tus anthrópus = the men [plural, accusative case, object of a verb or preposition].
ton anthrópon = of the men [plural, genitive or dative case, possession or indirect object]

*"Man" in the sense of "human being", without the gender-specificity 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.:
káno = I do [present tense, first person singular].
kánis = you do [present tense, second person singular].
káni = he/she/it does [present tense, third person singular].
kánome = we do [present tense, first person plural].
kánete = you do [present tense, second person plural].
kánun = they do [present tense, third person plural].
ékana = I did [past tense, first person singular]
ékanes = you did [past tense, second person singular]
ékane = he/she/it did [past tense, third person singular]
ekáname = we did [past tense, first person plural]
ekánate = you did [past tense, second person plural]
ékanan = they did [past tense, second person plural]


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:

hundred= 100d[cardinal]
hundredth= 100thd
= 1/100d
[ordinal]
[reciprocal]
thousand= 1000d[cardinal]
thousandth= 1000thd
= 1/1000d
[ordinal]
[reciprocal]
million= 1,000,000d[cardinal]
millionth= 1,000,000thd
= 1/1,000,000d
[ordinal]
[reciprocal]


So here we have words for cardinal numbers, slightly altered by a systematic ending, to give them different meanings as ordinal or reciprocal numbers.

QUOTE
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.

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"?
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Stella of the Sapphire
Posted: Apr 5 2015, 04:03 AM


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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 'hex-qua' means twelve ('-qua') to the sixth ('hex-') power, and 'hex-cia' one-twelfth ('-cia') to the sixth power and even 'un-tri-qua' as twelve to the dozen('un-')-and-third('tri-') power, right? Something like 'bi-try-on' (2-3-'positive exponent'?) or 'bi-try-no' (2-3-'negative exponent') or 'my-lli-m-bi-tri-on' (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 here for source of the 'myllion' system referenced here)
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