This forum contains discussion related to the UUS.

The Universal Unit System and its notaions

Takashi
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Takashi
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Jul 4 2010, 12:10 PM #1

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
- black-body radiation in the ice melting point
- density of water
- surface tension of water
- the half of specific heat of water
- the twice of Stephan-Boltzmann constant
etc.

The unit quantities and constant expressions are shown in the table retrievable at
http://www.asahi-net.or.jp/~dd6t-sg/uni ... densed.xls.

See also http://z13.invisionfree.com/DozensOnlin ... c=371&st=9

Please give your opinions about the Universal Unit System and its notation.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Takashi
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Jul 4 2010, 12:11 PM #2

# This is a comment to [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=137&st=32]http://z13.invisionfree.com/DozensOnline/i...topic=137&st=32[/url] In the paper [url=http://dozenal.com]http://dozenal.com[/url], I proposed Variation 1 and Variation 2-A. Variation 2-B was proposed in the Dozens Online. After discussion, I newly discovered Variation 2-C. 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 2-A. - If the unit 'hour' is disregarded, the variation 2-C. I think that Variation 2-C 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 2-A and 2-B. See also [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=5]http://z13.invisionfree.com/DozensOnline/i...wtopic=371&st=5[/url] Please give your opinions. ------ Variation 1 : This variation is corresponding to the Calendar 1 described in §D.1.1 of [url=http://dozenal.com]http://dozenal.com[/url]. Variation 2-A : This variation is corresponding to the Calendar 2 described in §D.1.2 of [url=http://dozenal.com]http://dozenal.com[/url]. Variation 2-B : This variation is proposed by Mr. icarus in the article [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=137&st=30]http://z13.invisionfree.com/DozensOnline/i...topic=137&st=30[/url]. Variation 2-C : A new variation [code] <Present system>                   <Variation 1>  over range                   over range      |                            |      : powers of 10               : powers of 12      |                            |    century                       octal century -+      | 100                        |             |    *year                          |             | 2^6 (= 8^2)      | 12                         |             |    *month                         |           *year      | 28-31                      |               |    *day                           |1.0020*12^6    | 1.0020*3^6/2      | 2 * 12                     |               |    *hour                          |           *day      | 60                         |             |    *minute                        |             | 2^7 (= 2 * 8^2)      | 60                         |             |    *second                      *clock ---------+      |                            |      : powers of 10               : powers of 12      |                            |  under range                  under range    <Variation 2-A>                <Variation 2-B>                <Variation 2-C> over range                     over range                     over range    |                              |                              |    : powers of 12                 : powers of 12                 : powers of 12    |                              |                              |   octal century -+               octal century -+               octal century -+    |             |                |             |                |             |    |             | 2^6 (= 8^2)    |             | 2^6 (= 8^2)    |             | 2^6 (= 8^2)    |             |                |             |                |             |    |           *year              |           *year              |           *year    |               |              |               |              |               |    |               | 1.0020*3^6   |               | 1.0020*3^6   |               | 1.0020*3^6/2    |1.0020*12^7    |              |1.0020*12^7    |              |1.0020*12^9    |    |            half a *day       |            half a *day       |           *day    |             |                |             |                |             |    |             | 12             |             | 2^3 (= 8)      |             | 12^3    |             |                |             |                |             |    |           *hour              |           *octal hour        |           milli day    |             |                |             |                |             |    |             | 2^6 (= 8^2)    |             | 2^3*12 (=8*12) |             | 2^7 (=2*8^2)    |             |                |             |                |             |  *octal minute --+              *octal minute --+              *milli clock  --+    |                              |                              |    : powers of 12                 : powers of 12                 : powers of 12    |                              |                              | under range                    under range                    under range * The ratio of these units cannot be approximated by integer powers of their base number. [/code]
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Takashi
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Jul 8 2010, 09:48 AM #3

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 [url=http://dozenal.com]http://dozenal.com[/url]. ** '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. The part enclosed with '()' can be omitted. ------------ The above-proposed is an explanation of the prefixes put on the unit. As for how to count the pure numbers, I propose base twelve [url=http://en.wikipedia.org/wiki/-yllion]myriad system[/url] replacing 10/ten/hundred with 12/dozen/gross.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 8 2010, 10:58 AM #4

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.) [url=http://www.dozenal.org/archive/DuodecimalBulletinIssue402-web.pdf]http://www.dozenal.org/archive/DuodecimalB...ssue402-web.pdf[/url] . * 'si' is not used.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Takashi
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Jul 10 2010, 06:09 PM #5

If the variation 2-C is selected, the earth local extension for the Universal Unit System may become a following system: ***** A mil(li day) is equal to H. C. Churchman's 'moment'.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 11 2010, 01:18 AM #6

The variations are due to the following intention. [The Variation 2-A] 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 2-B] 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 1-10;(1-12.) into 1-8, and the speed of the minute hand is adjusted to 2/3. An 'hour' is 1 and half times greater than the variation 2-A and a 'minute' is the same as the variation 2-A. [The Variation 2-C'] 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 2-A and 2-B. 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 Titius-Bode law, the orbital semi-major 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.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 11 2010, 07:32 AM #7

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 [url=http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls]http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls[/url] . -------- [EDIT] The unit of thermodynamic temperature has been changed. The new unit is one-10000;th of the old unit. Quantities are updated using [url=http://physics.nist.gov/cuu/Constants/index.html]CODATA(2010)[/url] [EDIT 2012-02-03] The power prefixes are revised.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 11 2010, 11:44 AM #8

The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit) become a following system: -------- [EDIT] The unit of thermodynamic temperature has been changed. The new unit is one-10000;th of the old unit. Quantities are updated using [url=http://physics.nist.gov/cuu/Constants/index.html]CODATA(2010)[/url]
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 12 2010, 10:52 PM #9

The comparison of time units of the Universal Unit Systems
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 13 2010, 01:06 PM #10

The point at issue is as follows:

Q1> Which Universal Unit System should be selected?
( See http://z13.invisionfree.com/DozensOnlin ... c=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/DozensOnlin ... c=371&st=1 )
1. Variation 1
2. Variation 2-A
3. Variation 2-B
4. Variation 2-C
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/DozensOnlin ... c=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/DozensOnlin ... c=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
[Q1-1, Q2-1 or 2, Q3-1, Q4-"don't care"].

If this is not acceptable from the viewpoint of human activity,
I propose another answer [Q1-3, Q2-4, Q3-1, Q4-1].

Please show your opinions.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Shaun
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Shaun
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Joined: Aug 2 2005, 04:09 PM

Jul 14 2010, 08:55 AM #11

This, I find, is all going over my head.
I still think the hour should be kept.
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.
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Takashi
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Jul 14 2010, 03:17 PM #12

[quote="Shaun @ Jul 14 2010, 08:55 AM"]I still think the hour should be kept.[/quote] 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 [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=26&st=25]http://z13.invisionfree.com/DozensOnline/i...wtopic=26&st=25[/url] and [url=http://z13.invisionfree.com/DozensOnline/index.php?showtopic=26&st=30]http://z13.invisionfree.com/DozensOnline/i...wtopic=26&st=30[/url] . This presumption indicates another variation 2-D. The variation 2-C' and 2-D don't contradict each other. The variation 2-C' 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.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 18 2010, 07:36 AM #13

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 [url=http://dozenal.com]http://dozenal.com[/url] . Non coherent supplementary constants (powers of radian)
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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The Mighty Dozen
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Jul 18 2010, 03:28 PM #14

Shaun @ Jul 14 2010, 08:55 AM wrote: This, I find, is all going over my head.
I still think the hour should be kept.
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.
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With cold and stone-hard stares and unmoved mind,
Is just to make him see what's plainly true:
He's like an animal, nay, is one too.
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Takashi
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Jul 22 2010, 01:54 PM #15

Shaun and Bryan, thank you for your opinions. The following calendar time notations can coexist: '10;-hour clock' notation -> (AM|PM)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.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 22 2010, 01:55 PM #16

The symbols of the Universal Unit System are brought together in the quartets. Therefoe, they can be arranged as follows:
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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icarus
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icarus
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Joined: Apr 11 2006, 12:29 PM

Jul 25 2010, 01:40 AM #17

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 24-cell 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.
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Ruthe
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Jul 27 2010, 08:31 PM #18

icarus @ Jul 25 2010, 01:40 AM wrote: 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.
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!
Why a Roman pocket abacus? They used dozenal fractions as their main form of fractions, 12 inches per foot & originally 12 oz per pound (inch=ounce=uncia=1/12). Columns 1 & 2 of the abacus are for dozenal fractions, column two for twelfths and column one, dozenal fractions of a twelfth. Columns 3 through 8 provided a decimal place value system with values from 1s to millions where each lower bead counts as 1 & the upper beads count 5 of a column's base 10 power, Is, Vs, Xs, Ls, Cs ,Ds, Ms etc.
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Cymbyz
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Jul 28 2010, 02:16 AM #19

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 number-bases (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).
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Shaun
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Jul 28 2010, 04:21 PM #20

and there's also the "ten-headed beast", isn't there?
I use the following conventions for dozenal numbers in my posts.

* prefixes a dozenal number, e.g. *50 = 60.
The apostrophe (') is used as a dozenal point, e.g. 0'6 = 0.5.
T and E stand for ten and eleven respectively.
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Cymbyz
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Jul 28 2010, 05:37 PM #21

Yes. Actually, all sorts of numerological what's-its in the Bible, a minefield to trip up the ardent literalist--or even the amateur "decoder."
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Takashi
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Aug 2 2010, 03:34 AM #22

icarus @ Jul 25 2010, 01:40 AM wrote:If you've got a fancy system, show me
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.
Ruthe @ Jul 27 2010, 08:31 PM wrote: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.
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.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Aug 2 2010, 03:35 AM #23

The angle is a good example what consideration being done for the consistency.

I think that non-rational units (rad,sr) and rational units (&#937;1=2pi rad,&#937;2=4pi sr) are both necessary.
The typical example is shown in Appendix B of http://dozenal.com.
Non-rational 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 high-dimensional hyperspheres in general.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Aug 10 2010, 09:24 AM #24

This is comment to the post
1. h vs &#295;

The Plank constant h appears only in shape 'h &#957;', where &#957; is frequency.

On the other hand, &#295; appears directly in the canonical commutation relation,
[X,P] = XP - PX = i &#295;,
that is basic related to the uncertainty principle.
Therefore usage of &#295; is not limited to the cycle phenomenon, and &#295; is used widely.

So I decided that it was more effective to express not h but &#295; 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 &#937;/ sr = 376.730 313 461 &#937;/ &#937;2.
Therefore the dimension of electric charge is not dimension of sqrt(energy * time / The characteristic impedance of vacuum).
If 376.730 313 461 &#937; 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.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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