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Title: The Universal Unit System and its notaions
Description: The Universal Unit System


Takashi - July 4, 2010 12:10 PM (GMT)
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/univunit-e/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 - July 4, 2010 12:11 PM (GMT)
# 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 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 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 2-A : This variation is corresponding to the Calendar 2 described in §D.1.2 of http://dozenal.com.
Variation 2-B : This variation is proposed by Mr. icarus in the article
http://z13.invisionfree.com/DozensOnline/i...topic=137&st=30.
Variation 2-C : A new variation

[doHTML]
<TABLE BORDER=1>
<TR><TD>Variation</TD><TD>Connection Range</TD><TD>Non Coherent Units</TD></TR>
<TR><TD>Present system</TD><TD>-</TD><TD>year,month,day,hour,minute</TD></TR>
<TR><TD>Variation 1</TD><TD>675s-1day</TD><TD>year,day</TD></TR>
<TR><TD>Variation 2-A</TD><TD>56.25s-1.0hour,1.0hour-1day</TD><TD>year,day,hour</TD></TR>
<TR><TD>Variation 2-B</TD><TD>56.25s-1.5hour,1.5hour-1day</TD><TD>year,day,octal hour</TD></TR>
<TR><TD>Variation 2-C</TD><TD>0.390625s-50s</TD><TD>year,day</TD></TR>
</TABLE>
[/doHTML]

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.

Takashi - July 8, 2010 09:48 AM (GMT)
The following descriptions are ideas for discussion
about prefix notations of the Universal Unit System.
------------
The symbol of the unit of the Universal Unit System is a symbol
that adds the suffix to the symbol of the corresponding SI unit.

Because the Universal Unit System is designed that the ratios of
some fundamental physical constants and the corresponding unit quantities
become integer powers of 12.^8(*), we cannot adopt SI prefixes
out of range between 1/12.^3 and 12.^3.

* See the last paragraph of §3.3 of the paper http://dozenal.com.

[doHTML]
prefix example
<TABLE BORDER=1>
<TR><TD colspan=2>prefix name</TD><TD>value[dozenal]</TD><TD>value[decimal]</TD><TD colspan=2>prefix name</TD><TD>value[dozenal]</TD><TD>value[decimal]</TD></TR>
<TR><TD>da</TD><TD>(do)deka</TD><TD>10;<sup>1</sup></TD><TD>12.<sup>1</sup></TD><TD>d</TD><TD>(do)deci</TD><TD>10;<sup>-1</sup></TD><TD>12.<sup>-1</sup></TD></TR>
<TR><TD colspan=4>-</TD><TD>s</TD><TD>septi **</TD><TD>2<sup>-7</sup></TD><TD>2<sup>-7</sup></TD></TR>
<TR><TD>h</TD><TD>hecto</TD><TD>10;<sup>2</sup></TD><TD>12.<sup>2</sup></TD><TD>c</TD><TD>centi</TD><TD>10;<sup>-2</sup></TD><TD>12.<sup>-2</sup></TD></TR>
<TR><TD>k</TD><TD>kilo</TD><TD>10;<sup>3</sup></TD><TD>12.<sup>3</sup></TD><TD>m</TD><TD>milli</TD><TD>10;<sup>-3</sup></TD><TD>12.<sup>-3</sup></TD></TR>
<TR><TD colspan=2>semi-cosmic</TD><TD>10;<sup>4</sup></TD><TD>12.<sup>4</sup></TD><TD colspan=2>semi-atomic</TD><TD>10;<sup>-4</sup></TD><TD>12.<sup>-4</sup></TD></TR>
<TR><TD colspan=2>(uni-)cosmic</TD><TD>10;<sup>8</sup></TD><TD>12.<sup>8</sup></TD><TD colspan=2>(uni-)atomic</TD><TD>10;<sup>-8</sup></TD><TD>12.<sup>-8</sup></TD></TR>
<TR><TD colspan=2>bi-cosmic</TD><TD>10;<sup>14;</sup></TD><TD>12.<sup>16.</sup></TD><TD colspan=2>bi-atomic</TD><TD>10;<sup>-14;</sup></TD><TD>12.<sup>-16.</sup></TD></TR>
<TR><TD colspan=2>tri-cosmic</TD><TD>10;<sup>20;</sup></TD><TD>12.<sup>24.</sup></TD><TD colspan=2>tri-atomic</TD><TD>10;<sup>-20;</sup></TD><TD>12.<sup>-24.</sup></TD></TR>
<TR><TD colspan=2>quadri-cosmic</TD><TD>10;<sup>28;</sup></TD><TD>12.<sup>32.</sup></TD><TD colspan=2>quadri-atomic</TD><TD>10;<sup>-28;</sup></TD><TD>12.<sup>-32.</sup></TD></TR>
<TR><TD colspan=2>quinti-cosmic</TD><TD>10;<sup>34;</sup></TD><TD>12.<sup>40.</sup></TD><TD colspan=2>quinti-atomic</TD><TD>10;<sup>-34;</sup></TD><TD>12.<sup>-40.</sup></TD></TR>
<TR><TD colspan=2>sexti-cosmic</TD><TD>10;<sup>40;</sup></TD><TD>12.<sup>48.</sup></TD><TD colspan=2>sexti-atomic</TD><TD>10;<sup>-40;</sup></TD><TD>12.<sup>-48.</sup></TD></TR>
<TR><TD colspan=2>hepti-cosmic ***</TD><TD>10;<sup>48;</sup></TD><TD>12.<sup>56.</sup></TD><TD colspan=2>hepti-atomic ***</TD><TD>10;<sup>-48;</sup></TD><TD>12.<sup>-56.</sup></TD></TR>
</TABLE>[/doHTML]
** 'septi' (SEventh Power of Two Inversed) is only for the earth local extension.
*** Greek prefix is used to distinguish from 'septi'.

SI units are combined only with the decimal figures, and
units of the Universal Unit System are combined only with dozenal figures.
Therefore, if prefix 'milli' is used with dozenal figures or units,
'milli' expresses 1/12.^3.

[doHTML]
unit example
<TABLE BORDER=1>
<TR><TD>[prefixed] unit name</TD><TD>symbol</TD><TD>symbol[plain text]</TD><TD>value</TD><TD>refer to</TD></TR>
<TR><TD>universal second</TD><TD>s<sub><i>u</i></sub></TD><TD>s_u</TD><TD>1; (universal) second</TD><TD>-</TD></TR>
<TR><TD>semi-cosmic (universal) meter</TD><TD>m<sub>s+<i>u</i></sub></TD><TD>m_s+u</TD><TD>10;<sup>4</sup> (universal) meter</TD><TD>-</TD></TR>
<TR><TD>(uni-)cosmic (universal) meter</TD><TD>m<sub>+<i>u</i></sub></TD><TD>m_+u</TD><TD>10;<sup>8</sup> (universal) meter</TD><TD>the speed of light in vacuum</TD></TR>
<TR><TD>uni(- and )s(emi)-cosmic (universal) meter</TD><TD>m<sub>1s+<i>u</i></sub></TD><TD>m_1s+u</TD><TD>10;<sup>10;</sup> (universal) meter</TD><TD>-</TD></TR>
<TR><TD>(uni-)atomic (universal) (do)deci meter</TD><TD>dm<sub>-<i>u</i></sub></TD><TD>dm_-u</TD><TD>10;<sup>-9</sup> (universal) meter</TD><TD>the Bohr radius</TD></TR>
<TR><TD>bi-atomic (universal) Coulomb</TD><TD>C<sub>2-<i>u</i></sub></TD><TD>C_2-u<TD>10;<sup>-14;</sup> (universal) Coulomb</TD><TD>the charge of an electron</TD></TR>
<TR><TD>tri-atomic (universal) gram</TD><TD>g<sub>3-<i>u</i></sub></TD><TD>g_3-u<TD>10;<sup>-20;</sup> (universal) gram</TD><TD>the unified atomic mass unit</TD></TR>
</TABLE>
[/doHTML]
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 myriad system
replacing 10/ten/hundred with 12/dozen/gross.

Takashi - July 8, 2010 10:58 AM (GMT)
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...ssue402-web.pdf .

[doHTML]
prefix example
<TABLE BORDER=1>
<TR><TD>prefix name</TD><TD>Hymnus in Ioannem</TD><TD>value[dozenal]</TD><TD>value[decimal]</TD></TR>
<TR><TD>fa</TD><TD>4 Famuli tuorum</TD><TD>10;<sup>3</sup></TD><TD>12.<sup>3</sup></TD></TR>
<TR><TD>so</TD><TD>5 Solve polluti</TD><TD>10;<sup>2</sup></TD><TD>12.<sup>2</sup></TD></TR>
<TR><TD>la</TD><TD>6 Labii reatum</TD><TD>10;<sup>1</sup></TD><TD>12.<sup>1</sup></TD></TR>
<TR><TD>si*</TD><TD>7 Sancte Ioannes</TD><TD>10;<sup>0</sup></TD><TD>12.<sup>0</sup></TD></TR>
<TR><TD>do</TD><TD>1 Ut queant laxis</TD><TD>10;<sup>-1</sup></TD><TD>12.<sup>-1</sup></TD></TR>
<TR><TD>re</TD><TD>2 Resonare fibris</TD><TD>10;<sup>-2</sup></TD><TD>12.<sup>-2</sup></TD></TR>
<TR><TD>mi</TD><TD>3 Mira gestorum</TD><TD>10;<sup>-3</sup></TD><TD>12.<sup>-3</sup></TD></TR>
</TABLE>
[/doHTML]
* 'si' is not used.

Takashi - July 10, 2010 06:09 PM (GMT)
If the variation 2-C is selected, the earth local extension for the Universal Unit System
may become a following system:

[doHTML]
The earth local extension for the Universal Unit System with the GCD unit
<TABLE BORDER=1>
<TR><TD colspan=2>Non coherent unit / prefix type</TD><TD>Non coherent unit / prefix name</TD><TD>symbol</TD><TD>symbol[plain text]</TD><TD>value</TD></TR>
<TR><TD rowspan=5>calendar time</TD><TD>prefix</TD><TD>septi</TD><TD colspan=2 align=center>s</TD><TD>2<sup>-7</sup></TD></TR>
<TR><TD rowspan=4>units</TD><TD rowspan=2>day</TD><TD rowspan=2 colspan=2 align=center>d</TD><TD>Ω<sub>1</sub>(=2 pi rad) ***</TD></TR>
<TR><TD>86,400. s</TD></TR>
<TR><TD>year</TD><TD colspan=2 align=center>y</TD><TD>365. 31./128. days</TD></TR>
<TR><TD>octal century</TD><TD align=center>C<sub><i>o</i></sub></TD><TD>C_o</TD><TD>64. years</TD></TR>
<TR><TD rowspan=4 colspan=2>supplementary constants</TD><TD>the gravitational acceleration of the Earth (is called '-force')</TD><TD align=center>g<sub><i>E</i></sub>*</TD><TD>g_E</TD><TD>9.831209 m/s<sup>2</sup></TD></TR>
<TR><TD>the rotation period of the Earth (is called 'Earth solar')</TD><TD align=center>s<sub><i>E</i></sub></TD><TD>s_E</TD><TD>86,400. s/Ω<sub>1</sub></TD></TR>
<TR><TD>the meridian length of the Earth (is called 'Earth meridian')</TD><TD align=center>m<sub><i>E</i></sub></TD><TD>m_E</TD><TD>40,007,860. m/Ω<sub>1</sub></TD></TR>
<TR><TD>difference of thermodynamic temperature and the ice point</TD><TD align=center>°K<sub><i>e</i></sub>**,****</TD><TD>degree K_e</TD><TD>1; K<sub><i>e</i></sub>****</TD></TR>
</TABLE>
<PRE>
* The suffix E is used for the Earth characteristics as a celestial body.
g<sub><i>E</i></sub> is defined that the gravitational radius of the Earth is expressed as g<sub><i>E</i></sub> * (m<sub><i>E</i></sub> * rad / c<sub>0</sub>)<sup>2</sup>.
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<sub><i>e</i></sub> = 2<sup>-7</sup>10;<sup>-3</sup> day( correspondent to 0.390625 s)].
See a sheet 'Clock' in http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls .

[Variation 2-C']
over range
|
: powers of 10;
|
<u>octal century</u> -------+
| | 2^6
| <u>year</u>
|1;003628*10;^9 | 1;003628*3^6/2
| <u>day</u>
| | 10;^3
| <u>md [mil(li day)]</u> *****
| | 2^7
<u>smd [septi m(illi day)]</u>-+
|
: powers of 10;
|
under range
</PRE>[/doHTML]***** A mil(li day) is equal to H. C. Churchman's 'moment'.

Takashi - July 11, 2010 01:18 AM (GMT)
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.

[doHTML]
<table border=1>
<tr>
<td colspan=2 rowspan=3>calendar time range</td>
<td><p align=center>base ten</p></td>
<td colspan=4><p align=center>base twelve</p></td>
</tr>
<tr>
<td rowspan=2><p align=center>present calendar time</p></td>
<td rowspan=2><p align=center>variation 1</p></td>
<td colspan=3><p align=center>variation 2</p></td>
</tr>
<tr>
<td><p align=center>A</p></td>
<td><p align=center>B</p></td>
<td><p align=center>C'</p></td>
</tr>
<tr>
<td colspan=2><p align=center>century</p></td>
<td><p align=center>10.<sup>2</sup>years</p></td>
<td><p align=center>10;<sup>6</sup></p><p align=center>clock</p></td>
<td><p align=center>10;<sup>7</sup></p><p align=center>octal minutes</p></td>
<td><p align=center>10;<sup>7</sup></p><p align=center>octal minutes</p></td>
<td><p align=center>10;<sup>9</sup></p><p align=center>septi milli days</p></td>
</tr>
<tr>
<td colspan=2><p align=center>year</p></td>
<td><p align=center><b>year</b></p></td>
<td><p align=center><b>year</b></p></td>
<td><p align=center><b>year</b></p></td>
<td><p align=center><b>year</b></p></td>
<td><p align=center><b>year</b></p></td>
</tr>
<tr>
<td colspan=2><p align=center>month</p></td>
<td><p align=center><b>month</b></p></td>
<td><p align=center>10;<sup>-1</sup>year</p></td>
<td><p align=center>10;<sup>-1</sup>year</p></td>
<td><p align=center>10;<sup>-1</sup>year</p></td>
<td><p align=center>10;<sup>-1</sup>year</p></td>
</tr>
<tr>
<td rowspan=5><p align=center>day</p></td>
<td><p align=center>order(1)</p></td>
<td><p align=center><b>day</b></p></td>
<td><p align=center><b>day</b></p></td>
<td><p align=center><b>day</b></p></td>
<td><p align=center><b>day</b></p></td>
<td><p align=center><b>day</b></p></td>
</tr>
<tr>
<td><p align=center>order(1/10)</p></td>
<td><p align=center><b>hour</b></p><p align=center><b>(T<sub>110</sub>)</b></p></td>
<td><p align=center>10;</p><p align=center>clocks</p></td>
<td><p align=center><b>hour</b></p><p align=center><b>(T<sub>110</sub>)</b></p></td>
<td><p align=center><b>octal hour</b></p><p align=center><b>(T<sub>400</sub>)</b></p></td>
<td><p align=center>10;<sup>2</sup></p><p align=center>milli days</p></td>
</tr>
<tr>
<td><p align=center>order(1/10<sup>2</sup>)</p></td>
<td><p align=center>10. minutes</p></td>
<td><p align=center><b>clock</b></p><p align=center><b>(T<sub>700</sub>)</b></p></td>
<td><p align=center>10;</p><p align=center>octal minutes</p></td>
<td><p align=center>10;</p><p align=center>octal minutes</p></td>
<td><p align=center>10;<sup>1</sup></p><p align=center>milli days</p></td>
</tr>
<tr>
<td><p align=center>order(1/10<sup>3</sup>)</p></td>
<td><p align=center><b>minute</b></p><p align=center><b>(T<sub>111</sub>)</b></p></td>
<td><p align=center>10;<sup>-1</sup></p><p align=center>clock</p></td>
<td><p align=center><b>octal minute</b></p><p align=center><b>(T<sub>710</sub>)</b></p></td>
<td><p align=center><b>octal minute</b></p><p align=center><b>(T<sub>710</sub>)</b></p></td>
<td><p align=center>milli day</p><p align=center>(10;<sup>-3 </sup>day)</p></td>
</tr>
<tr>
<td><p align=center>order(1/10<sup>5</sup>)</p></td>
<td><p align=center><b>second</b></p><p align=center><b>(T<sub>112</sub>)</b></p></td>
<td><p align=center>10;<sup>-3</sup></p><p align=center>clock</p></td>
<td><p align=center>10;<sup>-2</sup></p><p align=center>octal minute</p></td>
<td><p align=center>10;<sup>-2</sup></p><p align=center>octal minute</p></td>
<td><p align=center><b>septi milli day</b></p><p align=center><b>(T<sub>730</sub>)</b></p></td>
</tr>
</table>
[/doHTML]
where Txyz = 2^(-x)*10;^(-y)*50;^(-z) day (= 2^(-x)*12.^(-y)*60.^(-z) day)

The ratio of the same column units indicated in boldface cannot be approximated by integer powers of their base number.

Takashi - July 11, 2010 07:32 AM (GMT)
[doHTML]
<pre>
The Harmonic Universal Unit System is a Universal Unit System (with the GCD Unit)
which uses 1001700;/R<sub>∞</sub> 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<sub><i>h</i></sub> and called 'harmonic universal meter',
and the time unit is s<sub><i>h</i></sub> and called 'harmonic universal second'.
</pre>
[/doHTML]The units of this system are listed in the following table.
[doHTML]
<table border=1>
<tr>
<td>Dimension</td>
<td>Unit Symbol</td>
<td colspan=2>SI expression</td>
</tr>
<tr>
<td>Length</td>
<td>m<sub><i>h</i></sub></td>
<td align=right>272.352206</td>
<td>mm</td>
</tr>
<tr>
<td>Time</td>
<td>s<sub><i>h</i></sub></td>
<td align=right>390.625115</td>
<td>ms</td>
</tr>
<tr>
<td>Energy</td>
<td>J<sub><i>h</i></sub></td>
<td align=right>64.084550</td>
<td>mJ</td>
</tr>
<tr>
<td>Thermodynamic temperature</td>
<td>K<sub><i>h</i></sub></td>
<td align=right>58.387545</td>
<td>μK</td>
</tr>
<tr>
<td>Amount of substance</td>
<td>mol<sub><i>u</i></sub></td>
<td align=right>132.007609</td>
<td>mol</td>
</tr>
<tr>
<td>Mass</td>
<td>g<sub><i>h</i></sub></td>
<td align=right>131.829278</td>
<td>g</td>
</tr>
<tr>
<td>Work</td>
<td>W<sub><i>h</i></sub></td>
<td align=right>164.056401</td>
<td>mW</td>
</tr>
<tr>
<td>Force</td>
<td>N<sub><i>h</i></sub></td>
<td align=right>235.300280</td>
<td>mN</td>
</tr>
<tr>
<td>Pressure</td>
<td>P<sub><i>h</i></sub></td>
<td align=right>3.172201</td>
<td>Pa</td>
</tr>
<tr>
<td>Charge</td>
<td>C<sub><i>u</i></sub></td>
<td align=right>28.896577</td>
<td>mC</td>
</tr>
<tr>
<td>Electrical current</td>
<td>A<sub><i>h</i></sub></td>
<td align=right>73.975215</td>
<td>mA</td>
</tr>
<tr>
<td>Impedance</td>
<td>Ω<sub><i>n</i></sub></td>
<td align=right>29.9792458</td>
<td>Ω</td>
</tr>
<tr>
<td>Electrical potential difference</td>
<td>A<sub><i>h</i></sub>Ω<sub><i>n</i></sub></td>
<td align=right>2.2177212</td>
<td>V</td>
</tr>
<tr>
<td>Electrical capacitance</td>
<td>s<sub><i>h</i></sub>/Ω<sub><i>n</i></sub></td>
<td align=right>13.029851</td>
<td>mF</td>
</tr>
<tr>
<td>Magnetic flux</td>
<td>C<sub><i>h</i></sub>Ω<sub><i>n</i></sub></td>
<td align=right>0.866298</td>
<td>Wb</td>
</tr>
<tr>
<td>Magnetic flux density</td>
<td>G<sub><i>h</i></sub>Ω<sub><i>n</i></sub></td>
<td align=right>11.678991</td>
<td>T</td>
</tr>
<tr>
<td>Inductance</td>
<td>s<sub><i>h</i></sub>Ω<sub><i>n</i></sub></td>
<td align=right>11.710646 </td>
<td>H</td>
</tr>
</table>
[/doHTML]
The physical, material and astronomical constants expressed by means of this system are presented in the following table.
[doHTML]
<table border=1>
<tr>
<td>Constants</td>
<td>Dozenal</td>
<td>Prefix</td>
<td>Unit Symbol</td>
</tr>
<tr>
<td>Fine Structure Constant</td>
<td>1;07399404E</td>
<td>centy</td>
<td>-</td>
</tr>
<tr>
<td>Avogadro constant</td>
<td><b>1;</b></td>
<td><b>try-cosmic</b></td>
<td>1/mol<sub><i>u</i></sub></td>
</tr>
<tr>
<td>Rydberg constant</td>
<td><b>1;001700</b></td>
<td>cosmic centy</td>
<td>1/m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Speed of light in vacuum</td>
<td><b>1;</b></td>
<td><b>cosmic</b></td>
<td>m<sub><i>h</i></sub>/s<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Quantum of action</td>
<td><b>1;</b></td>
<td>quadry-atomic hecty</td>
<td>J<sub><i>h</i></sub> s<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Boltzmann constant</td>
<td><b>1;</b></td>
<td><b>try-atomic</b></td>
<td>J<sub><i>h</i></sub>/K<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Gas constant</td>
<td><b>1;</b></td>
<td><b>-</b></td>
<td>J<sub><i>h</i></sub>/(mol<sub><i>u</i></sub> K<sub><i>h</i></sub>)</td>
</tr>
<tr>
<td>Unified atomic mass unit</td>
<td>1;0024073</td>
<td><b>try-atomic</b></td>
<td>g<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Bohr Radius</td>
<td>1;00447X743</td>
<td>atomic dour</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Elementary electric charge</td>
<td>1;0374439E3</td>
<td><b>by-atomic</b></td>
<td>C<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Electron mass</td>
<td>0;E48324X</td>
<td>try-atomic milly</td>
<td>g<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Newtonian constant of gravitation</td>
<td>4;1460</td>
<td>atomic centy</td>
<td>(m<sub><i>h</i></sub>/s<sub><i>h</i></sub>)<sup>4</sup>/N<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Newtonian gravitational force constant</td>
<td>2X;EE7</td>
<td>quinty-cosmic</td>
<td>N<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Planck length</td>
<td>2;0412</td>
<td><b>quadry-atomic</b></td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Stephan-Boltzmann
constant</td>
<td>1E;82E29</td>
<td>try-atomic</td>
<td>W<sub><i>h</i></sub>/m<sub><i>h</i></sub><sup>2</sup>/K<sub><i>h</i></sub><sup>4</sup></td>
</tr>
<tr>
<td>Black-body radiation at the ice point</td>
<td>0;EX8783</td>
<td>hecty</td>
<td>W<sub><i>h</i></sub>/m<sub><i>h</i></sub><sup>2</sup></td>
</tr>
<tr>
<td>Temperature of the triple point of water</td>
<td>1;6974X3</td>
<td>cosmic centy</td>
<td>K<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Molar volume of an ideal gas</td>
<td>1;025664</td>
<td>hecty</td>
<td>m<sub><i>h</i></sub><sup>3</sup>/mol<sub><i>u</i></sub></td>
</tr>
<tr>
<td>neutral pH * : -log(Sqrt([H+][OH-])/(mol<sub><i>u</i></sub>/m<sub><i>h</i></sub><sup>3</sup>))</td>
<td>7;2X71</td>
<td>-</td>
<td>B<sub><i>z</i></sub>(=log(10;))</td>
</tr>
<tr>
<td>Maximum density of water</td>
<td>1;092X47</td>
<td>hecty</td>
<td>g<sub><i>h</i></sub>/m<sub><i>h</i></sub><sup>3</sup></td>
</tr>
<tr>
<td>Density of ice at the ice point</td>
<td>0;E85E</td>
<td>hecty</td>
<td>g<sub><i>h</i></sub>/m<sub><i>h</i></sub><sup>3</sup></td>
</tr>
<tr>
<td>Specific heat of water</td>
<td>0;6045</td>
<td>-</td>
<td>J<sub><i>h</i></sub>/g<sub><i>h</i></sub>/K<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Surface tension of water at 25°C</td>
<td>0;EEE4</td>
<td>dour</td>
<td>N<sub><i>h</i></sub>/m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Standard atmosphere</td>
<td>1;659967</td>
<td>super</td>
<td>P<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Standard gravitational acceleration</td>
<td>5;5E21264</td>
<td>-</td>
<td>m<sub><i>h</i></sub>/s<sub><i>h</i></sub><sup>2</sup></td>
</tr>
<tr>
<td>Gravitational radius of the earth</td>
<td>2;4180317</td>
<td>centy</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Equatorial radius of the earth</td>
<td>0;7X145E</td>
<td>cosmic dour</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Meridian length of the earth / 4</td>
<td>1;0370649</td>
<td>cosmic dour</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Gravitational radius of the sun</td>
<td>3;1798E857</td>
<td>kily</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Astronomical unit</td>
<td>8;X55509X33</td>
<td>cosmic hecty</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td rowspan=2>Astronomical unit / c<sub>0</sub></td>
<td>8;X55509X33</td>
<td>hecty</td>
<td>s<sub><i>h</i></sub></td>
</tr>
<tr>
<td>9;E91731X53</td>
<td>-</td>
<td>milly day</td>
</tr>
</table>
* decimal pH 7.0 ± 7.0 is corresponding to dozenal pH (7 and quarter) ± (6 and half).
[/doHTML]

See a sheet 'Clock_by_Rydberg' in http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls .
--------
[EDIT]
The unit of thermodynamic temperature has been changed. The new unit is one-10000;th of the old unit.
Quantities are updated using CODATA(2010)
[EDIT 2012-02-03]
The power prefixes are revised.

Takashi - July 11, 2010 11:44 AM (GMT)
The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit) become a following system:

[doHTML]
The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit)
<TABLE BORDER=1>
<TR><TD colspan=2>Non coherent unit / prefix type</TD><TD>Non coherent unit / prefix name</TD><TD>symbol</TD><TD>symbol[plain text]</TD><TD>value</TD></TR>
<TR><TD rowspan=5>calendar time</TD><TD>prefix</TD><TD>septi</TD><TD colspan=2 align=center>s</TD><TD>2<sup>-7</sup></TD></TR>
<TR><TD rowspan=4>units</TD><TD rowspan=2>day</TD><TD rowspan=2 colspan=2 align=center>d</TD><TD>Ω<sub>1</sub>(=2 pi rad)</TD></TR>
<TR><TD>corresponding to 86,400. s<br>at the beginning of year 1900.</TD></TR>
<TR><TD>year</TD><TD colspan=2 align=center>y</TD><TD>365. 31./128. days</TD></TR>
<TR><TD>octal century</TD><TD align=center>C<sub><i>o</i></sub></TD><TD>C_o</TD><TD>64. years</TD></TR>
<TR><TD rowspan=4 colspan=2>supplementary constants</TD><TD>the gravitational acceleration of the Earth (is called '-force')</TD><TD align=center>g<sub><i>E</i></sub></TD><TD>g_E</TD><TD>5;611X63X m<sub><i>h</i></sub>/s<sub><i>h</i></sub><sup>2</sup></TD></TR>
<TR><TD>the rotation period of the Earth (is called 'Earth solar')<br>at the beginning of year 1900.</TD><TD align=center>s<sub><i>E</i></sub></TD><TD>s_E</TD><TD>0;EEEEEE153586 s<sub><i>h</i></sub>/septi milli Ω<sub>1</sub></TD></TR>
<TR><TD>the meridian length of the Earth (is called 'Earth meridian')</TD><TD align=center>m<sub><i>E</i></sub> *</TD><TD>m_E</TD><TD>4124,216E; m<sub><i>h</i></sub>/Ω<sub>1</sub></TD></TR><TR><TD>difference of thermodynamic temperature and the base point</TD><TD align=center>°S<sub><i>h</i></sub></TD><TD>degree(s) S (degree(s) semi-cosmic harmonic Kelvin)</TD><TD>10000; K<sub><i>h</i></sub> **</TD></TR>
</TABLE>
<PRE>
* 1; Ω<sub>1</sub> m<sub><i>E</i></sub> = 40,007,860. m (called 'Earth meridian circle': the total meridian length of the Earth)
1; rad m<sub><i>E</i></sub> = 6,367,449. m (called 'Earth meridian radian': the radius length of the Earth)
0;0001 Ω<sub>1</sub> m<sub><i>E</i></sub> = 1,929.391 m (called 'Earth meridian semi-atomic circle': dozenal nautical mile)

** 0.0 °S<sub><i>h</i></sub> is corresponding to 118,2356; K<sub><i>h</i></sub>(definition)
0.0 °C is corresponding to 51;5 °S<sub><i>h</i></sub>
14.0 °C is corresponding to 61;0 °S<sub><i>h</i></sub>
37.0 °C is corresponding to 78;0 °S<sub><i>h</i></sub>
100.0 °C is corresponding to 100;0 °S<sub><i>h</i></sub>
</PRE>
[/doHTML]--------
[EDIT]
The unit of thermodynamic temperature has been changed. The new unit is one-10000;th of the old unit.
Quantities are updated using CODATA(2010)

Takashi - July 12, 2010 10:52 PM (GMT)
The comparison of time units of the Universal Unit Systems
[doHTML]
<table border=1>
<tr>
<td rowspan=2 colspan=2>system name</td>
<td>Type I</td>
<td>Type II</td>
<td>Type III</td>
</tr>
<tr>
<td>the Universal System of Units Standard</td>
<td>the Universal Unit System with the GCD Unit</td>
<td>the Harmonized Universal Unit System (with the GCD Unit)</td>
</tr>
<tr>
<td>suffix</td>
<td>-</td>
<td><i>u</i></td>
<td><i>e</i></td>
<td><i>h</i></td>
</tr>
<tr>
<td>suffix meaning</td>
<td>-</td>
<td>'universal'</td>
<td>the GCD of calendar time units of the 'earth'</td>
<td>'human' or 'harmonized universal'</td>
</tr>
<tr>
<td>time unit called</td>
<td>-</td>
<td>'universal second'</td>
<td>'GCD second'</td>
<td>'harmonized universal second' or simply 'harmonized second'</td>
</tr>
<tr>
<td>length unit called</td>
<td>-</td>
<td>'universal meter'</td>
<td>'GCD meter'</td>
<td>'harmonized universal meter' or simply 'harmonized meter'</td>
</tr>
<tr>
<td>length unit definition</td>
<td>-</td>
<td>1000000;/R<sub>∞</sub></td>
<td>86400.s * c<sub>0</sub> / 128. / 12.^11.</td>
<td>1001700;/R<sub>∞</sub></td>
</tr>
<tr>
<td>basic ratio</td>
<td>-</td>
<td>R<sub><i>u/u</i></sub> = 1;</td>
<td>R<sub><i>e/u</i></sub> = 1;0016EE</td>
<td>R<sub><i>h/u</i></sub> = 1;001700</td>
</tr>
<tr>
<td>length unit quantity</td>
<td>m</td>
<td align=right>0.272102883</td>
<td align=right>0.272352126</td>
<td align=right>0.272352206</td>
</tr>
<tr>
<td>time unit quantity</td>
<td>s</td>
<td align=right>0.390267520</td>
<td align=right>0.390625000</td>
<td align=right>0.390625115</td>
</tr>
<tr>
<td>mass unit quantity</td>
<td>kg</td>
<td align=right>0.131950058</td>
<td align=right>0.131829304</td>
<td align=right>0.131829266</td>
</tr>
<tr>
<td>time unit * 128. * 12.^3</td>
<td>s</td>
<td align=right>86,320.9312</td>
<td align=right>86,400.0000</td>
<td align=right>86,400.0255</td>
</tr>
<tr>
<td>difference from 86400.s</td>
<td>ms</td>
<td align=right>-79,068.7564</td>
<td align=right>0.0000</td>
<td align=right>25.4611</td>
</tr>
<tr>
<td>(time unit * 128. * 12.^3) just becomes 1 day</td>
<td>-</td>
<td>about 4.7 million years ago</td>
<td>the beginning of 20th century</td>
<td>about 1400. years later</td>
</tr>
</table>
[/doHTML]

Takashi - July 13, 2010 01:06 PM (GMT)
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 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/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
[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.

Shaun - July 14, 2010 08:55 AM (GMT)
This, I find, is all going over my head.
I still think the hour should be kept.

Takashi - July 14, 2010 03:17 PM (GMT)
QUOTE (Shaun @ Jul 14 2010, 08:55 AM)
I still think the hour should be kept.

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 2-D.

[doHTML]
<PRE>
[Variation 2-A'] [Variation 2-D]
over range over range
| |
: powers of 10; : powers of 10;
| |
<u>octal century</u> -------+ <u>octal century</u> -------+
| | 2^6 | | 2^6
| <u>year</u> | <u>year</u>
|1;003628*10;^9 | 1;003628*3^6/2 |1;003628*10;^9 | 1;003628*3^6/2
| <u>day</u> | <u>day</u>---+
| | 20; | | |20;
| <u>hour</u> | 10;^3| <u>hour</u>
| | 2^6 | | |60;
| <u>octal minute</u> | <u>md [mil(li day)]</u>
| | 10;^2 | | 2^7
<u>smd [septi m(illi day)]</u>-+ <u>smd [septi m(illi day)]</u>-+
| |
: powers of 10; : powers of 10;
| |
under range under range
</PRE>
[/doHTML]
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.

Takashi - July 18, 2010 07:36 AM (GMT)
The Universal Unit System uses not pi radian but 2 pi radian as a plain angle unit.
This is necesary in order to guarantee the consistency of plane and solid angle.

See §3.2.2 of http://dozenal.com .

Non coherent supplementary constants (powers of radian)
[doHTML]
<table border=1>
<tr>
<td>dimension</td>
<td>symbol</td>
<td>called name</td>
<td>aliased name</td>
<td>value</td>
</tr>
<tr>
<td>plane angle</td>
<td align=center>Ω<sub>1</sub></td>
<td>circle</td>
<td>day (for calendar time),<br>
cycle (for periodical phenomena)
</td>
<td>2 pi rad</td>
</tr>
<tr>
<td>solid angle</td>
<td align=center>Ω<sub>2</sub></td>
<td>sphere</td>
<td>turn (for magnetic units)</td>
<td>4 pi sr</td>
</tr>
</table>
[/doHTML]

The Mighty Dozen - July 18, 2010 03:28 PM (GMT)
QUOTE (Shaun @ Jul 14 2010, 08:55 AM)
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.

Takashi - July 22, 2010 01:54 PM (GMT)
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.

[doHTML]
<PRE>
[Variation 2-D']
over range
|
: powers of 10;
|
<u>octal century</u> -------+
| | 2^6
| <u>year</u>
|1;003628*10;^9 | 1;003628*3^6/2
| <u>day</u>---+
| | | 2
| | <u>half-day(AM/PM)</u>
| 10;^3 | |10;
| | <u>hour</u>
| | |60;
| <u>md [mil(li day)]</u>
| | 2^7
<u>smd [septi m(illi day)]</u>-+
|
: powers of 10;
|
under range
</PRE>
[/doHTML]

Takashi - July 22, 2010 01:55 PM (GMT)
The symbols of the Universal Unit System are brought together in the quartets.
Therefoe, they can be arranged as follows:
[doHTML]
<table border=1>
<tr>
<td>category</td>
<td>name / symbol</td>
<td>description</td>
<td>category</td>
<td>name / symbol</td>
<td>description</td>
<td colspan=2>category</td>
<td>name / symbol</td>
<td>description</td>
<td colspan=2>category</td>
<td>name / symbol</td>
<td>description</td>
</tr>
<tr>
<td rowspan=4>base units<br>that are<br>natural units</td>
<td><b>naper</b></td>
<td>logarithm of Napier's constant</td>
<td rowspan=4>non-coherent<br>supplementary<br>constants</td>
<td><b>B<sub>k</sub></b></td>
<td>logarithm of an integer<br>(B<sub>1</sub> is called 'bit',<br>B<sub><i>z</i></sub> is called 'Bel',<br>B<sub>8</sub> is called 'byte')</td>
<td rowspan=4 colspan=2>minor prefix</td>
<td>(do)<b>d</b>eci</td>
<td>10;<sup>-1</sup></td>
<td rowspan=4 colspan=2>major prefix</td>
<td>(do)<b>d</b>ek<b>a</b></td>
<td>10;<sup>1</sup></td>
</tr>
<tr>
<td><b>rad</b></td>
<td>plane angle<br>(rad is called 'radian',<br>rad<sup>2</sup> is called 'steradian')</td>
<td><b>Ω<sub>k</sub></b></td>
<td>total solid angle of a hypersphere<br>(Ω<sub>1</sub> is called 'circle' or 'cycle',<br>Ω<sub>2</sub> is called 'sphere' or 'turn')</td>
<td><b>c</b>enti</td>
<td>10;<sup>-2</sup></td>
<td><b>h</b>ecto</td>
<td>10;<sup>2</sup></td>
</tr>
<tr>
<td><b>Ω<sub><i>n</i></sub></b></td>
<td>natural unit of impedance</td>
<td><b><i>e</i></b></td>
<td>elementary electric charge (is called 'electron')</td>
<td><b>m</b>illi</td>
<td>10;<sup>-3</sup></td>
<td><b>k</b>ilo</td>
<td>10;<sup>3</sup></td>
</tr>
<tr>
<td><b><i>N<sub>A</sub></i><sup>-1</sup></b></td>
<td>per Abogadro constant</td>
<td><b>mol<sub><i>u</i></sub></b></td>
<td>universal mol</td>
<td><b>atomic</b></td>
<td>10;<sup>-8</sup></td>
<td><b>cosmic</b></td>
<td>10;<sup>8</sup></td>
</tr>
<tr>
<td rowspan=4>base units<br>that are not<br>natural units</td>
<td><b>m<sub><i>h</i></sub></b></td>
<td>harmonized meter</td>
<td rowspan=4>defining<br>constants</td>
<td><b><i>R<sub>∞</sub></i></b></td>
<td>the Rydberg constant</td>
<td rowspan=4 colspan=2>non-coherent<br>Earth local<br>constants</td>
<td><b>m<sub><i>E</i></sub></b></td>
<td>the meridian length of the Earth<br>(is called 'Earth meridian')</td>
<td rowspan=8>power<br>prefix</td>
<td rowspan=4>low order</td>
<td><b>semi-</b></td>
<td>square root</td>
</tr>
<tr>
<td><b>s<sub><i>h</i></sub></b></td>
<td>harmonized second</td>
<td><b><i>c<sub>0</sub></i></b></td>
<td>the speed of light in vacuum(is called 'light') </td>
<td><b>s<sub><i>E</i></sub></b></td>
<td>the rotation period of the Earth<br>(is called 'Earth solar')<br>at the beginning of year 1900.</td>
<td><b>uni-</b></td>
<td>1st power</td>
</tr>
<tr>
<td><b>J<sub><i>h</i></sub></b></td>
<td>harmonized Joule</td>
<td><b><i>ħ</i></b></td>
<td>the quantum of action</td>
<td><b>g<sub><i>E</i></sub></b></td>
<td>the gravitational acceleration of the Earth<br>(is called '-force')</td>
<td><b>bi-</b></td>
<td>2nd power</td>
</tr>
<tr>
<td><b>K<sub><i>h</i></sub></b></td>
<td>harmonized Kelvin</td>
<td><b><i>k<sub>B</sub></i></b></td>
<td>the Boltzman constant</td>
<td><b>°S<sub><i>h</i></b></td>
<td>difference of thermodynamic temperature and the base point</td>
<td><b>tri-</b></td>
<td>3rd power</td>
</tr>
<tr>
<td rowspan=4>derived units of<br>dynamical quantities</td>
<td><b>g<sub><i>h</i></sub></b></td>
<td>harmonized gram</td>
<td rowspan=4>derived units of<br>electro- magnetic quantities</td>
<td><b>C<sub><i>h</i></sub></b></td>
<td>harmonized Coulomb</td>
<td rowspan=4>non-coherent<br>Earth local<br>calendar time</td>
<td rowspan=3>units</td>
<td><b>o</b>ctal <b>c</b>entury</td>
<td>2<sup>6</sup> years</td>
<td rowspan=4>high order</td>
<td><b>quadri-</b></td>
<td>4th power</td>
</tr>
<tr>
<td><b>W<sub><i>h</i></sub></b></td>
<td>harmonized Watt</td>
<td><b>A<sub><i>h</i></sub></b></td>
<td>harmonized Ampere</td>
<td><b>y</b>ear</td>
<td>365. 31./128. days</td>
<td><b>quinti-</b></td>
<td>5th power</td>
</tr>
<tr>
<td><b>N<sub><i>h</i></sub></b></td>
<td>harmonized Newton</td>
<td><b>O<sub><i>h</i></sub></b></td>
<td>harmonized Oersted</td>
<td><b>d</b>ay</td>
<td>Ω<sub>1</sub>(= 2πrad)<br>corresponding to 86400. s<br>at the beginning of year 1900.</td>
<td><b>sexti-</b></td>
<td>6th power</td>
</tr>
<tr>
<td><b>P<sub><i>h</i></sub></b></td>
<td>harmonized Pascal</td>
<td><b>G<sub><i>h</i></sub></b></td>
<td>harmonized Gauss</td>
<td>prefix</td>
<td><b>s</b>epti</td>
<td>7th power of two inversed</td>
<td><b>hepti-</b></td>
<td>7th power</td>
</tr>
</table>
[/doHTML]

icarus - July 25, 2010 01:40 AM (GMT)
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.


Ruthe - July 27, 2010 08:31 PM (GMT)
QUOTE (icarus @ Jul 25 2010, 01:40 AM)
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!

Cymbyz - July 28, 2010 02:16 AM (GMT)
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).

Shaun - July 28, 2010 04:21 PM (GMT)
and there's also the "ten-headed beast", isn't there?

Cymbyz - July 28, 2010 05:37 PM (GMT)
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."

Takashi - August 2, 2010 03:34 AM (GMT)
QUOTE (icarus @ Jul 25 2010, 01:40 AM)
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.

QUOTE (Ruthe @ Jul 27 2010, 08:31 PM)
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.

Takashi - August 2, 2010 03:35 AM (GMT)
The angle is a good example what consideration being done for the consistency.

I think that non-rational 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.
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.

Takashi - August 10, 2010 09:24 AM (GMT)
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/ Ω2.
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.

Takashi - August 11, 2010 02:37 AM (GMT)
'Harmonized' means that human activity and fundamental physical constant are harmonized.
There is a word 'harmonic' that matches 'cosmic' and 'atomic' to the rhyme.
Is it natural for native speakers to use 'harmonic' instead of 'harmonized'?

dgoodmaniii - August 11, 2010 05:40 PM (GMT)
Well, at least Takahashi's given us the first real competition against TGM for a coherent dozenal system of units. I think you used LaTeX to produce the paper? Have you seen the dozenal package for producing real dozenal characters rather than the makeshift "A" and "B"?

Also, your section on the advantages of the dozenal system was brilliant. I, for one, had never noticed these characteristics of dozenal factorials before; testing them with dozdc it sticks out most obviously, but I never would have noticed had you not pointed it out.

Still, I have to ask: why marry the unit system to physical constants that are really quite far removed from the daily quantities that normal people have to deal with? The speed of light in a vacuum, for example; for most purposes that most people encounter, the speed of light might as well be instantaneous. It's certainly not a speed that anyone ever regularly observes or can easily relate to, since it's incredibly fast. And are you familiar with some research and theories indicating that the speed of light isn't really a constant?

I'm also not sure I understand your explanation of choosing the exponents for determining your base units. You explain it on page 13. Doesn't this meant that there's no 1:1 correspondence between units? Won't that make it unnecessarily difficult for users to combine and separate different unit types in calculations?

All in all, the systems strikes me as too abstract. In contrast, the customary and Imperial systems, and the better TGM, is very concrete. This is what I consider one of TGM's greatest strengths: it bases its system on quantities that are realities of our daily lives and with which we daily interact. It's also got a 1:1 correspondence between unit types, which I think is important.

By the way, why is the summary of units on page 15 in decimal? It appears to be, at least.

Takashi - August 14, 2010 07:53 AM (GMT)
dgoodmaniii,
thank you for your opinion.
---
I wrote "For putting these coincidences to use, the duodecimal system is the only choice."
in Chapter 2 "Why the duodecimal system?" in the paper http://dozenal.com .

We can make the standard gravitational accelaration the accelaration unit
regardless of decimal unit system or duodecimal unit system.
The density of water, the meridian length of the earth, too.

On the other hand, the unit system that can use the coincidences of the fundamental
constants is only the Universal Unit System that adopted duodecimal system.
All decimal unit systems cannot use the coincidences of the fundamental constants.

It is only the Universal Unit System that can answer the decimal people's question
why must be duodecimal unit system.
---
There was an arrangement of discussion that we should distinguish conceptual origin of
the unit and definition of the unit. I want to replace 'conceptual origin' with 'human scale'.

1. The unit quantity should be human scale. (See also here)
2. The unit defintion should guarantee commonness and reproducibility as much as possible in large range.
(See the 2nd paragraph of Chapter 1 of the paper http://dozenal.com .)

It is the best choice to use the fundamental constants for the unit definitions for Item 2.
Especially, the speed of light in vacuum and the quantum of action are vary common and stable
in the largest range in current physics paradigm.
At the viewpoint of definition, all proposed unit systems such as SI, imperial, TGM
use the speed of light in vacuum.

SI : meter = (second/299792458.) * c_0,
imperial : foot = 0.3048 meter = (0.3048 second/299792458.) * c_0,
TGM : Graft = Tim/*4XE49923; * c_0,
where c_0 is the speed of light in vacuum.

The fundamental constants themselves and Item 1 don't need to relate.
The coincidences of the fundamental constants originally contain factors of integer
powers of twelve. (See Section 2.1 of the paper http://dozenal.com ).
Therefore, it is natural that the units are defined as integer powers of twelve
multiple of the fundamental constants.
---
I discussed about coherent unit system in Appendix A.3 of the paper http://dozenal.com .
The concept of unit coherence is important, but not absolute.

A day is non-coherent unit for allmost all proposed unit systems such as SI, TGM, and
the Universal Unit System. But we cannot prohibit using a day as a unit.
Either radian or degree cannot be prohibited, too.

I think that we would rather control than prohibit non-coherent units.
It only has to clarify the rule of the usage.

In this viewpoint the 1st sentence of Chapter 1 of the paper http://dozenal.com is important.
| A unit of measure is "a quantity that is used as the basis for expressing a given quantity,
| and is of the same type as the quantity that is to be expressed".
I learned this perception through the Japanese translated version of M.L. McGlashan's
"Physicochemical Quantities and Units(2nd Edition)" - The Royal Institute of Chemistry(1971).
---
About factorials see also here.

dgoodmaniii - August 15, 2010 06:23 AM (GMT)
QUOTE
It is only the Universal Unit System that can answer the decimal people's question
why must be duodecimal unit system.


I don't know about that; there are lots of arguments for using the dozenal system for units, many of which are much more convincing than coincidences in fundamental constants in terms of daily applicability. Even the fundamental constant coincidences, while extremely interesting (and I'm glad you uncovered them, as I'd never seen them before), are only approximate, if I'm reading your paper right. Is it more convincing to say, "A dozenal unit system is better because of these relationships between constants which you rarely encounter," or, "A dozenal unit system is better because you can easily get exactly one third of a unit without repeating fractional parts?"

QUOTE
There was an arrangement of discussion that we should distinguish conceptual origin of
the unit and definition of the unit. I want to replace 'conceptual origin' with 'human scale'.


I agree, and it's an important distinction.

QUOTE
1. The unit quantity should be human scale. (See also here)


Agreed.

QUOTE
2. The unit defintion should guarantee commonness and reproducibility as much as possible in large range.
(See the 2nd paragraph of Chapter 1 of the paper http://dozenal.com .)

It is the best choice to use the fundamental constants for the unit definitions for Item 2.
Especially, the speed of light in vacuum and the quantum of action are vary common and stable
in the largest range in current physics paradigm.


Here's where I start to wonder. First, our measurements for these things are constantly getting more refined; will you redefine your human-scale units to match up with these newer, more specifically measured fundamental constants? The difference will, of course, be minute, but it's a valid question.

Second, what if these refinements render the coincidences in fundamental constants less coincidental?

Finally, why is using these values any more common or reproducible? If SI gets along well enough by defining a meter as the distance travelled by light in a totally arbitrarily-chosen period of time (picked really to closely correspond to the length of a platinum bar sitting in a vault somewhere in Paris), does using a fundamental constant really lend any additional stability? Terrible as SI is in its principles and decimal base, it's certainly stable within the limits of even the most fastidious practitioners.

QUOTE
Therefore, it is natural that the units are defined as integer powers of twelve
multiple of the fundamental constants.


I understand that. But how do you decide which integer power of the dozen to use for the human-scale unit? Is it an arbitrary choice based on the one that comes out approximately the right dimension, in your opinion? Or is there some system to it? The paper didn't make that clear, at least to me.

QUOTE
I think that we would rather control than prohibit non-coherent units.
It only has to clarify the rule of the usage.


Agreed. Non-coherent units don't bother me much, as long as the system itself is coherent. But I do find that a 1:1 correspondence of basic units is extremely helpful, and without this I think it's hard to say a system is coherent. As I understand it, you've got 1:1 correspondence with your fundamental constants, but not with the human-scale units, which are set by more or less arbitrary (by which I mean only "chosen without systematic justification; it's not meant as pejorative) integer exponents on those fundamental constants. But it's the human-scale units that will be used the vast majority of the time. So while there's a 1:1 correspondence in the fundamental, base units, there is no such correspondence in the human-scale units. Is this correct?

Takashi - August 22, 2010 02:24 AM (GMT)
dgoodmaniii,
Thank you for agreeing to a lot of points.

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
will you redefine your human-scale units to match up with these newer, more specifically measured fundamental constants?

There is no possibility from the viewpoint of 'reproducibility'.
Each fundamental constants used for the definition in the Universal Unit System is, not a measured quantity,
but a quantity which measures another quantities of the same dimention with enough reproducibility.

But, of course, there is always a possibility from the viewpoint of 'commonness' when a new paradigm shift outside expectation happens.
A coming expected paradigm shift changes the conceptual position of the gravitational constant.
There is no influence because I have dealt with this by considering in Appendix C of http://dozenal.com .

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
But how do you decide which integer power of the dozen to use for the human-scale unit?

Fundamental constants that relate to nature scale are shown Table 1.
Human scale and cosmic/atomic scale are mainly connected through factor 12.^8.
This is important for human recognition to nature scale.
Moreover, the units should be human scale as the pivot that connects cosmic scale with atomic scale.

[doHTML]
Table 1
<table border=1>
<tr>
<td>Constants</td>
<td>Dozenal</td>
<td>Prefix</td>
<td>Unit Symbol</td>
</tr>
<tr>
<td>Age of the universe</td>
<td>6;0</td>
<td>bi-cosmic</td>
<td>s<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Speed of light in vacuum</td>
<td>1;</td>
<td>cosmic</td>
<td>m<sub><i>h</i></sub>/s<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Bohr Radius</td>
<td>1;00447X724</td>
<td>atomic (do)deci</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Elementary electric charge</td>
<td>1;0374439X4</td>
<td>bi-atomic</td>
<td>C<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Unified atomic mass unit</td>
<td>1;0024074</td>
<td>tri-atomic</td>
<td>g<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Planck length</td>
<td>2;0413</td>
<td>quadri-atomic</td>
<td>m<sub><i>h</i></sub></td>
</tr>
<tr>
<td>Planck time</td>
<td>2;0413</td>
<td>quinti-atomic</td>
<td>s<sub><i>h</i></sub></td>
</tr>
</table>
[/doHTML]

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
you've got 1:1 correspondence

It is not 1:1 correspondence.
The number of fundamental constants is more than the number of dimensions of the unit.
Therefore, the relation shown in a dimensionless ratio comes out between fundamental constants.
See 2.1 of http://dozenal.com and Table 1.

Because the consideration of coherency of the unit is described in Appendix A.3 of http://dozenal.com, I don't repeat it.
If you worry about coherency, you can limit the units used only to the 16. coherent units of the table.
- base units that are natural units
- base units that are not natural units
- derived units of dynamical quantities
- derived units of electro- magnetic quantities
This is one of the variations of the Universal Unit System, too.

dgoodmaniii - August 23, 2010 02:05 PM (GMT)
QUOTE
dgoodmaniii,
Thank you for agreeing to a lot of points.


Well, it would be silly not to agree when you're right, which of course you often are.

QUOTE

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
will you redefine your human-scale units to match up with these newer, more specifically measured fundamental constants?

There is no possibility from the viewpoint of 'reproducibility'.
Each fundamental constants used for the definition in the Universal Unit System is, not a measured quantity,
but a quantity which measures another quantities of the same dimention with enough reproducibility.

Right. But when they refine the velocity of light by another few akis (to use TGM nomenclature), this will slightly but truly alter the dimensions that you measure via the velocity of light. (Or rather, more accurately, the accuracy of the dimensions measured with the velocity of light will correspondingly increase, altering however slightly your practical values.) Do you incorporate these into your system or not?

Also, wouldn't the truth of Dirac's decreasing constants idea wreak considerable havoc with this system?

QUOTE

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
But how do you decide which integer power of the dozen to use for the human-scale unit?

Fundamental constants that relate to nature scale are shown Table 1.
Human scale and cosmic/atomic scale are mainly connected through factor 12.^8.
This is important for human recognition to nature scale.
Moreover, the units should be human scale as the pivot that connects cosmic scale with atomic scale.


Right, I know where they're listed, but they seemed arbitrary; that is, not chosen systematically, but more because they simply produce human-sized units that seemed right to you. Am I correct?

(Multiples here in decimal, since the entire basic unit table is in decimal.) For example, your distance is 12^8, but your time and energy are 12^16, and your temperature is 12^-4. Mass is 12^32, and field strength is 12^-8. All of these, minus the outlier of temperature being 12^-4, are multiples of 8, it's true; but how did you choose these particular multiples of 8 for these particular units? Was it systematic, or was it arbitrary (in other words, based on your opinion of what would yield easy human-sized units)?

QUOTE

QUOTE (dgoodmaniii @ Aug 15 2010, 06:23 AM)
you've got 1:1 correspondence

It is not 1:1 correspondence.
The number of fundamental constants is more than the number of dimensions of the unit.
Therefore, the relation shown in a dimensionless ratio comes out between fundamental constants.
See 2.1 of http://dozenal.com and Table 1.


I thought it wasn't 1:1, and I think that's a problem. Not having a 1:1 correspondence compels mankind to an eternity of miscalculated exponents and other basic calculation errors for no good reason. TGM is a model here, in my opinion. Once the basic unit, the Tim, is selected, every other unit flows from there with an easy, 1:1 correspondence. So once we have the Tim, we can easily measure the unit of acceleration (1 Gee = 1 unit per Tim per Tim), which yields us the unit of velocity (1 unit per Tim) and length (1 Grafut), and so on.

Note that this is *not* an objection to your having noncoherent units in your system; as I said before, I don't really have a problem with that. Human needs are many and varied, and it's impossible for any system to anticipate convenient units for every single one of them. TGM, for example, embraces noncoherent units, such as the tumblol (about halfway between an imperial and a customary pint, equal to 3 _2Vm (three duniVolms), a convenient size for a mug of beer. They are given, as Pendlebury says, on a "take or leave basis." New ones can easily be developed as needed. But that doesn't change the fact that the basic units of the system are all related to one another on a 1:1 basis.

It's not the coherency of units actually used that's the problem; it's that there doesn't seem to be coherency in the units underlying them.

To elucidate: my theory is that, were TGM to become the common system, most of the time scientists would be using TGM units. The hoi polloi (like myself) would often also use some of these noncoherent derived units, like the tumblol and the galvol. But there's still a set of units available for easy use that are coherent; that is, that have a 1:1 correspondence and are systematically derived from very accurately measured base unit(s). These kind of correspondence greatly facilitates calculations.

Your system appears to have no such coherency. Rather, there are multiple base units from which different dimensions are derived, and those base units only correspond to one another approximately by multiples of the dozen. You derive human-scaled units from these base units in a nonsystematic manner. Is that correct?

Please note that I'm not trying to be belligerent here; I'm just trying to make sure I understand your system correctly. I had trouble following some of the paper and I want to ensure that I've got the system correct before I form a definite opinion about it.

Takashi - August 28, 2010 01:32 AM (GMT)
dgoodmaniii,
Thank you for your comments.

QUOTE (dgoodmaniii @ Aug 23 2010, 02:05 PM)
Also, wouldn't the truth of Dirac's decreasing constants idea wreak considerable havoc with this system?

The small change of the gravitational constant doesn't influence the definition of the Universal Unit System as commented previous time.
However, it is necessary to delete Plank length from last paragraph of Chapter 1 of http://dozenal.com
if there is too big change that corresponds to paradigm shift.

The change of the fine structure constant revises the ratio of the elementary electric charge
and the unit of electrical charge. But the quantity of unit of electrical charge doesn't change.

QUOTE (dgoodmaniii @ Aug 23 2010, 02:05 PM)
Do you incorporate these into your system or not?

I think that the improvement of the measurement precision of space and time indirectly
leads to the revision of a dimensionless constant like the fine structure constant.

In the paradigm of present physics, time and space are combined into the single space-time continuum.
The conversion coefficient of the space metric and time metric of the space-time continuum is called 'the speed of light in vacuum'.
Therefore, there is no influence on the structure of the Universal Unit System as long as the paradigm shift
that urges the revolution of recognition of space-time continuum doesn't happen.

QUOTE (dgoodmaniii @ Aug 23 2010, 02:05 PM)
I know where they're listed, but they seemed arbitrary; that is, not chosen systematically, but more because they simply produce human-sized units that seemed right to you. Am I correct?

There is finally very little arbitrariness though it was based on human scale which has arbitrariness.
The decision details are explained at the last paragraph of 3.3 of http://dozenal.com.

- the speed of light in vacuum : 12^P times velocity unit
- elementary electric charge : 12^Q times charge unit
- unified atomic mass unit : 12^R times mass unit

In the above relations, I selected the factor so that the greatest common divisor of P, Q, and R becomes the maximum.
The relation between the quantum of action and the elementary electric charge limits arbitrariness.
Equation (11) at 2.1.3 of http://dozenal.com is an important scale factor that means the ratio of typical nuclear energy and chemical energy.
This ratio contains factor 12^8, too.
When the numbers other than 8 (including 0) are chosen, The structure of Table 1 cannot be made.

The unit of thermodynamic temperature was changed along with the introducing of the Earth local extension.
The new unit is one-10000;th of the old unit.

QUOTE (dgoodmaniii @ Aug 23 2010, 02:05 PM)
Rather, there are multiple base units from which different dimensions are derived, and those base units only correspond to one another approximately by multiples of the dozen.

The quoted topic and the topic of the relation between the units and the fundamental constants are another topics.
There is only one 'base' unit for coherency corresponding to each dimension.
These base units assemble 'derived' units by using coherency.

There are 8 base units as shown in the table:
- base units that are natural units
- base units that are not natural units (# It means that 'defining constants' are not 'base' units.)

There are 8 named derived units in addition to the above-mentioned.
- derived units of dynamical quantities
- derived units of electro- magnetic quantities
These derived units are automatically coherent according to the definition of word 'derived'.

All coherent named units are covered by these.

Takashi - September 4, 2010 10:24 AM (GMT)
I quote http://dozenal.com as a supplementation.

Reproducibility
Each fundamental constant used for the definition in the Universal Unit System is, not a measured quantity,
but a quantity which measures another quantities of the same dimention. Therefore we will find the improvement of
reproducibility by reviewing dimensionless ratios descrived in Chapter 2.1 of http://dozenal.com.

The definition of the Universal Unit System is
QUOTE (the last paragraph of page.2 of http://dozenal.com)
the unit system that is constructed by using the dozenal system and using 'the speed of light in vacuum', 'the quantum of action', and the Boltzmann constant as the defining constants in such a way that these constants become strict multiples of integer powers of 12 of the unit quantities, and the Rydberg constant, the atomic mass unit, the Bohr radius, and 'half the value of the Planck length' can be approximated by multiples of integer powers of 12 of the unit quantities.

We have already acquired reproducibility enough to guarantee that these approximations are possible.
Therefore, it will not result in the revision of the definition even if reproducibility will improve in the future.
Appendix E of http://dozenal.com is for reference only. Table of constants is not part of the Universal System of Units Standard.

Commonness
I descrived the concept of 'paradigm shift' in the paragraph
QUOTE (the 3rd paragraph of page.1 of http://dozenal.com)
The history of units of measure, on the other hand, is the history of the establishment of new concepts that have accompanied the development of natural science. The laws of nature describe the 'relationship' between 'a given quantity' and 'another quantity' specified as mathematical expressions. The 'given quantity' and 'another quantity' referred to here are often quantities that correspond to 'newly established or greatly transformed concepts' that are born of new discoveries, as occurred with mass, energy, and electrical charge. As this process goes on, the need arises to deal with quantities of a new concept and a quantity is selected as a standard for that purpose. That quantity becomes a new unit.

The great transformation of concept ruins commonness of the corresponding definition constant.
Such paradigm shift has the possibility of resulting in the revision of the definition of the Universal Unit System.

Takashi - September 6, 2010 09:29 AM (GMT)
QUOTE (Takashi @ Aug 11 2010, 02:37 AM)
'Harmonized' means that human activity and fundamental physical constant are harmonized.
There is a word 'harmonic' that matches 'cosmic' and 'atomic' to the rhyme.
Is it natural for native speakers to use 'harmonic' instead of 'harmonized'?

If there is no comment, I will change 'harmonized' to 'harmonic'.

Takashi - September 20, 2010 02:27 AM (GMT)
This is a supplementation about the arbitrariness of the decision of the integer power of twelve for base units.
(the last paragraph of 3.3 of http://dozenal.com)

(1) the speed of light in vacuum : 12.^P * velocity unit
(2) elementary electric charge : 12.^Q * charge unit
(3) unified atomic mass unit : 12.^R * mass unit

if we put P=n,Q=-2n, and R=-3n based on the nature of the quantities, then
length unit = 12.^(-16. + 2n) * universal meter
time unit = 12.^(-24. + 3n) * universal second
mass unit = 12.^(-24. + 3n) * universal gram

It is only case n=8 that all units become human scale.
There is arbitrariness that originates in the definition of human scale.

Then, I shelve human scale once, and pay attention to other constants.
(4) Typical nuclear energy : 1 * 12.^8 * typical chemical energy (+)
_(+) descrived by Equation (11) at 2.1.3 of http://dozenal.com.
(5) Age of the universe : 6 * 12.^(+40. - 3n) * time unit
(6) Planck time : 2 * 12.^(-16. - 3n) * time unit
The ratio of (5) and (6) is 3 * 12.^(7*8) regardless of the value of n.

In order to use these all relations (1)-(6), n should be an integer multiple of 8:
length unit = 12.^(-16.*x) * universal meter
time unit = 12.^(-24.*x) * universal second
mass unit = 12.^(-24.*x) * universal gram

It is only the decision to adopt human scale that we need to determine the quantities of the base units.

Luke-Jr - March 10, 2011 02:19 AM (GMT)
I can't comprehend this unit specification at all. Can someone put it in simple terms, perhaps similar to Nystrom's Tonal unit definitions?

1. What are the names of the basic units for measurement, weights, temperatures, etc, and what are their imperial/metric equivalents? Why were these values chosen?

2. What are the prefixes/suffixes used to denote larger or smaller amounts of these units? For example, SI has mega, kilo, hecto, deca, centi, milli, micro, nano, while Tonal has bong, mill, san, ton.

Takashi - March 12, 2011 01:22 AM (GMT)
Luke-Jr,
I thank for your having been interested in the Universal Unit System.

QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
Why were these values chosen?

See chapter 2.1 and appendix D.1 of http://dozenal.com .

QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
1. What are the names of the basic units for measurement, weights, temperatures, etc, and what are their imperial/metric equivalents?

See the #6 of this thread and 'Clock_by_Rydberg' sheet of http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls .

QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
2. What are the prefixes/suffixes used to denote larger or smaller amounts of these units?

See the #15 of this thread .

As commented in the #32 of this thread, I changed the word 'hermonized' to 'hermonic' in order to match end rhyme with 'atomic' and 'cosmic'.
Please substitute 'hermonized' into 'hermonic' in the #6 and #15 of this thread.

Luke-Jr - March 12, 2011 01:50 AM (GMT)
QUOTE (Takashi @ Mar 12 2011, 01:22 AM)
QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
Why were these values chosen?
See chapter 2.1 and appendix D.1 of http://dozenal.com .
I guess there are good reasons? I can't really make any sense out of this site.
QUOTE (Takashi @ Mar 12 2011, 01:22 AM)
QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
1. What are the names of the basic units for measurement, weights, temperatures, etc, and what are their imperial/metric equivalents?

See the #6 of this thread and 'Clock_by_Rydberg' sheet of http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls .
I'm afraid this still seems too complicated. How many SI or (even better) US/imperial units are each of the new ones?
QUOTE (Takashi @ Mar 12 2011, 01:22 AM)
QUOTE (Luke-Jr @ Mar 10 2011, 02:19 AM)
2. What are the prefixes/suffixes used to denote larger or smaller amounts of these units?

See the #15 of this thread .
The first through third exponents seem sensible enough, but then it jumps immediately to 8th exponent? How would one handle 1,000,000 units of whatever? And since cosmic/atomic lack abbreviations(?), one has to write out the full word? What is larger/smaller than cosmic/atomic? After all, a cosmic byte (no new data unit?) would only be equivalent to 430 MB...

Takashi - March 21, 2011 10:59 AM (GMT)
QUOTE (Luke-Jr @ Mar 12 2011, 01:50 AM)
The first through third exponents seem sensible enough, but then it jumps immediately to 8th exponent?
See the last paragraph of chapter 3.3 of http://dozenal.com/ and #30,#33 of this thread .

QUOTE (Luke-Jr @ Mar 12 2011, 01:50 AM)
What is larger/smaller than cosmic/atomic?
See the second table of #6 of this thread and prefix column of 'Clock_by_Rydberg' sheet of http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/condensed.xls .

QUOTE (Luke-Jr @ Mar 12 2011, 01:50 AM)
How many SI or (even better) US/imperial units are each of the new ones?
See chapter 4 and the last 2 paragraphs of chapter 3.5 of http://dozenal.com/ .

QUOTE (Luke-Jr @ Mar 12 2011, 01:50 AM)
And since cosmic/atomic lack abbreviations(?), one has to write out the full word?
There are not abbreviations, but notations. I am making a summary now.

Takashi - April 1, 2011 11:23 AM (GMT)
The more a quantity leaves human scale, the less the use frequency of the quantity expression becomes.
It is natural that the length of expression is in inverse proportion to frequency for which the corresponding concept is used.
Therefore, I think that the abbreviation of 'atomic' and 'cosmic' is unnecessary.

Rather I want to express 'dodeci meter' and 'octal century' by shorter words.
I want suggestion of native speakers.

Luke-Jr - April 1, 2011 02:03 PM (GMT)
Please explain how one would easily write 1,000,000,000,000,000; bytes, or even 1,000,000,000,000.




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