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 The Universal Unit System and its notaions, The Universal Unit System
Takashi
Posted: Jul 4 2010, 12:10 PM


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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.
Top
Takashi
Posted: Jul 4 2010, 12:11 PM


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# 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

VariationConnection RangeNon Coherent Units
Present system-year,month,day,hour,minute
Variation 1675s-1dayyear,day
Variation 2-A56.25s-1.0hour,1.0hour-1dayyear,day,hour
Variation 2-B56.25s-1.5hour,1.5hour-1dayyear,day,octal hour
Variation 2-C0.390625s-50syear,day


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.
Top
Takashi
Posted: Jul 8 2010, 09:48 AM


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The following descriptions are ideas for discussion
about prefix notations of the Universal Unit System.
------------
The symbol of the unit of the Universal Unit System is a symbol
that adds the suffix to the symbol of the corresponding SI unit.

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

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

prefix example
prefix namevalue[dozenal]value[decimal]prefix namevalue[dozenal]value[decimal]
da(do)deka10;112.1d(do)deci10;-112.-1
-ssepti **2-72-7
hhecto10;212.2ccenti10;-212.-2
kkilo10;312.3mmilli10;-312.-3
semi-cosmic10;412.4semi-atomic10;-412.-4
(uni-)cosmic10;812.8(uni-)atomic10;-812.-8
bi-cosmic10;14;12.16.bi-atomic10;-14;12.-16.
tri-cosmic10;20;12.24.tri-atomic10;-20;12.-24.
quadri-cosmic10;28;12.32.quadri-atomic10;-28;12.-32.
quinti-cosmic10;34;12.40.quinti-atomic10;-34;12.-40.
sexti-cosmic10;40;12.48.sexti-atomic10;-40;12.-48.
hepti-cosmic ***10;48;12.56.hepti-atomic ***10;-48;12.-56.

** 'septi' (SEventh Power of Two Inversed) is only for the earth local extension.
*** Greek prefix is used to distinguish from 'septi'.

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

unit example
[prefixed] unit namesymbolsymbol[plain text]valuerefer to
universal secondsus_u1; (universal) second-
semi-cosmic (universal) meterms+um_s+u10;4 (universal) meter-
(uni-)cosmic (universal) meterm+um_+u10;8 (universal) meterthe speed of light in vacuum
uni(- and )s(emi)-cosmic (universal) meterm1s+um_1s+u10;10; (universal) meter-
(uni-)atomic (universal) (do)deci meterdm-udm_-u10;-9 (universal) meterthe Bohr radius
bi-atomic (universal) CoulombC2-uC_2-u10;-14; (universal) Coulombthe charge of an electron
tri-atomic (universal) gramg3-ug_3-u10;-20; (universal) gramthe unified atomic mass unit

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.
Top
Takashi
Posted: Jul 8 2010, 10:58 AM


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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 .

prefix example
prefix nameHymnus in Ioannemvalue[dozenal]value[decimal]
fa4 Famuli tuorum10;312.3
so5 Solve polluti10;212.2
la6 Labii reatum10;112.1
si*7 Sancte Ioannes10;012.0
do1 Ut queant laxis10;-112.-1
re2 Resonare fibris10;-212.-2
mi3 Mira gestorum10;-312.-3

* 'si' is not used.
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Takashi
Posted: Jul 10 2010, 06:09 PM


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If the variation 2-C is selected, the earth local extension for the Universal Unit System
may become a following system:

The earth local extension for the Universal Unit System with the GCD unit
Non coherent unit / prefix typeNon coherent unit / prefix namesymbolsymbol[plain text]value
calendar timeprefixseptis2-7
unitsdaydΩ1(=2 pi rad) ***
86,400. s
yeary365. 31./128. days
octal centuryCoC_o64. years
supplementary constantsthe gravitational acceleration of the Earth (is called '-force')gE*g_E9.831209 m/s2
the rotation period of the Earth (is called 'Earth solar')sEs_E86,400. s/Ω1
the meridian length of the Earth (is called 'Earth meridian')mEm_E40,007,860. m/Ω1
difference of thermodynamic temperature and the ice point°Ke**,****degree K_e1; Ke****
*  The suffix E is used for the Earth characteristics as a celestial body.
   gE is defined that the gravitational radius of the Earth is expressed as gE * (mE * rad / c0)2.
   See §C.1 of http://dozenal.com .
** See §A.3.1 of http://dozenal.com .
*** It seems that the dimension of the quantity of a day can be plane angle rather than physical time.
  The calendar time is, in a word, the rotation angle of the earth derived
  by using the direction of the sun as a coordinate origin.
  See Seaman,Rob (April 2003). "Proposal to Upgrade UTC"
  retrievable at http://iraf.noao.edu/~seaman/leap/ .
**** the units suffixed e is units of the Universal Unit System with the GCD unit
   [calendar time unit se = 2-710;-3 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;
      |
   octal century -------+
      |                 | 2^6
      |                year
      |1;003628*10;^9   | 1;003628*3^6/2
      |                day
      |                 | 10;^3
      |             md [mil(li day)] *****
      |                 | 2^7
smd [septi m(illi day)]-+
      |
      : powers of 10;
      |
  under range
***** A mil(li day) is equal to H. C. Churchman's 'moment'.
Top
Takashi
Posted: Jul 11 2010, 01:18 AM


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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.

calendar time range

base ten

base twelve

present calendar time

variation 1

variation 2

A

B

C'

century

10.2years

10;6

clock

10;7

octal minutes

10;7

octal minutes

10;9

septi milli days

year

year

year

year

year

year

month

month

10;-1year

10;-1year

10;-1year

10;-1year

day

order(1)

day

day

day

day

day

order(1/10)

hour

(T110)

10;

clocks

hour

(T110)

octal hour

(T400)

10;2

milli days

order(1/102)

10. minutes

clock

(T700)

10;

octal minutes

10;

octal minutes

10;1

milli days

order(1/103)

minute

(T111)

10;-1

clock

octal minute

(T710)

octal minute

(T710)

milli day

(10;-3 day)

order(1/105)

second

(T112)

10;-3

clock

10;-2

octal minute

10;-2

octal minute

septi milli day

(T730)


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.
Top
Takashi
Posted: Jul 11 2010, 07:32 AM


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The Harmonic Universal Unit System is a Universal Unit System (with the GCD Unit)
which uses 1001700;/R as a length unit.
A letter 'h', which means 'human' or 'harmonic universal',
is suffixed to the corresponding SI unit symbols to use in place of
the new symbols required by the Harmonic Universal Unit System (with the GCD Unit).
For example, the length unit is mh and called 'harmonic universal meter',
and the time unit is sh and called 'harmonic universal second'.
The units of this system are listed in the following table.
Dimension Unit Symbol SI expression
Length mh 272.352206 mm
Time sh 390.625115 ms
Energy Jh 64.084550 mJ
Thermodynamic temperature Kh 58.387545 μK
Amount of substance molu 132.007609 mol
Mass gh 131.829278 g
Work Wh 164.056401 mW
Force Nh 235.300280 mN
Pressure Ph 3.172201 Pa
Charge Cu 28.896577 mC
Electrical current Ah 73.975215 mA
Impedance Ωn 29.9792458 Ω
Electrical potential difference AhΩn 2.2177212 V
Electrical capacitance shn 13.029851 mF
Magnetic flux ChΩn 0.866298 Wb
Magnetic flux density GhΩn 11.678991 T
Inductance shΩn 11.710646 H

The physical, material and astronomical constants expressed by means of this system are presented in the following table.
Constants Dozenal Prefix Unit Symbol
Fine Structure Constant 1;07399404E centy -
Avogadro constant 1; try-cosmic 1/molu
Rydberg constant 1;001700 cosmic centy 1/mh
Speed of light in vacuum 1; cosmic mh/sh
Quantum of action 1; quadry-atomic hecty Jh sh
Boltzmann constant 1; try-atomic Jh/Kh
Gas constant 1; - Jh/(molu Kh)
Unified atomic mass unit 1;0024073 try-atomic gh
Bohr Radius 1;00447X743 atomic dour mh
Elementary electric charge 1;0374439E3 by-atomic Ch
Electron mass 0;E48324X try-atomic milly gh
Newtonian constant of gravitation 4;1460 atomic centy (mh/sh)4/Nh
Newtonian gravitational force constant 2X;EE7 quinty-cosmic Nh
Planck length 2;0412 quadry-atomic mh
Stephan-Boltzmann constant 1E;82E29 try-atomic Wh/mh2/Kh4
Black-body radiation at the ice point 0;EX8783 hecty Wh/mh2
Temperature of the triple point of water 1;6974X3 cosmic centy Kh
Molar volume of an ideal gas 1;025664 hecty mh3/molu
neutral pH * : -log(Sqrt([H+][OH-])/(molu/mh3)) 7;2X71 - Bz(=log(10;))
Maximum density of water 1;092X47 hecty gh/mh3
Density of ice at the ice point 0;E85E hecty gh/mh3
Specific heat of water 0;6045 - Jh/gh/Kh
Surface tension of water at 25°C 0;EEE4 dour Nh/mh
Standard atmosphere 1;659967 super Ph
Standard gravitational acceleration 5;5E21264 - mh/sh2
Gravitational radius of the earth 2;4180317 centy mh
Equatorial radius of the earth 0;7X145E cosmic dour mh
Meridian length of the earth / 4 1;0370649 cosmic dour mh
Gravitational radius of the sun 3;1798E857 kily mh
Astronomical unit 8;X55509X33 cosmic hecty mh
Astronomical unit / c0 8;X55509X33 hecty sh
9;E91731X53 - milly day
* decimal pH 7.0 ± 7.0 is corresponding to dozenal pH (7 and quarter) ± (6 and half).

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.
Top
Takashi
Posted: Jul 11 2010, 11:44 AM


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The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit) become a following system:

The Earth local extension for the Harmonic Universal Unit System (with the GCD Unit)
Non coherent unit / prefix typeNon coherent unit / prefix namesymbolsymbol[plain text]value
calendar timeprefixseptis2-7
unitsdaydΩ1(=2 pi rad)
corresponding to 86,400. s
at the beginning of year 1900.
yeary365. 31./128. days
octal centuryCoC_o64. years
supplementary constantsthe gravitational acceleration of the Earth (is called '-force')gEg_E5;611X63X mh/sh2
the rotation period of the Earth (is called 'Earth solar')
at the beginning of year 1900.
sEs_E0;EEEEEE153586 sh/septi milli Ω1
the meridian length of the Earth (is called 'Earth meridian')mE *m_E4124,216E; mh1
difference of thermodynamic temperature and the base point°Shdegree(s) S (degree(s) semi-cosmic harmonic Kelvin)10000; Kh **
 *   1; Ω1 mE  = 40,007,860. m (called 'Earth meridian circle': the total meridian length of the Earth)
     1; rad mE =  6,367,449. m (called 'Earth meridian radian': the radius length of the Earth)
0;0001  Ω1 mE  =      1,929.391 m (called 'Earth meridian semi-atomic circle': dozenal nautical mile)

** 0.0 °Sh is corresponding to 118,2356; Kh(definition)
   0.0 °C is corresponding to   51;5 °Sh
  14.0 °C is corresponding to   61;0 °Sh
  37.0 °C is corresponding to   78;0 °Sh
 100.0 °C is corresponding to  100;0 °Sh
--------
[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)
Top
Takashi
Posted: Jul 12 2010, 10:52 PM


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The comparison of time units of the Universal Unit Systems
system name Type I Type II Type III
the Universal System of Units Standard the Universal Unit System with the GCD Unit the Harmonized Universal Unit System (with the GCD Unit)
suffix - u e h
suffix meaning - 'universal' the GCD of calendar time units of the 'earth' 'human' or 'harmonized universal'
time unit called - 'universal second' 'GCD second' 'harmonized universal second' or simply 'harmonized second'
length unit called - 'universal meter' 'GCD meter' 'harmonized universal meter' or simply 'harmonized meter'
length unit definition - 1000000;/R 86400.s * c0 / 128. / 12.^11. 1001700;/R
basic ratio - Ru/u = 1; Re/u = 1;0016EE Rh/u = 1;001700
length unit quantity m 0.272102883 0.272352126 0.272352206
time unit quantity s 0.390267520 0.390625000 0.390625115
mass unit quantity kg 0.131950058 0.131829304 0.131829266
time unit * 128. * 12.^3 s 86,320.9312 86,400.0000 86,400.0255
difference from 86400.s ms -79,068.7564 0.0000 25.4611
(time unit * 128. * 12.^3) just becomes 1 day - about 4.7 million years ago the beginning of 20th century about 1400. years later
Top
Takashi
Posted: Jul 13 2010, 01:06 PM


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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.
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Shaun
Posted: Jul 14 2010, 08:55 AM


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This, I find, is all going over my head.
I still think the hour should be kept.
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Takashi
Posted: Jul 14 2010, 03:17 PM


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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.

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

The variation 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.
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Takashi
Posted: Jul 18 2010, 07:36 AM


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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)
dimension symbol called name aliased name value
plane angle Ω1 circle day (for calendar time),
cycle (for periodical phenomena)
2 pi rad
solid angle Ω2 sphere turn (for magnetic units) 4 pi sr
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The Mighty Dozen
Posted: Jul 18 2010, 03:28 PM


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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.
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Takashi
Posted: Jul 22 2010, 01:54 PM


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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.

[Variation 2-D']
  over range 
      |
      : powers of 10;
      |
   octal century -------+
      |                 | 2^6
      |                year
      |1;003628*10;^9   | 1;003628*3^6/2
      |                day---+
      |                 |    | 2
      |                 | half-day(AM/PM)
      |           10;^3 |    |10;
      |                 |   hour
      |                 |    |60;
      |             md [mil(li day)]
      |                 | 2^7
smd [septi m(illi day)]-+
      |
      : powers of 10;
      |
  under range
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Takashi
Posted: Jul 22 2010, 01:55 PM


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The symbols of the Universal Unit System are brought together in the quartets.
Therefoe, they can be arranged as follows:
category name / symbol description category name / symbol description category name / symbol description category name / symbol description
base units
that are
natural units
naper logarithm of Napier's constant non-coherent
supplementary
constants
Bk logarithm of an integer
(B1 is called 'bit',
Bz is called 'Bel',
B8 is called 'byte')
minor prefix (do)deci 10;-1 major prefix (do)deka 10;1
rad plane angle
(rad is called 'radian',
rad2 is called 'steradian')
Ωk total solid angle of a hypersphere
1 is called 'circle' or 'cycle',
Ω2 is called 'sphere' or 'turn')
centi 10;-2 hecto 10;2
Ωn natural unit of impedance e elementary electric charge (is called 'electron') milli 10;-3 kilo 10;3
NA-1 per Abogadro constant molu universal mol atomic 10;-8 cosmic 10;8
base units
that are not
natural units
mh harmonized meter defining
constants
R the Rydberg constant non-coherent
Earth local
constants
mE the meridian length of the Earth
(is called 'Earth meridian')
power
prefix
low order semi- square root
sh harmonized second c0 the speed of light in vacuum(is called 'light') sE the rotation period of the Earth
(is called 'Earth solar')
at the beginning of year 1900.
uni- 1st power
Jh harmonized Joule ħ the quantum of action gE the gravitational acceleration of the Earth
(is called '-force')
bi- 2nd power
Kh harmonized Kelvin kB the Boltzman constant °Sh difference of thermodynamic temperature and the base point tri- 3rd power
derived units of
dynamical quantities
gh harmonized gram derived units of
electro- magnetic quantities
Ch harmonized Coulomb non-coherent
Earth local
calendar time
units octal century 26 years high order quadri- 4th power
Wh harmonized Watt Ah harmonized Ampere year 365. 31./128. days quinti- 5th power
Nh harmonized Newton Oh harmonized Oersted day Ω1(= 2πrad)
corresponding to 86400. s
at the beginning of year 1900.
sexti- 6th power
Ph harmonized Pascal Gh harmonized Gauss prefix septi 7th power of two inversed hepti- 7th power
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icarus
Posted: Jul 25 2010, 01:40 AM


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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
Posted: Jul 27 2010, 08:31 PM


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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!
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Cymbyz
Posted: Jul 28 2010, 02:16 AM


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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
Posted: Jul 28 2010, 04:21 PM


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and there's also the "ten-headed beast", isn't there?
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Cymbyz
Posted: Jul 28 2010, 05:37 PM


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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
Posted: Aug 2 2010, 03:34 AM


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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.
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Takashi
Posted: Aug 2 2010, 03:35 AM


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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.
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Takashi
Posted: Aug 10 2010, 09:24 AM


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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.
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