Takashi
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Jul 10 2011, 06:18 AM #49

I put A Conveter to a Web server.
It is not yet tested enough.
--------
[Edit]
New physical quantities are supported.
A configuration page is added.
The collective conversion to plural units is implemented.
The Tonal System is added.
Mixed radix format for date and time is supported.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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icarus
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Jul 10 2011, 11:51 AM #50

Takashi, it's a little technical but works nicely!
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Takashi
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Jul 11 2011, 04:10 PM #51

icarus @ Jul 10 2011, 11:51 AM wrote:Takashi, it's a little technical
Please point out refinements.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 19 2011, 12:35 PM #52

Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Jul 29 2011, 04:04 AM #53

Mr. Pendlebury's Brite scale (the last page of the [url=http://www.dozenalsociety.org.uk/pdfs/TGMbooklet.pdf]TGM booklet[/url]) seems to harmonize with the Universal Unit System. The photon scale is based on the fact that a 540MHz photon's energy is approximately 1 bi-atomic Joule.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Sep 19 2011, 06:12 AM #54

There are some reasons why the Universal Unit System assumes not 12^12 but 12^8 a prefix interval.

(1) 12^8 is led naturally by relations between fundamental constants as I explained before.
Mass and amount of substance are three dimensional quantities. Therefore,
an atomic scale mass unit should be triple atomic quantity of human scale mass unit, and
an atomic scale amount of substance unit should be triple atomic quantity of human scale amount of substance unit.
An atomic scale mass unit has to be an atomic mass unit, and
an atomic scale amount of substance unit has to be reciprocal Avogadro constant.
These relations require that an atomic factor cannot help becoming not 12^-12 but 12^-8.

(2) 12^4 is a upper limit as for the ratio of quantities that a human being can feel intuitionally.
The human being can grasp numbers only countable in a work day or a night intuitively.
(Example: step counts per day, number of sheep to count at a night)
We cannot but grasp the further numbers logarithmically.

Therefore I gave quantities to become the base points and designed to express
all quantities between the upper and lower 12^4 of these base points.

The interval between these base points becomes bigger, the expression becomes more intuitive.
This is because situation using the same base point becomes frequent.
We come to recognize these base points as XX scale. (such as cosmic scale, atomic scale, ..)
Example:
It is easy to recognize the relations of atomic km and atomic dm if used to harmonic km and harmonic dm.

However, we cannot adopt 12^12 as the base point interval because 12^6 exceeds the limit that we can grasp intuitively.

(3) 12^8 and myriad system have high affinity.
--------------------------------------------------------
SI definition document 2.2.2 explains derived units with special names and symbols.

Without the special reason including the influence on health of the human body,
The SI did not give new special names to derived units.
It is expensive to add new words to common vocabulary.

Because the new words disturb the spread,
I designed the Universal Unit System to add new words as few as possible.

In addition, I reused the words that there had been already in common vocabulary
based on the commonality of the meaning. (such as 1000-ness)
But I designed the prefix system so that slight difference in expression
did not bring big difference in content.

Therefore, I adopted entirely different words in 12^3 and 12^-3.

Unfortunately because there is no single word with 10000-ness except 'myriad'
in common vocabulary, I cannot give single word expressions to 12^4 and 12^-4.

Expression of 12^4 is longer than expression of 12^8.
This is a left problem.

--
First Paragraphs are edited 2011-11-27
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Nov 6 2011, 10:04 PM #55

I intend to use [url=http://en.wikipedia.org/wiki/Knuth_-yllion]the myriad system[/url] to express pure numbers with the universal unit system. The table shown below explains how the myriad system will be modified for duodecimal system. We find "centy-" and "milly-" in the last part of this table. It means that we give "centy-" a meaning of 12[sup]2[/sup] and "milly-" a meaning of 12[sup]3[/sup]. If we adopt these words, 12[sup]2[/sup] will have two different expressions with "centy-" and "centi-" in same duodecimal context, because "centi-" is used for power prefix. 12[sup]3[/sup], too. This is not desirable. So, I revised power prefixes to accord with the myriad system. [url=http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf]http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf[/url] ( [url=http://dozenal.com/]http://dozenal.com/[/url] )
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Kodegadulo
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Nov 6 2011, 11:09 PM #56

Is there any difference in pronunciation between, for instance, "million" and "myllion"?
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Takashi
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Nov 7 2011, 12:22 PM #57

Please click the table shown above.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Nov 7 2011, 12:23 PM #58

The SI units definition will be changed.
There does not seem to be the influence on the Universal Unit System.

http://www.bipm.org/utils/common/pdf/24 ... tion_A.pdf

takes note of the intention of the International Committee for Weights and Measures to propose a revision
of the SI as follows:
• the International System of Units, the SI, will be the system of units in which:
• the ground state hyperfine splitting frequency of the caesium 133 atom ƒ¢ƒË(133Cs)hfs is exactly 9 192 631 770 hertz,
• the speed of light in vacuum c is exactly 299 792 458 metre per second,
• the Planck constant h is exactly 6.626 06X ~10-34 joule second,
• the elementary charge e is exactly 1.602 17X ~10-19 coulomb,
• the Boltzmann constant k is exactly 1.380 6X ~10-23 joule per kelvin,
• the Avogadro constant NA is exactly 6.022 14X ~1023 reciprocal mole,
• the luminous efficacy Kcd of monochromatic radiation of frequency 540 ~1012 Hz is exactly 683 lumen per watt,
<snip>
(ii) the symbol X in this Draft Resolution represents one or more additional digits to be added to the
numerical values of h, e, k, and NA, using values based on the most recent CODATA adjustment
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Kodegadulo
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Nov 7 2011, 02:04 PM #59

Takashi @ Nov 7 2011, 12:22 PM wrote: Please click the table shown above.
When I click on it, my Webroot security software blocks it as a suspicious site. However, I just noticed the caption at the bottom of the image indicating that the "y" has a long /a&#618;/ sound rather than a short /&#618;/ sound. This is odd, because if the myllion system is based on myriad /'m&#618;.r&#618;.&#601;d/ the "y" in the latter has a short /&#618;/ sound.
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Kodegadulo
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Nov 7 2011, 02:10 PM #60

Takashi @ Nov 7 2011, 12:23 PM wrote: • the ground state hyperfine splitting frequency of the caesium 133 atom ƒ¢ƒË(133Cs)hfs is exactly 9 192 631 770 hertz,
What symbol did you mean to write there?
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Takashi
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Nov 8 2011, 03:48 AM #61

-y- seems to be pronounced like mile to distinguish -y- from -i- in verbal communication.
Please see a search result.

Anyway I am thankful if you suggest better pure number name system or unit prefix system,
which can be used with revised version of http://dozenal.com/ and,
which adapts to the policy and requirement.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Nov 8 2011, 03:50 AM #62

The time unit 'second' will not be changed.
ƒ¢ƒË(133Cs)hfs means 'the ground state hyperfine splitting frequency of the caesium 133 atom'.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Kodegadulo
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Nov 8 2011, 05:12 AM #63

Takashi @ Nov 8 2011, 03:50 AM wrote:The time unit 'second' will not be changed.
ƒ¢ƒË(133Cs)hfs means 'the ground state hyperfine splitting frequency of the caesium 133 atom'.
I understand what (133Cs)hfs means. But there are what seem to be garbage characters just before that:
- script f
- cent mark
- script f
- capital E umlaut

It seems obvious you didn't intend those characters. I have seen my own posts get corrupted with similar characters when I use special symbols sometimes. So once again, what was the actual symbol you meant there?
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Takashi
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Nov 8 2011, 09:39 AM #64

Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Kodegadulo
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Nov 8 2011, 12:07 PM #65

Takashi @ Nov 8 2011, 09:39 AM wrote:Please see page.2 of http://www.bipm.org/utils/common/pdf/24 ... tion_A.pdf
So then it's captial-delta nu: &#916;&#957;
As of 1202/03/01[z]=2018/03/01[d] I use:
ten,eleven = ↊↋, ᘔƐ, ӾƐ, XE or AB.
Base-neutral base annotations
Systematic Dozenal Nomenclature
Primel Metrology
Western encoding (not by choice)
Greasemonkey + Mathjax + PrimelDozenator
(Links to these and other useful topics are in my index post;
click on my user name and go to my "Website" link)
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Takashi
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Nov 13 2011, 08:06 AM #66

The attention point of agreed revision is that an elementary electric charge becomes the definition constant.

- the elementary charge e is exactly 1.602 17X x 10-19 coulomb

This means that the permittivity of vacuum turns into measured quantity.
The fine structure constant and the permittivity of vacuum become to link strictly each other.

The electromagnetic interaction observed at the macroscopic distance is the renormalized result of
interaction between naked electric charge effect and quantum vacuum effect.
The fine structure constant may fluctuate by the change of the quantum vacuum in terms of time.

Strictly speaking, the following 1) is different from 2) as a concept each other.

1) The quantity of cahrge causing the electromagnetic interaction
2) The number of charges as the quantity of preservation of the quantum mechanics

The old definition uses 1), and the new definition uses 2).

For example, the quantity which we use for design of motor is 1) but 2).
In my opinion, the old definition is more appropriate and
we should have treated 2) as kind of 'amount of substance'.

# The SI notes "when the mole is used, the elementary entities must be specified and may be
# atoms, molecules, ions, electrons, other particles, or specified groups of such particles."
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Nov 17 2011, 01:38 PM #67

I minimized the kind of words which have to be added to common vocabulary. The added words are listed in the following table:
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Nov 27 2011, 06:24 AM #68

1)
In English common vocabulary, the words to express digits are the following 9 or 10 words:
'zero', 'one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine'

On the other hand, the words for positional representation are the following 5 words
within daily used range from 1 to 10^12:
'ten', 'hundred', 'thousand', 'million', 'billion'

There are more former kinds than latter kinds.
Such a phenomenon is not limited to only English.
This is a result optimized by the following policies after longtime real use:

- Relatively important concepts are discriminated from each other more finely and named more finely.
- Relatively non important concepts are discriminated from each other more coarsely and named more coarsely.

2)
In English common vocabulary, the words for positional representation of duodecimal numbering system
already exist:

dozen : 12
gross : 12^2
great gross : 12^3

and some dictionaries describe great gross as dozen gross.

It means that we can already express pure numbers smaller than 12^4 using duodecimal numbering system.

--------
The duodecimal myriad system is almost only numbering system
which is comprised of a simple rule to satisfy policies 1),
and which is connectable to system 2) at the lower limit.

I think that it is not accidental but Dr. Knuth's design that the myriad system satisfies polies 1).

People (including myself thirty years ago) who assign single word for 12^11 are
rare and special people feeling importance of the same degree in 11 and 12^11.
Such a feeling is a feeling only for the people who have a special interest in numbers and quantities.

There is not the situation using the big number such as 12^11 for daily use if we use appropriate units.
I think that this feeling is far apart from the feeling of common people.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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icarus
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Nov 27 2011, 12:50 PM #69

On page 87 of Dr. Anton Glaser's History of Binary and Other Nondecimal Numeration, Hermann Hankel is described as having evaluated number bases for their economy of concepts in 1874. He considered the number of concepts required to express a given number up to a certain power of the base, and decided base four was the most economical.

This seems a silly and unimportant measure of "best base" because humanity assigns hundreds of concepts even to relatively inconsequential notions such as popular culture and fantasy. Surely, being spare with counting concepts is simply being intellectually miserly. This might not have much to do with Takashi's post, but that is what I am left thinking about with the first part of the most recent post.

The concepts you are describing are names for "numeral" and "rank", according to my recollection of Karl Menninger's Number Words and Number Symbols. He describes numeral and rank at great length across cultures (but mostly across European cultures). Georges Ifrah also has a book but I've read a lot of discrediting for it. Perhaps only some parts of it are not solid. He too compares numeral and rank (doesn't use those terms necessarily) across cultures.

Truly English does have an inchoate system of duodecimal nomenclature, and Knuth's extension and several others that are related do well in connecting the lower range to upper ranges that become necessary for nomenclature in a system of measure that has a full range of concepts. The great thing about accessing this lower-range extant duodecimal nomenclature is that we engage an already-intelligible nomenclature and minimize what people need to know to use duodecimal numeration in everyday life. Other naming schemes may be more attractive, but most people are already equipped to understand duodecimal numbers up to just under the duodecimal 4th power. This represents the predominance of everyday use for most people. (Technical people easily exceed that). We can say there were four dozen six (or four and a half dozen) at last week's parish breakfast, rather than "about fifty" or "fifty-four". We can say Saturn has five dozen one moons, or Chicago is one gross ten dozen nine miles from St. Louis. English has more or less common words for some uncials: one sixth, one quarter, one third, one half, two thirds, three quarters, five sixths, and well understood words for divisors of the gross: one eighth, one sixteenth, etc. It needs help below the radix point as well as above the 4th power.

The significance of the eleventh power of any number (except perhaps those divisible by eleven) would seem rather low. Eleven is the fifth prime. From observations of the "real world", eleven-ness seems pretty rarely encountered. Because the naming convention for powers of the base often are modular, beginning with names for the lowest powers that are used everyday, we tend not to have single-word names for the eleventh power. There will be x names, with x being a small integer easily retained in memory. So we might have three, four, or six names. This isn't true in other cultures, perhaps only a western manifestation. Then compounds can be used to produce names for larger numbers. Pendlebury and Kodegadulo both have produced names for rank that operate like a second set of numeral names. This is effective because we then have standard nomenclature for a relatively large range of number. In English, we have standard names up to the hundred million, then differences arise at "billion-milliard", and in the American lexicon, the common person can understand up to "hundred trillion" even if the person might not grasp the correct magnitude of the number (most would think "very very big number" if presented by such). "Quadrillion" isn't yet a concept in the common vocabulary (believe me, the American government is working on it! We don't yet have debt that large!) when we need access to large ranks and want a short word that can be "prefixed" we turn to kilo-/mega-/giga-/tera-/peta-, with the latter two not quite as well known. Most people haven't heard of exa- and above.
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m1n1f1g
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Nov 27 2011, 09:12 PM #70

The great benefit of the Pendlebury-style rank names is that they are very easy to use. Just count the digits, take away one and turn that number into the corresponding name. This is easier than long scale, where division by six is needed, as well as short scale, which requires researching to be sure of large numbers - unless you are willing to sound like Brian Cox, for which division by nine is needed.

The myriad scale is similarly hard to use as the long or Cox scales. It requires a knowledge of binary powers that we are not easily familiar with. Is 28&#8242; = 25 or 26? As a programmer, I've bothered learning them, but a lot of people haven't. It's a reasonable and logical suggestion, but so is binary. Also, the myriad system suffers from the short scale problem: "byllion" is not 'bi'-anything.
A few little conventions:
- Dozenal integers suffixed with prime (&#8242;). This is the uncial point.
- Decimal integers suffixed with middle dot (·). This is the decimal point.

You may see me use * prefix for messages before 11&#400;7-03-1X, and a whole range of similar radix points. I will often use X and &#400; for :A and :B.

Sometimes, I will imply that an integer is in dozenal, so I won't add any marks to it. You should be able to tell that "10 = 22 * 3" is in dozenal.
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Dec 3 2011, 11:15 PM #71

For putting coincidence of fundamental physical constants to use, the duodecimal number system is the only choice. I do not know any other proposal except the Universal Unit System which can uniquely specify duodecimal number system. An approach such as follows may be good to have common 'decimal' people accept duodecimal number system. ------- [url=http://en.wikipedia.org/wiki/Planck_units]Planck unit system[/url] is a natural unit system to consider to be G=c[sub]0[/sub]=ħ=k[sub]B[/sub]=Z[sub]P[/sub]=1. We exchange G with 35G and can constitute a Universal Unit System which defines 35G, c[sub]0[/sub], ħ, k[sub]B[/sub] and Z[sub]P[/sub] as units for each dimension. We call this variaton of the Universal Unit System '[url=http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/gravitic.pdf]The gravitic Universal Unit System[/url]'. When we use the gravitic Universal Unit System, the gravitational equation is expressed by the following formula: The values of constants in this unit system become like the following list. If the universe will be over in the time of the 12[sup]56[/sup] units, it is beautiful, but probably will not become so. ------- Of course the gravitic Universal Unit System is not a practical unit system because precision of G is insufficient. Therefore, the gravitic Universal Unit System does not take the position of the harmonic Universal Unit System. ------- See also [url=http://en.wikipedia.org/wiki/Talk:Planck_units#Other_possible_normalizations]http://en.wikipedia.org/wiki/Talk:Planck_u..._normalizations[/url]
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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Takashi
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Dec 4 2011, 02:03 AM #72

uncia:

Google finds about 234,000 results for "great gross", about 1,110,000 results for "uncia".
How common is the word 'uncia'? Because I'm not native English speaker, I do not know well.
I didn't choose 'uncia' as 12-ness word in duodecimal myriad system because I want to make an initial of 12-ness word 'd'.

hundred trillion:

Hundred trillion is nearly equal to dozen myriadd myllion.
With the small number like this, common people will not be conscious of the binariness of the myriad system.

Units of the gravitic Universal Unit System are examples of non appropriate units.
In this case we will be conscious of octalness of the myriad system in scientific field.

The exponential notation of the Bohr radius will be '1;00*M2@6' gravitic meter and
read 'one point zero zero times myllion to the power two point six gravitic meter'.
(';' is duodecimal radix point and '@' is octal radix point.)
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.
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