## The Universal Unit System and its notaions

 Posts 187
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Takashi
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Joined: Apr 12 2010, 02:24 PM
'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'?
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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dgoodmaniii
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Joined: May 21 2009, 01:45 PM
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.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use or X; for elv, I use or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!

 Posts 187
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Takashi
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Joined: Apr 12 2010, 02:24 PM
dgoodmaniii,
---
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'.

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.
&#124; A unit of measure is "a quantity that is used as the basis for expressing a given quantity,
&#124; 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).
---
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.

Dozens Demigod
dgoodmaniii
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Joined: May 21 2009, 01:45 PM
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?"
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.
Agreed.
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.
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.
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?
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use or X; for elv, I use or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!

 Posts 187
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Takashi
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Joined: Apr 12 2010, 02:24 PM
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?[/quote] 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 [url=http://dozenal.com]http://dozenal.com[/url] . [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?[/quote] 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. [quote="dgoodmaniii @ Aug 15 2010, 06:23 AM"]you've got 1:1 correspondence[/quote] 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 [url=http://dozenal.com]http://dozenal.com[/url] and Table 1. Because the consideration of coherency of the unit is described in Appendix A.3 of [url=http://dozenal.com]http://dozenal.com[/url], I don't repeat it. If you worry about coherency, you can limit the units used only to the 16. coherent units of [url=http://s13.invisionfree.com/DozensOnline/index.php?showtopic=371&st=15]the table[/url]. - 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.
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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dgoodmaniii
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Joined: May 21 2009, 01:45 PM
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.
dgoodmaniii @ Aug 15 2010, 06:23 AM wrote: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?
dgoodmaniii @ Aug 15 2010, 06:23 AM wrote: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)?
dgoodmaniii @ Aug 15 2010, 06:23 AM wrote: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.
All numbers in my posts are dozenal unless stated otherwise.
For ten, I use or X; for elv, I use or E. For the digital/fractional/radix point, I use the Humphrey point, ";".
TGM for the win!

 Posts 187
Regular
Takashi
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Joined: Apr 12 2010, 02:24 PM
dgoodmaniii,
dgoodmaniii @ Aug 23 2010, 02:05 PM wrote: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.
dgoodmaniii @ Aug 23 2010, 02:05 PM wrote: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.
dgoodmaniii @ Aug 23 2010, 02:05 PM wrote: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.
dgoodmaniii @ Aug 23 2010, 02:05 PM wrote: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.
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.

 Posts 187
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Takashi
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Joined: Apr 12 2010, 02:24 PM
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
the last paragraph of page.2 of [url=http://dozenal.com]http://dozenal.com[/url] wrote: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
the 3rd paragraph of page.1 of [url=http://dozenal.com]http://dozenal.com[/url] wrote: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.
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.

 Posts 187
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Takashi
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Takashi @ Aug 11 2010, 02:37 AM wrote:'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'.
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.

 Posts 187
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Takashi
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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 [url=http://dozenal.com)]http://dozenal.com)[/url]

(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.
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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Luke-Jr
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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.

 Posts 187
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Takashi
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Luke-Jr,
I thank for your having been interested in the Universal Unit System.
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote:Why were these values chosen?
See chapter 2.1 and appendix D.1 of http://dozenal.com .
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote: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/uni ... densed.xls .
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote: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.
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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Luke-Jr
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Takashi @ Mar 12 2011, 01:22 AM wrote:
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote: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.
Takashi @ Mar 12 2011, 01:22 AM wrote:
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote: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/uni ... densed.xls .
I'm afraid this still seems too complicated. How many SI or (even better) US/imperial units are each of the new ones?
Takashi @ Mar 12 2011, 01:22 AM wrote:
Luke&#045;Jr @ Mar 10 2011, 02:19 AM wrote: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...

 Posts 187
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Takashi
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Luke&#045;Jr @ Mar 12 2011, 01:50 AM wrote: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 .
Luke&#045;Jr @ Mar 12 2011, 01:50 AM wrote: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/uni ... densed.xls .
Luke&#045;Jr @ Mar 12 2011, 01:50 AM wrote: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/ .
Luke&#045;Jr @ Mar 12 2011, 01:50 AM wrote: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.
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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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.
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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Luke-Jr
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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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Luke-Jr,

You can derive the expressions easily if you read the documents which I referred in an article
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 @ Apr 1 2011, 11:23 AM wrote:Rather I want to express 'dodeci meter' and 'octal century' by shorter words.
'octal century' = 64 year
- half of the Least Common Multiple (LCM) of the length of a day and a tropical year
- two times human generation approximately
Is there a word to apply to them?
The word that an initial is H or S is better.

'dodeci meter' = 2.27 cm
- The unit corresponding to inch
Probably high use frequency.
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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I refined the table of #15 of this thread.
and http://www.asahi-net.or.jp/~dd6t-sg/uni ... tables.pdf .
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<edited May 29 2011, 02:00 PM >

<edited June 5 2011, 05:00 AM >
tables.pdf is updated using CODATA(2010)
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 @ Apr 5 2011, 10:11 PM wrote:'octal century' = 64 year
- half of the Least Common Multiple (LCM) of the length of a day and a tropical year
- two times human generation approximately
Does the word 'Span' apply to the above unit?
Is it too abstract when we omit 'life' of 'life Span'?
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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Luke-Jr,

I reflected discussions of this thread and revised documents of http://dozenal.com.
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.

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How do the constants and the units that the TGM system uses for definitions turn out in the Universal Unit System? I made the following list. The numerical value of above list is all decimal and the factors of powers of twelve are ignored.
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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I tried to summarize the policy of the Universal Unit System naming rule.

1.Policy of the naming of the unit terms

Code: Select all

`````` &nbsp;1.1 The length of the unit terms
&nbsp; &nbsp;1.1.1 The unit terms to be used more frequently are shorter.
&nbsp; &nbsp; &nbsp;But,
&nbsp; &nbsp; &nbsp; &nbsp;It is not necessary to extremely shorten them.
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;There are many words more frequently used in daily use than unit terms.
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;Unit terms don't have priority over these words.
&nbsp; &nbsp; &nbsp; &nbsp;Don't shorten the term which distinguish an important difference.
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&#40;example&#41; Identification of the plus and minus of the power prefix.
&nbsp; &nbsp;1.1.2 The unit terms not to be used so frequently are longer.
&nbsp; &nbsp; &nbsp;&#40;reference&#41; The policy of http&#58;//en.wikipedia.org/wiki/-yllion is right.

&nbsp;1.2 Don't do novel naming in vain.
&nbsp; &nbsp;&#40;exception&#41;
&nbsp; &nbsp; &nbsp;Units&#40;time, length, volume and mass&#41; and lower power&#40;1-4&#41; prefixes used most frequently
&nbsp; &nbsp; &nbsp;may attach new names or abbreviations.
&nbsp; &nbsp;It is difficult to learn mass novel names.
&nbsp; &nbsp; &nbsp;Errata are not avoidable even in proposer.
&nbsp; &nbsp;Because unit terms for decimal and duodecimal are identifiable in context,
&nbsp; &nbsp;we can reuse words used widely for decimal as words for duodecimal.
&nbsp; &nbsp; &nbsp;Unit terms for decimal should be combined only with the decimal numbers.
&nbsp; &nbsp; &nbsp;Unit terms for duodecimal should be combined only with duodecimal numbers.
&nbsp; &nbsp;You can omit the self-evident element in context.

&nbsp;1.3 The peculiar name of the units
&nbsp; &nbsp;1.3.1 Give the peculiar name to a useful unit suitable for a start point of the deriving.
&nbsp; &nbsp; &nbsp;Because the unit system is coherent, how to derive units is free.
&nbsp; &nbsp; &nbsp;Therefore, it is not realistic to give a new derived unit a peculiar name one by one.
&nbsp; &nbsp; &nbsp; &nbsp;&#40;It is the introduction of mass novel names.&#41;
&nbsp; &nbsp; &nbsp;I choose useful units suitable for start points of the deriving
&nbsp; &nbsp; &nbsp;to become easy to understand how all derived units were derived,
&nbsp; &nbsp; &nbsp;and only give peculiar names to these useful units.

&nbsp; &nbsp;1.3.2 Collision with the conventional variable name
&nbsp; &nbsp; &nbsp;If there is no special circumstances, choose the name with the initial letter
&nbsp; &nbsp; &nbsp;which is different from a conventional variable name of the corresponding dimensional quantity.
``````
2.Policy of the symbol definition

Code: Select all

`````` &nbsp;2.1 The length of the symbol
&nbsp; &nbsp;Should be as short as possible.

&nbsp;2.2 Correspondence with the &nbsp;naming of the unit terms
&nbsp; &nbsp;2.2.1 The element which is not self-evident in context
&nbsp; &nbsp; &nbsp;Express all them by a letter.
&nbsp; &nbsp; &#40;example&#41; The identification of the plus and minus of the power prefix depends on
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;existence &#40;+/-&#41; of the letter not the position of the letter.
&nbsp; &nbsp;2.2.2 The element which is self-evident in context
&nbsp; &nbsp; &nbsp;In general, don't omit these elements, too.
``````
Decimal figures are indicated by a period “.” as the radix point, and duodecimal figures are indicated by a semicolon“;” as the radix point. Both notations may use a comma “,” and “_” as the digit group separator. ‘X’ expresses ten, ‘E’ expresses eleven and ‘M’ expresses 1_0000,0000;(=12.^8). Octal figures are indicated by an at sign “@” as the radix point.

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This is a follow up article of here

The mass of nucleon of aluminium is approximately equal to one tri-atomic universal gram(1 g3-u).
The mass of nucleon of iron (=The lightest nucleon) is approximately equal to one tri-atomic harmonic gram(1 g3-h).

The mass density of H2O is approximately 109; gh/mh3 (water:109; gh/mh3, ice:E8; gh/mh3)
The molar mass of H2O is approximately 16; gh/molu

Therefore, The molar density of H2O is approximately (109; gh/mh3) / (16; gh/molu) = 8;6 molu/mh3

It means that the molar density of H2O is approximately 8;6 H2O / m-h3 = 1;09 H2O / (m-h/2)3

In other words, a cube of one side of half atomic meter(= 6 times Bohr radius) includes about one H2O molecule.
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(1/2) mh * (1/2) mh * (3/4) mh is equal to one U.S. liquid gallon.
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.