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Pages: (5) « First ... 3 4 [5]  ( Go to first unread post )

 Day Gravity Water Spreadsheet, Crosby in the Cloud
Oschkar
Posted: Jan 17 2018, 01:28 AM


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You left out a colon in the link, by the way.
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Kodegadulo
Posted: Jan 17 2018, 01:33 AM


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QUOTE (Oschkar @ Jan 17 2018, 01:28 AM)
You left out a colon in the link, by the way.

Thanks. Fixed.
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Double sharp
Posted: Jan 17 2018, 11:40 AM


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QUOTE (Kodegadulo @ Jan 17 2018, 01:10 AM)
I do think that makes this metrology stink a little, so I've designated the brand prefix pu•. smile.gif

That's exactly how the symbol for plutonium became Pu (instead of, as might have been expected, Pl). happy.gif

Do you intend "pu" to be pronounced as individual letters (as if it were an acronym), or as a word? Because I think the former has a much higher chance of being taken seriously. wink.gif
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Kodegadulo
Posted: Jan 17 2018, 07:10 PM


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QUOTE (Double sharp @ Jan 17 2018, 11:40 AM)
QUOTE (Kodegadulo @ Jan 17 2018, 01:10 AM)
I do think that makes this metrology stink a little, so I've designated the brand prefix pu•. smile.gif

That's exactly how the symbol for plutonium became Pu (instead of, as might have been expected, Pl). happy.gif

Do you intend "pu" to be pronounced as individual letters (as if it were an acronym), or as a word? Because I think the former has a much higher chance of being taken seriously. wink.gif

Yes, well, ultimately the object lesson from that article is that some science is not to be taken seriously and is in fact a joke. If you have any doubts, just consider the SI prefixes.
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wendy.krieger
Posted: Jan 18 2018, 08:34 AM


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What do i find Crosby's system under? Will it include what Crsoby suggested for electrical units?

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Kodegadulo
Posted: Jan 19 2018, 05:00 AM


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QUOTE (wendy.krieger @ Jan 18 2018, 08:34 AM)
What do i find Crosby's system under?  Will it include what Crsoby suggested for electrical units?

In the DGW spreadsheet for small bases, I have added a new Crosby metrology, depicting (as near as I can determine, and such as it is) the system of measures which one Private William S. Crosby sketched out in his letter, "Uncial Jottings of a Harried Infantryman", published in the second issue of the Duodecimal Bulletin, June 1161z=1945d, near the end of World War II. In honor of Crosby's enlistment in the U.S. Army at that time, I have used Unicode Character 'CROSSED SWORDS' (U+2694) ⚔ as the brand mark for this metrology, since such cross swords are the traditional insignia for the U.S. infantry.

Although Crosby pioneered the idea of basing a system of measure on a dozenal fraction of the day, Earth's gravity, and the density of water, his system fell somewhat short of being thoroughly "coherent". He did designate an "ell"* as his lengthel, based on gravity and the "twinkling"* or pentcia·day (just like Tertiel or Sunny's system). However, he did not go on to derive the "ell-mass"* (a cubic ell of water) as his massel. Instead, he emulated SI by throwing in an extraneous third-power factor, taking the tricia of the "ell-mass", a kilogram-like "hand-mass"*, as his massel. (In effect, he did not use water·density as his densitel, but rather the tricia·water·density, just as SI uses the milli·water·density.)

The temperature scale Crosby suggested was simply Fahrenheit or Rankine degrees, but counted dozenally, zeroed at a fictitious point slightly below absolute zero, so that freezing would be at exactly 350z=492d rankine, and boiling at 480z=672d rankine. This, of course, does not make the massic heatability (specific heat capacity) of water a coherent unit, so the equivalence of work and heat will be less obvious.

As for Crosby's EM system, the problem is that he was somewhat tenuous about specifying it, and we are missing a critical bit of what he did plan to say. In fact, here is the complete text of what he wrote (italics indicated dozenal numbers):

QUOTE (Crosby @ Jun 1 1945, 12:00 PM)
Electrical Units, offer a big field for controversy, and I have come to no definite conclusions so far. Defining the permeability of space as 10?? or 10?? of unit permeability, and writing Ampere's law in Heaviside's "rational" form would define units of fairly convenient size.

The question marks I'm showing above represent missing characters in the text of the Duodecimal Bulletin, where clearly Crosby meant to have some exponents, but the publishers neglected to pen them in. Likely, these were 10−6z or 10−7z, but this is only a guess. If we take \(\mu_0\) = 1 ⚔hexcia·inductivitel = \(\mathrm{4\pi{\times}10^{-7}_d\ \frac{N}{A^2}}\), and assume "Ampere's law in Heaviside's 'rational' form" simply means what was rapidly becoming the modern rationalized formulation, with the onset of SI:

\(\displaystyle \frac{dF}{d\ell} = 2k_A\frac{I_1I_2}{r} = 2\frac{\mu_0}{4\pi}\frac{I_1I_2}{r} = \frac{\mu_0}{2\pi}\frac{I_1I_2}{r}\)

then we get ⚔currentel ≈ 2.2359d ampere, ⚔electrelic·potentialel ≈ 14.2837d volt, ⚔impedancel ≈ 6.3884d ohm, and so forth. If we assume \(\mu_0\) = 1 ⚔septcia·inductivitel = \(\mathrm{4\pi{\times}10^{-7}_d\ \frac{N}{A^2}}\), then we get ⚔currentel ≈ 6.4504d ampere, ⚔electrelic·potentialel ≈ 49.4491d volt, ⚔impedancel ≈ 76.6610d ohm, and so forth. In either case, as Crosby indicated, the results are "units of fairly convenient size".

It really took Pendlebury to demonstrate Crosby's idea in a (nearly) completely coherent way, including strict adherence to water density as the densitel (Denz), with the volumel (Volm) and hence the massel (Maz) derived strictly from the lengthel (Grafut); and including a coherent temperature scale (Calg) based on the massic heatability of water (Calsp); all without any extraneous factors, not even "powers of the base". Nevertheless, we surely must must acknowledge Crosby's sketch was a key inspiration for Pendlebury's system, and through Pendlebury, for Primel and the rest of these DGW systems. Hence the subtitle for this thread.

(*Note: The terms "twinkling", "ell-mass", and "hand-mass" are of course my own coinages, as are quantitels as names for coherent units, and of course Crosby wouldn't have called the negative fifth power of twelve of a day a "pentcia·day" (nor a "twinkling"). But I was pleasantly surprised to find he had identified his lengthel as an "ell", since I had completely independently stumbled on that as a colloquial name myself, before I discovered Crosby's letter.)

Moderator's Edit: Wendy responded to this with a post that contained a number of off-topic elements, and blatant inaccuracies, with the evident intent to divert this thread into her usual tropes. So I have moved it, as well as my response, to the Off Topic thread. If Wendy wishes to talk about her usual agenda, she is welcome to start a thread about it in her own Cough forum. In any event, I have little interest in entertaining her obsolete notions yet again, certainly not here.
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Kodegadulo
Posted: Jan 19 2018, 02:08 PM


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QUOTE (Kodegadulo @ Jan 19 2018, 05:00 AM)
In the DGW spreadsheet for small bases, I have added a new Crosby metrology, depicting (as near as I can determine, and such as it is) the system of measures which one Private William S. Crosby sketched out in his letter, "Uncial Jottings of a Harried Infantryman", published in the second issue of the Duodecimal Bulletin, June 1161z=1945d, near the end of World War II.

I went back and took a closer look at the section of Crosby's letter regarding his ⚔massel:

QUOTE (Crosby @ Jun 01 1945 @ 12:00 PM)
Mass. Here we can be guided fairly well by the metric example of giving the density of water a value of some power of the numerical base in units of the system.  At the same time I have allowed myself some leeway here, since the density of water changes with temperature and purity, and have used this leeway to try to insure that the new unit of pressure will work out so that the present "Standard Atmosphere" can be fairly accurately expressed in some round number. The result of these efforts to date is a compromise: let the unit of mass be defined such that one metric gram = 0.001 986unc of it, precisely; then the density of water will be around 1000 unit mass/ell³ at ordinary temperature, and the present "Standard Atmosphere', now expressed as 760 mm of mercury, will be almost exactly 8900unc of the new unit of pressure.

So Crosby jiggered his ⚔massel such that:

1 triqua·gram = 1.986z ⚔massel = \(\mathrm{\left(\frac{375}{2^5{\cdot}3^2}\right)_z}\)⚔massel, precisely

Given that he also equated 11z millimeter = 17z ⚔tricia·lengthel (⚔tricia·ell, colloquially), this leads to:

1 ⚔triqua·densitel ≈ 998.7155d kilogram/meter³
1 atmosphere = 101325d pascal ≈ 8900.6244z ⚔pressurel

So his (scaled-down) ⚔densitel seems to be based on water's density at slightly colder than 20°d celsius, hence fairly close to what was being used as "standard conditions" at the time. But he was slightly off of his goal of making the standard atmosphere round to 8900z ⚔pressurel. It's unclear at this great remove of time whether that may have been due to "standard atmospheric pressure" being slightly different back then (760d mm Hg ≈ 101325d pascal); or whether, without benefit of computers or pocket calculators, and probably limited to paper and pencil, he simply miscalculated slightly. It was, after all, only a sketch.

I've adjusted the spreadsheet in accordance with the above. I've also added a couple handy rows on the main Metrology tab:
  • Row 44 now shows atmospheric pressure in SI units (on the left, cell D44), and in target pressurels (on the right, cell N44).
  • Row 22 now shows lightspeed in SI units (on the left, cell D22), and in target velocitels (on the right, cell N22).
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Kodegadulo
Posted: Jan 19 2018, 09:09 PM


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QUOTE (Kodegadulo @ Jan 19 2018, 02:08 PM)
So Crosby jiggered his ⚔massel such that:

1 triqua·gram = 1.986z ⚔massel = \(\mathrm{\left(\frac{375}{2^5{\cdot}3^2}\right)_z}\)⚔massel, precisely
...
But he was slightly off of his goal of making the standard atmosphere round to 8900z ⚔pressurel.  It's unclear at this great remove of time whether that may have been due to "standard atmospheric pressure" being slightly different back then (760d mm Hg ≈ 101325d pascal); or whether, without benefit of computers or pocket calculators, and probably limited to paper and pencil, he simply miscalculated slightly. It was, after all, only a sketch.

Nevertheless, the principle he was demonstrating was sound: If there is some range or leeway in the values for a key constant used as a basis for deriving a coherent unit, it's okay to take liberties with the value if it helps achieve a subsidiary goal, such as establishing exact equivalences between units in the target metrology and customary units, or making some key value a rounded number, so long as this choice doesn't wander outside of the "natural" range or stray too far from an "average" value. In this case, if Crosby had had access to the kind of computing resources we take for granted today, he might have found some other simple-integer correspondence rather than 11z millimeter = 17z ⚔tricia·lengthel, that could have edged an atmosphere closer to 8900z ⚔pressurels.

Pendlebury used this principle himself in TGM in certain places, and of course I have done so in Primel. But we can see it applied at least as far back as Crosby.
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Kodegadulo
Posted: Jan 19 2018, 11:19 PM


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QUOTE (Kodegadulo @ Jan 19 2018, 05:00 AM)
In honor of Crosby's enlistment in the U.S. Army at that time, I have used Unicode Character 'CROSSED SWORDS' (U+2694) ⚔ as the brand mark for this metrology, since such cross swords are the traditional insignia for the U.S. infantry.

Hah! It honestly didn't occur to me until now: the pun between crossed swords and Crosby! biggrin.gif All the more apt, then...
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Kodegadulo
Posted: Jan 22 2018, 02:21 AM


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QUOTE (Kodegadulo @ Jan 19 2018, 02:08 PM)
I've also added a couple handy rows on the main Metrology tab:
  • Row 44 now shows atmospheric pressure in SI units (on the left, cell D44), and in target pressurels (on the right, cell N44).
  • Row 22 now shows lightspeed in SI units (on the left, cell D22), and in target velocitels (on the right, cell N22).

I realized that inserting these rows right there was a bad idea, because I was relying on the quantitel rows on the Metrology tab mirroring the order of the rows in the Quantitels tab. So I moved those insertions down to the bottom of the Metrology tab, past the block of quantitels, and then added some more useful quantities. So now it has the following:
  • lightspeed
  • inverse lightspeed
  • atmospheric pressure
  • vacuum impedance
  • vacuum admittance
  • vacuum elastivity
  • vacuum capacitivity
  • vacuum inductivity
  • vacuum reluctivity
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Oschkar
Posted: Jan 22 2018, 04:06 AM


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Fixed a small bug where integer values that due to floating point error ended up slightly below the intended value weren’t converting properly to the target base.

I also added a version of Planck’s constant to the list of useful quantities. Because Primel treats plane angle as a fundamental constants, h and ħ shouldn’t be viewed as two separate constants that differ by a factor of 2π, but as a single value that can be expressed in terms of either turns or radians. Since the coherent unit of plane angle in Primel is the radian, the value I’ve taken as fundamental is the rationalized ħ.
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Kodegadulo
Posted: Jan 22 2018, 01:33 PM


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Rescuing a bit of actually-on-topic material from the dustbin:

QUOTE (Kodegadulo @ Jan 21 2018, 02:07 PM)
... the International System of Units, or SI. It may be an acronym, but it is not an LMT acronym. It has explicitly abandoned that style. And it has explicitly abandoned "Metric" as a brand name, because that brand had gotten polluted by the proliferation of too many LMT systems created under its name. So there is one, and only one "international" lengthel, the meter. One and only one "international" massel, the kilogram. One and only one "international" timel, the second. One, and only one "international" electrel, the coulomb. And so forth.

Hmmm, does anyone know of a suitable character or emoji in Unicode that might convey the sense of "international?
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Oschkar
Posted: Jan 22 2018, 06:31 PM


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Try 🌐 GLOBE WITH MERIDIANS. It certainly conveys “internationality”, and the ISO logo is basically that with overlaid lettering.
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Kodegadulo
Posted: Jan 22 2018, 11:29 PM


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QUOTE (Oschkar @ Jan 22 2018, 06:31 PM)
Try 🌐 GLOBE WITH MERIDIANS. It certainly conveys “internationality”, and the ISO logo is basically that with overlaid lettering.

Perfect! biggrin.gif
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Kodegadulo
Posted: Jan 23 2018, 01:52 AM


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As you might have guessed, I just added the Système International (Int'l) metrology to the list. 🌐 as its brand mark. Well, true, it's not a DGW system, but I thought I'd include it for completeness. Funny, isn't it remarkable that each of its quantitels is exactly 1.000000000?? Downright uncanny.... wink.gif
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Kodegadulo
Posted: Jan 23 2018, 01:41 PM


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The globe with meridians is also an apt brand mark for SI, given that its lengthel, the meter, originated as a division of a meridian-quadrant.
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Paul Rapoport
Posted: Jan 23 2018, 04:17 PM


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Is there somewhere on the spreadsheets where some algebraic formulas are indicated? I mean what you have for derivation/decomposition for quantitels in the Primel pages. Room for that on the DGW quantitel page?
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Kodegadulo
Posted: Jan 23 2018, 08:02 PM


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QUOTE (Paul Rapoport @ Jan 23 2018, 04:17 PM)
Is there somewhere on the spreadsheets where some algebraic formulas are indicated? I mean what you have for derivation/decomposition for quantitels in the Primel pages. Room for that on the DGW quantitel page?

Sounds like a good idea. There's certainly room for that on the Quantitels tab. I'll add columns for Derivation and Decomposition this evening.
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Kodegadulo
Posted: Feb 9 2018, 02:22 PM


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Okay, let's get back to something more constructive...

QUOTE (Kodegadulo @ Jan 23 2018, 08:02 PM)
QUOTE (Paul Rapoport @ Jan 23 2018, 04:17 PM)
Is there somewhere on the spreadsheets where some algebraic formulas are indicated? I mean what you have for derivation/decomposition for quantitels in the Primel pages. Room for that on the DGW quantitel page?

Sounds like a good idea. There's certainly room for that on the Quantitels tab. I'll add columns for Derivation and Decomposition this evening.

I've gone back to the small-base DGW Spreadsheet and finished laying out the Derivation and Decomposition columns on the Quantitels tab. Here's an excerpt from that sheet:

QuantityQuantitelAbbrevDerivation  Decomposition  tmℓlgℓmsℓradsbℓtpℓεtℓ
timetimeltmℓ(selection)tmℓ1
frequencyfrequencielfqℓ = tmℓ\1/tmℓ1/tmℓ-1
accelerationaccelerelaccℓ(selection)lgℓ/tmℓ²-21
velocityvelocitelveℓaccℓ·tmℓlgℓ/tmℓ-11
lengthlengthellgℓveℓ·tmℓlgℓ1
lineiclengtheliclgℓ\1/lgℓ1/lgℓ-1
areaareanelarℓlgℓ²lgℓ²2
areicareanelicarℓ\1/arℓ1/lgℓ²-2
volumevolumelvoℓlgℓ³lgℓ³3
volumicvolumelicvoℓ\1/voℓ1/lgℓ³-3
densitydensiteldsℓ(selection)msℓ/lgℓ³-31
massmasselmsℓdsℓ·voℓmsℓ1
massicmasselicmsℓ\1/msℓ1/msℓ-1
momentummomentumelmmℓmsℓ·veℓmsℓ·lgℓ/tmℓ-111
actionactionelactℓmmℓ·lgℓmsℓ·lgℓ²/tmℓ-121
forceforcelfcℓmsℓ·accℓmsℓ·lgℓ/tmℓ²-211
weightweightelwtℓfcℓmsℓ·lgℓ/tmℓ²-211
energyenergielngℓfcℓ·lgℓmsℓ·lgℓ²/tmℓ²-221
workworkelwkℓnglmsℓ·lgℓ²/tmℓ²-221
potentialpotentialelptℓngℓmsℓ·lgℓ²/tmℓ²-221
influenceinfluencelnfℓfcℓ·arℓmsℓ·lgℓ³/tmℓ²-231
powerpowerelpwℓngℓ/tmℓmsℓ·lgℓ²/tmℓ³-321
intensityintensitelntsℓpwℓ/arℓmsℓ/tmℓ³-31
tensiontensioneltsℓfcℓ/lgℓmsℓ/tmℓ²-21
pressurepressurelpsℓfcℓ/arℓmsℓ/lgℓ/tmℓ²-2-11
dynamic viscositydynaviscositeldvsℓkvsℓ·dsℓmsℓ/lgℓ/tmℓ-1-11
kinematic viscositykineviscositelkvsℓveℓ·lgℓlgℓ²/tmℓ-12
plane angleradianrad(given)rad1
solid anglesteradiansrrad²rad²2
radiusradielrdℓlgℓ/radlgℓ/rad1-1
inverse radiusradielicrdℓ\1/rdℓrad/lgℓ-11
steradiussteradielsdℓrdℓ²lgℓ²/rad²2-2
inverse steradiussteradielicsdℓ\1/sdℓrad²/lgℓ²-22
angular displacementradielic·lengthelrdℓ\lgℓ = ∡lgℓlgℓ/rdℓrad1
angular velocityradielic·velocitelrdℓ\veℓ = ∡veℓveℓ/rdℓrad/tmℓ-11
angular accelerationradielic·accelerelrdℓ\accℓ = ∡accℓaccℓ/rdℓrad/tmℓ²-21
angular masssteradiel·masselsdℓ·msℓ = ∡msℓmsℓ·sdℓmsℓ·lgℓ²/rad²21-2
angular momentumradiel·momentumelrdℓ·mmℓ = ∡mmℓmmℓ·rdℓmsℓ·lgℓ²/tmℓ/rad-121-1
angular forceradiel·forcelrdℓ·fcℓ = ∡fcℓfcℓ·rdℓmsℓ·lgℓ²/tmℓ²/rad-221-1
amount of substancesubstancelsbℓ(10z msℓ carbon‑10z)sbℓ1
number concentrationconcentrelccℓ1/voℓ1/lgℓ³-3
substance concentrationsubstancel·concentrelsbℓ·ccℓ = sccℓsbℓ/voℓsbℓ/lgℓ³-31
mass concentrationmassel·concentrelmsℓ·ccℓ = mccℓdsℓmsℓ/lgℓ³-31
number solventagesolventelsvℓmsℓ\1/msℓ-1
substance solventagesubstancel·solventelsbℓ·svℓ = ssvℓsbℓ/msℓsbℓ/msℓ-11
mass solventagemassel·solventelmsℓ·svℓ = msvℓmsℓ/msℓ1
massic heatabilitymasselic·heatabilitelmsℓ\htbℓ(selection)lgℓ²/tmℓ²/tpℓ-22-1
heatabilityheatabilitelhtbℓmsℓ\htbℓ·msℓmsℓ·lgℓ²/tmℓ²/tpℓ-221-1
heatheatelhtℓngℓmsℓ·lgℓ²/tmℓ²-221
temperaturetemperatureltpℓhtℓ/htbℓtpℓ1
entropyentropielntpℓhtbℓmsℓ·lgℓ²/tmℓ²/tpℓ-221-1
quantity of electricityelectrelεtℓsqrt(actℓ/impℓ)εtℓ1
inverse electricityelectrelicεtℓ\1/εtℓ1/εtℓ-1
quantity of magnetismmagnetelμtℓεtℓ·veℓεtℓ·lgℓ/tmℓ-111
inverse magnetismmagnetelicμtℓ\1/μtℓtmℓ/εtℓ/lgℓ1-1-1
currentcurrentelctℓεtℓ/tmℓεtℓ/tmℓ-11
alternationalternationelaltℓctℓ/tmℓεtℓ/tmℓ²-21
electrizationelectrizationelεtzℓεtℓ/arℓεtℓ/lgℓ²-21
magnetizationmagnetizationelμtzℓμtℓ/arℓεtℓ/lgℓ/tmℓ-1-11
electrodensityelectrodensitelεdsℓεtℓ/voℓεtℓ/lgℓ³-31
magnetodensitymagnetodensitelμdsℓμtℓ/voℓεtℓ/lgℓ²/tmℓ-1-21
impedanceimpedancelimpℓ = εtℓ\μtℓ\nfℓ(selection)msℓ·lgℓ²/tmℓ/εtℓ²-121-2
resistanceresistancelrstℓ = εtℓ\μtℓ\nfℓimpℓmsℓ·lgℓ²/tmℓ/εtℓ²-121-2
reactancereactancelrctℓ = εtℓ\μtℓ\nfℓimpℓmsℓ·lgℓ²/tmℓ/εtℓ²-121-2
admittanceadmittanceladmℓ = nfℓ\εtℓ·μtℓ1/impℓεtℓ²·tmℓ/msℓ/lgℓ²1-2-12
conductanceconductancelcdcℓ = nfℓ\εtℓ·μtℓadmℓεtℓ²·tmℓ/msℓ/lgℓ²1-2-12
susceptancesusceptancelscpℓ = nfℓ\εtℓ·μtℓadmℓεtℓ²·tmℓ/msℓ/lgℓ²1-2-12
resistivityresistivitelrsvℓrstℓ·lgℓmsℓ·lgℓ³/tmℓ/εtℓ²-1312
conductivityconductivitelcdvℓ1/rsvℓεtℓ²·tmℓ/msℓ/lgℓ³1-3-1-2
elastanceelastancelescℓ = εtℓ²\ptℓptℓ/εtℓ²msℓ·lgℓ²/tmℓ²/εtℓ²-221-2
capacitancecapacitancelcpcℓ = ptℓ\εtℓ²1/escℓεtℓ²·tmℓ²/msℓ/lgℓ²2-2-12
inductanceinductancelndcℓndvℓ·lgℓmsℓ·lgℓ²/εtℓ²21-2
reluctancereluctancelrlcℓ1/ndvℓεtℓ²/msℓ/lgℓ²-2-12
elastivityelastivitelesvℓ = εtℓ²\nfℓimpℓ·veℓmsℓ·lgℓ³/tmℓ²/εtℓ²-231-2
capacitivitycapacitivitelcpvℓ = nfℓ\εtℓ²1/esvℓεtℓ²·tmℓ²/msℓ/lgℓ³2-3-12
inductivityinductivitelndvℓ = μtℓ²\nfℓimpℓ/veℓmsℓ·lgℓ/εtℓ²11-2
reluctivityreluctivitelrlvℓ = nfℓ\μtℓ²1/ndvℓεtℓ²/msℓ/lgℓ-1-12
electric influenceelectrelic·influencelεnfℓ = εtℓ\nfℓnfℓ/εtℓmsℓ·lgℓ³/tmℓ²/εtℓ-231-1
electric potentialelectrelic·potentialelεptℓ = εtℓ\ptℓεfcℓ·lgℓmsℓ·lgℓ²/tmℓ²/εtℓ-221-1
electric forceelectrelic·forcelεfcℓ = εtℓ\fcℓεnfℓ/arℓmsℓ·lgℓ/tmℓ²/εtℓ-211-1
electric tensionelectrelic·tensionelεtsℓ = εtℓ\tsℓεfcℓ/lgℓmsℓ/tmℓ²/εtℓ-21-1
electric pressureelectrelic·pressurelεpsℓ = εtℓ\psℓεfcℓ/arℓmsℓ/lgℓ/tmℓ²/εtℓ-2-11-1
magnetic influencemagnetelic·influencelμnfℓ = μtℓ\nfℓnfℓ/μtℓmsℓ·lgℓ²/tmℓ/εtℓ-121-1
magnetic potentialmagnetelic·potentialelμptℓ = μtℓ\ptℓμfcℓ·lgℓmsℓ·lgℓ/tmℓ/εtℓ-111-1
magnetic forcemagnetelic·forcelμfcℓ = μtℓ\fcℓμnfℓ/arℓmsℓ/tmℓ/εtℓ-11-1
magnetic tensionmagnetelic·tensionelμtsℓ = μtℓ\tsℓμfcℓ/lgℓmsℓ/lgℓ/tmℓ/εtℓ-1-11-1
magnetic pressuremagnetelic·pressurelμpsℓ = μtℓ\psℓμfcℓ/arℓmsℓ/lgℓ²/tmℓ/εtℓ-1-21-1


I've spoken about this in the past, but please note that I differ with SI regarding the definition of "base" and "derived" units or dimensions. Even though these DGW metrologies derive their units using a procedure that starts from certain selections ("mundane realities") for accelerel (Earth's gravity), densitel (water density), masselic·heatabilitel (massic heatability of water), and impedancel (vacuum impedance), I do not consider those to be "base" units, nor their dimensions to be "base" dimensions. Instead, I prefer to say that the following are "primitive" or "fundamental" dimensions (and their units):
  • time (timel)
  • length (lengthel)
  • mass (massel)
  • angle (radian)
  • amount of substance (substancel)
  • temperature (temperaturel)
  • quantity of electricity or electric charge (electrel)
And I treat all other dimensions (and their units) as "composite". So what you see in the rightmost columns is their "primitive decomposition", both as a formula and as an array of exponents. If some of the primitive units are back-calculated from values selected for related composite units, so be it. Just because SI acts as if its currentel (the ampere) is the more fundamental dimension than its electrel (the coulomb) doesn't mean that we must accept electric current rather than electric charge as the more fundamental phenomenon in nature. Likewise, just because this spreadsheet back-calculates the electrel needed to see to it that vacuum impedance is the impedancel should not be interpreted as indicating that impedance is somehow the more fundamental phenomenon than electric charge.

In fact, if you look at the Wikipedia pages for just about any of SI's electromagnetic units, you'll see long formulas giving numerous equivalences in terms of other SI units. Any of which might be interpreted as a "derivation" for that unit. To me, the procedure to calculate a unit is incidental. What makes it "primitive" is whether it provides the fundamental concept that characterizes a phenomenon. To my mind, the fact that electric charge exists as a kind of quantum in this universe is why all the phenomena of electromagnetism exist.

Moreover, the spreadsheet already includes some metrologies that aren't technically DGW's. Nevertheless, I've had to arrange (i.e., "kludge") it so their units go through the same calculation procedure, because that's just the way the spreadsheet is set up, even though that's not exactly how the originators of those metrologies went about it. Don't read anything into that. As the Scarecrow said, "You can get to Oz if you go that way ... or you can get to Oz if you go the other way ..."
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Kodegadulo
Posted: Feb 10 2018, 02:13 PM


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Oschkar posted a question here yesterday asking whether I had a story yet for the units of photometry ... but he later deleted his post, telling me offline that he thought we were just going to switch to a more modern channel for collaborating. This merits some branching discussions...

One of which would be here.

The other, following.
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Kodegadulo
Posted: Feb 10 2018, 03:29 PM


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I took a stab at Oschkar's question about photometry last night. I'm by no means happy yet with the naming and abbreviating conventions, and I'm on the fence now as to whether it's even necessary. But for what it's worth, here's what I came up with, on the Quantitels tab of the DGW Spreadsheet. (Just quoting some excerpts of the table here.)

QuantityQuantitelAbbrevDerivationDecompositiontmℓlgℓmsℓradsbℓtpℓεtℓλsℓ
. . .
powerpowerelpwℓngℓ/tmℓmsℓ·lgℓ²/tmℓ³-321
intensityintensitelntsℓpwℓ/arℓmsℓ/tmℓ³-31
radiant intensityradintensitel∡ntsℓ = sdℓ·ntsℓntsℓ·sdℓmsℓ·lgℓ²/tmℓ³/rad²-321-2
radianceradiancelrdncℓ = arℓ\∡ntsℓ∡ntsℓ/arℓmsℓ/tmℓ³/rad²-31-2
. . .
luminosity functionluminoselλsℓ(selected)λsℓ1
luminous energylumenergielλngℓ = λsℓ·ngℓλsℓ·ngℓλsℓ·msℓ·lgℓ²/tmℓ²-2211
luminous powerlumipowerelλpwℓ = λsℓ·pwℓλngℓ/tmℓλsℓ·msℓ·lgℓ²/tmℓ³-3211
illuminancelumintensitelλntsℓ = λsℓ·ntsℓλpwℓ/arℓλsℓ·msℓ/tmℓ²-311
luminous (radiant) intensitylumiradintensitelλ∡ntsℓ = λsℓ·∡ntsℓsdℓ·λntsℓλsℓ·msℓ·lgℓ²/tmℓ³/rad²-321-21
luminanceluminancelλmncℓλ∡ntsℓ/arℓλsℓ·msℓ/tmℓ³/rad²-31-21


And then as an example, here's an excerpt from the Metrology tab, set to Pendlebury's metrology (I've manually spliced in Pendlebury's actual unit names here, as a courtesy to his fans):

(Default to [d] for Google Sheets computed scientific notation.)

ABBREV PENDLEBURY QUANTITEL PRONUNCIATION SI COHERENT UNITSPendlebury's Unit Name
. . .
⊖pwℓ ⊖powerel pendle·powerel 4.31903205676495E+02 wattPov
⊖ntsℓ ⊖intensitel pendle·intensitel 4.94007989144366E+03 watt/meter²Penz
⊖∡ntsℓ ⊖radintensitel pendle·radintensitel 4.31903205676495E+02 watt/steradianquaraPenz
⊖rdncℓ ⊖radiancel pendle·radiancel 4.94007989144366E+03 watt/steradian/meter²quaraPenz/Surf
. . .
⊖λsℓ ⊖luminosel pendle·luminosel 6.83002000000000E+02 lumen/wattLytef
⊖λngℓ ⊖lumenergiel pendle·lumenergiel 2.05816263362609E-01 talbotLyqua
⊖λpwℓ ⊖lumipowerel pendle·lumipowerel 1.18550167696863E+00 lumenLypov
⊖λntsℓ ⊖lumintensitel pendle·lumintensitel 1.35596886494334E+01 luxLyde
⊖λ∡ntsℓ ⊖lumiradintensitel pendle·lumiradintensitel 1.18550167696863E+00 candelaquaraLyde
⊖λmncℓ ⊖luminancel pendle·luminancel 1.35596886494334E+01 candela/meter²quaraLyde/Surf


But to accommodate Pendlebury, I had to introduce a Luminosel Factor as another parameter in the DGW computation. It's a fudge factor, really. Pendlebury seems to have included an arbitrary factor of pentqua (105z) in his definition of his Lypov, apparently to get it to a convenient size, which is surprising because he was pretty uncompromising elsewhere in adhering to the program of 1:1 coherence. (Although come to think of it, Pendlebury did also use a factor of ennqua (109z) to give his Kur a reasonable size, deriving it from Ampere's law in a very SI-like fashion.)

Interestingly, Primel's generally already smaller units allowed me to leave the Luminosel Factor as 1 and still get pretty reasonable units:

ABBREV PRIMEL QUANTITEL PRONUNCIATION SI COHERENT UNITS
. . .
′pwℓ ′powerel prime·powerel 1.52954670597242E-03 watt
′ntsℓ ′intensitel prime·intensitel 2.27360171530696E+01 watt/meter²
′∡ntsℓ ′radintensitel prime·radintensitel 1.52954670597242E-03 watt/steradian
. . .
′λsℓ ′luminosel prime·luminosel 6.83002000000000E+02 lumen/watt
′λngℓ ′lumenergiel prime·lumenergiel 3.02281093539519E-02 talbot
′λpwℓ ′lumipowerel prime·lumipowerel 1.04468345927258E+00 lumen
′λntsℓ ′lumintensitel prime·lumintensitel 1.55287451875808E+04 lux
′λ∡ntsℓ ′lumiradintensitel prime·lumiradintensitel 1.04468345927258E+00 candela
′λmncℓ ′luminancel prime·luminancel 1.55287451875808E+04 candela/meter²


The ′lumipowerel and ′lumiradintensitel come quite close to a lumen and a candela, respectively. A ′lumintensitel of about 15d kilolux corresponds to an overcast day.

I haven't tried any of the other metrologies yet to see if they warrant fudge factors.

At any rate, the big question in my mind is whether an entire separate tier of photometry units was ever needed in the first place. Are they really distinct dimensions? You can see that I've reduced the feature of being a "luminous" quantity to just the primitive factor of having a "luminosel". (In a message to me offline, Oschkar came up with precisely the same idea independently, only calling it a luminel instead.)

But at this point it seems trivial. What are we measuring? How are photometry units qualitatively different from radiometry units? There's a certain amount of energy or power or intensity or radiant intensity to the light, which is physically there in total. A portion of it, in certain frequencies, is something the human eye can pick up -- but it's still just energy or power or intensity or radiant intensity and so forth. So once we have a set of units that cover radiometry, why not just use the same units to measure the visible portions of it? It would be analogous to saying that we can measure the detectable height of the atmosphere, and then also the maximum height where humans can breathe, and then assert those two kinds of height merit different dimension. Is that really needed?
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Kodegadulo
Posted: Feb 10 2018, 03:46 PM


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I'm noticing that the Unicode Character 'MEASURED ANGLE' (U+2221x) ∡ that I've been using as a sort of abbreviation for "angular" or "radiant", looks about the size of a lowercase character in the Chrome browser, but a bit tiny in Firefox.
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Kodegadulo
Posted: Feb 11 2018, 06:59 PM


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QUOTE (Kodegadulo @ Feb 10 2018, 03:29 PM)
How are photometry units qualitatively different from radiometry units? There's a certain amount of energy or power or intensity or radiant intensity to the light, which is physically there in total.  A portion of it, in certain frequencies, is something the human eye can pick up -- but it's still just energy or power or intensity or radiant intensity and so forth.  So once we have a set of units that cover radiometry, why not just use the same units to measure the visible portions of it?

After mulling over this conjecture and some off-line discussion with Oschkar, I think I need to back off from it. It's clear that the "standard luminosity function" used to derive these units is not in any way an attempt to account for all the radiant energy/power/etc in visible frequencies that is able to affect the human eye. In fact, all it is is an estimate of is the amount coming in on one characteristic wavelength (555d nm =1.4ᘔ07z ′quadcia·lengthel) in the yellow/green range, where human vision reaches its peak sensitivity. From that, we get a relative indication of how "bright" a human eye would perceive the light as a whole. To calculate the actual total power that would affect human vision is a much more complicated function that gets into quite a bit of weeds involving the biology of the rods and cones in the human retina. So at this point I'm persuaded that photometry units are indeed distinct dimensions from the corresponding radiometry units, related to them no doubt but that relationship is not necessarily straightforward.

I'm also persuaded, and I think Oschkar concurs (although he can speak for himself here, of course) that it was the right call to identify "luminous efficacy" or "luminosity function" as the essential primitive dimension here. So now the question is one of nomenclature for that. The candidates for a quantitel for that seem to be: (1) luminel, (2) luminosel, (3) luminositel, perhaps even something like (4) lumefficacel or lumefficel. I'm tending to be drawn to the first two, because they could serve as adjectives of a sort to form alternative compound names for the photometry units, piggy-backing on the names of the radiometry units:

lumenergiel (λngℓ) = luminosel·energiel (λsℓ·ngℓ)
lumipowerel (λpwℓ) = luminosel·powerel (λsℓ·pwℓ)
lumintensitel (λntsℓ) = luminosel·intensitel (λsℓ·ntsℓ)
lumiradintensitel (λ∡ntsℓ) = luminosel·radintensitel (λsℓ·∡ntsℓ)
luminancel (λmncℓ) = luminosel·radiancel (λsℓ·rdncℓ)

So, for instance a "luminosel·powerel" would be a measure of "luminous power". I like the fact that this includes an -os syllable echoing the -ous syllable in "luminous". "luminel·powerel" could be interpreted as measuring "luminal power", which might work as an adjective for the same thing, although it's not really a familar turn of phrase. "luminositel·powerel" as a measure of "luminosital power" seems a bit too ornate.

But if someone has a good counter argument I'm open to persuasion...
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Kodegadulo
Posted: Feb 12 2018, 03:27 AM


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Just for grins, I created a copy of the latest spreadsheet, with some modifications: Kodegadulo DGW System + SNN&on. What I did there was implement the idea I had in the SDN&on thread: Instead of conveying the idea of positional-place-value by concatenating digit roots together, I introduced an explicit positional-glue syllable: -on-. This would then mean that concatenation of any word forms would exclusively be interpreted as multipliciation. So for instance bi·tri would mean 2×3=6, whereas 23z would become bi-on-tri. Any bare digit root could then be used as a multiplier, with or without any multiplier glue syllable. So bi·triqua, tri·biqua, without the extra -na syllables, would more intuitively mean 2000z and 300z, respectively, and not 1023z and 1032z. To actually get the latter, you would need to say bi-on-triqua and tri-on-biqua instead. But this makes SNN&on Extra-Cripsy Recipe not entirely backward-compatible with Original Recipe SNN. For just that reason, SDN&on was roundly rejected when I first suggested it. People like Don had already been using the Original Recipe in public work, so there was a commitment to that scheme. But for what it's worth, this copy of the spreadsheet lets you see what SNN&on would have looked like.

EDIT: Meh, it's still a non-starter ... for better or worse, Pendlebury set the pattern of concatenating bare digit roots for positional-place-value inside a prefix, and those of us here following his legacy are far too used to that now to switch gears.
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