I personally favor a plankian system called centipace-ounce which has the main natural constants be powers of ten---c is a billion, hbar a nonillionth, G is a billionth, k, e, Avogadro all powers of ten etc. But I am curious about these other two systems trimmed metric and anglo-roman defined like this:

trimmed metric
time unit----second
speed unit, meter per second----1/(3E8) c
action unit, joule second----9.5E33 hbar

anglo-roman
time unit----second
speed unit, foot per second----E-9 c
action unit, footpound second----1.25E34 hbar

the values of the universal gravity constant G in the two systems are 6.6622E-11 for trimmed metric and
3.6325E-8 for anglo-roman.

I will calculate the mass of the sun. The sun is 500 lightseconds away and the earth's speed is a tenthousandth of light's. The mass of the sun can always be found by multiplying its distance by the square of the earth's speed and dividing by G.
It sounds complicated to find that mass of the sun but it turns out to be easy in either system.

angloroman
earth avg orbit speed E5 f/s (because a tenthousandth of c)
distance 500E9 feet

distxsq.speed 500E9 x E10 = 50E20
divide by G----50E20/3.6325E-8 slugs
13.76E28 slugs, if you do the arithmetic

trimmed metric
avg orbit speed 3E4 m/s
distance 500 x 3E8 = 15E10 meters

distxsq.speed 15E10 x 9E8 = 135E18
divide by G----135E18/6.6622E-11 kilograms
20.26E29 kilograms, if you do the arithmetic

At this point no reason to say one is better because that would depend on the problem and besides they both handled rather similarly. In either case there was just one step of real arithmetic which was dividing
50/3.6325 in one case and

135/6.6622 in the other case.

Hi Leonard--
That trimmed metric G is U-U-U-G-H-L-Y !!! Gag-gh!

wouldn't be surprised if you were kidding me
trimmed metric is actually a rather nice system
to use because several of the numbers are quite
a bit neater than in oldfashion untrimmed metric
and the G is no better or worse.
untrimmed G = 6.673E-11
trimmed G = 6.662E-11

So hardly any change in G, but c and hbar are much
nicer

trimmed c = 3E8 meter per second (exact 300 million)
untrimmed c = 299792458 meter per second

trimmed hbar = (1/0.95)E-34 joule second
untrimmed hbar = 1.05471596...E-34 joule second.

And finally it is nice because the sizes are hardly any different---everything is for all practical (physics coursework) purposes the same familiar old metric units, just with better arithmetic.

So no, I would not say trimmed G = 6.662E-11 is all that bad. In any case you'll never get a system where absolutely all the numbers are nice.

But centipace-ounce is a lot better----all the main ones including G are powers of ten and in fact G is simply a billionth---G = 1.00E-9 in centipaceounce terms.

Leonard, I have often noticed that you are a musical sort. I am not. But what particularly fascinates me about all this is that it has now become undeniable that there exists a "musical score" amongst both trimmed metric and planckian constants-- the main difference between these two being trimmed metric containing more of "minor chords" which are not so pleasing to the mind's ear as are the "major chords". This is nothing if not a recapitulation of the "music of the spheres that only the angels can hear". In this vein, i duly note your ramification that h-bar might be better defined as 1/.95E34. What happened to E-34 exactly? I am not well versed in the qualitative constitution of all the physical constants, so do not know how 1/.95E34 (relative to 1/E34) would impact many of the divers constants. Would this give "the greatest rotundity to the greatest number" (of consonants)? If so, then the term "metric martyr" might be seen to assume a new meaning that carries more epistomological import. So would i be correct in assuming that we might have to quarantine G and h-bar so that that the bulk of the inelegance of the coefficients in this trimmed system be confined to them in the greater interest of preventing the others from being infected by that same grotesquely disfiguring number disease which we have resolved to cure? To carry on with this analogy a bit further-- i was hoping that limiting the coefficients to two digits would suffice to immunize the majority of constants against all this inanely punctilious smallpox!!

Excuse me. I should have said h-bar=1/.95E-34. PLEASE don't tell Ralf about this!!

Hello pint,
just this moment woke up and had a sip of coffee. Pleased by the word "rotundity" for roundness and other details of style. I too like the harmonic series that forms the basis of many of the world's musical scales. Small fractions look nice and apparently pythagorus thought so too, or feel nice in the brain or something. Still just reacting and gradually waking up. So will simply quote this and try to think:

[Leonard, I have often noticed that you are a musical sort. I am not. But what particularly fascinates me about all this is that it has now become undeniable that there exists a "musical score" amongst both trimmed metric and planckian constants-- the main difference between these two being trimmed metric containing more of "minor chords" which are not so pleasing to the mind's ear as are the "major chords". This is nothing if not a recapitulation of the "music of the spheres that only the angels can hear". In this vein, i duly note your ramification that h-bar might be better defined as 1/.95E34. What happened to E-34 exactly? I am not well versed in the qualitative constitution of all the physical constants, so do not know how 1/.95E34 (relative to 1/E34) would impact many of the divers constants. Would this give "the greatest rotundity to the greatest number" (of consonants)? If so, then the term "metric martyr" might be seen to assume a new meaning that carries more epistomological import. So would i be correct in assuming that we might have to quarantine G and h-bar so that that the bulk of the inelegance of the coefficients in this trimmed system be confined to them in the greater interest of preventing the others from being infected by that same grotesquely disfiguring number disease which we have resolved to cure? To carry on with this analogy a bit further-- i was hoping that limiting the coefficients to two digits would suffice to immunize the majority of constants against all this inanely punctilious smallpox!!]

We can get closer to metrics presentday sizes if we use the fraction 18/19, I noticed yesterday. That is,

time unit---second
speed unit, meter per second---(1/3)E-8 c
action unit, joule second---(18/19)E34 hbar


These would be the definitions and they make the trimmed units come really close to the old ones which gives me a very good feeling about the system, actually.

Then to get what c and hbar are in terms of the trimmed units one must take reciprocals and that is easy with fractions---just turn them upside down and change E-8 to E8 etc.

c = 3E8 meters per second
hbar = (19/18)E-34 joule second.

I am going to finish my coffee and have another look at your post---the elegance issue in tradeoff versus the closeness of fit to existing sizes.

I should periodically unpack the notation because people come here and read and may not know what
3E8 means and stuff.

3E8 means 3 x 10^8

The reciprocal of that big number is a small number---one over 300 million (1/300,000,000)----and it can be written compactly various ways like

(1/3)E-8

which means 0.333333... x 10^-8


So if meter per second is defined as this slow fraction of the speed of light, namely

(1/3)E-8 c

then reciprocally the speed of light must be this fast big multiple of meter per second, namely

c = 3 E8 meter per second.

It is not clear why I am always putting parentheses in, I suppose it does no harm and may help avoid ambiguity, anyway it is very much like saying

penny is by definition (1/100) of dollar, so therefore
dollar = 100 pennies.

Same thing goes with the action unit joule second which is a very large amount of action (the physical quantity action is the product of energy combined with time and in metric the joulesecond is the unit for it)

joule second = big multiple of hbar = (18/19) x 10^34 hbar

hbar = tiny fraction of joule second = (19/18) x 10^-34 joule second.

And the notation compresses these numbers down into compact form like (18/19)E34 and (19/18)E-34.

readership still on the increase
I just checked log and it is over 1800 for month of march.

was just a handful of hits in jan
then for february there was an unexplained
increase to over 1400 (maybe people reading the
stories or physics examples)

now this month 1800 and not even the end of the month
so presumably will be even more for march.

I wonder if people like trimmed metric and if they find it interesting and likewise with the sort of trimmed anglo-roman system----or whether they just read some of the outrageous physics examples phrased in planckian units.

(18/19)E34 h-bar! That 18/19 is a fraction which represents a departure of >5%! It is like sandpaper to me. I am afraid there may not be anything practicable that can be done about it. However I await your caffeine enhanced perusal, Leonard. {:-P

This version of trimmed metric began with your suggestion, in the "Redneckystan" thread.
You suggested using 9.5E33
which is the same number as 0.95E34.

All I am doing now is considering replacing the 0.95
by 18/19. It is not very different and you can decide since it is your system.

Actually the 0.95 we were working with (at your suggestion) is equal to 19/20. So we are talking here the difference between 19/20 and 18/19. The latter just happens to get a slightly closer fit to presentday metric units.


Here is my 17March post and your reply, where you made what I thought was a good suggestion about the 9.5 approximation, or in this context 0.95.
I said:
[...Redneckystan is a multi-system society and uses a variety of units in an ad hoc pragmatic way. The government (while bad in several other respects) is not so anal and rigid that it forces society to use one uniform all-encompassing system.
.....<SNIP>....

As example of a time-speed-action system:

time unit----54 millisecond
speed unit----E-9 c---one billionth of light
action unit----E30 hbar---a nonillion times the natural unit of action.

This is probably how the metric system will be redefined in the next decade except with ugly numbers---metric is moving towards the same time-speed-action form of defintion and in fact top people in NIST and CODATA have proposed exactly this. It would work out about like this:

metric time unit-----one second
metric speed unit----1/299792458 of the natural speed unit, c.
metric action unit----9.48252355 E33 of the natural unit of action, hbar.

the speed unit is meter per second and defining it (using c) establishes the meter---this is how the meter is already officially defined

the action unit is the joulesecond and defining (using the natural unit hbar) establishes what the joule is. (this has been proposed and a vote at the CGPM has paved the way for it, but it is not settled yet)
having a natural-unit definition of joule will make the metal kilogram superfluous. one will chuck out the metal kilo. because a kilo is by definition simply equal to one joule sq.(second/meter).

In the future the important thing will be to define the action unit (joulesecond in metric case) and from that the joule and the kilogram mass standard can be derived.

However the metric numbers, 299792458 and 9.48252355 x E33 are disgusting.

In Redneckland we can hope to use an exact billion (E9) in place of 299792458 and an
exact nonillion (E30) in place of that 9.48252...garbage.

In the sample system I just described (using billion and nonillion) the length unit turns out to be a fingerwidth---one hundredth of the type of pace that is a thousandth of a mile: so a mile is 100 thousand of them. Don't change the roadsigns!

And in that (billion + nonillion) sample system the mass unit comes out to be ounce-size (more exactly 22 grams or 20 to a pound, but roughly ounce-size). It is a lab-scale system analogous to the old centimeter-gram-second still found among working physicists.

Lots of alternative time-speed-action options are open, this is just one.

In this system the main natural constants turn out to be powers of ten (electron charge, avogadro number, gas constant, boltzmann constant, temperature to eV conversion, etc)

The natural unit of action is found in every quantum of light. the photon's energy multiplied by the angular period of its vibration. Always equal to hbar. It is all around you now and on your computer screen. Like the speed of light--which is also all around everywhere all the time.
So give yourself a break and tune your units to what is.]

You said:
[YES. But let us also define the metre as 1/300 000 000 c and the action unit as 9.5E33. This would entail an adjustment of but .000692286 in the case of the metre and an adjustment of but .001843017 in the case of the action unit-- MUCH less than 1% in either case. This would involve NO change to the Planck derived units, only to SI, which has come to sprout a number of ugly warts of late. I think of this trimming as quite analogous to a dermatological removal of these warts (together with god-awfully ugly hairs emanating therefrom), not even as plastic surgery.]

I am not a physicist therefore don't always have this stuff at the ready on the tip of my cortex. I liked the .95 because it limited the coefs to 2 sigfigs. 18/19 is not *that* much different from 19/20. True enough. And 18/19 is closer to the present metric value. Also true enough. But now look at the decimal representation of 18/19: .94736842105... . Isn't THAT an elegant state of affairs!! True again, it is closer to .948252355 than is .95. But i would question whether the greater degree of approximation to the old value is worth the price of making that new coefficient equally as disgusting as the old one which it replaces. As long as it is going to change, why not hold that change within the limits of two sigfigs-- particularly when such can be done with a change of value <1%? Or am i missing something? BTW it is somewhat distracting here because i cannot get my eye off that bouncing blonde!! I am thinking of things *other than* physics!! She seems to be looking you right in the eye to see how she is doing!!

Hi p.d., I'm happy however things are done or if we try different notations out in different posts and see which is most comfortable. Also happy whichever you pick.

I'll read your post more carefully and try to reply thoughtfully in a while, but you basically call the shots on this one.

Oh yes the blond,
her half-closed eyes show she is enjoying it a lot.
all thought is impossible
by pulling the sliding bar at the side down just
a little bit I raise the page just enough that
she isnt there, only then, only then, can the mind
return to matters metrical and planckian

since she obviously has no pants on, why does she have that whatever undershirt-type top on? kinky. <SLIDE> She vanishes. Ahhhhh...

the basic number we are wrestling with is found in every handbook and every physics constant website and is:


hbar = 1.054571596 x 10^-34 joule second.

When you use a physical constant sometimes it is the number itself and sometimes you use ONE-OVER the number, the reciprocal. Same with c, same with G. You don't know at the outset which will most useful,

1.0545716E-34

or the reciprocal 1/(1.0545716E-34).


Now the reciprocal happens to be

0.948252...E34.

One way to handle it is to use a fraction as an approximation. Call the little number (20/19)E-34

and its reciprocal, the big number, (19/20)E34.

And never write either of them out as a decimal number.

But none of this is anything to worry about, it is a pretty nice system and this is just a little notational hang-nail. Reciprocals always give a little touble. Like, what is the reciprocal of 0.95?

BTW this is one reason I always gravitate to purely decimal systems, because the reciprocal of E9 is E-9,
the reciprocal of E30 is E-30. Never any bother.

Well at least h-bar OR its recip-- ONE of these should be a two digit deal. I am glad you threw in that coin on the matter of the constants because i see that you have turned over that coin and looked at the other side of it. My dutch uncle once said, "You can take a sheet of copper and compress it to your hearts content. You can hammer it down to a thickness of less than 1/1000 of an inch. But if you pick it up you will see that there is always another side."

stipulating that one or the other should be 2-digit
pretty much determines that it has to be
0.95
and perhaps the neatest way to write the reciprocal
of that is 20/19. Or do you have a different suggestion?

So in this system hbar has an exact value (as contrasted with the inexact presentday metric value)
of
(20/19) x 10^-34 joule second.


Presentday metric value 1.054571596 x 10^-34 joule second.
******************

I've been wrestling with another minor stubborn problem having to do with centipace ounce.
It is frustrating not to have a name for the unit
analogous to the metric watt

the "ounce" system is quite neat in several respects but it has as yet very few named units
it is as if, in metric, I was having to say "joule per second" all the time instead of "watt"

or "joule per coulomb" instead of "volt".

that is what the units of power and voltage actually are in metric, but they have one-syllable names for easy reference

Centipace ounce is the system that basically uses two numbers to define it----billion and nonillion (E30)

time unit (trice) ----- 54 milliseconds
speed unit ----- one billionth of c
action unit ----- nonillion hbar

the distance unit comes out to be the width of a finger, 1.6 cm, and the mass unit comes out ounce-size.
it is a lab-scale system.

the power unit turns out to be 36 milliwatts
roughly the power of an LED or a lightning bug (firefly).

BTW where I grew up in the east there were swarms of fireflies on summer eventings, used to catch them and let them go. there were as many as you ever wanted. dont know if they are still common back east but dont see them in California

just looked at log, March hits over 1970 so probably will pass 2000. still that unexplained increase starting from just a handful in january. maybe it is in part thanks to your participation p.d. Dialog is more interesting.
BTW interesting saying about things always having another side. As philosophy so so true, but in mathematics there is the klein bottle a surface with only one side. I met a man in Oakland recently who makes glass kleinbottles to sell, a home business. They are sort of pretty.

frustrated enough by lack of a name for the 36 milliwatt power unit that I may try calling it "bug"

ten thousand bugs is 360 watts, or half a horsepower.
I picture the bugs as either harnessed to pull a wagon, all ten thousand of them, or I picture an individual lightning bug (this was our slang for firefly as kids) flashing with about LED brightness.
usually it was a yellow green glow, not unlike some actual LEDs.

I know my resting metabolism, the averaged-out rate I burn food energy and produce heat, is about 3000 bugs----a bit over 100 watts, like a lightbulb.

I know that in direct sunlight a square fingerwidth area receives 10 bugs from the sun.

Would rating a car engine at a million bugs cause people to break out in a cold sweat and run off screaming, or merely smile pityingly. The trouble is a one-syllable handle on the power unit is rather necessary as a convenience because it comes up in so many contexts.

By ALL means Leonard. Let's nail down that action unit to 9.50E34 h-bar exactly. That way we will not only limit divergence to < 1%, but also will have at least one of the reciprocals of that constant limited to 2 digits. Question: will this impact any of the other physical constants to the extent of distorting them from this 2 digit standard that we have proferred-- the metre, k, c, Avogadro's N, e-,..., etc.?

There is that blonde again! I'll bet she is ACTUALLY doing it! Nice looking too. And she is looking better and better!