I have now become convinced by Leonard's system and would like to attempt to popularise it on this board as an acceptable solution to the problem of weights and measures.

One of the virtues of traditional English units, as has been pointed out, is its use of divisible numbers such as 12 and 16, where useful fractions work out to be integers - rather than 0.25 m or 0.333... m, we have 3" and 4". There is no number, however, that is more divisible than 60, and we can see its advantages in our traditional units of time and of angle. I do not propose we base an entire system on this base - too much like metric, I would say. But you will see that I have worked in the number in some places.

The only reason I support a new system is its compatibility with current standards, and without question, saving the inch is most important because of the necessity of precise measures of length in all manufacturing and the prevalence, even after 40 years of metric propaganda which has convinced more than a few companies to switch, of inch-base standards in most fields. The pound is next in importance, and in commercial context always means the pound of mass; hence, combined with the fact that mass can be measured conveniently to a higher accuracy than force, it convinces me that the pound mass is the standard. The pound force, hence, can be allowed to vary somewhat.

So, keeping in mind that I want to use physical constants where possible, without allowing them to get in the way of practicality as in Leonard's previous systems, it is a fortunate coincidence that the pound of force derived by setting the speed of light to be 600,000,000 inches per trice turns out to be within the allowable range; though the standard gravity thus calculated is on the high side (that at sea level and 75 deg. latitude), it is surely better to err that way when computing forces.

So, with that set, and keeping the inch and pound mass as near as could be required to the present values, I have evaluated here the set of three numbers that fully defines my base units.

The trice is equal to 467,308,981 cycles of the radiation from caesium used in atomic clocks.

The inch is that distance traveled by a photon in 1/600,000,000 trice.

The pound is the mass having equivalent energy equal to a collection of photons whose frequencies total 3.127637 * 10^48 cycles per trice.

Keep in mind, when I introduce the other units that are defined as integral parts of the system, that their establishment does not preclude the use of any traditional units of length, weight, or volume, so long as they are related to the base units.

First I establish the Roman pace, equal to 60 inches. I would hope for the replacement of feet and yards by this unit, especially in construction, but do not insist on it.

I define the point as 1/60 inch. This is taken from the point of typography, defined as 1/72 inch type height. For common fonts, though, it is very nearly 1/60 inch font height - the more useful as it determines the number of lines fitting any given vertical space. This also provides us with a unit comparable to the millimeter, one of the gaps in our traditional system - I find the millimeter to be the only SI unit I commonly think in terms of.

The point of using the Roman pace is to allow us to restore the mile of 1,000 paces or 60,000 inches. Now you see part of the reason for my fixing of the speed of light - it is equal to exactly 10,000 miles per trice!

The complete table of standard length units is therefore:

1 mil = 1/1,000 inch
1 point = 1/60 inch
1 inch = (base)
1 pace = 60 inches
1 mile = 1,000 paces

Any length sufficiently large or small that scientific notation is used should be generally expressed in the base unit - here inches. (This is also standard in metric.)

I have nothing to add for weight - the pound is the only unit I would like used scientifically. The previous discussion convinced me that England will not easily accept the US ton - perhaps we must remain different there. The grain, while of a useful size and, as far as I know, not subject to any conflicting definitions, is not used often enough to warrant its inclusion here.

Time is perhaps the most complicated for me to define because of the introduction of an unfamiliar unit that is not simply related to our traditional units. Its introduction though, is justified by the fact that all of us live on Earth and having our gravity equal unity is a considerable advantage. (More useful, I believe, than using the density of water as metric does - how many people need to know 62 lb/cu ft?)

I worried, though, about the complex conversion factor between seconds and trice. I know people will continue to used seconds, minutes, and hours for describing time periods and I see their evident utility. However, I do not like fudging such as that Leonard did in his problems by saying 1 trice = 1/20 second. I decided it should be exactly 20 - no more fudging.

This is achieved by having two distinct set of hours, minutes, and seconds. The set equal to our present standards I call 'clock time' and is based on the Earth's rotation. I define a new set, called 'scientific time', based on a second of 20 trice exactly. These two time standard, differing by about the 60th part, should not cause confusion. People will use 'clock time' to measure intervals on the clock for scheduling and such. 'Scientific time' will hopefully be used for all other measurements, not only in science and engineering but also in everyday life for measuring rates (miles per hour, gallons per minute) and, to name one more, for timing athletic events - not only track but football, soccer etc. as they are not intended to coincide with the true clock in any case. People will no doubt remember that there is a difference but not memorise the exact conversion factor.

Here is my 'scientific time':

1 trice = (base)
1 second = 20 trice
1 minute = 60 seconds
1 hour = 60 minutes

There are no units above the hour in that system. Compare 'clock time' as follows:

1 day = mean solar day from Earth
1 hour = 1/24 day
1 minute = 1/60 hour
1 second = 1/60 minute

The exact conversion, for anyone who would like to record it, is:

1 clock second = 0.983571057 scientific second

I do now believe that this pound-inch system is a worthy candidate and should be promoted for use. It satisfies the two criteria I would look for in such a candidate, that it is markedly superior compared with the two accepted systems, and that it is compatible with the great pound-inch tradition that I am unwilling to abandon.

(Leonard, you might want to chime in here!)

Andrew Usher

I would like to add another observation on time. The separation above has the advantage that as the Earth's rotation slows down - significant over millennia - the scientific standard will remain absolutely constant. It will not be necessary, as SI would have it, to insert 'leap seconds' with ever-increasing frequency, as the units of 'clock time' will simply stretch in accommodation.

With all due respect to Andrew and Leonard (I think that's the phrase to use when you're about to slag someone off) they seem to be trying to fix what ain't broke - and breaking it themselves in the process!

First, there's simply no need for radically new measurement systems. The ones we've got work fine. Imperial works fine for everyday applications and a great deal of engineering work. Metric works fine for scientific work, especially if you don't insist upon using only strict SI but allow every speciality its convenient and conventional usages. If we need new units we'll invent them when we need them.

I suspect that most people aren't willing to keep up with Leonard's challenges because they're bored with them. Whatever the theoretical merits of the inch-pound-trice system, neither ordinary people, nor scientists or engineers, are at all likely to use it. In practice, we can do those sort of sums well enough in SI, so we see no point going to the bother of doing it differently (pro-metric types who agree with me here might profit from reflecting that imperial users feel just the same way about doing the shopping, driving the car and doing DIY).

For mental arithmetic, g=10m/s/s is close enough. If you need more accuracy you use a calculator anyhow, so g=9.81m/s/s isn't much harder. I've never needed more precision than that. Likewise, scientists always use c=3x10**8m/s. It's easy to remember and easy to use. Only a very few specialists (metrologists mainly) ever need to go 2.997925...

This whole business of worrying about the value of g seems absurdly out-of-date. It's not a fundamental constant. Why treat it like one? By the end of this century most of the human race probably won't even live on this planet, and although most space colonies are likely to be spun to about one gee, it won't be exact (much of the habitat will have perhaps 5-10% lower gravity, as it falls off quite rapidly with height within the colony). Other planets will be different again (Venus has g=8.88m/s/s for instance).

Of all units, the second is the most universally used and humanly convenient (along with the minute, hour, day, week and year, of course). Why throw that away? Why use a unit too small to be readily appreciated (the trice) or add unnecessary complexity and the near-certainty of endless confusion with two similar but incompatible systems of time measurement? Ordinary wristwatches are good to better than one part per million, and are often used for timing races or scientific observations; having to convert between standards almost 2% different would be messy beyond belief.

Playing around with novel measurement systems is one thing, no worse than train-spotting or inventing new languages or alphabets, but seriously promoting their actual use seems to me dangerously close to allowing oneself to become a crank.

Hi Andrew,

I just saw your post.
The system you project, in which the
speed of light is exactly ten thousand
miles per time unit is graceful.

For my part I have chosen to avoid "fudging"
simply by using a time unit which is 1/19.65
and always calculating with that (when measuring
time) but DESCRIBE it every so often (to give an intuitive feel for its size) as roughly
a twentieth of a second. Then nothing else
needs to be changed (inch is same, pound mass
is same, mile is same, hours and minutes are same...)

I want to keep the 1/19.65 system available as a
tool to bash metric--by undermining the
metric pretense of physical convenience or
"scientifickiness". To work in discussion it has
to be quickly explainable to an unfriendly
or mixed audience. I suspect that I cannot use your more
beautiful 1/20 system (in which the technical time unit
trice is nicely connected with second by exact round
whole number relation) because it takes a few
more words to explain the time units and those
few words may cost listener's attention. We will
try it and see.

In any case we can learn from the 1/20 system. And maybe
use both for couching problems in. One thing that is
very nice is that

since light goes 10 thousand miles in trice
since earth's average orbit speed is within half
a percent of being 1/10,000 of light's

to fairly good approx. (half a percent) earth goes
one mile per trice. Correct me if I am wrong. I have
not yet had time to look at your post carefully--just
now saw it. Will try to reply more thoughtfully later.

BTW you referred to this kind of pound-inch system
as mine but it is at least as much your own invention
since you initiated my interest in pound-inch and
corresponded by email off the board during our
development of it. It may also have been worked out
in some other variant by other people (but don't know
of any specific case) and it may need to go through
further design iterations (can't think of any specific
modification to try at moment but things have a way
of improving with time.) It is actually a very nice
invention for college-level physics problems and
there is no reason you shouldn't take openly the share of authorship which
you know is yours. No time to proof read, hope
this post is OK

wow
just saw Paul's post
my physics problems are boring
(between reader and writer the reader, Paul
in this case, is the absolute arbiter)
and I, and possibly you Andrew, if we
persist in efforts of popularization,
risk the dreaded crank label.

I am not an arguer. I'm not sure what
to do.
Personally I see having several different systems
of units for physics problems (as we did
when I was college-age) as not cranky but
a plus.
And I see SI as badly in need of fixing
because of unphysical unsymmetric Maxwells
(leading people even now to use Gaussian cgs.)
So from my perspective anything that keeps
the units scene fluid, ununiform, uncongealed
is helpful. Not cranky.

However Paul's opinion (since informed and not biased by
narrow prejudice for SI) carries considerable weight
with me. What to do?

This all seems rather wonderful, which is a shame really, considering I don't really understand the half of it... ;) Anyway, suffice it to say, I wish to make two points:

1. We need to have a Imperial Scientific system that is as unified and whole as SI etc etc etc as one of the major "let's knock the Imp" points, is that Imperial is not scientific, or scientific enough.

2. I do not stand by the 5 foot pace- I don't really care if it is "nicer" because it has 60 inches, I personally a) prefer the three foor rule, and b) do niot view a "five foot rule", as it were, as being particularly helpful.

Just my (brief) thoughts.

>And I see SI as badly in need of fixing
>because of unphysical unsymmetric Maxwells

If that is the only problem SI has, I think 99.99% of the earth's population won't get why your system is superior to SI.
That includes me, I had to do some very ugly exams during my EE studies about electric/magnetic field distributions, but even then any symmetry wouldn't have helped me because solving the differential equations was the tricky part, which is a mathematical problem, not a problem of Maxwell's equations.

Ralf

Leonard: I don't want to stop you having fun with your inch-pound-trices, but I think you should face the fact that very few people will want to use them, even for the sort of problems you've been setting. Either they'll use one of the standard imperial systems, or one of the standard metric systems (or possibly some non-standard but convenient kludge).

Personally, I use all sorts of units in different circumstances, including mixtures of metric and British, whenever I find them convenient. For instance, I'll calculate forces in N from wind speeds in m/s and sail or wing areas in m**2 (useful because the density of air is about 1 kg/m**3 and water 1000 kg/m**3 and a L/D ratio of 10 moves neatly between N and kgf), but I'll convert into feet and knots for working out hull speeds (1.4xsqrt(length on waterline/ft)). Sometimes I use mainly SI, somtimes cgs, sometimes geometrodynamic units. When shopping, of course, I want mainly pounds and ounces, and pints or gallons. However - despite my unusually eclectic habits - I can't honestly think of any circumstances in which I'd genuinely find the inch-pound-trice system useful. Sorry.

Bryan: We already have several versions of the Imperial system which are perfectly adequate for engineering, and for which it is easy to give definitions in terms of fundamental physical constants (plus the less fundamental standard gravity). However, there aren't really any imperial versions of most of the electrical units. Unless that omission were rectified it would not be possible to use imperial as a unified general-purpose scientific system (unlike SI). And I cannot see much practical point in inventing a new set of units to fill the gaps (though Leonard and Andrew might like to try). I don't believe many people seriously want (or expect) to see a new imperial system become the international scientific standard; they just want to be free to keep using customary British units for their day-to-day transactions and activities, whenever they find it more convenient that way.

Ralf: SI is far from perfect; having 4.pi.epsilon-0 and mu-0 in the equations is less than elegant, and I know from experience that it's possible to forget to shove them in the right place and get absurdly wrong answers as a result, but I doubt whether Leonard will be able to find a way of avoiding such infelicites entirely. They're like wallpaper bubbles; get rid of one and another pops up to take its place.

Glad you mentioned electricity and magnetism Ralph.

These forces of nature have been known about for more than a century, and yet no one has developed an equivalent, for example, to the volt or the ampere in non-metric units.

All other measurable quantities in the natural world are covered by some combination metric units.

This shows that the metric system is now the only fully comprehensive system of measurement in use today.

P. S. I note that Paul had already observed this in his last post, while I was compiling this off line, but I thought I'd say it anyway.

In terms of electrical units, what could you come up with ?
If you redefine the ampere and the volt, then you also have to come up with something different than "watt", since [watt] = [volt]*[ampere] doesn't work anymore. If you redefine Watt, then forget the Joule since it's [watt]*[second].

In terms of higher order units (W,J,V,A etc.), everyone (including US and UK) is metric, let's just keep it at that...

Ralf

pip: there are plenty of units of voltage which
are not the volt. Units of current which are not
the amp. Some physicists prefer the non-volt non-amp
units because they work better in EM courses

and so at Princeton and MIT etc some profs require
using the non-SI units. Not that they are Imperial either.

Classical EM texts (Purcell Berkeley Physics series
vol. 2, or Jackson Classical Electrodynamics) are
still used partly because they were written with
non-SI.

So, pip, your suggestion that no-one has yet come up with alternative
units to volt and amp is not entirely right.

One automatically gets units for electricity in pound-inch from the charge unit if one wants them.

I did all the necessary defining back in my April 8
post on pound-inch thread. It is fine with me if you
just use pound-inch for non-electrical problems or if you use your favorite volt or amp or coulomb. I don't
make the rules for other people. BUT IF YOU WANT electrical units in pound inch, don't say they don't
exist. They all arise automatically once one says what the charge unit is. One possible charge unit was in my
April 8 post. I quote:

[[CHARGE: The pound-inch-trice unit of electrical charge is chosen to be exactly 1/19.65 coulomb so that the unit of current (the passage of unit charge in unit time) will turn out to be exactly one ampere. The unit of voltage works out to be 2.220... ordinary volts—-the same conversion factor as in the case of the power unit applies in the case of voltage. Rigorous definition along the lines of the 1990 electrical standards can be performed independently of metric units, since the 1990 electrical standards ultimately rest on fundamental constants and the atomic clock frequency standard.

To find inchpound in joules, 3131040 × 19.65 × 299792458^2/(135639274 × 600654080^2)

To find the metric watt equivalent of unit power (inchpound per trice), 3131040 × 19.65^2 × 299792458^2/(135639274 × 600654080^2)]]

It is fine with me if you just act bored or reject
the pound-inch electrical units. My present view
is that pound-inch is a kind of missile because of
pound-inch superiority in very simple (freshman)
physics problems. And because pound force and PSI
are more intuitive and familar to many people than
"newton" measure of force and "pascal".
the alternative units serve their purpose fine, in
my view, whether or not applied to electricity.
But it would be trivial to use them for electricity
if you wanted to and one could easily give them
the advantages of Gaussian cgs that cause many people
to prefer the non-SI system.
Hope this responds to the points you raised.
L

No, that's not quite true. Units of power and energy are used for in mechanics and thermodynamics - and a variety of imperial or customary units (horsepower, foot-pounds, BTU, calorie, etc.) are available and still widely used across the world (not only in the UK and USA). It's the equivalent of volts and amps (and the magnetic units) that are missing.

Pip, please remember that there is not one metric system, but many incompatible ones. It is true that MOST measurable natural phenomena can, often with some considerable inconvenience, be described using metric units - but not all (earthquakes, for instance - the Mercali and Richter scales don't directly correspond to Joules or Watts - or the Mohs scale hardness of minerals). A great many more natural phenonmena are almost invariably described in non-metric terms or units (for example, stellar types in the sequence WOBAFGKMRNS, periods of time in excess of a few hundred seconds, latitude and longitude, RA and declination, etc.).

I didn't realise/remember you'd earlier given some thought to e.m. units. But you'd need to go quite a bit further. If you stick with the ampere as a basic unit - although the metric people might still consider that a rip-off from SI - you need to name the others too, magnetic as well as electric (unless you insist that people only use combinations like ampere-trice for charge, etc.). Also, you'll need to specify the form Maxwell's equations are to take (in particular, where you stick the 4pi), and what the impedance of free space will be. My apologies if you've previously provided answers to these points.

Hi Bryan, Paul, Andrew, Pip, Ralf,

great to see all this discussion around Andrew's
carefully thought-out variant of pound-inch!

My view is that Andrew's version is beautiful, but
takes more time to explain and get across.

The variant I offered in April is probably more
useful as a missile. The thing about it is that
NOTHING IS DIFFERENT. pound is same, inch is same,
mile (if you want it) is same. You just add a small
time unit that is available when you want it for
use with physics problems (and you keep on telling
time in conventional hours and minutes otherwise).

The official figure for gravity is hardly (less than
one degree latititude) different from the official SI
metric figure for gravity. So there is no perceptible
or practical change in moving over.

You just have to ADD to the picture a time unit
which is exactly 1/19.65 second. You always deal
with as 1/19.65 second and get answers in those terms
but you can DESCRIBE it to someone who hasn't used
it before as "about a twentieth of a second".

So you adjoin a new small time unit to some familiar
customary units and you can beat SI metric in simple
problems over and over again. That's all. It is a
trivial business. you just show SI metric to be inferior (and it is easy to do) in a certain context.

One MIGHT after using my crude version of pound-inch
as one of several monkey wrenches, move on to a more beautiful version like Andrew's which has some elegance but is
somewhat more involved in its definitions.

Personally I would be glad if any version or versions of pound-inch can help torpedo SI metric because SI
threatens total engulfment by exclusive uniform use.
horrifying chasm I find between Paul's education
and Ralf's (doesn't know symmetric Maxwell or connection to Special Rel, probably believes in
epsilon mu naughts that physicists know to be
fictional, does not QUESTION what has been taught
in EE). Uniformizing brain-deadening disaster to
education to have exclusive SI use prevail. The
evidence is already among us in form of engineers
taught only one system of units.

I have not set my heart on any one version of pound
inch.

At this particular board I expect flat-out rejections
of any alternative or innovative unit systems and I
expect to learn from these reactions, to learn more
probably than the rejectionists will learn from me.

But if (million to one chance) there would be some
expression of pleasure at Andrew's system, by Paul
say, I would immediately drop my version and make
up the best problems I could think of to demonstrate
Andrew's. I am not selfishly stuck on one variant.
I believe in test driving alternative.

We can improve on SI metric (this is a no brainer
since it is bad in so many ways) and do you know
a better way to go?

No time to proof. Hope this is not to full of mistakes.

Yeah, but how many watts are there in a horsepower ?
How many calories in a BTU ?

Those units have absolutely no meaning to an everyday person, it's only a number of which you know "oh, this one means it's strong, this one means its weak".

I can only speak for Germany, but a few years ago they made it mandatory to put the power output of your car in Watts into this small specification leaflet.
And: Voila ! Suddenly you could relate it to for example light bulbs, you knew how much your AC (also measured in Watts, not BTU) or your stereo drains from you car when you turn it on etc. etc.
Same thing with calories for food, you have to state the amount in Joules now. And again, you can relate it to light bulbs, saying "oh, this pizza would produce this many hours of light"

You may say we lost some diversity at that point, I only noticed a loss of obscurity.

Ralf

BTW, this was in response to Paul's post (doesn't make too much sense after Leonard's post, it just took me a while to write)
Ralf

Hi Ralf,

Back in early 70s I was a big metric booster
because of similar feelings to yours about
watts (vs. hp) and joules (vs food calories).

In your post here you come across very sympatico
as someone who loves the clarity given by
systematic (sometimes called coherent) units
of energy and power.

Back then I wished all cars were rated in kilowatts
and that food could be counted in kiljoules.
Like you say you would then know how long a
certain pizza would (subject to conv. eff.) run
a lightbulb or a car. This is great.

Systems of units are, if not works of art, at
least works of craftmanship and ergonomic
design--fitting nature to the hand in some way.
It is OK to have feelings of enthusiastic appreciation
for how well systems of units can work to relate one
to nature and cars and food and whatever.

Since my artistic sensibility is probably very similar
in some respects to yours I have OF COURSE done the
very same thing in pound inch units.

There is an inchpound corresp to joule,
and ip/trice corresponds to watt.
Food energy is in inchpounds, and heat and
all energy, not just mechanical.

The only difference is that (while in SI metric
it is "meter newton" which equals joule) it
is inch pound which equals inchpound.

It is always the energy delivered by exerting
unit force through unit distance.

People who have no sense of the (admittedly very
simple but still real) beauty of systems of units
are impossible to talk to.

Pity you so closeminded in rejection of pound inch.
Try seeing something good in them. since you see
something good in metric.

A thousand pound C-programmer is sitting in
his kitchen, which is illuminated solely by
one 100 ip/trice (in other words 220 watt) bulb.

The programmer has focused his attention on
a large pizza with many kinds of toppings. The
pizza contains food energy of 36 million ip
(that is to say 4 million joules.)

Being of a philosophical turn of mind, the
highly respected systems engineer, who works from home
programming servers for sun workstations, wonders how
long the pizza's energy would run the lightbulb.

THE METRIC EQUIVALENTS ARE APPROXIMATE and intended
to facilitate the metric solution.

Pound-inch solution: 36 million inchpounds divided
by the 100 ip/tr power is 360 thousand trice.
Roughly 5 hours.

Metric solution: 4 million joules divided by 220
joules/second is about 18 thousand seconds.
Roughly 5 hours.

The above problem is intended to show neither
system to disadvantage. It happens to have been
written using 1/19.65 variety of pound-inch but
the ones just presented us by Andrew do not seem
all that different at this level so the problem
might perhaps do for them as well.

As a welcome to Andrew's new version of pound-inch
I decided to calculate the frequencies of various
colors of light in his units.

Please correct me if I am wrong but I believe
typical (angular format, vacuum) wavelengths for
red, green, blue are

4, 3, 2.5 millionths inch

So, always in angular format, the frequencies
are just what you get by dividing 600 million
(the speed of light) by the wavelengths.

600/4, 600/3, and 600/2.5 trillion per trice.

And as Andrew would immediately notice 600 is
very divisible so the arithmetic to find the
frequencies of the various colors of light is
instant and gives

150, 200, and 240 trillion per trice.

(frequencies of red, green, blue in Andrew's pound-inch
system)

I guess the only part that might intimidate some
people is that million divided by millionth is
trillion. 10^6 divided by 10^-6 is 10^12. But that
seems pretty tame.

Reliving that old broadway show tune (Annie get yr gun)
"anything you can do inch can do better
pound can do anything better than you!"

Come on, don't chicken out, let's have a complete set of e.m. units and show us where to put the constants in Maxwell: dF=0 & divF=4piJ.

Paul I just saw your post
and read it with delight! It is
a very friendly suggestion.

Though I should refrain
(it is completely Andrew's choice
what to do and last word from him I
think he wanted to keep a mixed system
with usual SI electrical units)
though I should refrain
(so as not to glaze the eyes of
technically unconcerned readers)
though I should refrain
(BTW its fair game would YOU like
to add electrical units to the system?)
PROBABLY I shall get around
to writing Lorentz force eqn and
Maxwell's for at least some version
of pound-inch.
Very kind of you to mention it!
Maybe should be back in old (April)
thread so as not to interfere too much
with Andrew's new version. Look for
the keyword "chicken".

Yes, I would very much appreciate that as well to end my unknowingness about symmetric Maxwells...

Cheers,
Ralf

Actually, I just looked at your web page www.planck.com to see what you mean by symmetric Maxwells. If understand it correctly, you get rid of mu0 and epsilon0, replacing it by a common factor, right ?
Although I admit that they look nicer that way, that beauty is confined to the case in which mu_r and epsilon_r are both 1.0, ie in vacuum.
In case of a real world scenario, both mu_r and epsilon_r are not 1.0, that's the reason why Maxwell's equations are usually written involving D and H and not just solely with E and B.
Apart from that, when trying to solve Maxwell's equations for a certain scenario, the least of your concern is some prefactors, getting the boundary conditions right and solving the differential equations consumes 99% of your time...

Ralf

Not without "Korbelima!"

Ralf gives us a valuable reminder of the
real-world difficulties of getting meaningful
solutions of M. equations especially in
dense media where the speed of light is less
than it is in vacuum. The solutions I think he
would say (were he not a bit laconic) become
beautiful when boundaries are defined (as by
a resonant chamber or a waveguide or the
geometry of antennas. A moment of respectful
silence for the tens of thousands of anonymous
craftsmen who have solved M. eq. over more than a century
in hundreds of different types of circumstances
and who have thereby built the corbelled arches and
carved the gargoyles of our civilization as much
as any other class of master artisan ever did. Or
so IMHO it could be argued.

I am sitting here wondering if "Korbel lima" should
have two ells or (as that nameless poster wrote it)
just one ell. The nameless one is trying to raise
the level of culture here, or show his own, I guess.

But right now it seems as if we should be looking
at ANDREW'S VERSION of pound-inch which is mainly
different from my April version (which Andrew
also instigated) because mine had exactly 1/19.65 second
and his has approximately 1/19.67 ordinary second but
based directly on atomic clock, not on second.

And it
strikes me that his version has an exact Planck's h
that is not terribly hard to write, namely

36/3.127637 x 10^-32 inchpound trice.

And I find this mildly amusing. Dammit, I find it
actually pleasant. In metric the h number is not
exact and it is a long number that goes on forevever
and you never know how many digits of it you are
going to want. But Andrew has somehow managed to
define some units in which h is exactly something.
You just have to be able to divide 36 by 3.127637.
OK I did that and it is about 11.51. So Planck h
is 11.51 x 10^-32.

I had better check it. his c is 600 million and his mass unit is defined by the exact frequency
3.127637 x 10^48. (This is where BRIAN KIBBLES
extremely accurate MOVING COIL BALANCE comes in.
It provides the weight measurement paradigm in
which one WANTS to have mass unit defined by freq.
in fact MUST HAVE mass unit defined by freq. Or
otherwise moving coil balance is used to measure
h experimentally, which is current practice in SI.)

So, well, h is always equal to c squared divided by
the mass unit frequency so that is 600 million squared divided by 3.127637 x 10^48, so indeed it is
11.51 x 10^-32 inchpoundtrice in Andrew's terms.

And the 11.51 is exactly 36/3.127637.

Like a mosquito Usher has gone in under the radar
again and left a tiny bite on metric which tomorrow
will itch. Perhaps my guess is wrong? Let's see
if tomorrow it doesn't itch that SI metric has
no simple exact value of Planck's constant. Kudos
Andrew.

Friendly approximation.
I really like what Andrew has done in getting a pound
inch system with speed of light exactly 600 million.
I can't think of anyone else to whom it would have
occurred to do that.

Today I was experimenting with a system which is
a close approximation to it but easier for me to
calculate in.

time unit: 1/19.67142 ordinary second. (Andrew will
not like because he favors basing unit directly on
cesium atomic clock but this is convenient for
calculations going back and forth betw. poundinch and
metric and VERY close to Andrew's subject to that
concession)

inch: same idea, speed of light exactly 600 million
inch per trice

mass unit: same idea but with frequency given
as 36/11.51031 x 10^48 cycles per trice.

Logically equiv. to defining mass unit by declaring
that Planck's h is exactly 11.51031 x 10^-32 in
terms of the system.

Relatives from st. p. on the way. Can't write
anymore today. Will not pursue if Andrew thinks
I shouldn't but seems convenient for some things.

Here for comparison Andrew's orig. def.

[[So, with that set, and keeping the inch and pound mass as near as could be required to the present values, I have evaluated here the set of three numbers that fully defines my base units.

The trice is equal to 467,308,981 cycles of the radiation from caesium used in atomic clocks.

The inch is that distance traveled by a photon in 1/600,000,000 trice.

The pound is the mass having equivalent energy equal to a collection of photons whose frequencies total 3.127637 * 10^48 cycles per trice.]]

Well, I see 25 replies! I should specify which I am answering to avoid confusion.

I will start with Leonard's, being the latest.

I do not mind defining exact h instead. It is cleaner in use, though the definition of mass will have a complex fraction in it (36/11.51029). I also do not insist of using the number of caesium cycles, so long as it has the same meaning. I find those just technical issues, not the real substance of the system.

Your 'pizza and lightbulb' problem highlighted a difficulty with all coherent measuring systems - the unit of energy being unreasonably small. This is why we use watthours, etc. - more convenient units. I think we need a name for (inchpound/trice), and then use (ip/tr)-hr for energy. It would equal 72,000 inchpounds or 2.22 W-hr.

Paul:

Most of your criticisms were addressed in my original post itself. I do not think I need to rehash my reasoning - we simply have a difference of opinions, I guess. I would like someone to take a look in more detail and react to specific decisions - that is one reason I posted it, I wanted suggestions on what features might be problematic.

Yes, g is not a 'fundamental constant', but it is very important to us, perhaps the most used constant. After all, we do live on this planet alone and will a long time into the future. If nothing else, it is superior to what metric takes as its 'fundamental constant', the density of water. Your assertion that g was 'absurdly out-of-date' sounds suspiciously like a pro-metric argument, actually.

Leonard, perhaps we should continue via e-mail. Discussions about Maxwell's equations and the arcane aspects of metrology really do not belong on this board.

Andrew Usher

>And it
>strikes me that his version has an exact Planck's h
>that is not terribly hard to write, namely
>36/3.127637 x 10^-32 inchpound trice.

To stay with Paul's analogy of wallpaper bubbles, doesn't fixing "h" mean that some other unit will be subject to variability then ?

Ralf

Ralf, yes.

Fixing Planck's h by any means will cause Coulomb's k to be no longer fixed - it must be determined experimentally. This is a good trade off I think.

Andrew Usher

It would inevitably take a long time for a system like this to take over from the current metric systems (if ever). By then, a large fraction of mankind will no longer be living on Earth, and the central position of g will seem a curious skiamorph. Already most scientific work makes little or no use of g, or deals with gravity fields significantly different from Earth's surface gravity. By contrast, the 1000kg/m**3 density of water is valid (and convenient) everywhere in the universe.

However, the reason I definitely dislike your scheme (as distinct from Leonard's) is your use of two different sorts of time. I might just about accept an everyday "clock time" slightly different from standard time. But not a scientific time 2% off from the present standard, especially one that tries to use the same names. The confusion this would cause is hard to overstate. All sorts of times and frequencies would become plain wrong. Even the FM channels on your radio would be impossibly off. Practically every scientific book or paper ever published would have to be thrown away or translated, and the confusion of old and new copies, and the perpetual ambiguity in the meaning of the second, would continue to cause endless trouble, even deaths. And to what end? So that the speed of light can have a slightly tidier value, even though most other fundamental constants will still have awkward values. No, I'm sorry, but it's not on. Your priorities are upside down here - ordinary people, even ordinary scientists, won't buy into them.

I think one of the strongest original motivations
for looking at this type of pound-inch system was
that people use pound-force (as in psi for pressure)
as well as pound mass in the vernacular.

For Andrew and me the challenge was, can we make up a coherent system
that will have these two very popular units of
mass and force?

The result (still unfinished and now the joint work of several
people because even a primarily critical presence
can be very helpful and even essential to arriving
at something workable) seems appealing enough to
me to use sporadically in the present.

Or at least have as one of several benchmark examples of
alternatives with which to compare metric.
I was never quite satisfied with the slug/pound or
with the pound/oldpoundal alternatives because they
were both so much at odds with popular usage.

I think everything I've said in this post was already
clear to you from the start. You understand all these
issues and know how I think about them.

What to do? Is this pound-inch system fun enough
to continue test-driving? You are absolutely right
that we cannot tamper with the worlds existing second,
minute hour! On the other hand Andrew's idea of
exact round c is appealing, at least to me.
Would you be willing to make a judgement call?
If I keep on making problems up in pound-inch would
it be better for me to stick with 1/19.65 and
gravity very very close to metric standard namely
that of around Bordeaux france latitude but light
going 600,654,080. Or should I move over to what
Andrew suggests which is essentially 1/19.67142
and light going 600 million but gravity closer to
Spitzbergen Norway latitude and about 2 tenths of
percent stronger? Or is this an uninteresting question
about which one should be indifferent. From the
viewpoint of someone composing physics problems
or working them it almost doesn't matter (0.2 percent
is so small) but do you still have a feeling one way
or the other?

BTW the point about units appropriate to life
off-earth certainly makes sense but does not cause
me to embrace SI metric since I picture
future people thinking for themselves and
retaining some cultural diversity and freedom of choice and being able to do better than
SI metric in that environment as well, with still
other systems. I think you do too maybe.

There's certainly nothing wrong with the basic idea of an updated pound-poundal system in which, for convenience, the value of Earth's surface gravity comes out close to one. Nor one in which the speed of light is close to 6E8. But to create gross inconveniences (like Andrew's non-standard seconds) for the sake of such minor ornaments is no real improvement.

Your system, with a new and distinct unit of time (the trice) has at the very least sound educational value. I myself am finding my understanding deepened by this debate, especially in regard to the symmetrical e.m. units, which are a real step forward. But Andrew's ambiguous seconds, I'm afraid, would tend more to confuse than to enlighten, for students and scientists alike; far too high a price for his scheme's slightly tidier values of c and s/t.

So my advice would definitely be to stick with the standard second and 19.65 trice per second, and accept that the speed of light is 0.1% away from the moderately neat but by no means overwhelmingly beautiful value of 6E8. Remember too that (working with your system) converting from trice to seconds is something people would want to do a lot, so a figure that is exactly 19.65 is much better than one that goes meandering off into the blue of umpteen decimal places; whereas only occasionally would one need to calculate with a more accurate value for the speed of light than 6E8 for your 6.0065408E8, which after all is almost identical in accuracy to 3E8 in SI.

>Leonard, perhaps we should continue via e-mail. >Discussions about Maxwell's equations and the arcane >aspects of metrology really do not belong on this board.

This board is still a good place to talk. I will keep
Maxwell's equations confined over in the April
pound-inch thread (to whatever extent discussed)
and out of this thread. Write email ALSO.

>Well, I see 25 replies! I should specify which I am answering to avoid confusion.

Yeah, congratulations on starting an intriguing thread.

right now I think you should drop the alternative
second/minute/hour idea (in cultural attack mode quickness of self-definition is essential, you die
all the time you spend explaining who you are) and
go ahead with the c = 600 million idea.

Let's see if we can make your system very quickly
explainable. It can always be refined later if it
wins some areas of acceptance or excites some interest.

1.You choose your time unit defined in terms of
second (to make introductions quick and reach people
who don't know what caesium is)

2.You say 600 million.

3.You say planck h is 11.51029 (this was your number
mentioned in previous post?) x 10^-32. Or something
like that.

Bang. system defined. Then problems in it. And it will turn out that
unit force is the (pound) weight of unit mass in
standard ("Norway") gravity. Which is 0.2 percent
stronger than what Frenchmen are familiar with but
machs nichts.

And lots of people will be put off by the fact that
you said what h is exactly and did not say what
mass unit was exactly and you will lose the
attention of some of those people. But on other
counts you will win.

And Mohr and Taylor (CODATA doyens that I respect a
whole lot) have already in at least one paper suggested
that eventually SI metric could be defined by
specifying exact h instead of mass unit by frequency. Logically
equivalent and somehow simpler to say.



>I do not mind defining exact h instead. It is cleaner in use, though the definition of mass will have a complex fraction in it (36/11.51029). I also do not insist of using the number of caesium cycles, so long as it has the same meaning. I find those just technical issues, not the real substance of the system.

YES!!!! You are saying here just what I was talking
about. If you don't mind trying the definition by
means of h then we are in business with a trial
vehicle. It may fail but it is interesting.

If it does nothing else, it enlivens the morning.
And it may help bog down metric advance. Very
happy about this. Cheers,
L

Hello Andrew, I seem to be always stealing your ideas first about doing a pound-inch system and then about having c be 600 million. Well I try to give credit but get intrigued and involved as well.

Anyway I tried to find a common ground between your idea of a clean speed of light and Paul's concern to make the expression for time unit concise and came up with a compromise which works if inch can be allowed to grow by 70 ppm (7 thousandths of a percent). I think that might be allowable for educational use although not in high-precision industrial contexts. Of course things might change in the future and definitions change but for now here is a kind of compromise:

1. trice is 1/19.67 second
2. c is 600 million inches per trice
3. h is 11.5095 E-32 inchpoundaltrice

All three are exact and together they define the
base units. I'm using Paul's suggested name of
poundal (really a "new poundal") I still have no clear
idea of my own how to distinguish verbally between
pound mass and pound force (should one say 'libra'
for the mass and 'pound' for the force? the Romans
had two names for their pound: libra and pondo).
I kind of like reserving the name pound for the force
and saying something else like libra or "poundmass" for the inertia.
So if I weigh 190 pounds my mass is 190 libras.
I like pound for the force so I can say inchpound
for energy and poundpersquareinch for pressure. But generally speaking Paul has been sorting out the names
and as long as he wants to say poundal for the force I will
go along with it. the system sort of grows by snowball
gathering the work of whoever works on it.

How are you feeling about developments? I am worried
that since you have a kind of parental interest in
pound-inch the rough-and-tumble may be disappointing
you.

Let me know if the above 3-point definition seems good
to you.

It has at least the virtue that many of the numbers
are short: it is 19.67 instead of 19.67142 and it
is 6E8 instead of 6.0065408E8.




To get the number for h I took
Taylor and Mohr's most recent published proposed
frequency definition for kilogram, multiplied
by 0.45359237 (the official pound number) and
divided by 19.67.
Most recently Taylor and Mohr (IEEE Trans. on Instrumentation and
Measurement, vol 50 no. 2 April 2001) proposed
135639277E42 hertz for the kilogram.

Doing that to their number gives what they would
have been proposing if it had been for the standard
pound and using trice. Then dividing 36E16 by that
gives the 11.5095...value for h. You've done those
calculations several times already on your own. We
seem to be going through design iterations.
***********

One of the more hopeful things I've heard recently
was Paul's comment in one of the preceding posts:

"Your system, with a new and distinct unit of time (the trice) has at the very least sound educational value."

I think this is an unprejudiced objective assessment.
I think it is true. Pound inch in at least some
version (which we have already or have not yet got)
has potential educational value and it would make
sense to accumulate some physics problems in it on
the web.
At the head of the web-page with the problems there
should be a concise definition and description of
the units and that is what we are hashing over now.
I think the hashing is nearly complete. Please let
me know what you think either on board or by mail.

L

I can not agree with changing the inch. One of the virtues of the system is allowing the present inch-base engineering standards to continue, and a 70 ppm change would destroy that.

Also, I found that the reason our values of h disagreed is that I was using US survey measure, i.e. 1 inch = 1/39.37 meter. I suppose I will have to bow to a metric definition for once and use 1 inch = .0254 meter.

Using this definition, we can come up with the same number of caesium cycles as I already had (467,308,981); we could use 1/19.67142 second, but I feel that has so many digits that one might as well use the atomic-clock definition.

As far as the mass unit is concerned, if you believe fixing h preferable to number of cpt, I will go along with that. Then h = 11.51031 e-32 ipt, or the pound = 3.12763 cpt (notice changes).

I will accept either - you make the call.

For now I give up my nonstandard second, minute, hour; I do not retract my comment that the slowing of the Earth's rotation will eventually cause problems with this approach, and the scientific unit of time - the trice - can not be allowed to change.

Andrew Usher

The slowing of the Earth doesn't cause any problems for the standard or scientific second (or for that matter the trice), or even really for the clock second. The length of the day is only 86400 seconds exactly for the date 1900.0. All that the Earth's slowing means is the occasional inclusion of a leap second; it will be about sixty thousand of years, at the present rate of change, before there'll need to be more than one leap second a day.

Long, long before that we'll be used to days on other planets needing plus or minus several leap hours a day - or more - and none of this need or should change the standard second one jiffy. We will probably then use digital watches in which one enters the length of day in standard hours, minutes, seconds and hundredths of a second, just like setting the alarm. On its local time setting the watch will count up to the full length of day (on Mars, 24h 49m 35s if I've calculated right) then reset to 00h 00m 00s. It will keep track of standard time simultaneously. In fact, it could easily keep track of an arbitrary number of local times the same way.

Paul: 60,000 years? I was thinking much faster than that. Nevertheless, the basic dilemma remains: do we keep the present time units and thereby codify the length of the day on one planet at one time, or do we let the units vary?

I take it you would keep the constant minute and hour as well, and hence the day would become longer than 24 hours over time.

I notice that in your scheme, all populations on all planets in the future will suffer the inconvenience of having time units based on Earth c. 2000 AD. And did you not just criticise me for using Earth's standard gravity (which is at least constant with time) in my system?

The reason I commented of this time question is that it would simply offend my sense of beauty to not have the clock equally divided. So I came up with a solution - the only as far as I can see - divorcing the units of (Earth-based) timekeeping from the units of measure.

Andrew Usher

<<I can not agree with changing the inch. One of the virtues of the system is allowing the present inch-base engineering standards to continue, and a 70 ppm change would destroy that.>>

You have a point and this version is yours to decide
all such questions. I like the idea of having several
different versions of pound-inch visible on web because it lets the reader decide for him or herself
which is personally most appealing.

GO WITH EITHER 467,308,981 clock cycles or 1/19.67142
of atomic clock second. As you said one time it doesn't really matter which. Both give you an inch that is indistinguishable from present inch and that
is very nice.
Maybe it is slightly better to go with the clock cycles because the more digits the finer precision.
Yes I think I marginally prefer that in your version
of the system.

But I also love a version of pound-inch that is very
quick to define (only four-digit accuracy and four-
digit numbers) and I want to have a page on it at
my site. It derives from you idea of having a clean
round speed of light (unexpected bonus of pound-inch)
and I hope this is all right with you.



<<As far as the mass unit is concerned, if you believe fixing h preferable to number of cpt, I will go along with that. Then h = 11.51031 e-32 ipt, or the pound = 3.12763 cpt (notice changes).

I will accept either - you make the call.>>

You Andrew are the final arbiter. I like the approach using h. Mohr Taylor have even suggested it recently
for metric system to redefine kilo (before they just
said use frequency but now they say could use h
instead, and there is no essential difference as you
have pointed out and as they observe as well).

Looks like today we have to be busy on
homerepair fixit stuff so
I'm not going to get to read and post at
bwma but must send this now.
Bravo on the pound-inch, it continues
to look interesting,

L

I can understand why you'd prefer to keep a neat twenty four hour day for ordinary use (though as I say the difference won't matter on Earth for a very long time). Most artifically constructed space habitats are likely to use the standard day too, so no problem there either. Many terraformed planets will also have their solettas arranged to provide them with a standard 86400 second day.

However, other planets, and a minority of habitats, will have days of differing lengths. The least awkward option is then as I suggested - to stick to the standard second, minute and hour, and allow clocks and watches to reset after the full local day, at whatever time that turns out to be. The alternative of re-adjusting the units of clock time to give a twenty four hour (or other round number) day would be horribly messy, and differently messy on every planet, because of the impact on all the other things for which one uses units of time, velocity, frequency, etc. No doubt some planets will end up with such idiosyncratic time measurements, but I suspect most will prefer standardisation, because of the difficulty of maintaining two sets of incompatible units (for clock and scientific time), especially since there can be no reasons of tradition to make them choose otherwise.

Paul has posted a description of his version of
pound-inch units at his www.paulbirch.net site

http://www.paulbirch.net/InchPoundTrice.html

The exposition is clear and it is an interesting
version. You might want to have a look.


It seems like a good idea to have several variants
of pound-inch on the web.

We have two now going on three. Pauls and the two
that Andrew and I are developing which are turning
out to be fairly close.

The problems posted here to show metric clumsiness
and demonstrate pound-inch's superiority (as more
modern decimal system) in college physics area work
equally well in any variant of pound inch units.

The same problems work for all.

VISIBILITY: For a couple of months the visibility on
Google has been that if you put in two words [pound
inch] and do a search then Google's number one, in
the list of what it finds, is the exposition of
pound-inch units at my planck.com site.

Now there has been some improvement. Now we have the first four positions on the list. Two refer to
pages at planck.com and two refer to metricsucks.com.

For one of the two metricsucks you have to use "cache"
to find the pound-inch place because metricsucks is so huge. But mostly you get directly to pound-inch exposition and problems.

I expect Google to pick up Paul's page now that he has put it up on the web. If you are reading this and you have a site, consider checking out Paul's page. If you like it and link to it this increases visibility of the new system (Google ranking is based on links to).

Pound-inch is a superior system and is fun to use.

Now I have some basic grasp of physics, I understand this proposal, so say this:

Here are my proposals (in a nutshell):

Trice = 1/19.65 secs
Acceleration = Axxel/atsel (a)
Force = poundatsel/accel (lba, la)
Work = strenue (sn)
Power = potes (po)

Mass:
10,000 myriounces/mroz (yoz) = 1 ounce
10,000 myripounds/myrl (ylb) = 1 pound
16 ounces = 1 pound
20lb = 1 cent
100 cents = 1 ton

Andrew’s system of length, but pace and new mile for technical purposes only.

Light speed to be either 600,600,000 (or some similar figure) inches per trice
G at 45 degrees.