People interested in preserving the pound as a traditional unit of mass might consider that there is a widely recognized natural mass unit and that 48 pounds is (as close as can be measured) equal to a billion times the natural unit.

A quick way to find out some things about the natural unit is to use Google and search with keywords such as [planck mass], [natural units], [planck units]. My site will show up on Google's list but you are encouraged to look at everybody else's instead if you want. Or just go to the NIST site on fundamental constants and look up planck mass directly.

It is a bizarre coincidence that a billion times the natural mass unit (which physicists and cosmologists like so much and believe is so basic) should be equal as closely as can be measured to 48 pounds.

People interested in preserving the traditional pound unit (even if they are non-scientists) should consider trying to UNDERSTAND how the natural unit arises from the built-in proportions in light and gravity.

Even if you think you expect it's too complicated, you might find it's not. I will think about a concise explanation and perhaps post one as a continuation of this later.

48, being divisible by both 12 and 16, is one of the greatest numbers in existence.

There is an overwhelmingly prevalent physical quantity that is all around you in every bit of light. This is the bit of light's energy-length product and it's the same for every quantum of light.

Every bit of light has a small cargo of energy that it carries and it also has a wavelength. Multiplying the two things gives the same answer for every bit of light.

Bits that carry more energy have shorter wavelength. So they have the same energy-length product as bits that carry less energy and have longer wavelength. For each bit it equalizes out so that the product of its energy with its length is the same.

The conventional physicist SYMBOL for this ubiquitous all-pervasive energy-length product is ---well dammit it doesn't matter what the symbol is! that is just the historical accident of physics symbols!---but anyway the symbol is h-bar c.

So this quantity h-bar x c is everywhere all around you at all times and especially in patches of sunlight where there are jillions of quanta and therefore jillions of individual occurrences of this exact quantity of energy times length.

I AM GOING TO GET THE SQUARE OF THE NATURAL MASS UNIT from THIS ENERGY-LENGTH PRODUCT. This is actually automatic. The fundamental ratio in gravity is itself a ratio between energy-length products and squared mass. If you know that it is a cinch, but some people don't so I'll stop here and think about how to introduce the basic gravity idea in another post as a continuation.

BTW in Bryan units which are so nice for relating to nature with, the energy unit is kibblebone and the length unit is bone. So the unit of energy multiplied by length is kibblebonebone which is unit force times unit area. The natural quantity is a power-of-thousand fraction of the bryan unit force times unit area. Indeed the bryan unit is a trilliontrillion times the natural thing present in all light. (part of what "seminatural" means, related to natural units by powers of thousand).

10 is the greatest number on earth !

^ Not according to nature, it isn't.

^ Mind over matter !

Ralf

"What is the mind? Is it a series of electronic impulses, or is it something more tangible?"
"What is mind? No matter. What is matter? Nevermind. Heh heh heh. Now you get to sleep boy"

"...ELECTRIC..."

"damn, I should have taken the blue pill..."

the sunlight is blindingly bright out on the
terrace and it is hot. when I walk outside it is like having a sack of sugar dumped on my head except it is a sack of quanta light-grains and each
tiny sparkle of light has the same energy-wavelength product

If I could catch a trilliontrillion bits of light (of whatever mix of wavelengths) and measure the energy each one carries and its wavelength and multiply them and add them up--all trilliontrillion--it would add up to
just one Bryan unit of force x area, in other words one kibble x square bone. Bryan Seminatural units were set up (partly by nature and partly by us) so it would be that way.

In lab they can deal with individual quanta and tell how much energy an individual carries and its wavelength and such, but I can't. So I just walk outside
and get hit by a blast of sunlight quanta and know that
the energy-wavelength product for every one is the same and that a trilliontrillion would add up to something I know.

Here's how I know it: bone is the width of my little finger at knuckle and
kibblebone is energy of lifting something that weighs a kibble by one fingerbreadth. so I know a kibblebonebone. or I can think of it as kibble force multiplied by square bone area (easy to picture a little square that is fingerbreadth wide).

The really strange and interesting thing, I think, is that every MASS has a distinctive force x area product connected with it. Maybe I should say "force x square distance" product.

If you take two copies of the mass (say for example two 1000 dog masses, two 48,000 pound masses) and put them some distance apart and measure the force of attraction. Then the force x square distance apart is ALWAYS THE SAME. Increasing the distance and thus the square distance will make the force less! So it equalizes out no matter what distance apart!

In the case of two 48,000 pound masses the force x square distance apart will always be one kibblebonebone--the thing you get from the light.

Down at level of natural units. two natural mass units
(each a billionth of the 48 pound mass) have a pull x squaredistance product that is the SAME AS THE energy x wavelength product for an individual quantum of light.

This is one way of thinking about why natural mass unit is what it is. It has the same somethingorother
as every quantum of light in the universe.

The somethingorother is a physical quantity that
in Bryan units turns out to be a trilliontrillionth of a kibblebonebone. Maybe it makes it more confusing to
say that because it sounds a bit absurd but how else to say how much the actual quantity is.

There are neater more algebraic ways to say this
that take a sentence or two and some symbols but
this is with concrete ideas like the bag of sugar
and the two masses, which I hope help rather than
the opposite!

Someone else want to throw in a random, and yet still relevent quote? No...? I will then, just for the sheer hell of it!

"My car gets 9 rods to the hogshead, and that's the way I likes it!!!"
-You know, when you know what this is from, it could actually be taken as a mocking of Imperial *or* of metric... Also, his car really isn't all that efficient: 1 hogshead= 52½ gallons, 1 rod= 5½ yds

I think old Abe actually said he got 40 rods to the hogshead.

He also prefaced that comment with "the metric system is the tool of the devil!"

He must be a Stonecutter, eh?

Most likely. And, you know, 40 rods to the hogshead still isn't a particularly efficient car (another way of putting it is that he goes 220 yards on 52½ gallons)

you know what Rotclar said about 48
has a ring of truth
it is a pretty good number

I agree Leonard. You know, 48 has to be the perfect number for combining the two superior numbers (16 and 12) and 60 is the best number for combining 12 and 10.

You mentioned the rods/hogshead quote from Abe
on Simpsons. I went looking to see if I could
find the quote.

I found it on a strange site:

http://xocxoc.home.att.net/math/metrics.htm

The site expresses REGRET at the slowness of metrication in US. On the other hand it has the
Abe quote and makes some interesting observations
about things which undermine popularity of metric.

One thing this site claims is that some research
showed that 1/100 inch is the a practical limit on
human eye (I guess for workers using measuring rods).
It said that some US manufacturers have switched to
"decimal inch" because in some sense it works better
and that this has had a domino effect or something
which has tended to further delay adoption of metric in industry and some types of engineering.

I don't know if this is true but it comes from a
seemingly pro-metric source and it basically says that 1/100 of inch (0.254 mm) is better in some ways than millimeter. Millimeter is OK but the human eye can
do better than millimeter. However the eye cannot
work down to a TENTH of a millimeter. So hundredths
of inch have a sort of advantage.

(I would think one would be using calipers and
electronic measuring tools anyway, but at least this
source implies that decimal inch suits human eye well.)

Not sure this has any place in discussion. Just came
across it looking for Old Abe hogshead quote.

Hmm, I don't see how a length can be used to indicate the resolution of the human eye.
The only metric that makes sense is the smallest angle the eye can distinguish, which is the only way I've read about it so far.

BTW, that reminds me: Has anyone on this forum ever used stuff like arc minutes and arc seconds in calculations ? I must say that I always used decimals (eg 5.2432°), even though it has nothing to do with the metric system...

Ralf

Leonard, remember my idea for 48ths of an inch (4 quarters of 12 lines each)? I think it is a good number and a good size.

Yes I do remember! Do you recall what thread
that was? I believe I remember BWMA had something
to say about it too. It was perceived as a problem
that ordinary inch-fractions don't go down as small as a millimeter.

But if we can trust what this "xocxoc" site says, some precision manufacturing is done with hundredths of inch which (being 0.254 mm) would be FOUR TIMES more precise than millimeter.

If workers holding stuff at "reading distance" can
use rulers marked in hundredths of inch then your
1/48 inch rulings would seem to be quite workable.
(as well as numerically convenient for some things).

BTW I am most embarrassed! The idea that the King
personally adjusted the stone to suit the fisherman was my own foolish embellishment of the story. I was
just reminded of that as I was trying to find your
earlier post about fractions of inch. But who else
would have authority to adjust the weight of so venerable a unit as the stone? Could it have been done at some local level, by a council of Burghers or by the Lord Mayor of London. My guess is that one group of tradesmen want stone to be 16 pounds and one group wanted it to be 12 pounds and a COMMITTEE of some sort
came up with a compromise 14 pound stone that did not
really please anybody but which put the problem on hold. It seems self-evident that the stone ought be a division of 48 pounds.



Recalling what you and BWMA were talking about back a while was one thing that made me notice what this
guy "xocxoc" said. For reference here is the quote about decimal inch
from xocxoc site:



[The Metrics killer: The Decimal Inch

Manufacturing and some engineering disciplines have abandoned traditional measures as well, but not in favor of metrics. They have discovered an even better system of measure called the decimal inch. It has been discovered that the smallest distance of separation visible to the unaided eye is 0.01 inches, or 0.26 mm. What this means is that being accurate to within a hundredth of an inch is better than being within a millimeter. Four times better as a matter of fact. The only way metrics can be better is if rulers used half and quarter millimeters, but adding fractions defeats the whole purpose of decimal measurement. So now manufacturing and engineering have embraced the decimal inch, a standard inch divided into tenths and hundredths. This has set off a chain reaction, if manufacturing does not have to convert to metrics, why should we?]

>But if we can trust what this "xocxoc" site says,
>some precision manufacturing is done with hundredths
>of inch which (being 0.254 mm) would be FOUR TIMES
>more precise than millimeter

Yes, Leonard, isn't that an amazing feature of the number 100 ?

Ralf

I'm not sure I understand your question (I think
you know i wasn't talking about the number 100 but
was asking about precision manufacturing in US)

I'm hoping someone helps get the facts straight.
Is there a trend towards using decimal inch (as this
fellow suggests)? I would not have expected this. It
would be a pleasant surprise.

I am told the US automotive industry is completely metric. Can any one confirm this? What major industry in US is NOT metric, if you know any? I mean one
involving precision manufacture. Aircraft? Is decimal
inch a factor there?

Does anybody here know if the decimal inch issue raised by this "xoc" fellow is relevant at all, and
in what way? Since I know nothing about him I am
skeptical of what he says.

I have only hearsay about manufacturing (other than microwave tubes where I have a little direct knowledge)
so would appreciate some relable report.

Leonard, I did say that the stoy about he King was something that *you* had added. Oh well...

Ralf, we do not have a phobia of the numbers 10,100, 1000 etc. Also, STOP ENDING ALL OF YOUR POSTS WITH DOT DOT DOT (...)!!!

The resolution of the human eye is about 1/3000 radian (pupil diameter in wavelengths). At the near point for normal vision (around 25 - 30 cm) this implies a linear resolution of about 0.1 mm, or about 300 dots per inch, which is where the basic dot matrix resolution comes from. Ordinarily one could expect to be able to measure and work down to within a factor of two or three of that (ie 0.01") without excessive strain or reliance upon perfect vision - remembering too that the resolution varies with light level, being highest when the pupil is widest open and least in BRIGHT light.

Astronomers mostly use arc-minutes and arc-seconds. Or sometimes microradians. Seldom if ever decimal degrees.

The first time I tried explaining this it was too long and I want to try radically boiling it down. The first attempt at an explanation began this way:

[There is an overwhelmingly prevalent physical quantity that is all around you in every bit of light. This is the bit of light's energy-length product and it's the same for every quantum of light.

Every bit of light has a small cargo of energy that it carries and it also has a wavelength. Multiplying the two things gives the same answer for every bit of light.

Bits that carry more energy have shorter wavelength. So they have the same energy-length product as bits that carry less energy and have longer wavelength. For each bit it equalizes out so that the product of its energy with its length is the same.

The conventional physicist SYMBOL for this ubiquitous all-pervasive energy-length product is ---well dammit it doesn't matter what the symbol is! that is just the historical accident of physics symbols!---but anyway the symbol is h-bar c.

So this quantity h-bar x c is everywhere all around you at all times and especially in patches of sunlight where there are jillions of quanta and therefore jillions of individual occurrences of this exact quantity of energy times length.]

IF YOU TAKE THAT QUANTITY AND DIVIDE BY the universal gravity constant G THEN YOU GET THE SQUARE OF A MITE-SIZED MASS that just happens to be a billionth of, you guessed it, 48 pounds.

Pairs of natural mass have an attraction for each other characterized by the same quantity that characterizes every quantum of light. That uniquely determines the natural mass unit and it's one way of describing what singles it out and makes it be (by an odd coincidence and to within experimental error) a billionth of 48 pounds.

I'll have another go at this and try to get the pieces to come together in a brief paragraph.

The formula for the mass unit (which is the mass of
a barely visible mite or flea, the size of a period in ordinary printed material) is SQRT (h-bar c/G).
Algebra. It discourages many people. All this says
is that if you take two copies of the mass and multiply them together and multiply that squared-mass by G you get the omnipresent h-bar c thing. G is the
universal ratio of the product of two masses and the force x distance-squared product that defines their attraction for each other.

Sometimes I think I will go to the arts-and-crafts store and buy 48 pounds of clay and make a statue of a dog to put out by the rose bushes in the garden but
probably my wife would not like this.

This mass of 48 pounds is a good one.

It has nice divisions
and it is a billion times the natural unit.

Can you think of anything that could be done
to generate awareness of it?

Is there anything that is regularly sold in
48 pound bags that one could stick a label on?

shall I go down to the waterfront park where there
are stones and grass and make a pile of stones
that has 48 pound mass.

Bryan did you happen to see the documentary film about
the Scotch artist Andy Goldsworthy who
works with natural material like leaves, running water,
driftwood, stones, bracken. The film is called
"Rivers and Tides." He has a heavy perhaps north of England or Scots accent and is often hard to understand but the documentary is worth seeing.

I'd like to do something to fix that 48 pound mass
in people's minds. no ideas at the moment.

It's an amazing coincidence that a billion natural units is (as closely as can be measured) equal to 48 pounds. Here's how to check this for yourself, if you care to, from data readily available on the web.

The agreement is to within 2.5 percent of a percent (0.00025) and the natural mass unit itself is only known with an uncertainty of 7.5 percent of a percent (0.00075). So the agreement is closer than the precision with which the natural mass can currently be measured. Can't get any better than that at least for now.

Anybody who wants should be able to verify this. It is easy to do. Google with the keywords [planck mass] or even better [codata planck mass]. You quickly find that a billion times planck mass is 21.767 kilos.

The exact conversion to pounds is to divide by 0.45359237. this the official figure for the kilograms in a pound: any good handbook will have it.

The number 21.767 you easily get off the web and when you divide that by 0.45359237 you get 47.988033. How close is that to 48 exactly?

It is within 2.5 percent of a percent. To check that divide 48 by 47.988 and see that the result is 1.00025.

The experimental uncertainty in the planck mass figure of 21.767 is something you can also get off the web: it's 7.5 percent of a percent. (CODATA will say 7.5 x 10**-4 and that is what it means).

CODATA is the best supplier of fundamental physical data on the web so searching with [codata planck mass] is a way of making sure you get the current best value. But pretty much any site with the fundamental constants will say that planck mass, which is the natural unit of mass intrinsic in light and gravity everywhere in the universe, is 2.1767 x 10**-8 kilogram. To find out how much a billion of those is you just multiply by 10**9 and you get 21.767 kg.

So that is why a billion natural mass units is a level 48 pounds.

It is improbable it should be something like 48.00 when what one would expect is a garbage number like 21.767.
It means that pounds are accidentally in a simple
relation to the underlying units of nature.

this is an unlikely coincidence similar to the surprising fact that the mile in everyday use is within half a percent of being a power-of-ten multiple of the natural unit length.

a sixteenth of an inch is within 2 percent of
being 10**32 natural lengths


the mile is within half a percent of being 10**38
and that means really close. half a percent doesn't
matter for a lot of purposes. and the coincidence in
the case of mile is pretty surprising

a 2 percent coincidence is not so remarkable
and just occurs with sixteenths not with inches per se.

but I mention it in case anyone has a ruler
marked in sixteenths and wants a handle on the natural unit of length

I continue trying to join the natural units to the customary units

with the help of some unexplained coincidences

hoping that a combined natural+customary system will be more resistant to encroachment by metric.

THE MILE is bryan is half a percent longer than present mile.
If we specify 1740 yards to mile (instead of 1760)
then something nice happens:

1/16 " is practically equal to a millionth of a mile

10/16" is the fingerwidth bone unit length

100/16" which is 6 and 1/4 inches is equal to the
convenient auxilliary length unit (with of palm with thumb extended) we've been calling a bryan.

the cost of making this neat a joint between customary and natural units is that there are 5220 feet in a mile instead of the 5280 which everybody is used to.

In this adjustment, the foot is made slightly larger so that there are slightly fewer (5220) feet in a mile.
The mile stays what it was (in metric terms 1616 meters) and yard feet and inches grow (a factor of 5280/5220, one percent).

I was intending to edit the preceding post
at one point there was a typo: "is" instead of "in"
but otherwise it's all right I think.

this version of bryan units or seminatural units
whatever you want to call them
is remarkable in that its pound is
practically indistinguishable from the present pound

and 10/16 " (of if you prefer 5/8") is exactly a bone.

AND the constants are powers of thousand:
gravity is a millionth
light speed is a billion
h-bar is 10**-33

inch and foot are somewhat over one percent longer
(less than two percent) but if you can stand having
inch and foot slightly longer well here is a
unified customary and natural system

I've copied this from another board.
This version of the system has pounds, inches, feet, yards and all that good stuff but also has natural constants that are powers of thousand:

Bryan seminatural units are a an attempt to adapt customary units like pound, mile, gallon so that they can be joined with natural units in a unified system (which, it is hoped, will be successful in resisting metric encroachment).

In the bryan system the main natural constants (G, c, h-bar, e) are powers of thousand--approximately in the case of G and exactly in the other cases.

Gravity is a millionth, light speed is a billion, h-bar is 10**-33 and e is 10**-18.

Time is told in the usual hours/minutes/seconds terms but there is an additional small time unit snicker which is exactly 1/18.55 second.

1/16" is defined as the distance traveled by light in vacuum in one tenmillionth of a snicker.

The base length unit "bone" is fingerwidth size and is defined as 5/8". The standard speed for light is a billion bone per snicker.

The customary units inch, foot, yard turn out to be slightly longer (but by less than two percent).

The mile is defined as 1740 yards (5220 feet) so it turns out only about half a percent longer than present mile.

To close approximation light travels ten thousand miles per snicker.

By a remarkable coincidence the mass unit turns out to be so nearly 48 conventional pounds that the pound can be defined as 1/48 of the system's mass unit (called the "dog") without perceptible change.

Technically the dog unit mass is defined as 10**33 h-bar snicker per square bone. One can just think of it as 48 pounds though, without going into the details of that definition.

Anyone with a ruler marked in sixteenths of an inch has a handle on the natural unit of length

10/16" is the fingerwidth bone unit length

100/16" which is 6 and 1/4 inches is equal to the convenient auxilliary length unit (with of palm with thumb extended) we've been calling a bryan.

A gallon is a cubic bryan. Equivalently a thousand cubic bones. A special pint will be provided so as not to disappoint beerdrinkers (I've been warned, this gallon is considerably larger than US but still smaller than UK gallon.)

The associated units of energy, pressure, temperature etc. have been defined and discussed in other posts on this board.