There is a set of units built into nature—based on proportions intrinsic to light and gravity—called the natural units or Planck units. Human-scale versions of the natural units are fun to play around with and convenient to use for some purposes.
In the version described here, natural units have been scaled by powers of ten to give them handy sizes. The natural units of time, length, and mass are things you can find on the web—e.g. just google with "fundamental constants" and select "universal". You will get a short list of universal fundamental physical constants with the accepted values of the Planck units, as well as things like c, G, h-bar, on which the natural units themselves are based.
It just happens that when you scale the mite-sized natural mass unit up by a billion, to make it human-size, you get a mass which is (within a fraction of a percent) equal to 48 conventional pounds, about what a classical talent weighed. The natural length unit, scaled up by a power of ten, is (within half a percent of) an ordinary mile. The time unit, likewise scaled by a power of ten to give it a familiar size, comes out to be (within two tenths of a percent) 1/1600 of a day, or nine tenths of a conventional minute. This is just how things turn out, and it indicates the real, but not impossible, hurdles involved in getting used to human-scale natural units. It means getting accustomed to using a reduced minute in certain technical situations—for definiteness the minute in these stories will be 54 seconds, ten percent less than the conventional one—and to describing masses and lengths with convenient fractions of the talent and mile.
Together with the minute, the talent and mile specify a unit of force which is somewhat more than the weight of a kilogram in normal sealevel gravity—more precisely about 2.7 pounds. There is a traditional unit of this size used in parts of eastern Europe and the mediterranean which is called the ocque or oke—the spelling here is simplified to oc. An oc is the force needed to accelerate talent mass by one mile a minute per minute. The ocmile unit of energy, about 5 food Calories worth, is that delivered by a mile-long oc push. These are essentially Planck units of force and energy scaled by powers of ten to make them a practical human size.
Technically the Talent Mile units used in the stories are defined by specifying exact round values for the main physical constants:
the speed of light, c = E7 miles per minute (E7 stands for 107, ten million.)
Planck's hbar = E-40 ocmile minute
Boltzmann's k = E-25 ocmile per grade.
It turns out that with these definitions the gravitation constant G takes an approximately power-of-ten value.
G = 1.00E-15 cubicmile/squareminute per talent.
Reform is not urged here. You are urged to continue using ordinary pounds and miles, or metric units if you prefer, and the customary hours and minutes of the clockface. But for certain kinds of physics calculations it can be fun to switch over to "talent mile units"— units connected to nature and to the proportions built into light and gravity, in terms of which the most important natural constants take on power-of-ten values.
Three units (time, length, mass) are defined and then used to specify others, particularly some smaller subdivisions.
This makes the mile come out to be 1618.88 meters (a fraction of a percent longer than the conventional one) and the talent come out 21.73 kilograms. The pace, one thousandth of a mile, is used as a convenient subdivision. If we need to describe volume, one thousandth of a cubic pace is gallon-sized and will be called so.
I also divide the talent mass into 1000 ounces. In one story there is a 100 ounce rabbit and a 10 ounce frog. This ounce is roughly 3/4 of a conventional avoirdupois ounce. It seems to work fairly well and so far I have not needed any other subdivision of the talent.
Talent Mile units do not have much extra terminology—the units are simply based on minute, mile, talent, and the oc force that arises from them. The unit of power is that which supplies unit energy (ocmile) in unit time (minute). One ocmile per minute works out to be about 360 conventional watts or half a horsepower: a good nickname for it is pony.
Copyright 2002 Leonard Cottrell. All rights reserved.
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