Laotzu was visiting a planet where the skimspeed, the speed of the closest circular orbit, was 100 miles per minute. This was a smaller planet than Earth, where the skimspeed is 260 miles per minute. The planet's density, on the other hand, was nearly that of earth, and regardless of differences in size, planets with the same density have the same skimtime—the time it takes to travel the length of a radius in skimming orbit. In the earth's case this is just under 15 minutes (14.94 to be precise) and on the planet he was visiting Laotzu found it was slightly over 15 minutes.
It happened to be New Year's Day there, which in many places is a kind of birthday party for the planet. People have a special meal commemorating, among other things, the energy that binds them to the planet. They reckon the energy in talent (mile/minute)2, a unit (for want of a better name) equal to about five food Calories. So a light snack might contain ten or twenty energy units and a substantial meal might contain several hundred.
Each of us is bound to our planet by a definite amount of energy that would have to be supplied to liberate us from the planet's hold. We are in hock for that amount — that's what binding energy means. A person's energy ransom must somehow be supplied if they are to go their own way around the star.
On large planets like the one Laotzu was visiting a person's energy bond is more than anyone could ever eat in one meal. But as a remembrance of this bond, on New Year's you eat a bit of the brittle Freedom Cracker with just enough energy in it to free one of your ounces. This custom has the advantage that, since an ounce is the same for everybody, everybody gets the same-sized piece. It's just a token mouthful to enjoy as part of the whole meal.
Laotzu was delighted to realize that the feastday meal is like the Jewish feast of Passover, in which there are prescribed things to be said and done by specific persons. As the honorary Chinese uncle he got to help the youngest arithmetician at the table square the skimtime, best done with a calculator although some would use an abacus. The precise figure for the planet's skimtime, which is remarkably similar to Earth's, is 15.45 minutes.
WHAT THE YOUNGEST RECKONER TELLS THE OTHERS
On the planet's feastday we remember that her gravity is what retains the air we breathe and keeps our seas from running away. This day we are mindful of the planet's mass and after dark go out to watch satellites sailing overhead. The skimtime here is 15.45 minutes, nearly the same as the old planet's, and it tells us the volume occupied by a talent of her mass. Squaring 15.45 and multiplying by 4 pi/3 gives 1000, which tells us that on average the volume occupied by each talent is a gallon.
The people on this planet say talent for the 48-pound unit of mass. And they say gallon for the thousand cubic fingerwidth volume which just happens to be a trillionth of a cubic mile. In conventional earth terms their gallon is roughly halfway between the present US and British gallons. A young reckoner is allowed to ask an older person for help with the squaring and can, if they wish, simply multiply by 4 instead of 4pi/3 since the effect is pretty much the same. This planet's density is one talent per gallon, slightly less but very close to that of Earth.
WHAT THE NEXT YOUNGEST RECKONER SAYS
At our planet's feast we remember that the speed of the fastest orbit circling her, the ground-skimming orbit, is 100 miles per minute. Escape velocity, which something needs to get free of the planet and take its own orbit around the sun, is always equal to the skimspeed times the square root of 2. Since the square root of 2 is 1.414, we know that our planet's escape speed is 141.4 miles per minute. This is how fast a person seeking full independence needs to go.
A person traveling at escape velocity has accumulated a kinetic energy which is equal to the energy binding them to the planet. An ounce of mass which is going 141.4 miles per minute has acquired energy of motion equal to its bond.
WHAT THE OLDEST RECKONS FOR THE OTHERS
Then the oldest person at the table who still likes working with numbers reckons the kinetic energy in one ounce traveling at escape velocity. This decides how much Freedom Cracker each person gets because it is the ransom energy needed by each ounce to break loose from the planet. An ounce is one thousandth of a talent—as a grown person you probably have several talents of mass and so contain several thousand ounces.
In accordance with the time-honored formula of the elders, the units of kinetic energy in an ounce equals the square of the miles per minute divided by 2000. The oldest at the table squares 141.4 to get 20 thousand and divides by 2000 to get 10. This shows everyone that the energy needed to liberate one ounce is 10 units. The oldest reckoner announces that each person's share of Freedom Cracker is 10 units (in conventional Earth terms we would say 50 Calories.) and then someone at the table breaks the bread.
LAOTZU BREAKS THE BREAD
If you had been a seven-year-old there at the time of Laotzu's visit then very likely your mass would have been 1000 ounces—typical for seven-year-olds—and your binding energy to the planet would have been a ten thousand units. Your share of Bread would have contained enough energy to free a thousandth of your mass, just a small token but something anyway.
That day they gave Laotzu, their guest, the job of breaking the Freedom Cracker into the necessary shares: each one containing just 10 units of energy. You could well have been the youngest reckoner that year, and he would have offered you the first piece.
Copyright © 2002 by Leonard Cottrell. All rights reserved.
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