Postscript 2 — Human-scale Planck Units

The Planckian Fables are stories told in human-scale Planck measure. The units used in the fables are the ton of force and dime of speed, the minute, the pace, and the grade of temperature.

The minute in our system is just defined outright as a certain fraction of the conventional minute, namely 1/1.113 or, if you'd rather not see a decimal point in the denominator, 1000/1113. The rest of the units can be characterized by the values which some fundamental physical constants take on in terms of them. In particular TPM units are characterized by:

The speed of light (c) = 1 × 10¹⁰ pace per minute

Planck's constant (h-bar) = 1 × 10^-40 ton pace minute

Boltzmann's constant (k_B) = 1 × 10^-25 tonpace per grade

Since the minute has a definite size measured by the atomic clock, our adopted value for the speed of light determines the pace. Then, since the pace and minute are determined, our value for h-bar determines what the ton has to be. Then, since ton and pace are determined, and from them the tonpace unit of energy (equivalent to about 4.7 food Calories), our value for Boltzmann's constant determines what the temperature unit, the grade, must be.

One of many byproducts of the definitions is the keynote frequency/temperature ratio (k_B/h-bar) which appeared in the "French Thermometer" story. This ratio is easily calculated from values already given for Planck's constant and Boltzmann's constant. It is 1 × 10¹⁵ per minute per grade

Another byproduct is that the gravitational constant (G) = 1.000 (pace/minute)⁴/ton. It equals unity to the accuracy with which the constant is currently measured which is to about four decimal places.

In the later version of Apollo's invention of the lyre, some fundamental constants were given fanciful names such as Helix and Gê. Under whatever names, they are proportions deeply engrained in nature and operating at all times as a pervasive part of our experience. They are so basic to our lives that it makes sense, in my view, to give them simple power-of-ten values in our units. Human-scale Planck units are what results if one adjusts familiar-sized units so that the fundamental physical constants acquire values which are powers of ten.

To imagine the world and to reckon in terms of a set of quantities one does not always need to know their precise metric equivalents. For most purposes intuitive ideas of the units' sizes suffice. But to equip you with a pocket tool-kit for any possible encounter with the venerable metric system, here are some Planck sizes in metric terms:

pace: 1.616 meters
minute: 1000/1113 of an ordinary minute
ton: 12104 newtons (a force of about 2700 pounds)
grade: 141.7 kelvin
middle D frequency: 1855 [radians] per second, 100 thousand per minute.