Postscript 2 — Human-scale Planck Units

The Serious Units Fables are stories told in human-scale Planck measure. The basic units used in the fables are the talent mass, the mile distance, and the Planck minute.

The minute is defined as a 9/10 fraction of a conventional one. There are 1600 minutes in a day. The other two base units are determined by the values which fundamental physical constants take when expressed in terms of them. Additional units arise as combinations of the base units. In particular, one oc is the force required to give unit mass the unit acceleration---talent mile per square minute--- and the ocmile unit of energy is the amount delivered by a mile-long oc push.

The units are characterized by:

The speed of light c = E7 (ten million) miles a minute

Planck's h-bar = E-40 ocmile minute

Boltzmann'sk = E-25 ocmile per grade

One of many byproducts of the definitions is the ratio h-bar/k which appeared in the "French Thermometer" story is E-15 minute grade. This relates each temperature to the keynote frequency in the thermal glow at that temperature.

Another byproduct is that the gravitational constant G = 1.00E-15 (mile/minute)⁴/oc.

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:

mile: 1620 meters
pace: 1.62 meters
Planck minute: 9/10 of an ordinary minute
oc: 12 newtons (a force of about 2.7 pounds)
talent: 21.7 kilograms (a mass of 48 pounds)
grade: 141.45 kelvin
middle D frequency,100 thousand per minute: 18.5 [radians] per second.