Postscript 3 — The Auspiciousness of Miles

This postscript is about the auspiciousness not only of miles but of minutes, gallons, tons and ounces as well. But that would have made the title too long.

Think of the old Roman mile (mille passuum, a thousand paces) and the associations we have with it. It seems almost incredible that its modern descendant, our conventional statute mile (in metric, some 1609 meters), is actually within half a percent of the corresponding power-of-ten scale-up of Planck length, namely 1616 meters.

What an amazing coincidence! The thousand-pace mile is a good example of something in our language which we need to keep alive if we ever want our units to align well with nature's. No metric quantity comes anywhere near as close to being Planckian or natural. All we would need to do is tweak the statute mile from its present 1609 meters to a barely larger 1616 meters and we would have a power-of-ten scale-up of Planck length.

The two-step, five-foot Roman pace that once measured out the miles across Europe and the Mediterranean world was practically speaking equal to 10³⁵ Planck lengths. The half-foot dichas of the Greeks, which they thought of as the width of both palms side-by-side, was also surprisingly Planckian — essentially 10³⁴ Planck lengths.

The half-foot cube, so nearly a power-of-ten scale-up of the Planck volume, happens by another remarkable coincidence, to be gallon-sized. (At 4.2 liters, in metric terms, it's halfway between the US and the British gallons.) A gallon of water is roughly how much a Roman soldier could carry in his galeta, the common soldier's helmet, not that there was any linguistic connection. A gallon is roughly the size of a person's head, as you can see by inspecting gallon containers of milk and spring water at the supermarket. This half-foot cube volume has a long history — it has been found convenient. That the gallon should turn out to be Planckian as well is astonishing and makes this measure worth preserving and adapting.

The time-honored ton of force is remarkably close to being a power-of-ten scale-down of the Planck force. Likewise the quarter, which most recently was 25 pounds in the US and 28 pounds in Britain.

We would also do well to preserve and adapt the ounce as a measure of mass, with the new ounce being a million times Planck mass. Its metric equivalent would be 22 grams because the Planck mass itself is 22 micrograms (or more precisely 21.8.)

The traditional minute, again by a remarkable coincidence, is surprisingly close to the 10⁴⁵ multiple of Planck time. What may be the best arrangement is to make the Planck minute 1600 to a day and use it as an optional special-purpose time unit for problem-solving, while continuing to use ordinary time units in day-to-day life.

For me, the half-foot length which is a human-scale power-of-ten version of Planck length corresponds rather well either to the width of my palm with thumb extended or to the spread between the tips of my thumb and forefinger. I find myself using that manual span to measure things fairly often. Ten make a pace and tenthousand make a mile. A tenth of such a handspread is the width of my little finger at the knuckle. Almost without thinking about it I've begun using the natural units (adjusted by powers of ten) which were always there as functioning parts of the world.