A measure of a civilisation

On this 40th anniversary of the lunar landings, I was thinking about how we compare civilisations. A bit dull I know, but it passes the time. I think a fairly good measure is their physical size versus their sphere of exploration. The distinction is important. The ancient Roman Empire was the same approximate physical size as the United States, but the sphere of exploration of the Roman Empire didn’t extend much beyond their borders. By contrast the sphere of exploration of the USA can be taken as far as the lunar orbit.

Physical size would be a measure of that civilisation’s political or military might – its either been strong enough to expand of enlightened enough to form a political block – where as sphere of exploration is a measure of the civilisation’s technological and scientific ability. One could even split the sphere of exploration into that physically explored (humans have gone to the Moon) and that which they have direct, reasonably accurate information about (we’ve sent unmanned probes to the edge of the solar system).

I’d like to use a metric for these measures. We could use simple distance, but the numbers get very large, very quickly. I also want to avoid negative numbers, to start with a single person, and to have all real and fantasy civilisations/powers on a single scale. What I came up with was C = 1 + ( log₁₀(R) / 3 ) were R is the radius in km of the sphere in question. This normalises to the size of a person because an adult is about 2m tall, the radius is half of that (R=0.001 km), so C=0.0.

Your typical subsistence level European villager in a pre-industrial society could probably (just about) have found everything they need within a one kilometer of home, which is C=1. A modern nation or state (California, France, etc) is about 1,000 miles across, which gives a C-=2. Then next milestone after that is C=3.0 which is equivalent to the exploration of the Moon. I’ve summarised a few other milestones in the following table.

AU is astronomical unit – 1 AU equals the average Earth-Sun separation. LY is a light year – the distance light travels in 365 days, then MLY is millions of light-years and BLY is billions of lightyears.

We can express a civilisation as its physical size and its sphere of exploration using the values of C. Using our example of the present day USA, its size is continental (2.1), but its sphere of exploration is lunar (2.9) so C = 2.1/2.9. Contrast that to an 18th century European power (1.9) that has explored the world (2.3), C=1.9/2.3. So global powers are generally going to be two point something where as medieval or even fantasy regional powers are generally going to be one point something.

Star Trek’s Federation is fairly typical of a big science-fiction galactic-power – they take up a not insignificant part of a Quadrant (a quarter) of the Galaxy and have explored as far as the other side of the Galaxy (ST Voyager or the Ds9 wormhole). They’re probably equivalent to the DC Comics’s Dominion, Khunds, or other major interstellar powers. These fellows are going to have C=6.6/6.9.

Compare with the Kryptonians who, at their height, had some sort of interstellar empire (we don’t know exactly how big), but appear to have explored the local group of galaxies (Jor-El’s monology to Kal-El in Superman: The Movie) so they would have C=6.6/7.5.

There are some interesting contrasts that open up with isolationist cosmic powers. For example the Guardians of the Universe obviously have explored the Universe, but they’re actual home is only a single planet (Oa). They’d have C=2.3/8.9. The Star Wars Republic is a civilisation than spans a galaxy, but its also one that doesn’t seem to have explored much beyond the edges of their own civilsation. They’d have C=6.9/6.9 or at the every least 6.8/6.9.

The usefulness may not be in the decimal points, but the short hand of rounding C up to the next integer to given a civilisation level is certainly useful. A level 1 civilisation is a village, a level 4 civilisation is an interplanetary one, and a level 10 civilisation is one than spans parallel universes.