This was a very fun and enlightening 10 minute video by Numberphile. 58 and other Confusing Numbers He doesn't get to the Klingons until the very end but the whole thing was incredibly interesting. There's a whole lot of 'who knew' crammed into the 10 minutes. Who knew number systems based on counting on your ten fingers wasn't the norm in every society.
The Sumerian/Babylonian number system was base 60 - hence why we have 60 seconds in an minute and 360 degrees in a circle and so on. https://en.wikipedia.org/wiki/Babylonian_cuneiform_numerals
Someone on another forum noted that meant things like numbers on a clock could be divided without needing fractions. Ot it was the result.
I love thinking through things like this. For one sci-fi setting I got halfway through developing, I was thinking of an alien race colonizing planets using sub-lightspeed ships. Since they wanted to keep in touch with their colonists but knew that they would need to communicate with them thousands of years in the future, and after colonizing planets they couldn't know anything about in advance--what if after all that time or on a very alien planet, their descendants developed new systems of measurement that they wouldn't know how to convert? I figured they might come up with measurement systems based on universal constants rather than whatever customary system had developed on their homeworld. I thought the hydrogen line (or some fraction or multiple thereof) might be a good base unit of length for a roughly human-sized species. For a species with roughly human metabolism/cognitive speed, maybe the base unit of time could be in terms of the rotational period of some widely-visible pulsar. And so on.
Some tribes use base 12, and count using the knuckles instead of the fingers. Actually, most computer science people, at least the ones who work at low level, have learned to think and do basic math in base 16. It's very useful when a large amount of your operations involve some power of 2. It's also the most efficient way to look at raw memory, binary is too much data, converting it to decimal wouldn't let you see the bit data, but hexadecimal is perfect. An 8 bit byte has exactly FF unique states. That's migrated into my everyday life, when I number things I tend to go 1 2 3 4 5 6 7 8 9 a b c d e f 10....
@Naomasa298 mentions 60, it’s a lovely number that easily breaks up into even parts and can be used in all sorts of ways. The wikipage gives a great breakdown. Its very efficient without the need for fractions after several divides or multiplications most done in the head. The number zero came along much later on... Research Carl Sagan and CONTACT. He helped design the Gold discs on the Voyager Probes and other signals sent into space. How to get an Alien civilization to understand your message. Using Hydrogen as key like @Robert Musil said works. Just as long as what divisor you have works for you. Don’t have an answer but let us know how you get on... MartinM
That's not quite correct. An 8 bit byte actually has &100 (256) unique states. FF is 255, and doesn't include 0.
The big takeaway from that for me, the part I remember most, is that the first video transmission from Earth powerful enough to reach the distant stars was a Nazi rally. Nice 1st impression we make, eh? Just think, it's still expanding outward, reaching new star systems all the time. Tune in folks, just wait till you see Jerry Springer and Real Housewives!! I wouldn't blame 'em if they just nuke the site from orbit.
They'll watch Star Trek and eagerly await our noble explorers. Then we arrive and nuke THEM from orbit. Galaxy Quest, we ain't.
It seems likely that 360 was chosen because it's close to the number of days in a year. Perhaps 60 came about as a nice factor of 360, along with being highly factorizable itself. So we see number systems chosen because of the quirks of where we find ourselves: the days in our years, the digits on our hands, or possibly the number of knuckles. I suspect that aliens might choose their number systems in similar ways. Seven tentacles? Base seven will do. 450 days in a year? Base 50.
How about base 7 for the number of music notes? Pronouncing the numbers would be as simple as humming the notes. a, b, c, d, e, f, g, aa, ab . . . a = 1 aa = 7 aaa = 21 aaaa = 147 It would resist the brain's natural (natural?) urge to place music notes to a tune. Also, there's no "direction" in this system. One writes a "wheel of numbers," (all of which look the same from all angles) and the biggest numbers are read first. This would be represented in speaking. If I wanted to say "I am 22 years old," I would say a loud "a" note, a quieter "a" note, and a quieter still "b" note--in any order.
So aliens could in theory use the music scale for numeric countings? Hmm...Then I suppose they would do well to carry a synth and , us to know the notes. Take me to your bizaar, I have business to broker.
In the Conrad Stargard series (a riff on A Connecticut Yankee in King Arthur's Court) the MC goes back in time to Dark Ages Poland. No idea how historically based it was, but the noble there scoffs at using base 10 because it doesn't divide up neatly. Two groups of five, or five of two, and you're out. Base 12 however has two groups of six, six of two, four of three, and three of four. Much more variety in divvying things.