Plato argued that 7! was the ideal number of citizens in a city because it was a highly factorable number. Being able to cut numbers up is an time-tested favorite. That's why there are 360 degrees.
360 degrees in a circle predates Plato by quite a lot (2000 years I think!). It comes from the Summarians more than 4000 years ago. They used a method of counting on fingers that goes up to 12 on one hand and 60 using both hands, so their numbering system was based on 60. 360 is 6 * 60 and also roughly how many days in a year.
Later societies inherited that from them along with 60 minutes in and hour.
Not that these are exclusive, but I thought it's a rounding of 365.25 days a year stemming from Egypt. 360 is a pretty useful number of degrees for a starry sky that changes ince a night.
I just can't resist, pointing out that a "minute" is what you get when you split up an hour into 60 minute (i.e. the word pronounced my-newt) pieces, and a "second" is what you get if you break a minute into 60 pieces (i.e. you've performed the division a "second" time).
By this logic, 0.016 (recurring) seconds should be a called a "third".
I've always held opinion that ideal base for our day life computation is 12. It's close enough to 10, so most things would work just as well (like you just need to remember 2 more digits), but it's actually divisible by 3, 4, 6 which is a lot more useful than 5, compared to 10-base.
> "(like you just need to remember 2 more digits)"
"The standard among mathematicians for writing larger bases is to extend the Arabic numerals using the Latin alphabet, so ten is written with the letter A and eleven is written with the letter B. But actually doing it that way makes ten and eleven look like they're too separate from the rest of the digits so you can use an inverted two for ten and an inverted three for eleven. But those don't display in most fonts so you can approximate them with the letters T and E which also happen to be the first letters of the English words ten and eleven. But actually as long as we're okay for using the Latin alphabet characters for these digits then we might as well use X for ten like in Roman numerals. But actually now we're back to having them look too different from the other ten digits so how about instead we use the Greek letters Chi and Epsilon but actually if we're using Greek letters then there's no association between the X looking letter and the number ten, so maybe you can write ten with the Greek letter delta instead.
And all you really need to learn is those 'two new digits' and you're ready to use dozenal."
- Jan Misali in his comedy video on why base 6 is a better way to count than base 12 or base 10 https://www.youtube.com/watch?v=qID2B4MK7Y0 (which is a pisstake and ends up making the point that Base 10 isn't so bad).
("in dozenal, a seventh is written as 0.186X35 recurring because it's equal to one gross eight dozen ten great gross ten gross three dozen five eleven gross eleven dozen eleven great gross eleven dozen eleventh's").
Ideally you learn with what you are both with. It’s easy to have base 10 as you have ten fingers. If we only had 8 fingers we could have ended up with octal
Yeah, metric is cool and all, you can divide by ten and multiply by ten. But even better would be a hexadecimal system so that you could halve, third and quarter it. Plus it's n^2 so it's a perfect square \s
7! 5040 has the less than useful property of being quite large for interacting with human scales.
5! 120 however lacks fine precision required at human scale. Haven't done the math but it's probably something like using 3.1 as the analog of Pi.
360 seems like it might have been chosen based on a mix of precision and practicality. Many small prime factors ( 2 2 2 3 3 5 ). Also an extra prior prime factor for every added prime. 75600 too big, and 12 what analog clock faces use as their primary number.
And many of the conversions between metric and imperial align with the Fibonacci sequence on any order of magnitude. 130km/h is roughly 80mph simply because the fibo sequence has 8 and 13.
Obviously not an emergent property but shows how these things were designed.
I don’t think any common conversions fall near there other than miles->km. It’s certainly not the case that the systems were designed to have the golden ratio as conversions between the two.
1 mile = 1,000 [double] paces of 0.8m each = 1,600m
1m = 1e-10 times half-meridian from the North Pole to the equator, via Paris for a croissant, apparently.
So kind of a coincindence... But a very neat one. Meanwhile, ratio of adjacent Fibonacci numbers converves to some expression involving sqrt(5) which is approx 1.6
