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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 favor
by willis936 1y ago
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.
- gxs 1y agoOr 60 minutes in an hour 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60
- labcomputer 1y agoOr 5280 feet in a mile.
- ashirviskas 1y agoAnd one feet is 4 small foot toes and one big foot toe!
- ljm 1y agoAnd 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.
- thfuran 1y agoI 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.
- rich_sasha 1y ago1 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
- zveyaeyv3sfye 1y agoconverges
- speedgoose 1y agoIt wasn’t designed with British miles in mind. https://en.m.wikipedia.org/wiki/History_of_the_metre https://en.m.wikipedia.org/wiki/History_of_the_metre https://en.m.wikipedia.org/wiki/Arc_measurement_of_Delambre_and_M%C3%A9chain https://en.m.wikipedia.org/wiki/Arc_measurement_of_Delambre_...
- BobbyTables2 1y agoWonder why we don’t have 720 degrees… (6!)
- top_coder 1y agoMaybe because 360 is already divisible by 6, so 720 is not much of an upgrade over 5!. 7! On the other hand adds another prime factor to it.
- mjevans 1y ago7! 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.
- otabdeveloper4 1y ago360 is base 60. (6*60) Like minutes and seconds. The 12 hours in a day and the 12 months are also 60 / 5. This all connects to ancient Mesopotamia somehow.
- bregma 1y ago> 12 hours in a day I guess, for a sufficiently large value of 12.
- otabdeveloper4 1y agoYes, the original day was 12 hours. (Hence the legacy of "AM" and "PM" that some countries still use.)
- rich_sasha 1y ago> That's why there are 360 degrees. 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.
- jalk 1y agoI believe the 360 degrees is attributed to Babylonians, who were using the Sumerian base 60 number system (6*60=360)
- handsclean 1y agoTo elaborate a little, an advantage of this is there are many numbers it’s evenly divisible by. 60: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 100: 2, 4, 5, 10, 20, 25, 50 360: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180
- kps 1y ago60 and 360 are superior highly composite numbers¹. ¹ https://mathworld.wolfram.com/SuperiorHighlyCompositeNumber.html https://mathworld.wolfram.com/SuperiorHighlyCompositeNumber....
- AndrewOMartin 1y agoI 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".
- ralfd 1y ago> (i.e. the word pronounced my-newt) "minute" comes from latin "pars minuta" and the "i" should be pronounced like in "minimum" > By this logic, 0.016 (recurring) seconds should be a called a "third". It should be "tertia". I found that in German and Polish it was used that way, but don't know about english: https://de.wikipedia.org/wiki/Tertie_(Winkel) https://de.wikipedia.org/wiki/Tertie_(Winkel) https://pl.wikipedia.org/wiki/Tercja_k%C4%85towa https://pl.wikipedia.org/wiki/Tercja_k%C4%85towa
- almost 1y ago360 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.
- amelius 1y agoBut why wasn't the handcounting inherited too? It sounds useful to be able to count up until 60 on two hands.
- deleted 1y ago[deleted]
- vbezhenar 1y agoI'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.
- jodrellblank 1y ago> "(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 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").
- deleted 1y ago[deleted]
- DonHopkins 1y ago>...one gross eight dozen ten great gross ten gross three dozen five eleven gross eleven dozen eleven great gross eleven dozen eleventh's Now do PI! Then Tom Lehrer's New Math.
- nyeah 1y agoPlato is being annoying, and not for the first time. Sure, 7! has a lot of factors. But one person dies and you've got 5039. That's prime[1], so I guess your society breaks down? [1] https://prime-numbers.fandom.com/wiki/5,039#:~:text=5%2C039%20is%20a%20prime%20number,number%20between%205%2C001%20and%206%2C000. https://prime-numbers.fandom.com/wiki/5,039#:~:text=5%2C039%...