It was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long.<p>1 x 2 x 3 x 4<p>That way you could have half days, quarter days, or third of days.<p>An hour is divided into 60 minutes: 3 x 4 x 5<p>The word "second" means a "second division by 3 x 4 x 5"
Babylonian number system was based on 60 (which is why we have 60 minutes in an hour and 360 degrees). 60 is dope because it has divisors 2,3,4,5,6,10,12,15,20,30 which is a lot of divisors.<p>Bee tee dubs Babylonians were like way ahead of their time math-wise. They were aware of Fourier for example.<p><a href="https://en.wikipedia.org/wiki/Babylonian_mathematics" rel="nofollow">https://en.wikipedia.org/wiki/Babylonian_mathematics</a>
Unfortunately, the definition of one second as 9,192,631,770 energy transitions of the Cesium atom factorizes in a less pretty way:<p>2 x 3^2 x 5 x 7^2 x 47 x 44351
Previous discussion from last time the same OP made a tweet with the same content.<p><a href="https://news.ycombinator.com/item?id=15888591" rel="nofollow">https://news.ycombinator.com/item?id=15888591</a>
It's not a pure coincidence. Coefficients used for time measurements (12, 24, 60) were deliberately chosen to have as many (small) integer divisors as possible.
Ehhhhh, sort of? But more: "surprisingly close to one day", because if you want to do correct time-keeping, a real day (or rather, a sidereal day, the time in which the earth makes one full rotation wrt "fixed" stars) is currently 86164090.7 milliseconds long.<p>You could also look at the solar day (the time it takes the earth to rotate such that the sun appears in the same place), in which case a day is actually a little longer than 86400000ms.
And a related mnemonic: The number of seconds per day, in modern programming language notation, is 864e2 (That's 8-6-4-2 with an 'e' inserted before the last digit).<p>I generally prefer to have a SECS_PER_DAY constant, or write (24 * 60 * 60) to make the value clear, but when code golfing, and as a mnemonic, I remember that SECS_PER_DAY=86400=864e2
It is a pretty great coincidence, but there are things that helped improve the chances of this:<p>Numeric bases are often chosen to have many divisors. The numeric bases 60, 12 and 10 are used in time, which have many 2's, 3's and 5's as divisors.<p>So if you multiply them all, you get exactly such a product. The only coincidence is how nicely the powers line up.
Utter coincidence, and it only works at all if you throw in the milliseconds term, which makes it seem forced.<p>A lot of our numbering systems are inherited from early mathematics that dealt mainly with ratios of low whole numbers. And so selecting bases with many prime factors made the rational math easier. When your base is 60, it's easier to divide by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.<p>You might as well divide up the mean solar day into 10! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 = 2^8 * 3^5 * 5^2 * 7 = 3628800 chunks, which are each 1/42nd of a second. Or maybe make the 7 represent the 7 days in a week, and use 518400 chunks per day, each 1/6th of a second. You could divide up your time by <i>so many</i> whole factors.
This isn't much of a coincidence. We have days, hours, and minutes that are designed to be divided into 3's, 4's and 5's, and then there are lots of factors of 10's in the fifth hyperfactorial, getting us down to milliseconds. It's fun that it happens to work out to the hyperfactorial, but if it didn't, it was always going to be just a couple of additional or fewer 2s, 3s, and 5s away.
Speaking of factorials, this post I had written a few years ago may be of interest:<p>Permutation facts:<p><a href="https://jugad2.blogspot.in/2016/10/by-vasudev-ram-nicomachus-theorem-3d.html" rel="nofollow">https://jugad2.blogspot.in/2016/10/by-vasudev-ram-nicomachus...</a><p>It mentions many kinds of factorials and other interesting types of numbers too.
10! is the number of seconds in 7 weeks<p><a href="https://duckduckgo.com/?q=10!+-+(60*60*24*7*6)&t=canonical&ia=calculator" rel="nofollow">https://duckduckgo.com/?q=10!+-+(60*60*24*7*6)&t=canonical&i...</a>
Despite being well aware that 60 was chosen to be evenly divisible by small numbers, I find it a really cool coincidence that the exponents fell into place so perfectly.
Factoid:<p>The reason the number 108 recurs in Hinduism and Buddhism is that as the third hyperfactorial it was esoteric knowledge discoverable by sacred geometers.<p>(3³×2²×1¹ = 27×4×1 = 108)
yeah but as other comments explain, this isn’t some numeric “property” as such, giving insight into anything. It is by definition.<p>Furthermore, a day is not even a day. We need leap seconds to sync up the solar day.