13 ms·
The fifth hyperfactorial: 5⁵×4⁴×3³×2²×1¹=86400000 milliseconds is exactly 1 day
- JoeAltmaier 8y agoWell, a civil day anyway. A solar day is 86400002
- jvolkman 8y agooff by 2
- mattdeboard 8y ago4 hard problems in computer science
- forinti 8y agoApparently, 86400000 was exact two centuries ago: https://www.theguardian.com/science/2016/dec/07/earths-day-lengthens-by-two-milliseconds-a-century-astronomers-find https://www.theguardian.com/science/2016/dec/07/earths-day-l...
- arthurcolle 8y agosigns of The Architect
- daveFNbuck 8y agoI assume you're referring to a god here. I'm curious as to why you think this has anything to do with a god. Did it manipulate us to choose highly divisible numbers for timekeeping? Or is it responsible for 24 * 60 * 60 * 1000 being equal to the fifth hyperfactorial? Is it evidence of The Architect every time two seemingly unrelated numbers are equal, or is there something about these two in particular that points to The Architect?
- arthurcolle 8y agoIt was a Matrix joke. Lighten up
- dlhavema 8y agowe're only 15 years past the release date of the 2nd movie... unless you go with XKCD's theory/view about the matrix - https://xkcd.com/566/ https://xkcd.com/566/
- gvx 8y agoNext year, that xkcd strip will have been published closer to the original release of The Matrix than to the current day. I can't believe I've been keeping up with xkcd for so long.
- andai 8y agoNo
- SketchySeaBeast 8y agoThe Architect was off in terms of the ACTUAL time it takes for the earth to rotate - 86,164,100 milliseconds. What a "stellar" mistake for numerical perfection. Did The Architect screw up the math?
- arthurcolle 8y agoIf I ever meet the referenced fictional character from the Matrix trilogy I'll be sure to ask.
- SketchySeaBeast 8y agoThere was never a Matrix trilogy, there was one very good movie and that was it.
- vignesh_m 8y agoOur "original" definition of seconds was in term of our earth's rotation so it is exactly OPs number. We just changed our definition to a more constant second that slightly varies from our old definition.
- SketchySeaBeast 8y agoBut "milli" implies the metric system's version of a second, which is defined as per the decay of a caesium-133 atom. I doubt very much The Architect wanted us to mix our units of measure, unless The Architect was referring to that window of time where "milli" existed, but we hadn't yet changed the second to a uniform length of time (as opposed to one that would be affected by the variable rotation of the earth). If so, we are already past His golden age.
- coldtea 8y agoErr, we created the "seconds in a day" metric, by picking the time span of seconds. The earth's rotation takes a constant K time. Whether the time is 86400000 seconds or 50 seconds or 642552 seconds, is based on whatever arbitrary value we pick to mean "a second".
- simonvc 8y agoIt was useful for sailors to be able to divide the day into shifts, so our day is the most divisible number of hours long. 1 x 2 x 3 x 4 That way you could have half days, quarter days, or third of days. An hour is divided into 60 minutes: 3 x 4 x 5 The word "second" means a "second division by 3 x 4 x 5"
- simulate 8y agoThanks for this! I loved this explanation and I had never heard that divisibility is the reason we have 24 hours in a day and 60 minutes in an hour. After reading your comment, I found this article in Scientific American that gave additional detail: https://www.scientificamerican.com/article/experts-time-division-days-hours-minutes/ https://www.scientificamerican.com/article/experts-time-divi...
- BuildTheRobots 8y agoI believe divisibility is also the reason we have 360-degrees in a circle.
- xamuel 8y agoAnd 12 inches in a foot, etc. Perhaps in centuries to come, the US will be vindicated for its metric system resistance :)
- gpvos 8y agoIt would have been nice if numbers had developed into a base-12 instead of a base-10 system. But it's even nicer that the number system (now 10-based) and the measurement system (now metric) are in sync.
- JdeBP 8y agoThey in fact did, many years ago. This is discussed elsewhere on this very page.
- test6554 8y agoThe fifth hyperfactorial: 5⁵×4⁴×3³×2²×1¹=86400000 milliseconds is exactly 24 hours. 24 hours is approximately 1 earth day.
- vertexFarm 8y agoIt would be very suspicious if our day was such an even number of milliseconds. It isn't, but still pretty cool! Things like this are what leap years are for, after all. Or does that count? Is that caused by a partial day in the revolution of the earth around the sun or a failure of a day to fit into exactly 24 hours? Or both? Are we talking solar or sidereal days?
- brlewis 8y agoLeap years account for a year not being exactly divisble into days. Leap seconds account for a day not being evenly divisible.
- bwbw223 8y agoHow so? Hours, minutes, seconds, and milliseconds are all man-made units. It’s the failure of 24 hours not fitting exactly into a day, not the inverse. Leap years have nothing to do with milliseconds in a day- it’s days that fail to fit into a year; days and years are defined by the orbit and rotation of the earth. Leap seconds, however, are another story...
- vertexFarm 8y agoI know they are man-made units, but I don't think the men who made the second could measure the length of a day and split it into 86,400,000 units accurately.
- jvkersch 8y agoHence, a very poor approximation to pi is given by 365 × 5⁵ × 4⁴ × 3³ × 2² × 1¹ / 10^10.
- OskarS 8y agoWhy would "the number of milliseconds in a year divided by 10 billion" have anything to do with pi?
- leetcrew 8y agono real reason. it's just that 86400000 / 10^2 ~= 0.01 and 365 is relatively close to pi shifted two places. there's no direct relationship between orbital period and length of day.
- Shadow6363 8y agoDon't think Hacker News notifies you of sibling comments, but there is actually a reason. See my answer at https://news.ycombinator.com/item?id=17084159 https://news.ycombinator.com/item?id=17084159
- efaref 8y agoIt's pure coincidence, but "pi seconds is a nanocentury" is a useful mnemonic.
- Shadow6363 8y agoDon't think Hacker News notifies you of sibling comments, but it's not actually pure coincidence. See my answer at https://news.ycombinator.com/item?id=17084159 https://news.ycombinator.com/item?id=17084159
- Shadow6363 8y agoI feel like I was just nerd sniped, but this drove me crazy until I thought about it for a bit. If we treat Earth's orbit as a perfect circle, then the number of milliseconds in a year would be its circumference. To get to pi then, we just need to divide that by its diameter or 2*its radius. In addition, we have the circumference in ms so we want to convert that into a distance or the radius into ms so we need the speed the Earth is rotating around the sun. The average radius of the Earth to the Sun is 149,600,000 km so the diameter is 299,200,000 km. Earth's average orbital speed is 30 km/s or 0.03 km/ms. Combining these two numbers to get ms, (299,200,000 km / 0.03 km/ms) = 9,973,333,333.333 ms, which is very nearly 10 billion.
- Aardwolf 8y agoIt is a pretty great coincidence, but there are things that helped improve the chances of this: 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. So if you multiply them all, you get exactly such a product. The only coincidence is how nicely the powers line up.
- Xophmeister 8y agoAn equally uninteresting coincidence is that 10! seconds is 6 weeks
- mxwsn 8y agoUnfortunately, the definition of one second as 9,192,631,770 energy transitions of the Cesium atom factorizes in a less pretty way: 2 x 3^2 x 5 x 7^2 x 47 x 44351
- adamnemecek 8y agoBabylonian 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. Bee tee dubs Babylonians were like way ahead of their time math-wise. They were aware of Fourier for example. https://en.wikipedia.org/wiki/Babylonian_mathematics https://en.wikipedia.org/wiki/Babylonian_mathematics
- shagie 8y ago60 is a preferred number for many card game decks as it works for 2, 3, 4, 5 And 6 players. 52 has difficulty with even deals for 3, 5, and 6 players.
- gr3yh47 8y agothis assumes the entire deck being dealt, which is really rare
- deleted 8y ago[deleted]
- bryanlarsen 8y agoBut is that rarity cause or effect?
- joliv 8y agoBridge, Hearts, Pinochle, Spades, BS/Cheat, and President off the top of my head all deal the full deck. The first four tend to be played only with 4 players because it's an even deal, which is too bad
- gowld 8y agoYou can throw away the As or Ks to get a lovely (2^4 * 3)-card deck.
- 8y ago
- aetherson 8y agoThis 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.
- drivers99 8y ago24 hr per day, 60 min per hour, 60 s per min, 1000 ms per s 24 : 2 3 4 60 : 3 4 5 60 : 3 4 5 1000 : 2 4 5 5 5 ------- count: 2 3 4 5
- m0skit0 8y agoA "real" day is 86164100 milliseconds (23h 56m 4.100s)
- rimliu 8y agoAnd what makes stellar day real, and mean solar day not real? Having day defined in terms of the star Earth is orbiting around has a benefit of having more or less consistent time for noon. Having a day defined in terms of the mean sun instead of the real one has a benefit of having noons at exactly 24h apart instead of variable inter between noons of the real sun (see https://en.wikipedia.org/wiki/Equation_of_time https://en.wikipedia.org/wiki/Equation_of_time).
- jschwartzi 8y agoI never understood this until now. Thank you.
- jonsen 8y ago... what makes stellar day real, ... ? It's not really real, just side-real.
- m0skit0 8y ago"Real" is not real.
- cdelsolar 8y agoA solar day is still not exactly 86,400 seconds long.
- 8y ago
- jiveturkey 8y agoyeah but as other comments explain, this isn’t some numeric “property” as such, giving insight into anything. It is by definition. Furthermore, a day is not even a day. We need leap seconds to sync up the solar day.
- oytis 8y agoIt'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.
- mywittyname 8y agoI was going to make a comment to this effect -- I think this is by design. This is a logical alternative to our metric system. We use powers of ten for increasing units because we operate in base-10. Older civilizations created larger units by multiplying a smaller unit by either an existing member of the set, or the next largest factor. So you end up with a sequence like 2, 6 (3x2), 12 (3x2x2), 60 (5x3x2x2), 360 (6x5x3x2x2), 2520 (7x360), etc. In effect, this is akin to saying a kilogram is 10^3 grams. It's novel to use because we were not taught to think that way. I bet a Babylonian would find this tweet to be kind of obvious.
- TheRealPomax 8y agoEhhhhh, 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. 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.
- vignesh_m 8y agoThat's basically because our definition of second is no longer based on the rotation of the earth. If it was it would be exactly that.
- deleted 8y ago[deleted]
- aaroninsf 8y agoFactoid: The reason the number 108 recurs in Hinduism and Buddhism is that as the third hyperfactorial it was esoteric knowledge discoverable by sacred geometers. (3³×2²×1¹ = 27×4×1 = 108)
- vignesh_m 8y agoLol. Its just because its a highly divisible number. Saying basic multiplication is "esoteric" shows how little you expect of ancient civilisations. They estimate the circumference of the fuckin earth and you say its "esoteric" to think 108 is holy.
- jobigoud 8y agoI would say that considering a number as "holy" is esotric by definition.
- brolover 8y ago10 factorial seconds is 42 days.
- ChuckMcM 8y agoAnd perhaps in our lifetime the next hyper factorial (6^6 * 5^5 * 4^4 * 3^3 * 2^2 * 1^1) will be a lifetime (127.8 years (approximately)
- logfromblammo 8y agoUtter coincidence, and it only works at all if you throw in the milliseconds term, which makes it seem forced. 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. 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 so many whole factors.
- gowld 8y agoPrevious discussion from last time the same OP made a tweet with the same content. https://news.ycombinator.com/item?id=15888591 https://news.ycombinator.com/item?id=15888591
- dmix 8y ago5 months for an exact repost by the same person getting a similar amount of upvotes/comments. That's a new one for me...
- DenisM 8y agoIn related news a (typical) year is 10^2 + 11^2 + 12^2 == 365 days. Also known as 13^2 + 14^2.
- mike_ivanov 8y ago> exactly Which day, specifically? https://en.wikipedia.org/wiki/Day_length_fluctuations https://en.wikipedia.org/wiki/Day_length_fluctuations
- sandov 8y agoIt would be impressive if days and seconds weren't defined arbitrarily.
- beagle3 8y agoAnd 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). 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
- vram22 8y agoSpeaking of factorials, this post I had written a few years ago may be of interest: Permutation facts: https://jugad2.blogspot.in/2016/10/by-vasudev-ram-nicomachus-theorem-3d.html https://jugad2.blogspot.in/2016/10/by-vasudev-ram-nicomachus... It mentions many kinds of factorials and other interesting types of numbers too.
- brlewis 8y agoDespite 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.
- partycoder 8y agoYou can divide a day in any arbitrary manner. This is just a coincidence.
- stretchwithme 8y agoSo is 5^5 * 4^4 * 3^3 * 2^2 * 1^1 * 0^0
- mbfg 8y agoalmost like the person who thought up time keeping, thought about how it would be most useful.
- aembleton 8y ago10! is the number of seconds in 7 weeks https://duckduckgo.com/?q=10!+-+(60*60*24*7*6)&t=canonical&ia=calculator https://duckduckgo.com/?q=10!+-+(60*60*24*7*6)&t=canonical&i...
- zimpenfish 8y ago6 weeks? Unless I'm radically misunderstanding that multiplication.
- aembleton 8y agoYes, 6 weeks. Not sure why I typed 7.
- juancn 8y agoAnd 10! seconds is exactly 6 weeks.