10 ms·
The fifth hyperfactorial: 5⁵ × 4⁴ × 3³ × 2² × 1¹ milliseconds is exactly 1 day
- greenleafjacob 9y agoUnits of time are specifically chosen to have 5, 2, and 3 as factors. It doesn't look so pretty when you compare with universal fundamentals: > 1.000692286 milliseconds – time taken for light to travel 300 km in a vacuum
- gerdesj 9y ago60 is the really important number. It does happen to have rather a lot of convenient factors. Cheers Babylon. (I have checked the assertion and it is correct)
- ngcc_hk 9y agoFinally less hate if barbarian. Sorry Babylonian. 10 hour 10 second easier. A quarter pass 7. (Actual 12 is a human number of look from earth. Both chi-na and ... is it a copy.)
- stephengillie 9y agoIt's always bugged me there's no "metric time". 1 metric minute = 100 seconds = 1.667 Babylonian minutes 1 metric hour = 100 metric minutes = 166.7 Babylonian minutes = 2.78 Babylonian hours. 1 day = 8.61 metric hours = 1436 Babylonian minutes = 23.93 Babylonian hours. Thoughts?
- todd8 9y agoI've always thought that if we are redefining time units a better solution might be 100000 metric seconds in a day (making them a bit shorter than the existing 86400 in a day) and otherwise the same relationships you've suggested: 1 metric minute = 100 metric seconds 1 metric hour = 100 metric minutes 1 day = 10 metric hours.
- VMG 9y agoIf rather switch to a base-12 number system
- theoh 9y agohttps://en.wikipedia.org/wiki/Decimal_time https://en.wikipedia.org/wiki/Decimal_time
- collinmanderson 9y agoI believe they split up a circle into 360 degrees because it's close to the number of days in the year.
- TekMol 9y agoUnits of time are specifically chosen to have 5, 2, and 3 as factors. Why not 4?
- tehlike 9y ago4=2^2?
- greenleafjacob 9y agoI think that is fair as well. 60/4=15 but 30/4 is not a whole number.
- gerdesj 9y agoNo it isn't but a quarter of a half hour is still understandable and is seven and one half minutes which is 7' 30". The ancient Babylonian idea of using 60 (and 360 for angles) is absolute genius. If you think about it, it is a bit weird but makes so much sense working in base 60. We all do it all of the time.
- collinmanderson 9y agoI believe 360 for angles came from 365 days in a year.
- jacquesm 9y agoBecause you want prime factors.
- arnarbi 9y ago60 is indeed handy since it divides into 2, 3, 4, 5, and 6. 30 would be much less convenient. Better to drop the 5 (as evidenced by 12 and 24) I think the gp just generalized a bit to much. Units of time weren't chosen for those (prime) factors. People had simply figured out long time ago that a dozen is a nice round number.
- mkl 9y ago300km is the wrong number. Metres are defined based on the speed of light, and it's 299,792,458 m/s (not pretty!). This is for historical compatibility reasons, and without any goal of nice factors. It takes exactly 1 ms for light to travel 299.792458 km. Physicists often use "natural" units [1] where the speed of light is 1. [1] https://en.wikipedia.org/wiki/Natural_units https://en.wikipedia.org/wiki/Natural_units
- konschubert 9y agoThe speed of light in natural units is 1c. Usually people omit c because it's power can be inferred. And then they fail to mention to students that they're just omitting the c, causing a hilarious amount of confusion, half-truths and cargo-culting on the topic of natural units... ------ Saying that the speed of light in natural units is 1 is like saying that one meter in SI units is 1. (s, m, kg, 10) can be seen as basis vectors of a vector space. (Multiplication is "addition", power is "multiplication".) Another base of this vector space is (h, c, GeV, 10).
- mkl 9y agoTrue. We're talking about the prettiness and factors of the numerical values, and the terms in the original hyperfactorial don't have units at all.
- adrusi 9y agoThe speed of light has the dimension distance/time. Distance is a relative measure of space (length, height, depth), time is a measure of... time. When we talk about relativity, the distinction between space and time isn't very useful, so those are actually the same kind of measure. So distance/time is the same thing as distance/distance or time/time or 1. I suspect this is precisely the half truths and cargo cutting you're referring to. Maybe you could explain what the problem here is.
- konschubert 9y ago*its
- monochromatic 9y agoSlightly off topic, but my favorite units for c are feet per nanosecond. In those units c = 1 (plus or minus a couple of percent).
- 18nleung 9y agoThat's really interesting - only about 2% off. Conversion Here: https://www.wolframalpha.com/input/?i=speed+of+light+in+feet+per+nanosecond https://www.wolframalpha.com/input/?i=speed+of+light+in+feet...
- contravariant 9y agoIt's even closer if you use a 'metric foot' of exactly 30 cm. Then you're only off by 0.1%.
- monochromatic 9y ago> metric foot Why is that a thing?
- sixothree 9y agoMaybe because 30cm is very close to 12 inches.
- contravariant 9y agoNot sure, but most of those 'metricised' units are leftovers from Napoleon's push to make everything metric.
- letlambda 9y agoWhich leads to my favorite way to think about it. One foot per clock tick of a 1Ghz processor.
- stephengillie 9y agoDoes this mean circuits in a 1 GHz processor can't be longer than 12 inches?
- zokier 9y agoSpeed of light is by choice too; the numerical value is in no way "fundamental"
- Scooty 9y ago[5, 4, 3, 2, 1].map(n => Math.pow(n, n)).reduce((a, b) => a * b) === 1000 * 60 * 60 * 24 true
- gerdesj 9y agoBlimey, I just used a spreadsheet 8) I'm not sure what language you are using but it actually comes close to looking like a proper proof - all the inputs are on show and the construction is reasonably obvious. My spreadsheet is trivially correct as well but some of the working is not on obvious show unless you inspect the cells. Also, my spreadsheet is unavailable unless I share it. Nice one.
- warent 9y agoIt's JavaScript, ES2015
- gerdesj 9y agoThanks. Google ECMAScript to me is the odd thing I had to learn (I have a really odd accent when speaking it) to get Novell's DirXML working.
- Jach 9y agoBe careful accepting JS numerical proofs, since they're all doubles. e.g. > 12345678910111210 + 1 == 12345678910111211 true > 12345678910111210 + 1 == 12345678910111212 true
- Franciscouzo 9y agoMy favorite one is disproving Fermat's last theorem: > 19774**3 + 257049**3 == 257088**3 true
- thomastjeffery 9y ago> Be careful ... e.g. > two true statements What?
- deleted 9y ago[deleted]
- em3rgent0rdr 9y agoSo what? Coincidences occur all the time. Unless they expose a deeper hidden scientific/mathematical truth (which is not the case here), they aren't worth mentioning. Since the number of things that can be compared is astronomically huge (and increases every day), the chances of having coincidences is huge (and increases every day). The birthday paradox is an example of how common coincidences really are. Numerologists of centuries past wasted lots of intellectual potential by obsessing over simple coincidences.
- macawfish 9y agomaybe it's just cool?
- Froyoh 9y agoSome people are just party poopers.
- IanCal 9y agoNobody is claiming any amazing connection, it's just a fun little detail.
- gerdesj 9y agoYou are right this is a bit of whimsy. However it is not too obvious and I don't think it is fair to compare it with some of the dafter ideas that numerology has spat out in the past. Obviously our concept of time is based on 60 and 24 because there are loads of factors in those numbers which enables lots of convenient clock based shenanigans. However, is it obvious that the set of numbers {5,4,3,2,1} when raised to their own power and multiplied together is equal to the number of milli-seconds in one day? It is when it is pointed out. I doubt that there is any deeper meaning but it is simply a bit of fun. I recall that an Indian bloke who was close to death noted that the number of a taxi that some British mathematician took to get to the hospital was fleetingly interesting. If Ramanujan and Hardy can play silly games with numbers then why the hell can't us mere mortals.
- 9y ago
- danislu2 9y agoThis is the final and clinching proof of the non-existence of God. "The argument goes something like this: 'I refuse to prove that I exist,' says God, 'for proof denies faith, and without faith, I am nothing.' 'But, says Man, this is a dead giveaway, isn't it? It could not be chance. It proves you exist, and, by your own arguments, you don't. QED.' 'Oh dear,' says God, 'I hadn't thought of that,' and vanishes in a puff of logic. 'Oh, that was easy,' says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing
- akkat 9y ago> and without faith, I am nothing. Care to elaborate? I think virtually all religions believe that God existed before humans and therefore existed when no one had faith in God.
- knolan 9y agoIt’s from Douglas Adams’ Hitchhiker’s Guide to the Galaxy. From this and other similar works such as Terry Pratchett’s Small Gods or Neil Gaiman’s Ameeican Gods, deities pop into existence from the pure belief of people. It’s a great literary conceit.
- JorgeGT 9y agoAnd also a very old one; Man is certainly stark mad: he cannot make a worm, yet he will make gods by the dozen. Michel de Montaigne, 1533-1592. (Still, Small Gods is one of the best revisions of the topic!)
- akkat 9y agoBut that's what I don't understand. Either God 'A' who is believed by Religion 'X' exists or doesn't exist. If 'A' exists, then even if 'X' didn't believe in 'A', 'A' would still exist. (At least assuming that 'X' is a subset of all religions that I know) If 'A' doesn't exist then 'X' believing in it doesn't make 'A' exist anymore. I can't think of any religion where pure belief of people cause deities pop into existence. Unless of course you are calling the fact that people talk about the deity as popping them into existence. In that case, you can say that JK Rowling caused Voldemort to pop into existence (how evil of her).
- mavhc 9y ago(5 * 5 * 5 * 5 * 5) * (4 * 4 * 4 * 4) * (3 * 3 * 3) * (2 * 2) = (4 * 3 * 2) * (5 * 4 * 3) * (5 * 4 * 3) * ((5 * 5 * 4) * (5 * 2)) = 24 * 60 * 60 * 1000
- ngcc_hk 9y ago42 = 10! In one of the tweet there is another surprise.
- deleted 9y ago[deleted]
- GIFtheory 9y agoObligatory xkcd: https://xkcd.com/1047/ https://xkcd.com/1047/
- baddox 9y agoAlso, 10 factorial seconds is exactly 6 weeks.
- gerdesj 9y agoOK, so far we have a Javascript and possibly C based "proof". Could someone manage a Brain Fuck proof or perhaps ASM?
- jsjohnst 9y ago++++++++++[>+>+++>+++++++>++++++++++<<<<-]>>>--.>+++++++++++.<<++.>>++++++++++.----------.++++++.<<.>>---.-------------.----.+++++++++++..+++++++++++++.<<.>>-----.------------.+.+++++.---.<<.>>+++++++++.------------.+.++++++++++.<<.>>----------------.++++++++++++.--..--------.+++++++++.++++++.<<.>>-----.---------..-.+++++++++++++.-------------.-.<<.>>---.+++++++++++++.+++++++++++.<<.>>---.---------------------.+++++++++++.+++++++++.----------------.<-----.
- srtjstjsj 9y agoHaskell: > (product . map (Control.Monad.join (^)) $ [1..5]) == (1000 * 60 60 24) True
- abhisuri97 9y agoconst hyperFactorial = (n) => [...Array(n+1).keys()].map(Math.pow).reduce((a,b) => a * b)
- LearnerHerzog 9y agoIt is one day according to our clocks; it has no real significance in when compared to an actual day which is 23 hours 56 minutes 4 seconds- the time it takes the earth to make one full rotation.
- toth 9y agoLeap year rules have to do with the actual length of the year being 365.24219 days - not with days not being 24 hours.
- zokier 9y agoThe difference between solar day (about 24h+-30s) and sidereal day (about 23h56min) has nothing to do with leap years
- teilo 9y agoCome again? If that were true, then the clock would advance past the actual time of day 2 hour for every month (30.5 days to be precise). And that would mean that in 6 months, midnight would be at high noon. So...
- hodgesrm 9y agoIndeed. But the earth is simultaneously orbiting about the Sun, which changes the apparent length of a day by approximately 3.95 minutes. (I.e., approximately 24 * 60 / 365 minutes).
- deleted 9y ago[deleted]
- teilo 9y agoRight. A sidereal day. Sorry. His point flew right over my head. I see it now.
- zokier 9y agoDo you think "actual" years also have 366 days?
- MPSimmons 9y agoThis is only true if you have no idea of how many milliseconds are in a day. On the other hand, it IS very close to a day, which is neat. But it's not exactly a day. Within a few miliseconds, days drift quite a bit because of shifts in the center of gravity and the moment of inertia. The Three Gorges Dam and the Boxing Day quake both measurably changed the rate of the Earth's spin.
- hanbura 9y agoIt is exactly the length of a civil day in TAI (International Atomic Time). It also happens to match almost all civil days in UTC-derived timezones (with the exception of leap seconds, daylight savings, and timezones switching to a different UTC offset) It doesn't match solar days, but most people don't actually use solar days.
- didhshz 9y agog in SI units is very close to pi^2. And the weird thing is that it almost is not a coincidence! The meter was almost defined as a second pendulum (implying pi^2 is exactly g) but then the variability in g was considered to impractical. So then they choose the first meter definition (1/4 circ. if the earth)... which is suspiciously close to what they wanted to define the meter with in the first place
- danjoc 9y agoOff by one https://www.timeanddate.com/time/earth-rotation.html https://www.timeanddate.com/time/earth-rotation.html
- deleted 9y ago[deleted]
- beagle3 9y agoAnother neat trick: the number of seconds in a day is 864e2 (easier to remember than 86400 for me)
- juancn 9y agoAlso 10! seconds is exactly six weeks.