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greenleafjacob
Units 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
60 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
Finally 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
It'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
I'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
If rather switch to a base-12 number system
collinmanderson
I believe they split up a circle into 360 degrees because it's close to the number of days in the year.
TekMol
Units of time are specifically chosen to have 5, 2, and 3 as factors.

Why not 4?

greenleafjacob
I think that is fair as well. 60/4=15 but 30/4 is not a whole number.
gerdesj
No 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.

jacquesm
Because you want prime factors.
arnarbi
60 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
300km 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

konschubert
The 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
True. 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
The 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.

monochromatic
Slightly off topic, but my favorite units for c are feet per nanosecond. In those units c = 1 (plus or minus a couple of percent).
contravariant
It's even closer if you use a 'metric foot' of exactly 30 cm. Then you're only off by 0.1%.
monochromatic
> metric foot

Why is that a thing?

sixothree
Maybe because 30cm is very close to 12 inches.
contravariant
Not sure, but most of those 'metricised' units are leftovers from Napoleon's push to make everything metric.
letlambda
Which leads to my favorite way to think about it. One foot per clock tick of a 1Ghz processor.
stephengillie
Does this mean circuits in a 1 GHz processor can't be longer than 12 inches?
jeffwass
I always like the fact that there are π seconds in a nanocentury (within half a percent)
Cerium
Mine are gigahertz * inches. 11.8ghz * in is the speed of light. Gives you a feel for it and is practical. Want to find an antenna length? Ghz*inches are your friend.
boyce
That is great, never heard that one. Thanks
zokier
Speed of light is by choice too; the numerical value is in no way "fundamental"
Scooty
[5, 4, 3, 2, 1].map(n => Math.pow(n, n)).reduce((a, b) => a * b) === 1000 * 60 * 60 * 24

true

gerdesj
Blimey, 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
It's JavaScript, ES2015
gerdesj
Thanks. 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
Be careful accepting JS numerical proofs, since they're all doubles. e.g.

    > 12345678910111210 + 1 == 12345678910111211
    true
    > 12345678910111210 + 1 == 12345678910111212
    true
Franciscouzo
My favorite one is disproving Fermat's last theorem:

    > 19774**3 + 257049**3 == 257088**3
    true
thomastjeffery
> Be careful ... e.g.

> two true statements

What?

mvkg
The two 'true' statements show that 12345678910111211 == 12345678910111212 transitively, which is obviously not possible.
sedro
Look closely. Or, equivalently

  > n=12345678910111210
  > n+1 === n+2
  true
progval
Shorter version (which actually checks for 0⁰ × 1¹ × 2² × 3³ × 4⁴ × 5⁵):

> [0, 1, 2, 3, 4, 5].map(Math.pow).reduce((a, b) => a * b) === 1000 * 60 * 60 * 24

true

vortico 

  a=1;for(i=1;i<=5;i++)a*=Math.pow(i,i);a === 1000 * 60 * 60 * 24

  a=1;i=1;while(i++<5)a*=Math.pow(i,i);a === 1000 * 60 * 60 * 24
TekMol
Even shorter version that simply does the calculation from the title of this post:

    5**5*4**4*3**3*2**2*1**1===24*60*60*1000
    
    true
vortico
Nice ES7. But if we're not constrained by leaving 5 as a "general" number, then

  864e5 === 24 * 60 * 60 * 1000
mkl
This skips the power calculation, which is the entire point!
warent
If we remove some of the cruft on the righthand side, we can save a few bytes:

  864e5;
irth
1 (because it's a bool anyway)
vortico
!0 if we actually want the exact value `true` :)
atonalfreerider
A better title: The fifth hyperfactorial: 5⁵ × 4⁴ × 3³ × 2² × 1¹ milliseconds is exactly 24 hours.

A sidereal day is not exactly 24 hours, it is closer to 23 hours 56 minutes and 4.1 seconds.

hanbura
The word day is ambiguous, but calling it 24 hours is not perfect either. A 24 hour period can include leap seconds, meaning it can be one second longer or shorter than 24 * 60 * 60 seconds.

(At least that's how ISO8601 defines time periods: 11pm-12am is a one hour period even if leap seconds cause the last minute to have 59 or 61 seconds)

goodcanadian
When people talk about a day, they are usually thinking more of a solar day than a sidereal day. A solar day varies, but on average it is about 24 hours. That is after all how hours were originally defined.
bouvin
I've always found it odd that English, which otherwise is fairly rich vocabulary-wise, does not have a specific word for this. In Danish, we have 'dag' (day), 'nat' (night), and 'døgn' (a day and a night). A 'døgn' contains all the leap seconds that may be necessary.
hughdbrown
I thought it was ruby at first.

(1..5).map{|n| n n}.reduce(:) == 24 60 * 60 * 1000

godd2
Looks like you need to indent that code

  (1..5).map{|n| n**n}.reduce(:*) == 24 * 60 * 60 * 1000
Or if we're golfing

  (1..5).reduce{|t,n|t*n**n}
[dead] yaccz 

  (foldl (*) 1 $ map (\x -> x**x) [0..5]) == 3600*24*1000
  True
18nleung
Looks nice in Haskell too.

  product (map (\n -> n ^ n) [1..5]) == 1000 * 60 * 60 * 24
  => True
oerpli
I recommend looking at . and $ to make code more readable (by preventing unnecessary brackets)

    product $ map (\x -> x^x) [1..5]

    (.) :: (b -> c) -> (a -> b) -> a -> c
    ($) :: (a -> b) -> a -> b
=>

    f (g (h x)) == f . g . h $ 5
jonahx
Bow before J:

    (*/ 1000 60 60 24) = */ ^~ 1 2 3 4 5

1
bakul
K:

      (24*60*60*1000)=*/x^x:!6
    1
No stinking whitespace :-)
jonahx
That's preference. Can you say the same for that hideous variable name? :P
bakul
The following works too!

    (24*60*60*1000)=*/(!6)^!6
so does

    (24*60*60*1000)=1{x*y^y}/!6
but now you have two hideous parameters!
arpankapoor
q:

    (24*60*60*1000)=prd xexp[x;x]til 6
    1b
Slightly more readable :P
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em3rgent0rdr
So 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
maybe it's just cool?
Froyoh
Some people are just party poopers.
IanCal
Nobody is claiming any amazing connection, it's just a fun little detail.
gerdesj
You 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.

ajross
Those are the same criteria though. Any product of a bunch of timekeeping numbers is, because of all the small integer factors (which are there by design!) going to be a product of a bunch of small integers! Now, it's sort of a coincidence that there are exactly five 5's, 4 4's, etc... But that's not that big a search space in the first place.
falsedan
Ramanujan’s observation about 1729 is actually quite interesting and not at all whimsical or silly. It was that is is the smallest number expressible as the sum of two cubes in two different ways:

  1^3 + 12^3
  10^3 + 9^3
Ramanujan probably derived this on the spot (by familiarity with the low cubic powers, and eliminating all the other sums of the low cubics [(n-2)^3 + (n-1)^3 only exceeds n^3 for n>7]). But he may have already been familiar with this property, since it was first found by Frenicle (along with 4 other, higher numbers expressible as such a pair of sums of cubes) as a solution to a challenge put forth by Euler.
falsedan
Please don’t steal my bank cards.
DonbunEf7
Ramanujan may have been aware of 1728 == 12² because of 12's recurrence within number theory. (Well, really, 24's recurrence. [1]) He wrote down several equations [2] which feature 12 and 24, and given the time in which he lived, he may have been acquainted with the work of Felix Klein and others [3] as well.

The other sum is 1000 + 729, much easier for a decimal-preferring mentat like Ramanujan to pull from thin air.

[1] http://math.ucr.edu/home/baez/numbers/

[2] https://en.wikipedia.org/wiki/Mock_modular_form

[3] https://en.wikipedia.org/wiki/J-invariant

srtjstjsj
That's not whimsical and silly?
falsedan
I don’t think so. I think it’s quite interesting! Especially trying to understand Ramanujan’s thought process that produced this insight!
PhasmaFelis
Nobody's obsessing wastefully. It's just interesting to people who find numbers interesting. Stop being such a grinch.
zokier
But this is not purely a coincidence; what it demonstrates is that our timekeeping leans heavily on the 5-3-2 prime factors, which is, while not very deeply hidden, a meaningful insight.
em3rgent0rdr
Still is a coincidence. If the original post emphasized this fact of reliance on 5-3-2 prime factors, then the post would have been only a bit more interesting. But even had the original post simply been "Our timekeeping leans heavily on 5-3-2 factors", that still isn't terribly impressive.

Little point in hacker news users upvoting every little such coincidence. There's a large number of similar trivial coincidences if one bothered to look.

packetslave
Says the guy who submitted a link to "Duck Penises Grow Bigger Among Rivals"
gbraad
Coincidences happen all the time ;-)
em3rgent0rdr
That was a scientific article, which was quite insightful to how evolution works...in summary:

Flightless birds can carry around the extra weight, so grow big penises to impress mates, while flying birds can't afford the weight and so must result to colorful feathers to impress mates.

thomastjeffery
> Numerologists of centuries past wasted lots of intellectual potential by obsessing over simple coincidences.

Do you seriously believe that "intellectual potential" is tied so closely to time or specific efforts?

These exercises may not be useful on their own, but as exercises, they are useful to [s]he who exercises.

danislu2
This 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
> 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
It’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
And 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
But 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).

knolan
Well yes, if you assume that gods are real and reveal themselves to the world they created. Then you go down he dreary path of prime motivators etc. That’s no fun.

If on the other hand you start with the premise that there is a magical world created somehow then lesser gods can exist and cease to exist for all manner of reasons. We can apply it to the real world in the context of cultural memes. J.K. Rowling didn’t cause Voldemort to pop into existence, the fans of the books and those who got hysterical over depictions of witchcraft did.

gerdesj
Well there's a thing.

You are of course correct but for a decent discussion of the issues around religion, I'll direct you to "Small Gods" by Sir Terry Pratchett. I don't think it is considered a classic by fans but for me I think it is close to being one of the great critiques about religion. If nothing else it is a damn good page turner.

Yetanfou
You forgot the attribution: Douglas Adams, "The hitchhikers guide to the galaxy" series.
mavhc
(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
42 = 10! In one of the tweet there is another surprise.
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baddox
Also, 10 factorial seconds is exactly 6 weeks.
gerdesj
OK, so far we have a Javascript and possibly C based "proof".

Could someone manage a Brain Fuck proof or perhaps ASM?

jsjohnst
++++++++++[>+>+++>+++++++>++++++++++<<<<-]>>>--.>+++++++++++.<<++.>>++++++++++.----------.++++++.<<.>>---.-------------.----.+++++++++++..+++++++++++++.<<.>>-----.------------.+.+++++.---.<<.>>+++++++++.------------.+.++++++++++.<<.>>----------------.++++++++++++.--..--------.+++++++++.++++++.<<.>>-----.---------..-.+++++++++++++.-------------.-.<<.>>---.+++++++++++++.+++++++++++.<<.>>---.---------------------.+++++++++++.+++++++++.----------------.<-----.
srtjstjsj
Haskell:

> (product . map (Control.Monad.join (^)) $ [1..5]) == (1000 * 60 60 24) True

abhisuri97
const hyperFactorial = (n) => [...Array(n+1).keys()].map(Math.pow).reduce((a,b) => a * b)
LearnerHerzog
It 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
Leap year rules have to do with the actual length of the year being 365.24219 days - not with days not being 24 hours.
zokier
The difference between solar day (about 24h+-30s) and sidereal day (about 23h56min) has nothing to do with leap years
teilo
Come 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
Indeed. 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).
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teilo
Right. A sidereal day. Sorry. His point flew right over my head. I see it now.
zokier
Do you think "actual" years also have 366 days?
MPSimmons
This 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
It 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
g 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

srtjstjsj
1/40,000
wcoenen
Still off by a factor 1000. That's the kilometer.
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beagle3
Another neat trick: the number of seconds in a day is 864e2 (easier to remember than 86400 for me)
juancn
Also 10! seconds is exactly six weeks.