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Comment by gerdesj | Hacker News Reader

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.

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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.

Please don’t steal my bank cards.

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

1728 = 12^3

That's not whimsical and silly?

I don’t think so. I think it’s quite interesting! Especially trying to understand Ramanujan’s thought process that produced this insight!

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.

It's just a bit of fun. Just like this: https://en.wikipedia.org/wiki/1729_(number)

You are a clever person and I'm not daft either. We can have a laugh over how some numbers do silly things.

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