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A wonderful coincidence or an expected connection: why π² ≈ g

roitman.io

11–20 of 352 posts

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#11
Awesome write up and a great surprise in the history of the definition of the meter.

Reading this reminds me a little of mathematicians like Ramanujan who spent a fair amount of time just playing around with random numbers and finding connections, although in this case, I imagine the author knew the history from the beginning.

Anyway, I feel like my math degree sort of killed some of that fun exploration of number relations — but I did like that kind of weird doodling / making connections as a kid. By the time I was done with the degree, I wanted to think about connections between much more abstract primitives I’d learned, but it seems to me there are still a lot of successful mathematicians that work this way — noticing some weird connection and then filling out theory as to why, which occasionally at least turns out to be really interesting.

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#14

As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)

As a physicist? When we did physics at school, and we were solving problems, the answer was always a number together with its unit. pi² might be 10 because it is a pure number, but g can never be 10, because it is an acceleration, a physical quantity, so it must be 10 of some unit.

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#15

This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.

Changing units in Electrodynamics for instance comes with unexpected factors in formulas though, indeed containing π. (CGS SI)

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#16

As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)

I assumed the pi / g connection was because cows that accelerate in a vacuum are spherical.

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#17

As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)

As a computer scientist this is not surprising either. After all there are only three numbers: 0 1 and n.

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#18

As a physicist, this makes sense. Pi = 3, pi^2 = 10, which is g Not sure why everyone is surprised. Ah, and a year is pi*10e9 seconds (IIRC)

As a computer scientist this is not surprising either. After all there are only three numbers: 0 1 and n.

You mean the legendary “i”. There is no n.

Re: A wonderful coincidence or an expected connection: why π² ≈ g

#19

This is interesting, but I have to quibble with this: > If you express this value in any other units, the magic immediately disappears. So, this is no coincidence Ordinarily, this would be extremely indicative of a coincidence. If you’re looking for a heuristic for non-coincidences, “sticks around when you change units” is the one you want. This is just an unusual case where that heuristic fails.

Actually no, the whole equation boils down to the definition of meter. Or rather, one of the earlier definitions.

Yeah, I read the post. What I’m saying is “this relationship vanishes when you change units, so it must not be a coincidence” is a bad way to check for non-coincidences in general.

For example, the speed of sound is almost exactly 3/4 cubits per millisecond. Why is it such a nice fraction? The magic disappears if you change units… (of course, I just spammed units at wolfram alpha until I found something mildly interesting).

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