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

Post by BrandoElFollito » Sat, Aug 10, 2024, 4:37 PM UTC

radiator wrote: post #14

BrandoElFollito wrote: post #7

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.

Post by GuB-42 » Sat, Aug 10, 2024, 4:41 PM UTC

mistercow wrote: post #99

mikequinlan wrote: post #83

Earlier quoted context omitted.

Pi is related to the circumference of a circle; the meter was originally defined as a portion of the circumference of the Earth, which can be approximated as a circle. "The meter was originally defined as one ten-millionth of the distance between the North Pole and the equator, along a line that passes through Paris."

But that connection actually is a coincidence. From what I can tell, when they standardized the meter, they were specifically going for something close to half of a toise, which was the unit defined as two pendulum seconds. So they searched about for something that could be measured repeatably and land on something close to a power of ten multiple of their target unit. The relationship to a circle there doesn’t have…

Post by john-aj » Sat, Aug 10, 2024, 4:47 PM UTC

klabb3 wrote: post #134

jeffwass wrote: post #57

Earlier quoted context omitted.

One of my old physics professors said something similar - there are only three numbers in the world - 0, 1, and infinity. No wait, zero is just one divided by infinity, so there are only two numbers, zero and one. So if the answer is not zero, it must be one. (ie, how to justify dimensional analysis and ignore any dimensionaless constant). Hysterical, especially for the fact that he quotes 'two' and 'three' in the se…

Another one would be philosophy: there’s nothing, something and everything. Or logic: ∃, ¬∃ and ∀. Just rambling here, but seems like universal concepts across fields.

Post by mistercow » Sat, Aug 10, 2024, 4:53 PM UTC

GuB-42 wrote: post #143

mistercow wrote: post #99

Earlier quoted context omitted.

But that connection actually is a coincidence. From what I can tell, when they standardized the meter, they were specifically going for something close to half of a toise, which was the unit defined as two pendulum seconds. So they searched about for something that could be measured repeatably and land on something close to a power of ten multiple of their target unit. The relationship to a circle there doesn’t have…

Not a coincidence. They defined the meter from the second using the pendulum formula, and the pandulum formula has a pi in it, so pi is going to appear somewhere. The reason there is pi is probably because a pendulum is defined by its length and follows a circular motion that has the length as its radius. We could imagine removing pi from the pendulum equation, but that would mean putting it back elsewhere, which wou…

Post by mistercow » Sat, Aug 10, 2024, 4:55 PM UTC

john-aj wrote: post #142

mistercow wrote: post #5

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.

I agree. But if you remove the "so", there is no contradiction. It is possible the author used "so" not to mean "in other words", but simply as a relatively meaningless discourse marker.