I laughed 3 times reading this article while pondering the novelty of standardization.
Is standardization the sans-serif of civilization?
A wonderful coincidence or an expected connection: why π² ≈ g
51–60 of 352 posts
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#52Sorry to ruin the party, but g is a quite random number, on other planets the corresponding acceleration is different. So π^2~g is a pure coincidence and not relevant. The Newtonian gravitational constant G is a real constant btw.
Have you read the article? The point is that the definition of the metre, which is used in g, originates from the length of a pendulum that swings once per second in the gravity field around Paris. So it is a matter of definitions, and the length of the metre originates from the duration of the second and the Earth's gravity field. The definitions of 1/40.000 of the Earth's circumference or ~1/300.000.000 of a light…
My intuitive assumption, then, is that on Mars they would have come up with a different meter such that π² ≈ 10 "mars meters" / s².
Or alternatively stated, that the Mars meter would be much shorter than Earth's meter if they used the same approach to defining it (pendulums and seconds).
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#53Earlier quoted context omitted.
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 intere…
Because the cubit is a measure of what a body can reach
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#54What an amazing post! Such an interesting investigation. These kinds of write-ups make me realize how truly far we are from AGI. Sure, it can write amazing code, poems, songs, but can it draw interesting conclusions from first principles? I asked both ChatGPT and Claude, the same question, and both failed at pointing out the connection the author states. This is not to deride feats of AI today, and I am sure it will…
> Sure, it can write amazing code, poems, songs, but can it draw interesting conclusions from first principles?
Can you?
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#55I've got a related one I like. Why are the Avogadro's number and Boltzmann's constant inverses of each other N ~ 1/k? The statement doesn't make sense because the units don't work out, but it is true in mks. It's because they multiply to the gas constant which is ~1. They both are numbers to transfer from the microscopic to human scale units and they cancel for the gas constant, which is about human scale experience…
But it's a coincidence, right? N*k=8.31 is pressure*volume/temperature for a mole of gas.
Temperature has a relatively small range (100-1000) and there's no reason why the range of P*V couldn't be far from that range, for example 0.01–0.1, with a different definition of meter, second or kilogram.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#56Earlier quoted context omitted.
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 intere…
X^2 is a lot more interesting than x*0.0000743 or whatever it is
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#57As 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.
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 sentence itself.
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#58No mention of ‘meter’ being the unit of measurement, make this like saying 3:14pm is related to pi.
There’s no correlation between a continuous number and a unit of measure. That’s truly apples to oranges comparison.
g can easily be expressed in ‘feet’ as ~32.1 ft/s^2
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#59Earlier quoted context omitted.
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 intere…
Because the cubit is a measure of what a body can reach
How does that explain the relationship to the speed of sound?
Re: A wonderful coincidence or an expected connection: why π² ≈ g
#60Very interesting! So if I understand correctly: the meter was defined using gravity and π as inputs (distance a pendulum travels in 1 cycle), so of course g and π would be connected.
On the hand, g is about 32.2 ft/s². So it's suddenly related to π³? I think there's no connection at all, it's just an accident. It would be really weird if some contemporary property of the earth were actually related to a fundamental mathematical constant. It's similar to finding a message among the digits of π that shouldn't be there, statistically speaking.
The bulk of the article is devoted to explaining that g = pi^2 in m/s^2 units (under an old definition of meter) because (that definition of) the meter was not selected arbitrarily, but selected in a way that makes the equation hold on purpose.