Comment by jds-67
1 year ago
Sorry 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 second came later.
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).
A Martian meter defined by martians should relate their average size, the number of fingers they have on their hands and some basic measure of the planet.
I mean, one meter is defined as 1/10^7 of the distance between the equator and the poles which leads to a round number in base 10.
A unit system is not just something that matches objective reality but something that has some cognitive ergonomy.
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I have to admit I only read half of the article. Even if there is some historical fact there (but it was not mentioned at the beginning of the article), from a physical standpoint this comparison is already dimensionally wrong and also coincidentally only correct if you choose appropriate units. That was the point I was trying to make. There is not anything "deep" here.
How strange.
"I only ran the first half of the program, but it didn't seem to give the correct answer, so it's obviously broken."
"I only read the first half of the proof, but the answer wasn't contained there, so I'm forced to conclude the proof is worthless."
You simply gave up before encountering the mathematical reason the relationship exists, why the units are different, and so on. You just ran with your incorrect initial assumption.
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I admit I scanned the article first and wondered what it was all about. The actual argument is not very clearly presented.
I’d suggest fully reading the article.
It's not about the values, but the units of measurement. g is in units of meter/second^2. The article discusses the dependency of the meter's original definition on the value of pi.
You are correct but the point is the way the meter is calculated, g in meters per second should come to pi squared.