211–220 of 352 posts
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Only because you're using metric seconds instead of "imperial seconds" (the time it takes for a 1 foot long pendulum to complete a full oscillation).
Sure, if you change either of the units you can always change the other one to fix the equation again.
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Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a m…
In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
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The equation holds in imperial units as well. The length of the 2 second pendulum needs to be in feet AND the value of g in ft/sec2.
π^2 ≈ 32 to you?
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No, the equality requires the length of a 2 second period pendulum be g / pi^2. Change your definition of length - that no longer holds true. g in imperial units is 32 after all. g has units; pi does not
A more natural way to say it is that equality requires that the unit of length is the length of an arbitrary pendulum and the unit of time is the half-period of the same pendulum. The pendulum is a device that relates pi to gravity.
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.
It’s really the best and only way to find non-coincidences involving the definition of units, though. All such non-coincidences will have this property
Earlier quoted context omitted.
Fun fact: pi is both the same, and not the same, in all of those places, too. Because geometry. If you consider pi to just be a convenient name for a fixed numerical constant based on a particular identity found in Euclidean space, then yes: by definition it's the same everywhere because pi is just an alias for a very specific number. And that sentence already tells us it's not really a "universal" constant: it's a m…
In non-euclidean spaces, your definition of pi wouldn't even be a value. It's not well defined because the ratio of circumference to diameter of a circle is dependent on the size of the circle and the curvature inside the circle. It's probably true that it's only well defined in euclidean space. Your relaxed definition, which I have never seen before, is not very useful.
1. Your parent was talking about projections from one space to another and getting it confused.
2. Pi is pi and their non-Euclidean pi is still pi (unless you want to argue that a circle drawn on the earth’s surface has a different value of pi).
The problem comes down to projections, then all bets are off.
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 don’t agree with this. You could literally redefine any unit (as we have done so multiple times in the past) and end up with zero coincidences. All measurement metrics are “fake” - nothing is truly universal, and can easily be correlated with another human made measure eg Pi.
There are just too many physical quantities we find significant, and too many ways to mix numbers together to make expressions that look notable.
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.
Not necessarily. One of the things I was taught when studying astronomy is that if you observe periodicity that is similar to a year or a day, that's probably not a coincidence, you probably failed to account for the earth's orbit or rotation.
The earths rotation coincides with the phenomenon, so it's likely a coincidence.
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Another bad way to check for non-coincidences is to use a value like g which changes depending on your location. Pi is the same everywhere in the universe. g on Earth: 9.8 m/s² g on Earth's moon: 1.62 m/s² g on Mars: 3.71 m/s² g on Jupiter: 24.79 m/s² g on Pluto: 0.62 m/s² g on the Sun: 274 m/s² (Jupiter's estimate for g is at the cloud tops, and the Sun's is for the photosphere, as neither body has a solid surface.)
My physics prof said g is actually a vector field. Because the acceleration has a direction and both magnitude and direction vary from point to point.
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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 incorre…