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

roitman.io

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

#71

Post by ants_everywhere »

brians wrote: post #53
mistercow wrote: post #19

Earlier 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

I never thought of the cubit this way. It's an interesting idea, but the cubit is the length of a forearm, whereas you can reach around yourself in a circle the length of your extended arm, from finger tip to shoulder.

That would be somewhere between 1.5 to 2 cubits for people whose forearm is about a cubit long.

I think the cubit is mainly a measure of one winding of rope around your forearm. That way you can count the number of windings as you're taking rope from the spool. This is the natural way a lot of us wind up electrical cables, and I'm sure it was natural back in the day when builders didn't have access to precise cubit sticks.

I don't see the connection with the units and sound that you're making. But it is kind of interesting to know that sound travels about 3/4 of a forearm length per millisecond. That's something that's easy to estimate in a physical space.

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

#72

Post by KeplerBoy »

karmakurtisaani wrote: post #10
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.

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

It does not? Pi has nothing to do with our arbitrary unit system.

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

#73

Post by [deleted] »

fouronnes3 wrote: post #17
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 computer scientist this is not surprising either. After all there are only three numbers: 0 1 and n.

[deleted]

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

#74

Post by [deleted] »

phkahler wrote: post #69
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.

Doesn't the relationship hold if we change units? It seems like it must. When I worked with electric water pumps I loved that power can be easily calculates from electrical, mechanical, and fluid measurements in the same way if you use the right units. Volts Amps, torque rad/sec, pressure*flow_rate all give watts.

[deleted]

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

#75

Post by mistercow »

jncfhnb wrote: post #56
mistercow wrote: post #19

Earlier 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…

X^2 is a lot more interesting than x*0.0000743 or whatever it is

Ok, then by that thinking, you should find it really interesting that Earth escape velocity is almost exactly ϕ^4 miles per second.

In fact, adding exponents here objectively makes it less interesting, because it increases the search space for coincidences.

What makes the case in the post most interesting to me is that it looks at first glance like it must be a coincidence, and then it turns out not to be.

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

#76

Post by syockit »

Anarch157a wrote: post #43
pansa2 wrote: post #22

Earlier quoted context omitted.

Remember that `i` is also a number. As in `for i = 0 to n`. Don’t believe those mathematicians when they tell you that `i` is “imaginary”.

All numbers are imaginary. sqrt(-1) should have been called w, for "weird".

I use w for the complex roots of 1 though, when rewriting FFT notes.

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

#78

Post by eigenket »

phkahler wrote: post #69
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.

Doesn't the relationship hold if we change units? It seems like it must. When I worked with electric water pumps I loved that power can be easily calculates from electrical, mechanical, and fluid measurements in the same way if you use the right units. Volts Amps, torque rad/sec, pressure*flow_rate all give watts.

Nope, it completely vanishes in other units. If you do all your distance measurements in feet, for example, the value of pi is still about 3.14 but the acceleration due to gravity at the earth's surface is about 32 feet s^(-2). If you do your distance measurements in furlongs and your time measurements in hours then the acceleration due to gravity becomes about 630,000 furlongs per hour squared and pi (of course) doesn't change.

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

#79

Post by eigenket »

KeplerBoy wrote: post #72
karmakurtisaani wrote: post #10

Earlier quoted context omitted.

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

It does not? Pi has nothing to do with our arbitrary unit system.

pi is always just pi, but g may be defined in terms of the meter.

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

#80

Post by Maken »

otabdeveloper4 wrote: post #36
karmakurtisaani wrote: post #13

Earlier quoted context omitted.

A standard free measure for distance? Sounds dubious.

No. The other way around. Two seconds is the period of a pendulum with a length of two Sumerian cubits. (One meter is thus two Sumerian cubits, but that's an artifact due to us still using Sumerian time measurements.) P.S. I don't know why Sumerians used a factor of two. Americans still divide the day into two 12 hour spans, according to Sumerian fashion. P.P.S. One second is 1/(2*12*60*60) of a solar day. 12 and 60…

Probably because 12 is a much better base than 10. 12 can be divided by 2, 3, 4 and 6 and still results in whole numbers, which helps a lot when doing rounding and fraccional numbers. The only reason we use base 10 is because is much easier to count with our fingers.
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