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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

#43

Post by Anarch157a »

pansa2 wrote: post #22
fouronnes3 wrote: post #17

Earlier quoted context omitted.

As a computer scientist this is not surprising either. After all there are only three numbers: 0 1 and n.

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".

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

#45

Post by IHLayman »

ahmedfromtunis wrote: post #33

[flagged]

I disagree… the article talks about defining the meter using the pendulum and the second. Other planets would have their own definition of second, but not their own definition of pendulum. Since one meter is prescribed though a pendulum because of the oscillation formula and dependent on the frequency alone (in this case, 2 seconds), no matter what planet you are on, how strong gravity, is or how long a second is, the pendulum describes a relationship between seconds and meters such that if using this method a planet’s scientists would always define their units such that acceleration of gravity was eerily equal to pi^2.

Makes me think of possible lunar scientists unwittingly making their meter 5/6th shorter(edit: english is hard) and then marveling at the same coincidence…

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

#46

Post by mjfisher »

ahmedfromtunis wrote: post #33

[flagged]

Nope, it's not a coincidence - it's an interesting exploration of the history of the definition of a metre. Read the article.

As it says, at some point there was an attempt to standardise the length of a metre in terms of a pendulum's length; which related it directly to g through Pi.

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

#47

Post by jameshart »

ahmedfromtunis wrote: post #33

[flagged]

On any planet where you want to define a system of units, you can start by defining a fixed time period (maybe use a fraction of the planetary rotation cycle or something), then make a pendulum that swings with that frequency, and derive a unit of distance from its length.

The local value of g will be roughly pi squared pendulum lengths per tick squared, in that system of measurement.

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

#49

Post by air7 »

shubhamjain wrote: post #27

What 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…

Arguably most humans can't do this either.
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