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

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

#151

Post by twojacobtwo »

mjburgess wrote: post #132
arcastroe wrote: post #121

Earlier quoted context omitted.

I'm surprised at the number of people disagreeing with your quibble. I had the exact same thought as you! If pi^2 were _exactly_ g, and the "magic" disappeared in different units, THEN we could say "so this is no coincidence" and we could conclude that it has to be related to the units themselves. But since pi^2 is only roughly equal to g, and the magic disappears in different units, I would likely attribute it to co…

It would be useful if people carried around some card with all the information that they understood on it, since opinions are largely symptoms of this. In almost all cases any apparent phenomenon specific to one system of measurement is clearly a coincidence, since reality is definable as that which is independent of measurement.

> since reality is definable as that which is independent of measurement.

In terms of quantum mechanics, would that mean the wave function is real until it collapses due to measurement? Or am I misunderstanding your use of measurement there?

Something about that is sticking in my mind in an odd way, but I can't put my finger on exactly what it is - which is intriguing.

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

#152

Post by dr_dshiv »

mistercow wrote: post #19
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.

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…

Alpha brainwaves are almost exactly 10hz, in humans and mice. The typical walking frequency (for humans) is almost exactly 2hz (2 steps per second). And the best selling popular music rhythm is 2hz (120bpm) [1].

Perhaps seconds were originally defined by the duration of a human pace (i.e. 2 steps). These are determined by the oscillations of central pattern generators in the spinal cord. One might suspect that these are further harmonically linked to alpha wave generators. In any case, 120bpm music would resonate and entrain intrinsic walking pattern generators—this resonance appears to make us more likely to move and dance.

Or it’s just a coincidence.

[1] https://www.frontiersin.org/journals/neurorobotics/articles/...

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

#153

Post by fireattack »

Totally unrelated to the content, but about the website itself.

The site completely breaks when I visit it. After some investigation, I found out that if I enable Stylus (a CSS injection extension) with any rules (even my global ones), the site becomes unusable. Since it's built using the React framework, it doesn't just glitch; it completely breaks.

After submitting a ticket and getting a quick response from the Stylus dev, it turns out that this website (and any site built with caseme.io) will throw an error and break if it detects any node injected into ``.

[1] https://github.com/openstyles/stylus/issues/1803

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

#154

Post by saghm »

mistercow wrote: post #19
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.

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…

Reminds me of https://xkcd.com/687/

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

#155

Post by jncfhnb »

satvikpendem wrote: post #66
jncfhnb wrote: post #56

Earlier quoted context omitted.

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

Why is it more interesting? Is it just more interesting because we use such bases, or can it be interesting inherently? That is the question that is being asked, and why some say it's merely a coincidence.

Well every number is the product of another number and some coefficient. If it’s a nice clean number then that implies it could be the result of some scaling unit conversion. But that should be sort of apparent. And it’s not super interesting if true.

If a number is another number squared then that implies some sort of mechanistic relationship. Especially when the number is pi, which suggests there’s a geometric intuition to understanding the definition.

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

#156

Post by nneonneo »

Waterluvian wrote: post #107
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…

Or the speed of light being almost a sweet 300 million m/s. Or after-atmosphere insolation being somewhat on average 1kw/m2.

Usefully, the speed of light is extremely close to one foot per nanosecond. This makes reasoning about things like light propagation delays in circuits much easier.

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

#157

Post by satvikpendem »

jncfhnb wrote: post #155
satvikpendem wrote: post #66

Earlier quoted context omitted.

Why is it more interesting? Is it just more interesting because we use such bases, or can it be interesting inherently? That is the question that is being asked, and why some say it's merely a coincidence.

Well every number is the product of another number and some coefficient. If it’s a nice clean number then that implies it could be the result of some scaling unit conversion. But that should be sort of apparent. And it’s not super interesting if true. If a number is another number squared then that implies some sort of mechanistic relationship. Especially when the number is pi, which suggests there’s a geometric intu…

In other bases, it does not actually imply much, even if it were squared. Maybe it really does make sense if it existed in base 10 but I cannot see much if it were part of other bases.

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

#159

Post by anon457437 »

mistercow wrote: post #149
john-aj wrote: post #142

Earlier quoted context omitted.

I agree. But if you remove the "so", there is no contradiction. It is possible the author used "so" not to mean "in other words", but simply as a relatively meaningless discourse marker.

Huh, interesting point. Writing unambiguously is ridiculously hard.

The comma differentiates. The comma indicates a short pause and a certain intonation in speech (the period means a longer pause and a different intonation). If you say that sentence with and without a pause/comma, you'll see (hear) that the sentence is correct. Reading unambiguously is also hard.

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

#160

Post by gpvos »

jds-67 wrote: post #103
gpvos wrote: post #29

Earlier quoted context omitted.

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…

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.

I admit I scanned the article first and wondered what it was all about. The actual argument is not very clearly presented.
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