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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

#251

Post by rat_on_the_run »

There is nothing meaningful about this. I can change the unit system to make g any value I want (this is done all the time in research). I try really hard to ignore all the physics-related articles posted here but this one is too egregious. It's not the usual thing where the author know nothing about the nouns they are using (enter, quantum). In this case the concepts are fairly simple. The fact that units can be freely changed should be taught in middle school.

Somehow I found programmers have a much higher probability of talking about physics than people in other professions. And unfortunately in all cases I've seen, they have no idea what they are talking about. Unlike programming, physics is hard enough that it needs to be studied in classes.

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

#252

Post by aaplok »

rat_on_the_run wrote: post #251

There is nothing meaningful about this. I can change the unit system to make g any value I want (this is done all the time in research). I try really hard to ignore all the physics-related articles posted here but this one is too egregious. It's not the usual thing where the author know nothing about the nouns they are using (enter, quantum). In this case the concepts are fairly simple. The fact that units can be fre…

This is addressed in the article, including the fact that you can change the unit system to change the value of g.

The article explains that the coincidence comes from the fact that the meter, as a unit, was defined (by Huygens) based on g and π. It was later redefined several times and the link between the two values became anecdotal. In other words, on another planet the gravitational constant would still have had a value of (approximately) π², and what would have been different is our unit length.

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

#255

Post by billforsternz »

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.

Agreed. Irrespective of how the story is later developed, "So, this is no coincidence", is a baffling thing to put immediately after apparently demonstrating a coincidence!

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

#256

Post by antonvs »

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…

> 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.

Yeah, it was a strange claim, which makes me think that the author may have had his conclusion in mind when writing this. I.e. what he meant to say may have been something more like:

"The relationship vanishes when you change units, which suggests the possibility that the relationship is a function of the unit definitions... and therefore not a coincidence."

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

#257

Post by kazinator »

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.

It is not unusual case. The heuristic you want is working. It's nothing more than a coincidence.

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

#258

Post by rat_on_the_run »

aaplok wrote: post #252
rat_on_the_run wrote: post #251

There is nothing meaningful about this. I can change the unit system to make g any value I want (this is done all the time in research). I try really hard to ignore all the physics-related articles posted here but this one is too egregious. It's not the usual thing where the author know nothing about the nouns they are using (enter, quantum). In this case the concepts are fairly simple. The fact that units can be fre…

This is addressed in the article, including the fact that you can change the unit system to change the value of g. The article explains that the coincidence comes from the fact that the meter, as a unit, was defined (by Huygens) based on g and π. It was later redefined several times and the link between the two values became anecdotal. In other words, on another planet the gravitational constant would still have had…

Yeah, I saw the author says it depends on the units. But like, why is this interesting? This is not physics, just some number coincidence in the metric unit system, and I'm sure one can find many more these kind of things by playing around with the constants. The fact the author calls this a "wonderful coincidence" is just... Like, a simple energy conservation or momentum conservation, taught in middle school, is infinitely worth being talked than this.

One philosophy in physics, is that the world and its rules are independent of human. We actively try to eliminate and downplay historical and human factors in the theory, and try to talk about just "the physics", because those factors often obscure the real physics (mechanism) and complicate the calculation. I mean people can find a historical thing interesting, but I guess I just feel disappointed that people find such a trivial thing so interesting, and maybe think that this is what physics is about, while physics is about anything but those pure coincidences.

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

#259

Post by mistercow »

kazinator wrote: post #257
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.

It is not unusual case. The heuristic you want is working. It's nothing more than a coincidence.

What are you disputing about the explanation given in the post? As far as I can tell, it’s basically accurate (although the pendulum unit was called the toise, and the meter seems to have targeted half a toise). If you accept that account, it’s not a coincidence.

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

#260

Post by aaplok »

rat_on_the_run wrote: post #258
aaplok wrote: post #252

Earlier quoted context omitted.

This is addressed in the article, including the fact that you can change the unit system to change the value of g. The article explains that the coincidence comes from the fact that the meter, as a unit, was defined (by Huygens) based on g and π. It was later redefined several times and the link between the two values became anecdotal. In other words, on another planet the gravitational constant would still have had…

Yeah, I saw the author says it depends on the units. But like, why is this interesting? This is not physics, just some number coincidence in the metric unit system, and I'm sure one can find many more these kind of things by playing around with the constants. The fact the author calls this a "wonderful coincidence" is just... Like, a simple energy conservation or momentum conservation, taught in middle school, is inf…

> why is this interesting?

Physicists need some precise definitions of units, and this is hard. Harder than most people expect. You can't do physics properly using your current king's foot size. This, more than the actual computations, was Huygens' valuable insight.

So you need a universal constant to serve as a standard, and it turns out very few things are in our world. One of them is the ratio of the perimeter of a circle over its diameter. So it's no wonder that this ratio comes up under various forms in our standard units, more often than chance would predict.

This is interesting because students of physics need to understand the complexity and importance of coming up with a standard set of measurement units, based on universal constants.

This is also interesting because the reason we need standard units is that we need science to be reproducible. If all I care about is to understand the world on my own then using the size of my own foot will do just fine as a unit.

Accessorily it's also useful to address the nonsense belief that such coincidences prove the existence of god or the perfection of nature.

None of this will come as radically insightful to you, but there are a lot of people in this world for whom this is not the case.

I'm also not a fan of over the top language, but this seems to be the norm of our attention-seeking times.

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