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Given our knowledge of physics, it must surely be a coincidence.

It so happens that $\pi$ can be experimentally observed, for instance by constructing circles out of wire. But there is a very biased causality here: The wire loop exhibits $\pi$ because our world is like the Platonic ideal of Euclidean sapce, not the other way around. Although it is worth noting that there is of course a reason why Euclid happened to start with exactly that kind of space, and not another.

You don't have to accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$. You can, for instance, make the disturbing but reasonable objection that mathematics is nothing but an artifact of the human brain, and is not universal but a posteriori. In a sense this position weak, because we have observed animals to have a similar understanding of mathematics, but of course that is only circumstantial evidence, not proof.

Given our knowledge of physics, this must surely be a coincidence.

It so happens that $\pi$ can be experimentally observed, for instance by constructing circles out of wire. But there is a very biased causality here: The wire loop exhibits $\pi$ because our world is like the Platonic ideal of Euclidean space, not the other way around. Although it is worth noting that there is of course a reason why Euclid happened to start with exactly that kind of space, and not another.

You don't have to accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$. You can, for instance, make the disturbing but reasonable objection that mathematics is nothing but an artifact of the human brain, and is not universal but a posteriori. In a sense this position is weak, because we have observed animals to have a similar understanding of mathematics, but of course that is only circumstantial evidence, not proof.

One can observe that while mathematics doesn't care about the world, the world does appear to obey mathematics. We have never observed the real world contradict mathematical logic. So, it is not impossible that one day, the true nature of $g$ will be understood, and it will turn out to have a geometrical origin (for instance), and we will find out that your observation is in fact meaningful, not mere coincidence. But as far as I know, no such geometrical explanation exists.

One can observe that while mathematics doesn't care about the world, the world does appear to obey mathematics. We have never observed the real world contradict mathematical logic. So, it is not impossible that one day, the true nature of $g$ will be understood, and it will turn out to have a geometrical origin (for instance), and we will find out that your observation is in fact meaningful, not mere coincidence. But as far as I know, no such geometrical explanation exists. I doubt this will ever happen either, because the relation works only on Earth, and not even everywhere on Earth.

You don't have to accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$. You can, for instance, make the disturbing but reasonable objection that mathematics is nothing but an artifact of the human brain, and is not universal but a posteriori. In a sense this position weak, because we have observed animals have a similar understanding of mathematics, but of course that is only circumstantial evidence, not proof.

If you do accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$, being that $\pi$ is obtained with no input from the physical world: Then whereas everyone's $\pi$ is necessarily equal, everyone's $g$ need not be. Thus the relation you observe would only hold in our universe, not in hell or Universe X. In other words, our universe "easily could have had" a different $g$ - it is unclear whether the laws of physics we know had no choice but to be the way they are, or if there was some kind of dice rolling to conjure up a bunch of random laws, and we "could have" ended up with a different set. It is not even clear if the laws have always held, or will hold in the future (although we have never observed them not holding so far).

Note 2: I didn't want to be mean and give you the boring answer right off the bat. For the sake of completeness, here it is: $\pi^2$ is like $g$... only if you use meters and seconds, two explicitly arbitrary units. In Planck units the relation does not exist. In fact, with the right units, you can make $g$ be like $e$, or your age, or any number you desire.

You don't have to accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$. You can, for instance, make the disturbing but reasonable objection that mathematics is nothing but an artifact of the human brain, and is not universal but a posteriori. In a sense this position weak, because we have observed animals to have a similar understanding of mathematics, but of course that is only circumstantial evidence, not proof.

If you do accept that $\pi_{earth}=\pi_{hell}=\pi_{alien}$, being that $\pi$ is obtained with no input from the physical world: Then whereas everyone's $\pi$ is necessarily equal, everyone's $g$ need not be. Thus the relation you observe would only hold in our universe, not in hell or Universe X. In other words, our universe "easily could have had" a different $g$ - it is unclear whether the laws of physics we know had no choice but to be the way they are, or if there was some kind of dice rolling to conjure up a bunch of random laws, and we "could have" ended up with a different set. It is not even clear if the laws have always held, or will hold in the future. Although we have never observed them not holding so far - except for the ones we did, but we don't talk about those anymore...

Note 2: I didn't want to be mean and give you the boring answer right off the bat. For the sake of completeness, here it is: $\pi^2$ is like $g$... only if you use meters and seconds, two explicitly arbitrary units. In Planck units the relation does not exist. In fact, with the right units, you can make $g$ be like $e$, or your age, or your ZIP code, or any other number you desire.