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 coincidence if I hadn't read the article.
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.
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.
I cannot measure santa clause into existence. But I can change the temperature of some water by measuring it with a very hot thermometer.
That measurement changes what is measured is the norm in almost all cases, except in classical physics which describes highly simplified highly controlled experiments. The only 'unusual' thing about QM is its a case in physics where measurement necessarily changes the system, but this is extremely common in every other area. It is more unusual that in classical physics, measurement doesn't change the system.