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Can math.atan2 return INF?

Steven D'Aprano <steve at pearwood.info>:

> Naive empirical falsification can, at best, be considered as a
> best-practice rule: if you have no way of falsifying something even in
> principle, then it's not scientific. But it doesn't really give you
> much in the way of practical guidance. What counts as falsification?

We cannot get any information on black holes proper because black holes
cannot come into existence according to the very theory that predicts
black holes. It will take infinitely long for an event horizon to form.
Speculating on what happens to an astronaut falling in is not much
different from speculating what happens after the end of the world.

> We have no way of seeing what goes on past the black hole's event
> horizon, since light cannot escape. But we can still see *some*
> properties of black holes, even through their event horizon: their
> mass, any electric charge they may hold, their angular momentum.

If an event horizon cannot come into existence, you can only see
properties of almost-black-holes. Even though there probably is
virtually no difference between the two astronomically, it relieves
physicists from answering some awkward questions on the goings-on inside
an event horizon.

> We can test the proposition that a black hole that forms from hydrogen
> is no different from one which forms from uranium. We can look for
> variations in randomness in the Hawking radiation emitted, we can test
> that the event horizon is where we expect, etc. An electrically
> neutral black hole with a magnetic field would likely falsify a lot of
> theories about what goes on inside the event horizon.

If an event horizon cannot ever form, you can't really test any of that