Can math.atan2 return INF?
Steven D'Aprano <steve+comp.lang.python at pearwood.info>:
> There's a common myth going around that black holes take an infinite
> amount of time to form,
That appears to be the case. (Identical discussion points here: <URL:
> or another way of putting it is that it takes an infinite amount
> of time for something to fall into a black hole,
That's not another way of putting it. That's a completely different
> and therefore "black holes can't really exist". This myth comes about
> because people don't fully understand the (admittedly mind-boggling)
> implications of General Relativity.
No, the fundamental question here is whether it makes scientific sense
to speculate about topics that are beyond the reach of science. Few
scientists speculate about what went on before the Big Bang, for
> First, you must accept that *your* experiences are not the only valid
> experiences. Just because *you* never see the black hole form, doesn't
> mean it doesn't form. You just don't get to experience it yourself.
The main point: the only direct information we can ever have about black
holes is by falling into one. Since none of that information can be
communicated back, it cannot be considered any more scientific than the
religions' beliefs about life after death (you can verify, say,
Christianity by dying but that doesn't make it valid science).
anyone that asserts a singularity exists inside a black hole is
simply saying that the mathematical model they're using says there is
> Neither is "right" and the other is "wrong", neither frame of
> reference is privileged over the other. BOTH are right, even though
> they contradict each other. That's the nature of the universe we live
Nobody has claimed otherwise.
> Tim is so engrossed by the view of the gravitational lensing that he
> forgets to fire the retro-rockets, and before he knows it, he's
> crossed the event horizon and there's no going back.
> For a sufficiently large black hole, he might not even have noticed
> the transition. From his perspective, he's still distant from the
> singularity (being so small and distant, he can't quite make out what
> it looks like), and space-time is still quite flat for a sufficiently
> large black hole. Tim can still see out, although the incoming light
> is getting bluer, and he's still receiving Bill's clock signals,
> though like Graham he sees them as drastically sped up.
By the time the event horizon hits Tim at the speed of light, Tim will
have received all of our Universe's signals at an ever accelerating
frequency and increasing power. He will have seen the End of the World
before leaving it.
We have no way of telling if your prediction would be true for Tim
inside the black hole.
> Tim's spaceship appears to be *asymptotically* approaching the event
> horizon, in some sort of horrible version of Zeno's Paradoxes: each
> minute that goes by, Tim gets closer to the event horizon by a
> *smaller* amount as time slows down for him (as seen by Bill and
> Graham on the space station).
Correct, and very relevant. In fact, that's the reason the even horizon
never even appears to form to us outsiders. The star just keeps on
collapsing for ever. That is true even for Tim who can't experience a
true black hole before it hits him.
> Although their perspectives are very different, neither is "more
> right" than the other.
No, but only one of them can be examined scientifically.
Heisenberg's uncertainty principle was at first presented as some sort
of limitation to what we can know. Nowadays, it is viewed more
fundamentally as a law of physics; en electron cannot fall in the
nucleus of an atom because it would end up violating Heisenberg's
Similarly, the Universe does not owe us an answer to what happens to
Tim. The Universe will come to an end (even for Tim) before the question
comes to the fore.
The cosmic teenage hacker who created our virtual world probably simply
typed this in that part of his code:
thus terminating Tim's thread.
> From our frame of reference, we seem them asymptotically approaching
> the event horizon, but never cross it.
More than that, we see the star collapsing but never quite being able to
create an event horizon.