Can math.atan2 return INF?

[Steven D'Aprano]

On Mon, 27 Jun 2016 09:08 am, Gregory Ewing wrote:

> Marko Rauhamaa wrote:
>>>The singularity being talked about there is an artifact of a
>>>particular coordinate system; the theory predicts that there is no
>>>*physical* singularity at the event horizon.
>> 
>> That theory can't be tested even in principle, can it? Therefore, it is
>> not scientific.
> 
> It can in principle be tested by a scientist falling into
> the hole. The only problem is that he won't be able to
> tell anyone outside what he finds out, but that's a
> practical difficulty, not a philosophical one.

Marko's complaint about black holes seems to be based on a very naive
definition of "scientific", specifically Karl Popper's naive empirical
falsification theory of science. Unfortunately, falsification is not even
close to a good description of what scientists do in their day-to-day work.

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? How do you falsify
historical events like "the Earth formed from a cloud of gas"? We weren't
there to observe it, we can't repeat the experiment, and the entire process
from start to finish takes too long for anyone to watch a cloud of gas
coalesce into a solid planet.

So, black holes... 

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. 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. 

And it may be that some future advance in quantum gravity theory will
suggest a way of testing the prediction of a singularity. There are
theories of black holes that predict "ring shaped" singularities, and
suggest that in principle one might "miss the singularity" and fall out of
a worm hole at the other end, although its doubtful that this would apply
to anything bigger than an atom.

I don't think many physicists actually believe that the singularity is a
real thing, rather than just a failure of our current gravitational
theories to correctly model matter under extreme conditions. After all,
we've been here before, with the prediction that a black-body should
radiate an infinite amount of energy at a finite temperature:

https://en.wikipedia.org/wiki/Ultraviolet_catastrophe

[...]
>> Religious theories about the afterlife face similar difficulties -- and
>> present similar extrapolations.
> 
> I don't think they're similar at all. Show me the equations
> for one of these religious theories and I might change
> my mind...

I don't think that the essential difference between a scientific theory and
a non-scientific one is the presence or absence of *equations*.

There's a lot of grey area between science and non-science, but I think a
good start is to ask, "how do you know?".

If the answer comes down to one of the following:


- divine revelation, including from gurus, angels and spirits;
- visions and inspiration;
- "it just stands to reason";
- "because otherwise, what would be the point?"

then its not scientific. The last means its wishful thinking. Maybe there is
no point. Perhaps things just are, and meaning is what we decide on, not an
inherent part of the universe. The third is just a cop-out. If you can't
explain the reason, there probably isn't one. And the first two are
necessarily subjective and forms of argument by authority:

All swans are white[1] because The Master said so, and who are you to
question The Master?

Whereas, I think that for a first degree approximation, we can say that
science must be *objective*. Often that does mean it involved equations,
after all the laws of mathematics are the same for all of us. But objective
fact does not necessarily require maths. Even in the ancient days of
humanity, we can be pretty sure that two Neandertals stepping out of their
cave to watch the sun rise in the east would agree on where the light was
coming from. If one faced into the sun and shaded her eyes, while the other
turned his back on the sun and shaded his eyes, we can be confident that
the second was mucking about :-)

And that's where all forms of religious revelation fail. Ultimately,
revelation divides the world into two:

- those who personally know the truth;
- and those who just have to take their word for it.


"God wants you to give me your money, honest. Oh, and he also doesn't want
you to eat carrots. Don't question the Lord!"






[1] Apart from black swans, which came as an awful shock for philosophers
when they learned of their existence.


-- 
Steven
“Cheer up,” they said, “things could be worse.” So I cheered up, and sure
enough, things got worse.