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Can math.atan2 return INF?

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  Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-22 03:50 +1000
    Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-21 20:01 +0200
      Re: Can math.atan2 return INF? Jussi Piitulainen <jussi.piitulainen@helsinki.fi> - 2016-06-21 21:32 +0300
        Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-22 11:40 +1000
          Re: Can math.atan2 return INF? Nagy László Zsolt <gandalf@shopzeus.com> - 2016-06-27 15:27 +0200
      Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-22 11:38 +1000
        Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-22 08:21 +0200
        Re: Can math.atan2 return INF? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-06-22 16:34 +0100
          Re: Can math.atan2 return INF? Random832 <random832@fastmail.com> - 2016-06-22 12:19 -0400
          Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-22 19:18 +0200
            Re: Can math.atan2 return INF? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-06-22 20:17 +0100
              Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-22 12:50 -0700
              Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-23 13:59 +1000
                Re: Can math.atan2 return INF? Dan Sommers <dan@tombstonezero.net> - 2016-06-23 04:40 +0000
                  Re: Can math.atan2 return INF? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-23 16:45 +1000
                    Re: Can math.atan2 return INF? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-06-23 15:39 +0100
                      Re: Can math.atan2 return INF? alister <alister.ware@ntlworld.com> - 2016-06-23 15:04 +0000
                        Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-24 02:44 +1000
                          Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-23 19:14 +0200
                            Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-23 20:22 +0300
                              Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-24 09:53 +0200
                                Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-24 13:38 +0300
                                  Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-26 11:43 +1200
                              Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-26 11:40 +1200
                                Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-26 10:09 +0300
                                  Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-27 11:08 +1200
                                    Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-27 12:59 +1000
                                      Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-27 09:40 +0300
                                        Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-27 06:15 -0700
                                          Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-27 16:45 +0300
                                            Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-27 07:01 -0700
                                              Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-27 17:12 +0300
                                                Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-27 07:27 -0700
                                                  Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-27 20:03 +0300
                                          Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-28 18:12 +1200
                                            Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-27 23:25 -0700
                                            Re: Can math.atan2 return INF? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-28 16:27 +1000
                                        Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-28 18:12 +1200
                                          Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-28 09:23 +0300
                                      Re: Can math.atan2 return INF? Random832 <random832@fastmail.com> - 2016-06-28 09:39 -0400
                                        Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-06-29 01:22 +1000
                                        Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-28 19:36 +0300
                                        Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-28 19:42 +0300
                                Re: Can math.atan2 return INF? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-29 19:35 +1000
                                  Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-29 13:54 +0300
                                    Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-29 18:33 -0700
                                      Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-29 19:13 -0700
                                        Re: Can math.atan2 return INF? Chris Angelico <rosuav@gmail.com> - 2016-06-30 12:38 +1000
                                        Re: Can math.atan2 return INF? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-30 18:24 +1000
                                          Re: Can math.atan2 return INF? Andreas Röhler <andreas.roehler@online.de> - 2016-06-30 11:35 +0200
                                            Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-30 02:42 -0700
                                              Re: Can math.atan2 return INF? Andreas Röhler <andreas.roehler@online.de> - 2016-06-30 12:13 +0200
                                          Re: Can math.atan2 return INF? Andreas Röhler <andreas.roehler@online.de> - 2016-06-30 12:11 +0200
                                            Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-07-01 03:18 +1000
                                          Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-30 08:28 -0700
                                            Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-07-01 04:03 +1000
                                              Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-07-01 07:19 -0700
                                                Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-07-01 18:20 +0300
                                              Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-07-29 22:46 -0700
                                                Re: Can math.atan2 return INF? Steven D'Aprano <steve@pearwood.info> - 2016-08-01 12:53 +1000
                                                  Re: Can math.atan2 return INF? Paul Rubin <no.email@nospam.invalid> - 2016-07-31 20:41 -0700
                                                    Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-07-31 20:54 -0700
                                                  Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-07-31 21:05 -0700
                                                    Re: Can math.atan2 return INF? Ian Kelly <ian.g.kelly@gmail.com> - 2016-08-01 01:05 -0600
                                          Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-07-24 19:48 -0700
                                      Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-30 09:24 +0300
                                        Re: Can math.atan2 return INF? Rustom Mody <rustompmody@gmail.com> - 2016-06-29 23:29 -0700
                                          Re: Can math.atan2 return INF? Dennis Lee Bieber <wlfraed@ix.netcom.com> - 2016-06-30 07:47 -0400
                                        Re: Can math.atan2 return INF? alister <alister.ware@ntlworld.com> - 2016-06-30 14:54 +0000
                                      Re: Can math.atan2 return INF? Paul Rubin <no.email@nospam.invalid> - 2016-06-29 23:57 -0700
                                        Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-30 00:16 -0700
                                          Re: Can math.atan2 return INF? Paul Rubin <no.email@nospam.invalid> - 2016-06-30 00:32 -0700
                                            Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-30 00:39 -0700
                                          Re: Can math.atan2 return INF? Steven D'Aprano <steve+comp.lang.python@pearwood.info> - 2016-06-30 18:27 +1000
                                      Re: Can math.atan2 return INF? Andreas Röhler <andreas.roehler@online.de> - 2016-06-30 09:17 +0200
                                        Re: Can math.atan2 return INF? Lawrence D’Oliveiro <lawrencedo99@gmail.com> - 2016-06-30 00:17 -0700
                                    Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-30 18:06 +1200
                                      Re: Can math.atan2 return INF? Marko Rauhamaa <marko@pacujo.net> - 2016-06-30 09:32 +0300
                                  Re: Can math.atan2 return INF? Random832 <random832@fastmail.com> - 2016-06-29 09:55 -0400
                          Re: Can math.atan2 return INF? Gregory Ewing <greg.ewing@canterbury.ac.nz> - 2016-06-26 11:15 +1200
                            Re: Can math.atan2 return INF? MRAB <python@mrabarnett.plus.com> - 2016-06-26 00:31 +0100
                        Re: Can math.atan2 return INF? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-06-23 20:04 +0100
                  Re: Can math.atan2 return INF? pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange) - 2016-06-23 19:07 +0200
                Re: Can math.atan2 return INF? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-06-23 15:37 +0100

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#110449

Marko Rauhamaa <marko@pacujo.net> wrote:

> Note that the "valid point of view for external observers" is the only
> valid scientific point of view.

For a scientific point of view, right. But tell this to the one that
will be close to a blackhole ;-)

-- 
Pierre-Alain Dorange               Moof <http://clarus.chez-alice.fr/>

Ce message est sous licence Creative Commons "by-nc-sa-2.0"
<http://creativecommons.org/licenses/by-nc-sa/2.0/fr/>

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#110451

pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange):

> Marko Rauhamaa <marko@pacujo.net> wrote:
>
>> Note that the "valid point of view for external observers" is the
>> only valid scientific point of view.
>
> For a scientific point of view, right. But tell this to the one that
> will be close to a blackhole ;-)

Then, you'd better consult a priest than a scientist.


Marko

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#110507

Marko Rauhamaa wrote:
> pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange):
> 
>>For a scientific point of view, right. But tell this to the one that
>>will be close to a blackhole ;-)
> 
> Then, you'd better consult a priest than a scientist.

But don't worry, you'll have an infinitely long time
to make your confessions -- from our point of view,
anyway.

-- 
Greg

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#110506

Marko Rauhamaa wrote:
> pdorange@pas-de-pub-merci.mac.com (Pierre-Alain Dorange):
> 
>>Near a black hole 3.7 seconds can last an infinite time...
> 
> Which phenomenon prevents a black hole from ever forming. Yet
> astronomers keep telling us they are all over the place.

Astronomers have observed objects whose behaviour is
entirely consistent with the existence of black holes
as predicted by general relativity.

>    Oppenheimer and his co-authors interpreted the singularity at the
>    boundary of the Schwarzschild radius as indicating that this was the
>    boundary of a bubble in which time stopped. This is a valid point of
>    view for external observers, but not for infalling observers.
> 
> Note that the "valid point of view for external observers" is the only
> valid scientific point of view.

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.

It's true that we outside can't be absolutely sure that things
are as predicted at the horizon itself, because any observer
we sent in to check would be unable to report back. But in
principle we can observe arbitrarily close to it. The
observations we've made so far all fit the theory, and the
theory doesn't present any obstacles to extrapolating those
results to the horizon and beyond, so we accept the theory
as valid.

There *is* a difficulty at the very center of the hole, where
there is a true singularity in the theory, so something
else must happen there. But for other reasons we don't
expect those effects to become important until you get
very close to the singularity -- something on the order of
the Planck length.

-- 
Greg

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#110510

Gregory Ewing <greg.ewing@canterbury.ac.nz>:

> Marko Rauhamaa wrote:
>> Which phenomenon prevents a black hole from ever forming. Yet
>> astronomers keep telling us they are all over the place.
> Astronomers have observed objects whose behaviour is entirely
> consistent with the existence of black holes as predicted by general
> relativity.

As far as I understand, all we can ever observe is black holes in the
making since the making can never (seem to) finish. IOW, the event
horizon never forms.

These almost-black-holes are virtually indistinguishable from black
holes proper. However, we don't have to speculate about the physics of
the insides of the black hole.

> 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's true that we outside can't be absolutely sure that things are as
> predicted at the horizon itself, because any observer we sent in to
> check would be unable to report back. But in principle we can observe
> arbitrarily close to it. The observations we've made so far all fit
> the theory, and the theory doesn't present any obstacles to
> extrapolating those results to the horizon and beyond, so we accept
> the theory as valid.

Religious theories about the afterlife face similar difficulties -- and
present similar extrapolations.

> There *is* a difficulty at the very center of the hole, where there is
> a true singularity in the theory, so something else must happen there.
> But for other reasons we don't expect those effects to become
> important until you get very close to the singularity -- something on
> the order of the Planck length.

That's my point: such speculation must remaing mere speculation. The
universe doesn't owe us an answer to a question that we can never face.


Marko

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#110542

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.

A lot of what the early Greeks found out got lost in
various library burnings, etc. Does that mean they
weren't being scientific?

> 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...

-- 
Greg

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#110551

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.

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#110563

Steven D'Aprano <steve@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
stuff.


Marko

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#110575

On Monday, June 27, 2016 at 12:10:21 PM UTC+5:30, Marko Rauhamaa wrote:
> Steven D'Aprano :
> 
> > 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
> stuff.

I am reminded of an argument I once had with a colleague about
infinite, lazy data-structures

I said that for the Haskell list [0..]

[0..] ++ [-1] == [0..]

++ is like python's list append +

This could equally apply to a Python generator like:

def nats():
  i=0
  while True:
     yield i
     i += 1

He said (in effect) yes that -1 would not be detectable but its still there!

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#110580

Rustom Mody <rustompmody@gmail.com>:

> I am reminded of an argument I once had with a colleague about
> infinite, lazy data-structures
>
> I said that for the Haskell list [0..]
>
> [0..] ++ [-1] == [0..]

[...]

> He said (in effect) yes that -1 would not be detectable but its still
> there!

Georg Cantor would probably be with your colleague, but then, Georg
Cantor was not a scientist.


Marko

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#110584

On Monday, June 27, 2016 at 7:16:03 PM UTC+5:30, Marko Rauhamaa wrote:
> Rustom Mody :
> 
> > I am reminded of an argument I once had with a colleague about
> > infinite, lazy data-structures
> >
> > I said that for the Haskell list [0..]
> >
> > [0..] ++ [-1] == [0..]
> 
> [...]
> 
> > He said (in effect) yes that -1 would not be detectable but its still
> > there!
> 
> Georg Cantor would probably be with your colleague, but then, Georg
> Cantor was not a scientist.

I'm mystified

Earlier (I thought) you were on the Platonist = {Cantor, Hilbert...} side
Now you sound like you are on the constructivist = {Kronecker, Brouwer } side

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#110588

Rustom Mody <rustompmody@gmail.com>:

> On Monday, June 27, 2016 at 7:16:03 PM UTC+5:30, Marko Rauhamaa wrote:
>> Georg Cantor would probably be with your colleague, but then, Georg
>> Cantor was not a scientist.
>
> I'm mystified
>
> Earlier (I thought) you were on the Platonist = {Cantor, Hilbert...}
> side
> Now you sound like you are on the constructivist = {Kronecker, Brouwer
> } side

I'm a formalist.


Marko

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#110591

On Monday, June 27, 2016 at 7:42:26 PM UTC+5:30, Marko Rauhamaa wrote:
> Rustom Mody :
> 
> > On Monday, June 27, 2016 at 7:16:03 PM UTC+5:30, Marko Rauhamaa wrote:
> >> Georg Cantor would probably be with your colleague, but then, Georg
> >> Cantor was not a scientist.
> >
> > I'm mystified
> >
> > Earlier (I thought) you were on the Platonist = {Cantor, Hilbert...}
> > side
> > Now you sound like you are on the constructivist = {Kronecker, Brouwer
> > } side
> 
> I'm a formalist.

Well then formalism is semantics-free: What matters it if an argument is
theological or scientific as long as it is (internally) consistent?

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#110601

Rustom Mody <rustompmody@gmail.com>:

> On Monday, June 27, 2016 at 7:42:26 PM UTC+5:30, Marko Rauhamaa wrote:
>> I'm a formalist.
>
> Well then formalism is semantics-free: What matters it if an argument
> is theological or scientific as long as it is (internally) consistent?

That's what I'm saying: black holes can't exist according to the very
theory that predicts their existence.

They might exist in reality, though...


Marko

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#110653

Rustom Mody wrote:
> I said that for the Haskell list [0..]
> 
> [0..] ++ [-1] == [0..]
> 
> He said (in effect) yes that -1 would not be detectable but its still there!

The code to generate it is there, but it will never
be executed, so the compiler is entitled to optimise
it away. :-)

He may have a point though. There are avenues of
mathematics where people think about objects such
as "all the natural numbers, followed by -42", and
consider that to be something different from just
"all the natural numbers".

So, a mathematician would probably say they're not
equal. A scientist would say they may or may not be
equal, but the difference is not testable.

An engineer would say "Lessee, 0, 1, 2, 3, 4, 5,
6, 7... yep, they're equal to within measurement
error."

-- 
Greg

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#110658

On Tuesday, June 28, 2016 at 11:42:29 AM UTC+5:30, Gregory Ewing wrote:
> Rustom Mody wrote:
> > I said that for the Haskell list [0..]
> > 
> > [0..] ++ [-1] == [0..]
> > 
> > He said (in effect) yes that -1 would not be detectable but its still there!
> 
> The code to generate it is there, but it will never
> be executed, so the compiler is entitled to optimise
> it away. :-)
> 
> He may have a point though. There are avenues of
> mathematics where people think about objects such
> as "all the natural numbers, followed by -42", and
> consider that to be something different from just
> "all the natural numbers".
> 
> So, a mathematician would probably say they're not
> equal. A scientist would say they may or may not be
> equal, but the difference is not testable.
> 
> An engineer would say "Lessee, 0, 1, 2, 3, 4, 5,
> 6, 7... yep, they're equal to within measurement
> error."

Yes there is a sloppiness in my statement above:

[0..] ++ [-1] == [0..]

What kind of '==' is that?
If its the Haskell (or generally, programming language implementation) version
that expression just hangs trying to find the end of the infinite lists.

If its not then a devil's advocate could well say:
"So its metaphysical, theological and can know the unknowable,
viz. that that -1 which is computationally undetectable is nevertheless present.

ie the '++' can be a lazy Haskell *implemented* function
The '==' OTOH is something at least quasi mystical

Mathematicians are more likely to say 'mathematical' than 'mystical'
Such mathematicians -- the majority -- are usually called 'Platonists'

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#110659

On Tuesday 28 June 2016 16:12, Gregory Ewing wrote:

> Rustom Mody wrote:
>> I said that for the Haskell list [0..]
>> 
>> [0..] ++ [-1] == [0..]
>> 
>> He said (in effect) yes that -1 would not be detectable but its still there!
> 
> The code to generate it is there, but it will never
> be executed, so the compiler is entitled to optimise
> it away. :-)
> 
> He may have a point though. There are avenues of
> mathematics where people think about objects such
> as "all the natural numbers, followed by -42", and
> consider that to be something different from just
> "all the natural numbers".
> 
> So, a mathematician would probably say they're not
> equal. A scientist would say they may or may not be
> equal, but the difference is not testable.
> 
> An engineer would say "Lessee, 0, 1, 2, 3, 4, 5,
> 6, 7... yep, they're equal to within measurement
> error."

And a programmer would write a script to compare the two, and then go to 
Stackoverflow asking for help to optimize it because it takes too long to 
complete.

Relevant:

https://blogs.msdn.microsoft.com/oldnewthing/20131029-00/?p=2803




-- 
Steve

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#110651

Marko Rauhamaa wrote:
> 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.

Only in some frames of reference.

By your reasoning, Zeno's paradox proves that a runner
can never reach the finish line in a race. But it really
only proves that if you measure time in such a way that
the finishing time is infinitely far in your future, you
will never see him finish.

That's obviously a screwy way to measure time in a
race, but something similar is happening with the black
hole. If you draw coordinate lines in a particular
way (corresponding to the inertial frame of an outside
observer stationary with respect to the hole) then
the time axis bends in such a way that it never
crosses the horizon.

But there's no reason you have to draw the coordinates
that way; there are plenty of others in which the time
axis does cross the horizon.

-- 
Greg

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#110657

Gregory Ewing <greg.ewing@canterbury.ac.nz>:

> Marko Rauhamaa wrote:
>> 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.
>
> Only in some frames of reference.
>
> By your reasoning, Zeno's paradox proves that a runner can never reach
> the finish line in a race.

In Zeno's case, the limit is finite. Zeno's error is not realizing that
you can pack an infinite number of jiffies in finite time. In the black
hole case, the limit is infinite.

> But it really only proves that if you measure time in such a way that
> the finishing time is infinitely far in your future, you will never
> see him finish.

An external observer never experiences any effect whatsoever (direct or
indirect) from an event horizon or a black hole.

> But there's no reason you have to draw the coordinates that way; there
> are plenty of others in which the time axis does cross the horizon.

Not where I'm standing.


Marko

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#110695

On Sun, Jun 26, 2016, at 22:59, Steven D'Aprano wrote:
> 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.

All objects, not just black holes, have those properties. The point here
is that we are in fact observing those properties of an object that is
not yet (and never will be) a black hole in our frame of reference.

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