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Groups > comp.lang.python > #110252 > unrolled thread
| Started by | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| First post | 2016-06-22 03:50 +1000 |
| Last post | 2016-06-23 15:37 +0100 |
| Articles | 20 on this page of 84 — 19 participants |
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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
Page 3 of 5 — ← Prev page 1 2 [3] 4 5 Next page →
| From | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| Date | 2016-06-29 01:22 +1000 |
| Message-ID | <57729648$0$22140$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #110695 |
On Tue, 28 Jun 2016 11:39 pm, Random832 wrote: > 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. So what? You say that as if our frame of reference is privileged. If you hop in your trusty rocket and fly towards the black hole, thinking that it's all fine, its not "really" a black hole because "black holes can't actually form", you'll be in for a really nasty surprise when you cross the event horizon. -- Steven “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse.
[toc] | [prev] | [next] | [standalone]
| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2016-06-28 19:36 +0300 |
| Message-ID | <87furxnudl.fsf@elektro.pacujo.net> |
| In reply to | #110695 |
Random832 <random832@fastmail.com>:
> 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.
A physicist once clarified to me that an almost-black-hole is
practically identical with a black hole because all information about
anything falling in is very quickly red-shifted to oblivion.
However, there is some information that (to my knowledge) is not
affected by the red shift. Here's a thought experiment:
----------
/ \
/ (almost) \ N
| black | |
| hole | S
\ /
\ /
----------
We have a stationary, uncharged (almost) black hole in our vicinity and
decide to send in a probe. We first align the probe so it is perfectly
still wrt the black hole and let it fall in. Inside the probe, we have a
powerful electrical magnet that our compass can detect from a safe
distance away. The probe is also sending us a steady ping over the
radio.
As the probe approaches the event horizon, the ping frequency falls
drastically and the signal frequency is red-shifted below our ability to
receive. However, our compass still points to the magnet and notices
that it "floats" on top of the event horizon:
----------
/ \
/ (almost) \ N
| black ||
| hole |S
\ /
\ /
----------
/
/ compass needle
/
[toc] | [prev] | [next] | [standalone]
| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2016-06-28 19:42 +0300 |
| Message-ID | <87ziq5mfiw.fsf@elektro.pacujo.net> |
| In reply to | #110695 |
(sorry for the premature previous post)
Random832 <random832@fastmail.com>:
> 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.
A physicist once clarified to me that an almost-black-hole is
practically identical with a black hole because all information about
anything falling in is very quickly red-shifted to oblivion.
However, there is some information that (to my knowledge) is not
affected by the red shift. Here's a thought experiment:
----------
/ \
/ (almost) \ N
| black | |
| hole | S
\ /
\ /
----------
We have a stationary, uncharged (almost) black hole in our vicinity and
decide to send in a probe. We first align the probe so it is perfectly
still wrt the black hole and let it fall in. Inside the probe, we have a
powerful electrical magnet that our compass can detect from a safe
distance away. The probe is also sending us a steady ping over the
radio.
As the probe approaches the event horizon, the ping frequency falls
drastically and the signal frequency is red-shifted below our ability to
receive. However, our compass still points to the magnet and notices
that it "floats" on top of the event horizon:
----------
/ \
/ (almost) \ N
| black ||
| hole |S
\ /
\ /
----------
/
/ compass needle
/
The compass needle shows that the probe is "frozen" and won't budge no
matter how long we wait.
Marko
[toc] | [prev] | [next] | [standalone]
| From | Steven D'Aprano <steve+comp.lang.python@pearwood.info> |
|---|---|
| Date | 2016-06-29 19:35 +1000 |
| Message-ID | <57739650$0$1601$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #110506 |
On Sunday 26 June 2016 09:40, Gregory Ewing wrote:
> 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.
Indeed.
There's a common myth going around that black holes take an infinite amount of
time to form, or another way of putting it is that it takes an infinite amount
of time for something to fall into a black hole, 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.
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.
So, let's consider a thought experiment. Imagine three astronauts, Tim, Bill
and Graham ("we do anything, anytime"). Tim and Graham are in separate space
ships, dropping straight towards a black hole under free fall. Bill is watching
them from a safely orbiting space station.
Graham drops towards the black hole, as does Tim. Neither can see the black
hole directly, or at least they can't see the *inside* of the black hole, since
no light can escape it, but they can see it by its effect on the starlight: the
black hole acts like a great big lens, bending light. If they line up their
space ships with the black hole directly between them and a distant star, they
will see one of the more amazing sights of the universe: gravitational lensing.
The (somewhat reddened) light from the star will be bent around the black hole,
so that the star will appear to be a donut of light with a black centre.
As Graham falls, he pays close attention to the distance from his ship to the
black hole. That's easy to do: he can tell how fast he is going thanks to
Bill's space station, which transmits a steady radio signal for him, a steady
clock sending one pulse per second.[1]
But as Graham gets closer and closer to the event horizon, he notices Bill's
radio signals have a higher and higher frequency, and appear to be sped up...
at the end, just before he loses his nerve and fires the retro-rockets before
crossing the event horizon, the signals are coming thousands of pulses per
second.
When Graham returns to the space station, he finds a *much* older Bill waiting
for him. Bill insists he was sending one pulse per second, as agreed, but that
Graham has been gone for many years. Graham insists that he has only been gone
a few days, and Bill has obviously been partying very hard indeed to look like
this after such a short time. But after sitting down with Albert Einstein's
head[2], they reconcile their two differing experiences:
As seen by Bill, in Bill's frame of reference far from the black hole, Graham's
experiences have been slowed down enormously. But Graham sees things
differently: he experiences his own frame of reference at the same speed he
always has, and see's *Bill's* frame of reference as being immensely sped up.
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 in.
What about Tim?
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.
If Tim has sufficiently powerful rockets with enough fuel, he could *not quite*
escape: he could change his space ship's trajectory enough to avoid the
hypothetical singularity for days, weeks, years, as long as the fuel lasts. But
nothing he can do will allow him to escape the event horizon. (Well, maybe
faster-than-light travel, if his hyperdrive will still work this close to a
black hole.)
And as invariably as tomorrow follows today, he's getting closer to the
supposed singularity, and long before he reaches it, both Tim and his space
ship will be torn apart into atoms by the ever-increasing tidal forces, and
then even the atoms torn apart. And then, well we really have no idea what
happens if you try to squeeze an electron into a volume of space a trillion
times smaller than a sphere with radius equal to the Planck Length...
Should Tim realise his fate, and decide that there's no point delaying the
inevitable, his free-fall drop into the supposed singularity will be over in a
relatively short amount of time, at least according to his own frame of
reference. (For a stellar size black hole, the time from crossing the event
horizon to reaching the supposed singularity is a small fraction of a second.)
For a large black hole where the Schwartzchild Radius is 1 a.u., and ignoring
any relativistic corrections, it will take Tim six months of free fall to
collide with the singularity. During that time he will have plenty of time to
reflex on the curious way that Bill's space station is running faster and
faster, sending clock ticks millions of times a second. (At least until he is
torn apart by tidal forces.)
Meanwhile, back on Bill's space station, they're still faithfully sending out
radio pulses at the rate of one per second. By looking in their most powerful
telescopes, they can see Tim's spaceship falling into the black hole, strangely
slowing down as it approaches, the light getting redder and redder, Tim's own
radio signals getting further and further apart. 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).
Graham decides to mount a rescue mission. He flies back towards the black hole,
and experiences the same speeding up of signals coming from Bill. But no matter
how closely he approaches the event horizon, Tim always appears to ahead of
him, like the turtle to Achilles (from Graham's frame of reference).
As seen by Bill, the closer Graham gets to Tim, the slower he appears to be
experiencing time, with his return clock ticks coming back one a day instead of
one per second, then one a week, one a month, ...
Unless Graham is willing to cross the event horizon too, he cannot catch up to
Tim. That's because, from Tim's perspective, Graham left the space station too
late. Tim has already experienced crossing the event horizon, so unless Graham
has a time machine, there's nothing Graham can do to reach Tim before he
crosses the event horizon. No matter how close Graham gets to the event
horizon, Tim will already be just a bit closer. Unless Graham is suicidally
willing to cross the event horizon too, he's going to have to pull out (after,
from his perspective, perhaps as little as a few hours of high-acceleration),
and return to the space station, where he will find that Bill has experienced
possibly many thousands of years.
So whose viewpoint is right? According to Bill and Graham, Tim is frozen just
before the event horizon, infinitely red-shifted, his radio signals coming in
infinitely slowly. But according to Tim, the opportunity for rescue is long
gone. He long ago watched Graham's idiotic rescue mission ("don't bother
Graham, I'm well past the event horizon, you can't save me now..."), the daring
flight almost to the event horizon, and Graham's eventual return to the space
station.
Although their perspectives are very different, neither is "more right" than
the other.
So does the black hole form? Do objects cross the event horizon? From the frame
of reference of such objects, yes, certainly, and in a fairly short period of
time too. From our frame of reference, we seem them asymptotically approaching
the event horizon, but never cross it. Both are equally correct.
[1] Or very possibly playing "A Walk In The Black Forest".
[2] In a jar.
--
Steve
[toc] | [prev] | [next] | [standalone]
| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2016-06-29 13:54 +0300 |
| Message-ID | <87mvm4uux1.fsf@elektro.pacujo.net> |
| In reply to | #110762 |
Steven D'Aprano <steve+comp.lang.python@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:
http://astronomy.stackexchange.com/questions/2441/does-matter-accumulat
e-just-outside-the-event-horizon-of-a-black-hole>.)
> 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
story.
> 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
example.
> 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
one
<URL: http://astronomy.stackexchange.com/questions/2441/does-matter-a
ccumulate-just-outside-the-event-horizon-of-a-black-hole#comment21507
_2448>
> 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
> in.
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
uncertainty principle.
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:
raise NotImplementedError()
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.
Marko
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| From | Lawrence D’Oliveiro <lawrencedo99@gmail.com> |
|---|---|
| Date | 2016-06-29 18:33 -0700 |
| Message-ID | <cc5f7978-e590-48a8-b88d-774230ceccb3@googlegroups.com> |
| In reply to | #110770 |
On Wednesday, June 29, 2016 at 10:55:03 PM UTC+12, Marko Rauhamaa wrote: > 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 > example. On the contrary. The cosmic microwave background is too smooth to be explained by a simple Big Bang. Hence the invention of cosmic inflation, to try to smooth it out. Trouble is, once you turn on the inflation field, how do you turn it off? But if you don’t turn it off, then you get an infinite series of Big Bangs, not just one. So you see, like it or not, we are drawn to the conclusion that there *was* indeed something before our particular Big Bang. Every time somebody tries to point to an example of a “topic that is beyond the reach of science”, it seems to get knocked over eventually.
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2016-06-29 19:13 -0700 |
| Message-ID | <f402ba31-bade-4d12-aa2b-fd49c661e222@googlegroups.com> |
| In reply to | #110794 |
On Thursday, June 30, 2016 at 7:03:30 AM UTC+5:30, Lawrence D’Oliveiro wrote: > On Wednesday, June 29, 2016 at 10:55:03 PM UTC+12, Marko Rauhamaa wrote: > > 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 > > example. > > On the contrary. The cosmic microwave background is too smooth to be explained by a simple Big Bang. Hence the invention of cosmic inflation, to try to smooth it out. Trouble is, once you turn on the inflation field, how do you turn it off? But if you don’t turn it off, then you get an infinite series of Big Bangs, not just one. > > So you see, like it or not, we are drawn to the conclusion that there *was* indeed something before our particular Big Bang. > > Every time somebody tries to point to an example of a “topic that is beyond the reach of science”, it seems to get knocked over eventually. What is the physics that you folks are talking of ... Ive no idea OTOH Computer Science HAPPENED because mathematicians kept hotly disputing for more than ½ a century as to what is legitimate math and what is theology/mysticism/etc: In particular the question: "Are real numbers really real?" is where it starts off... http://blog.languager.org/2015/03/cs-history-0.html
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| From | Chris Angelico <rosuav@gmail.com> |
|---|---|
| Date | 2016-06-30 12:38 +1000 |
| Message-ID | <mailman.117.1467254338.2358.python-list@python.org> |
| In reply to | #110795 |
On Thu, Jun 30, 2016 at 12:13 PM, Rustom Mody <rustompmody@gmail.com> wrote: > ... hotly disputing for more than ½ a century... You keep using that character. Is it just to show off that you can? I was always taught to match the style of the rest of the sentence, so this would be "half a century". Same for most of your other uses - it would be far more grammatically appropriate to use the word "half". ChrisA
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| From | Steven D'Aprano <steve+comp.lang.python@pearwood.info> |
|---|---|
| Date | 2016-06-30 18:24 +1000 |
| Message-ID | <5774d75d$0$1617$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #110795 |
On Thursday 30 June 2016 12:13, Rustom Mody wrote: > OTOH Computer Science HAPPENED because mathematicians kept hotly disputing > for more than ½ a century as to what is legitimate math and what is > theology/mysticism/etc: I really don't think so. Computer science happened because people invented computers and wanted to study them. What people like Turing did wasn't computer science, because the subject didn't exist yet. He was too busy creating it to do it. And as for Kronecker, well, I suspect he objected more to Cantor's infinities than to real numbers. After all, even the Pythogoreans managed to prove that sqrt(2) was an irrational number more than 3000 years ago, something Kronecker must have known. > In particular the question: "Are real numbers really real?" is where it > starts off... http://blog.languager.org/2015/03/cs-history-0.html The pre-history of what later became computer science is very interesting, but I fear that you are too focused on questions of "mysticism" and not enough on what those people actually did and said. For example, you state that Turing "believes in souls" and that he "wishes to put the soul into the machine" -- what do his religious beliefs have to do with his work? What evidence do you have for the second claim? What does it even mean to put "the" soul (is there only one?) into "the" machine? Besides, the whole point of science is to develop objective, rational reasons to believe things. The chemist Friedrich Kekulé was inspired to think of benzene's molecular structure as a ring through a dream in which a snake bit its own tail, but that's not why we believe benzene is a ring-shaped molecule. No chemist says "Kekulé dreamed this, therefore it must be true." The irrational and emotional psychological forces that inspire mathematicians can make interesting reading, but they have no relevance in deciding who is write or wrong. No numbers are real. All numbers are abstractions, not concrete things. If there is a universe of Platonic forms -- highly unlikely, as the concept is intellectually simplistic and implausible -- we don't live in it. Since all numbers are abstractions, the Real sqrt(2) is no more, or less, "real" than the integer 2. -- Steve
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| From | Andreas Röhler <andreas.roehler@online.de> |
|---|---|
| Date | 2016-06-30 11:35 +0200 |
| Message-ID | <mailman.129.1467279066.2358.python-list@python.org> |
| In reply to | #110830 |
On 30.06.2016 10:24, Steven D'Aprano wrote: > On Thursday 30 June 2016 12:13, Rustom Mody wrote: > > [ ... ] > Besides, the whole point of science is to develop objective, rational reasons > to believe things. Science is not about believing, but about models. Believing is important to make the career of a scientist maybe, it's for people outside.
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| From | Lawrence D’Oliveiro <lawrencedo99@gmail.com> |
|---|---|
| Date | 2016-06-30 02:42 -0700 |
| Message-ID | <9b17feea-9834-41d7-bebd-a562d2c4a10a@googlegroups.com> |
| In reply to | #110833 |
On Thursday, June 30, 2016 at 9:31:29 PM UTC+12, Andreas Röhler wrote: > Science is not about believing, but about models. The nice thing about science is, it works even if you don’t believe in it.
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| From | Andreas Röhler <andreas.roehler@online.de> |
|---|---|
| Date | 2016-06-30 12:13 +0200 |
| Message-ID | <mailman.132.1467281319.2358.python-list@python.org> |
| In reply to | #110834 |
On 30.06.2016 11:42, Lawrence D’Oliveiro wrote: > On Thursday, June 30, 2016 at 9:31:29 PM UTC+12, Andreas Röhler wrote: > >> Science is not about believing, but about models. > The nice thing about science is, it works even if you don’t believe in it. Thats it!
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| From | Andreas Röhler <andreas.roehler@online.de> |
|---|---|
| Date | 2016-06-30 12:11 +0200 |
| Message-ID | <mailman.131.1467281255.2358.python-list@python.org> |
| In reply to | #110830 |
On 30.06.2016 10:24, Steven D'Aprano wrote: > On Thursday 30 June 2016 12:13, Rustom Mody wrote: > > > The irrational and emotional psychological forces that inspire mathematicians > can make interesting reading, but they have no relevance in deciding who is > write or wrong. Hmm, so math is not inspired by solving real world problems, for example in physics or big-data? > No numbers are real. Numbers express relations, which are represented as symbols. So far they are real, as math exists, the human mind exists. We don't have any natural numbers, assume Kronecker made a joke. "Natural numbers" is the most misleading term in the field maybe.
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| From | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| Date | 2016-07-01 03:18 +1000 |
| Message-ID | <57755482$0$22140$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #110836 |
On Thu, 30 Jun 2016 08:11 pm, Andreas Rc3b6hler wrote: > > > On 30.06.2016 10:24, Steven D'Aprano wrote: >> On Thursday 30 June 2016 12:13, Rustom Mody wrote: >> >> >> The irrational and emotional psychological forces that inspire >> mathematicians can make interesting reading, but they have no relevance >> in deciding who is write or wrong. "Write" or wrong? Oh the shame :-( > Hmm, so math is not inspired by solving real world problems, for example > in physics or big-data? I didn't say that. Of course the work people do is influenced by real world problems, or their own irrational and subjective tastes. Why does one mathematician choose to work in algebra while another chooses to work in topology? As interesting as it may be to learn that (say) Pascal worked on probability theory in order to help a friend who was a keen gambler, the correctness or incorrectness of his work is independent of that fact. >> No numbers are real. > > Numbers express relations, which are represented as symbols. So far they > are real, as math exists, the human mind exists. They are real in the same way that "justice" and "bravery" are real. That is, they are *abstract concepts*, not *things*. -- Steven “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse.
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2016-06-30 08:28 -0700 |
| Message-ID | <0765346e-42a1-48b7-8b7d-e134f4165ce4@googlegroups.com> |
| In reply to | #110830 |
On Thursday, June 30, 2016 at 1:55:18 PM UTC+5:30, Steven D'Aprano wrote: > you state that Turing "believes in souls" and that he "wishes to > put the soul into the machine" -- what do his religious beliefs have to do with > his work? Bizarre question -- becomes more patently ridiculous when put into general form "What does what I do have to do with what I believe?" More specifically the implied suggested equation "soul = religious" is your own belief. See particularly "Christian faith" in the quote below. > What evidence do you have for the second claim? What does it even > mean to put "the" soul (is there only one?) into "the" machine? Excerpted from https://blog.sciencemuseum.org.uk/the-spirit-of-alan-turing/ ======================= Morcom was Turing’s first love, a fellow, older pupil at Sherborne School, Dorset, who shared Turing’s passion for mathematics (who died in 1930) He was profoundly affected by the death of his friend... Turing admitted that he ‘worshipped the ground he trod on’. Morcom’s death cast a long shadow. Turing turned away from his Christian faith towards materialism, and began a lifelong quest to understand the tragedy. As he struggled to make sense of his loss, Turing pondered the nature of the human mind and whether Christopher’s was part of his dead body or somehow lived on. The October after the loss of his friend, Turing went up to Cambridge, where he studied mathematics. Our exhibition includes an essay, entitled “Nature of Spirit” that Turing wrote the next year, in 1932, in which he talked of his belief in the survival of the spirit after death, which appealed to the relatively recent field of quantum mechanics and reflected his yearning for his dear friend. Around that time he encountered the Mathematical Foundations of Quantum Mechanics by the American computer pioneer, John von Neumann, and the work of Bertrand Russell on mathematical logic. THESE STREAMS OF THOUGHT WOULD FUSE when Turing imagined a machine that would be capable of any form of computation. Today the result – known as a universal Turing machine – still dominates our conception of computing. =================================== > And as for Kronecker, well, I suspect he objected more to Cantor's infinities > than to real numbers. After all, even the Pythogoreans managed to prove that > sqrt(2) was an irrational number more than 3000 years ago, something Kronecker > must have known. They -- reals and their cardinality -- are the identical problem And no, the problem is not with √2 which is algebraic See http://mathworld.wolfram.com/AlgebraicNumber.html It is with the transcendentals like e and π ℕ ⫅ ℤ ⫅ ℚ ⫅ A ⫅ ℝ is obvious almost by definition That upto A (algebraic numbers) they are equipotent is somewhat paradoxical but still acceptable (to all parties) See the Cantor pairing function https://en.wikipedia.org/wiki/Countable_set#Formal_overview_without_details parties However between A and ℝ something strange happens (where?) and the equipotence is lost. At least thats the traditional math/platonic view (Cantor/Hilbert etc) Constructivist view "Yes real numbers are not enumerable That means any talk of THE SET ℝ is nonsense (talk with language, symbols whatever can only be enumerable) Therefore Equipotence is like angels on a pin"
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| From | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| Date | 2016-07-01 04:03 +1000 |
| Message-ID | <57755efb$0$1604$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #110850 |
On Fri, 1 Jul 2016 01:28 am, Rustom Mody wrote: > On Thursday, June 30, 2016 at 1:55:18 PM UTC+5:30, Steven D'Aprano wrote: > >> you state that Turing "believes in souls" and that he "wishes to >> put the soul into the machine" -- what do his religious beliefs have to >> do with his work? > > Bizarre question -- becomes more patently ridiculous when put into general > form "What does what I do have to do with what I believe?" Lots of people do things that go against their beliefs, or their beliefs (at least, their professed beliefs) go against what they do. But I'll ask again: in what way does Turing's supposed beliefs about souls have anything to do with his mathematical work? Let's be concrete: In what way does the Halting Problem depend on the existence (or non-existence) of the soul? How was his work on breaking German military codes during World War 2 reliant on these supposed souls? (In the sense of a separate, non-material spirit, not in the figurative sense that all people are "souls".) > More specifically the implied suggested equation "soul = religious" > is your own belief. See particularly "Christian faith" in the quote > below. Of course belief in souls is a religious belief. It certainly isn't a scientific belief, or a materialistic belief. Don't make the mistake of thinking that materialism is a religious belief. It is no more a religious belief than "bald" is a hair colour. >> What evidence do you have for the second claim? What does it even >> mean to put "the" soul (is there only one?) into "the" machine? > > Excerpted from > https://blog.sciencemuseum.org.uk/the-spirit-of-alan-turing/ [snip irrelevancy about the death of Morcom] > Around that time he encountered the Mathematical Foundations of > Quantum Mechanics by the American computer pioneer, John von > Neumann, and the work of Bertrand Russell on mathematical > logic. THESE STREAMS OF THOUGHT WOULD FUSE when Turing imagined a > machine that would be capable of any form of computation. Today > the result – known as a universal Turing machine – still > dominates our conception of computing. "These streams of thought" being the work of von Neumann and Russell. Perhaps, and I'll accept this as a fairly unlikely by theorectically possible result, Turing was only capable of coming up with the concept of the Turing Machine *because of* his rejection of Christianity and his hopes and fears and beliefs about the supposed soul of his deceased friend Morcom. I'll grant that as a possibility, just as it is a possibility that had Friedrich Kekulé not eaten a late night snack of cheese[1] before going to sleep, he never would have dreamt of a snake biting its own tail and wouldn't have come up with the molecular structure of benzene, leaving it to somebody else to do so. But the idiosyncratic and subjective reasons that lead Turing to his discovery are not relevant to the truth or otherwise of his discoveries. >> And as for Kronecker, well, I suspect he objected more to Cantor's >> infinities than to real numbers. After all, even the Pythogoreans managed >> to prove that sqrt(2) was an irrational number more than 3000 years ago, >> something Kronecker must have known. > > They -- reals and their cardinality -- are the identical problem > And no, the problem is not with √2 which is algebraic > See http://mathworld.wolfram.com/AlgebraicNumber.html What reason do you have for claiming that Kronecker objected to non-algebraic numbers? Nothing I have read about him suggests that he was more accepting of algebraic reals than non-algebraic reals. (I'm not even sure if mathematicians in Kronecker's day distinguished between the two.) I daresay that the famous Kronecker comment about god having created the integers was not intended to be the thing he is remembered by. It was probably intended as a smart-arsed quip and put-down of Cantor, not a serious philosophical position. For is we take it *literally*, Kronecker didn't even believe in sqrt(2), and that surely cannot be correct. > It is with the transcendentals like e and π Both e and π can be written as continued fractions, using nothing but ratios of integers: e = (2; 1, 2, 1, 1, 4, 1, 1, 6, 1, 1, 8, ...) π = (3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, ...) so surely if Kronecker accepted square root of two: √2 = (1; 2, 2, 2, 2, ...) he has no reason to reject the others. I'm not entirely convinced that transcendentals deserve to be a separate category of numbers. "Algebraic numbers" seem quite arbitrary to me: what's so special about integer polynomials? Just because the Ancient Greeks had some weird ideas about integers doesn't mean that we have to follow along. I mean, sure, it's interesting to look at integer polynomials as a special case, just as we might look at (say) Diophantine equations or Egyptian Fractions as special cases. There might even be some really important maths that comes from that. But that doesn't necessarily make algebraic numbers any more *fundamental* than "Rustom numbers", the solutions to equations of the form: a0 + a1 * e**x + a2 + e**(x**2) + a3 * e**(x**3) + ... + an * e**(x**n) where the a's are all rational numbers where the numerator and denominator are co-prime. So I accept that transcendental numbers are interesting. I don't necessarily agree that they are fundamental in the same way integers, rationals and reals are. [1] Or perhaps if he *had* eaten a late snack of cheese. -- Steven “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse.
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2016-07-01 07:19 -0700 |
| Message-ID | <7b1b0a49-86ac-4d9e-8113-35c8f56500cc@googlegroups.com> |
| In reply to | #110855 |
On Thursday, June 30, 2016 at 11:33:58 PM UTC+5:30, Steven D'Aprano wrote: > On Fri, 1 Jul 2016 01:28 am, Rustom Mody wrote: > > > On Thursday, June 30, 2016 at 1:55:18 PM UTC+5:30, Steven D'Aprano wrote: > > > >> you state that Turing "believes in souls" and that he "wishes to > >> put the soul into the machine" -- what do his religious beliefs have to > >> do with his work? > > > > Bizarre question -- becomes more patently ridiculous when put into general > > form "What does what I do have to do with what I believe?" > > Lots of people do things that go against their beliefs, or their beliefs (at > least, their professed beliefs) go against what they do. But I'll ask > again: in what way does Turing's supposed beliefs about souls have anything > to do with his mathematical work? > > Let's be concrete: > > In what way does the Halting Problem depend on the existence (or > non-existence) of the soul? Lets change your question -- ever so slightly, given the Turing-context: In what way does the Turing Test depend on the existence (or non-existence) of the soul? > > How was his work on breaking German military codes during World War 2 > reliant on these supposed souls? (In the sense of a separate, non-material > spirit, not in the figurative sense that all people are "souls".) When you say "soul" you (seem to?) mean what has been called with justifiable derision, "dualistic notion of soul" - something for which Christianity gets bad press though its the invention of Descartes http://www.iep.utm.edu/descmind/ - something which caught on because of Descartes huge reputation as a scientist There are other more reasonable non-religious non-dualistic notions of soul possible: http://www.bu.edu/agni/poetry/print/2002/56-szymborska.html <snipped stuff on numbers> You are missing the point -- its not about specific numbers its about cardinality not adding up - Cantor theory points to uncountably many real numbers - All the sets upto algebraic are countable - So the uncountable fellas need to be transcendental - We only know two blessed guys -- π and e Where are all the others hiding?? And dont try saying that if e is transcendental so is 2e 3e 4e... And no use trying more such tricks -- they only multiply these two countably infinite times And you may produce a few more, more esoteric transcendentals --- a very finite set! Nor is it much good saying this is not much relevance to our field: https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument So our (computer scientists') predicament in short - our field is opposed to Cantor's non-constructivist *outlook* - At the foundation of CS are *methods* that.... come from Cantor... OOPS!
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| From | Marko Rauhamaa <marko@pacujo.net> |
|---|---|
| Date | 2016-07-01 18:20 +0300 |
| Message-ID | <87oa6hl710.fsf@elektro.pacujo.net> |
| In reply to | #110900 |
Rustom Mody <rustompmody@gmail.com>: > There are other more reasonable non-religious non-dualistic notions of > soul possible: Software engineers should have an easy time understanding what a soul is: a sufficiently sophisticated software system in execution. I'd say the minimum requirement for a soul is the capacity to suffer. I don't think anything built by humans has yet reached that level of sophistication, but insects probably can feel pain as authentically as humans. > - Cantor theory points to uncountably many real numbers > - All the sets upto algebraic are countable > - So the uncountable fellas need to be transcendental > - We only know two blessed guys -- π and e > > Where are all the others hiding?? Here: <URL: https://en.wikipedia.org/wiki/Transcendental_number>. > And dont try saying that if e is transcendental so is 2e 3e 4e... And > no use trying more such tricks -- they only multiply these two > countably infinite times And you may produce a few more, more esoteric > transcendentals --- a very finite set! The banal way of putting it that we can express only countably many individual items. The more philosophical point of view is that mathematics failed at circumscribing all of philosophy and is condemned to counting beans. Naive set theory was a Grand Unified Theory of Everything, but of course inconsistent. The bottom-up set theories are sane but completely fail at being the ultimate metalevel. Marko
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| From | Rustom Mody <rustompmody@gmail.com> |
|---|---|
| Date | 2016-07-29 22:46 -0700 |
| Message-ID | <d4e25cbd-38cd-4ca3-afde-4c67692e89ce@googlegroups.com> |
| In reply to | #110855 |
On Thursday, June 30, 2016 at 11:33:58 PM UTC+5:30, Steven D'Aprano wrote: > On Fri, 1 Jul 2016 01:28 am, Rustom Mody wrote: > > > On Thursday, June 30, 2016 at 1:55:18 PM UTC+5:30, Steven D'Aprano wrote: > > > >> you state that Turing "believes in souls" and that he "wishes to > >> put the soul into the machine" -- what do his religious beliefs have to > >> do with his work? > > > > Bizarre question -- becomes more patently ridiculous when put into general > > form "What does what I do have to do with what I believe?" > > Lots of people do things that go against their beliefs, or their beliefs (at > least, their professed beliefs) go against what they do. But I'll ask > again: in what way does Turing's supposed beliefs about souls have anything > to do with his mathematical work? > > Let's be concrete: > > In what way does the Halting Problem depend on the existence (or > non-existence) of the soul? > > How was his work on breaking German military codes during World War 2 > reliant on these supposed souls? (In the sense of a separate, non-material > spirit, not in the figurative sense that all people are "souls".) > > > > More specifically the implied suggested equation "soul = religious" > > is your own belief. See particularly "Christian faith" in the quote > > below. > > Of course belief in souls is a religious belief. It certainly isn't a > scientific belief, or a materialistic belief. > > Don't make the mistake of thinking that materialism is a religious belief. > It is no more a religious belief than "bald" is a hair colour. > > <snip> > > What reason do you have for claiming that Kronecker objected to > non-algebraic numbers? Nothing I have read about him suggests that he was > more accepting of algebraic reals than non-algebraic reals. > > (I'm not even sure if mathematicians in Kronecker's day distinguished > between the two.) > Lots of questions... I would guess rhetorical. However under the assumption that they are genuine (or could be genuine for others than you), I went back and checked. I recollected that I started thinking along these lines — viz. that philosophical disputes led to the genesis of computers — after reading an essay by a certain Adam Siepel... which subsequently seems to have fallen off the net I tracked him down and re-posted his essay here: http://blog.languager.org/2016/07/mechanism-romanticism-computers.html Just to be clear — this is Dr. Adam Siepel's writing reposted with his permission
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| From | Steven D'Aprano <steve@pearwood.info> |
|---|---|
| Date | 2016-08-01 12:53 +1000 |
| Message-ID | <579eb9b2$0$1611$c3e8da3$5496439d@news.astraweb.com> |
| In reply to | #112042 |
On Sat, 30 Jul 2016 03:46 pm, Rustom Mody wrote: > Lots of questions... I would guess rhetorical. They weren't rhetorical. You've made a lot of claims about the origins of computer science, and I've questioned some of your statements. Answers would be appreciated. > However under the assumption that they are genuine (or could be genuine > for others than you), I went back and checked. > I recollected that I started thinking along these lines — viz. that > philosophical disputes led to the genesis of computers — after reading an > essay by a certain Adam Siepel... which subsequently seems to have fallen > off the net > > I tracked him down and re-posted his essay here: > http://blog.languager.org/2016/07/mechanism-romanticism-computers.html > > Just to be clear — this is Dr. Adam Siepel's writing reposted with his > permission The essay is not awful, but I wouldn't shout its praises either. It looks to me like an undergraduate essay, taking a very narrow and rather naive view of the field. There's not a lot of references (only nine), which means the author is (in my opinion) excessively influenced by a small number of views, and I don't see any sign that he has even made a half-hearted attempt to seek out alternate views. The author makes a claim: "... Principia Mathematica, between 1910 and 1913, which in its attempt to place mathematics squarely in the domain of logic, represented the first new system of logic since Aristotle" but doesn't give any justification for the claim. Why single out the Principia and ignore the works of the Stoics, Peter Abelard, William of Ockham, Augustus DeMorgan, Gottlob Frege and most especially George Boole dismissed? I would think that if anyone truly deserved credit for creating a new system of logic, it should be Boole. But perhaps that's just a matter of opinion on where you draw the lines. http://www.iep.utm.edu/prop-log/#H2 That's not really central to his argument, but it does suggest that his views are quite idiosyncratic. To my mind, that feels like someone claiming that Stephen Hawking is the first genuinely original physicist since Newton. Einstein? Schrödinger? Dirac? Never heard of 'em. A rather large section of the essay is an irrelevant (and, I think, incorrect) digression about "Mechanists" and "Romantics", neither of which is really relevant to the philosophy of mathematics. He eventually mentions the Intuitionists, but I don't think he understands them. By linking them to the Romantics, he seems to think that the Intuitionist school of thought doesn't require mathematical proofs, or that they are satisfied with the "intuitively obvious truth" of axioms. But that's not what the Intuitionists were about: https://en.wikipedia.org/wiki/Intuitionism He mischaracterises and over-simplifies the argument over the foundations of mathematics: https://en.wikipedia.org/wiki/Brouwer–Hilbert_controversy with at least three separate groups involved (Logicists such as Russell, Formalists such as Hilbert, and Constructivists such as Poincaré -- four groups if you count Intuitionism separate from Constructionism). He exaggerates the death of the Logicist school of thought. It continues today with Second Order Logic. And I wonder why you are taking this essay as supporting your position. According to this essay, the Intuitionists won in mathematics. And yet Turing and Von Neumann (two major pioneers of computing) were "Mechanists". If Intuitionism influenced computer science, where is the evidence of this? Where are the Intuitionist computer scientists? On the contrary, academic CS seems to have come from the Logicist school of thought, and practical computer engineering from "whatever works" school of thought. None of this even *remotely* supports your assertions such as "[Turing] wishes to put the soul into the machine". Maybe he did. But this essay gives no reason to think so, or any reason to think that Turing's personal beliefs about souls is the slightest bit relevant to computer science. -- Steven “Cheer up,” they said, “things could be worse.” So I cheered up, and sure enough, things got worse.
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