 |
|
|
|
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Invisible" <voi### [at] dev null> wrote in message
news:483fee71@news.povray.org...
> Stephen wrote:
> > Obviously not an engineer. :)
> Hmm... so is "software engineer" not an engineer then? ;-)
True, programmers often pretend to be engineers, scientists and architects.
Thankfully, "software doctor" is not a term that has yet caught on..
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Stephen wrote:
> What part of "don't" do you not understand, Andrew? ;)
Um... the abbreviated part? :-}
> We've met, did I look like "an interested in games" type of person?
> On second thoughts, don't answer that :)
Well gee, I don't know. I mean I got the impression... oh wait, you said
DON'T answer that? ;-)
Heh. well screw the game. I just find the idea of a guy casually having
a beer and a sing-song in the middle of a warzone kinda humurous...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Invisible wrote:
> For example: How am I gonna stop some big bean mutha hubba from tearing
> me a new, structurally superflous behind? The answer: Use a gun. And if
> they don't work: Use MORE gun.
Reminds me of an old #xml channel topic. "XML is like violence. If it
doesn't solve the problem, use more."
(I don't agree with it)
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Fri, 30 May 2008 16:08:46 +0100, Invisible <voi### [at] devnull> wrote:
>
>Heh. well screw the game. I just find the idea of a guy casually having
>a beer and a sing-song in the middle of a warzone kinda humurous...
Yeah, I would not have thought that war zones were the best place for
a boozy sing song. Unless it was
Spam, spam, spam, spam, spam, spam, baked beans, spam, spam, spam and
spam
Spam, sausage, spam, spam, spam, bacon, spam, tomato and spam
--
Regards
Stephen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Nicolas Alvarez wrote:
> Reminds me of an old #xml channel topic. "XML is like violence. If it
> doesn't solve the problem, use more."
>
> (I don't agree with it)
"Sometimes, you have a problem, and you think 'hey, I could solve this
using Perl!' And then you have TWO problems..." ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Invisible <voi### [at] devnull> wrote:
> "Real-world problems are simply degenerate cases of pure mathematical
> problems."
Not related, but saw this today:
"Any sufficiently advanced magic is indistinguishable from technology"
-- Larry Niven's corollary to Clarke's Third Law.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mueen Nawaz wrote:
> And that theory is simply mathematically invalid (at least with the
> current state of mathematics).
I gave up when I learned what "spin 2" particles actually means. :-)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On 30 May 2008 11:34:54 -0400, Warp <war### [at] tagpovrayorg> wrote:
>Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
>"Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
That brought a smile to my face.
--
Regards
Stephen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Invisible wrote:
> Stephen wrote:
>
>> Obviously not an engineer. :)
>
> Hmm... so is "software engineer" not an engineer then? ;-)
>
definitely not. Engineer is (at least here in the Netherlands and the
US) a protected title. You are not allowed to call yourself an engineer
unless you have passed a final exam in one of the certified engineering
courses. It is therefor not hard to prove that nearly all software
engineers are breaking the law. I know the IEEE (of which I am an
associate member, because I am not an engineer) finds the software
engineers a treat to the perception of engineers by laymen. IIRC the
practice is so wide spread that they think it has become impossible to
enforce the law in these cases. That does not stop them from being annoyed.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
How true it is... ;-)
[...for example, I am speakin to a person I've never met, who is
currently in a country I've never visited. Cavemen would be astounded!]
In our lab, some joker put the following on the wall:
"Statinger's Law: It works better if you plug it in."
"Horner's Five Thumb Postulate: Experience varies directly with
equipment ruined."
"Snells Rule: Whatever we did, that was what we planned to do."
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
>
Hmm apparently a cookie thread. let's add another one:
I got this fortune cookie less than 24 hours ago:
"Our government has kept us in a perpetual state of fear -- kept us in
a continuous stampede of patriotic fervor -- with the cry of grave
national emergency... Always there has been some terrible evil to
gobble us up if we did not blindly rally behind it by furnishing the
exorbitant sums demanded. Yet, in retrospect, these disasters seem
never to have happened, seem never to have been quite real."
-- General Douglas MacArthur, 1957
(Possibly one of the offensive cookies)
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Orchid XP v8 wrote:
> Warp wrote:
>
>> "Any sufficiently advanced magic is indistinguishable from technology"
>> -- Larry Niven's corollary to Clarke's Third Law.
>
> How true it is... ;-)
>
> [...for example, I am speakin to a person I've never met, who is
> currently in a country I've never visited. Cavemen would be astounded!]
I think that one is covered by the original Third Law of Arthur C Clarke
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> Invisible <voi### [at] devnull> wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> Not related, but saw this today:
>
> "Any sufficiently advanced magic is indistinguishable from technology"
> -- Larry Niven's corollary to Clarke's Third Law.
Any technology distinguishable from magic is insufficiently advanced.
-- some other corollary to the 3rd Law.
--
Tim Cook
http://empyrean.digitalartsuk.com
-----BEGIN GEEK CODE BLOCK-----
Version: 3.12
GFA dpu- s: a?-- C++(++++) U P? L E--- W++(+++)>$
N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
D++(---) G(++) e*>++ h+ !r--- !y--
------END GEEK CODE BLOCK------
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Fri, 30 May 2008 16:16:48 -0400, Tim Cook <z99### [at] gmailcom>
wrote:
>
>Any technology distinguishable from magic is insufficiently advanced.
> -- some other corollary to the 3rd Law.
Cook's corollary to the 3rd Law? :)
--
Regards
Stephen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Stephen wrote:
> Cook's corollary to the 3rd Law? :)
Nah, I found it somewhere on the web.
--
Tim Cook
http://empyrean.digitalartsuk.com
-----BEGIN GEEK CODE BLOCK-----
Version: 3.12
GFA dpu- s: a?-- C++(++++) U P? L E--- W++(+++)>$
N++ o? K- w(+) O? M-(--) V? PS+(+++) PE(--) Y(--)
PGP-(--) t* 5++>+++++ X+ R* tv+ b++(+++) DI
D++(---) G(++) e*>++ h+ !r--- !y--
------END GEEK CODE BLOCK------
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
andrel wrote:
> "Our government has kept us in a perpetual state of fear -- kept us in
> a continuous stampede of patriotic fervor -- with the cry of grave
> national emergency... Always there has been some terrible evil to
> gobble us up if we did not blindly rally behind it by furnishing the
> exorbitant sums demanded. Yet, in retrospect, these disasters seem
> never to have happened, seem never to have been quite real."
> -- General Douglas MacArthur, 1957
>
> (Possibly one of the offensive cookies)
I've got a great book on Harry S Truman. You should see what he said
about MacArthur.
Unfortunately, I'm too lazy to dig it out :( Suffice it to say, he
called the guy an idiot.
...Chambers
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Sat, 31 May 2008 15:36:22 -0700, Chambers wrote:
> andrel wrote:
>> "Our government has kept us in a perpetual state of fear -- kept us in
>> a continuous stampede of patriotic fervor -- with the cry of grave
>> national emergency... Always there has been some terrible evil to
>> gobble us up if we did not blindly rally behind it by furnishing the
>> exorbitant sums demanded. Yet, in retrospect, these disasters seem
>> never to have happened, seem never to have been quite real."
>> -- General Douglas MacArthur, 1957
>>
>> (Possibly one of the offensive cookies)
>
> I've got a great book on Harry S Truman. You should see what he said
> about MacArthur.
Is the book "The Fifties" by David Halberstam? The quote that's listed
on wikiquote from there is about MacArthur's "Old soldiers never die"
speech - "Nothing but a d*mn bunch of BS" (paraphrased).
Jim
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Mueen Nawaz wrote:
> Invisible wrote:
>> "Real-world problems are simply degenerate cases of pure mathematical
>> problems."
>
> I recently attended a talk given by Arthur Jaffe, a (co)founder of
> the Clay institute and professor at Harvard (forgot if he's in the math
> or physics dept). His work is mathematical physics.
>
> I don't know his stance, but he knows many top physicists and
> perhaps mathematicians as well who'd disagree. Essentially, the (very
> boring) talk was about this very issue: Are mathematics and physics
> consistent with each other?
>
> A lot of the calculations in physics as currently performed are
> actually mathematically invalid. He gave this startling example. You see
> the g_s in the equation on this page?
>
> http://en.wikipedia.org/wiki/Magnetic_moment#Magnetic_moment_of_electrons
>
> It has now been measured to around 12 significant figures - perhaps
> the most precise measurement ever made. Those 12 figures agree with theory.
>
> And that theory is simply mathematically invalid (at least with the
> current state of mathematics).
I'm not sure that "mathematically invalid" means anything here. It
would be more precise to say that the model described by the mathematics
in question does not apply to the phenomena described.
Is .5c + .5c = 1c mathematically valid? Well, yes. If two observers,
moving at .5c relative to one observer, in opposing directions, observe
each other, do their observations of each others' motion equal 1.0c? We
now know that they will observe a lesser value (.75c, IIRC). .5c + .5c
=1.0c is still mathematically valid, but the math describes a model of
motion that does not apply to real-world motion (although the error is
important only at velocities that are significant fractions of c).
So it isn't a case of the math being wrong, it's a case of the math
being irrelevant, which is the reason for this famous physics quote by
Wolfgang Pauli: "This isn't right. This isn't even wrong."
Regards,
John
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
John VanSickle <evi### [at] hotmailcom> wrote:
> Is .5c + .5c = 1c mathematically valid? Well, yes.
The problem with that equation is that it lacks the proper context,
more precisely the topology used.
In a linear cartesian space that equation is correct. However, the
context of the equation is not a linear cartesian space. Thus, in context,
it makes it invalid.
I would say that mathematics can always be used to represent reality
when put in the proper context.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Chambers wrote:
> andrel wrote:
>> "Our government has kept us in a perpetual state of fear -- kept us in
>> a continuous stampede of patriotic fervor -- with the cry of grave
>> national emergency... Always there has been some terrible evil to
>> gobble us up if we did not blindly rally behind it by furnishing the
>> exorbitant sums demanded. Yet, in retrospect, these disasters seem
>> never to have happened, seem never to have been quite real."
>> -- General Douglas MacArthur, 1957
>>
>> (Possibly one of the offensive cookies)
>
> I've got a great book on Harry S Truman. You should see what he said
> about MacArthur.
>
> Unfortunately, I'm too lazy to dig it out :( Suffice it to say, he
> called the guy an idiot.
>
A couple of remarks:
- According to that most reliable source of wikipedia, it was Truman
that fired MacArthur for disagreeing with him. So I would be surprised
if he did not try to portrait him as an idiot. That is irrespective of
whether he was right or wrong. Simply the case that a president fires a
famous general dictates that the president should convince the public
that he was much better equipped than the general.
- The reason I found this quote interesting is that when you start
reading it you expect some left wing attack on president Bush for his
Iraq invasion. An then it isn't. Even if it had been a 50 year old quote
from a true idiot it would still be interesting.
- He is not the only general to show insights into the political process
after their active duty in a way that makes you wonder why they did not
resign themselves earlier. In fact that seems to hold also for
presidential spokesmen and the like.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> I would say that mathematics can always be used to represent reality
> when put in the proper context.
The fascinating thing to wonder about is ... why is this so?
Most people are so used to it that it's hard to even imagine a world
where this isn't true. Even the religious types try to come up with
"laws" that would govern the supernatural.
Of course, maybe that's just anthropogenic. If the universe didn't work
consistently, I'd (wild-ass) guess that it's likely that life capable of
wondering about it wouldn't have evolved.
And the thing about QED is there doesn't seem to be math at the bottom
level - it's random on an event-by-event basis. (Maybe there's a math
for that? I don't know of any. Statistics only deals with multiple events.)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New <dne### [at] sanrrcom> wrote:
> Of course, maybe that's just anthropogenic. If the universe didn't work
> consistently, I'd (wild-ass) guess that it's likely that life capable of
> wondering about it wouldn't have evolved.
I'm sure if you asked a physicist specialized in quantum mechanics he
would say that life would probably not be possible without the wild
uncertainties of quantum phenomena (such as particles physically being
at multiple locations at the same time).
Yet, even the counter-intuitive quantum phenomena can be subject to
mathematical formulation.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New wrote:
> And the thing about QED is there doesn't seem to be math at the bottom
> level - it's random on an event-by-event basis.
My personal theory is that it *isn't* random - we just can't see it well
enough to find a pattern. (As in, it's not possible to make the actual
measurements that would reveal a pattern.) But hey, what do I know?
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> Yet, even the counter-intuitive quantum phenomena can be subject to
> mathematical formulation.
A closed set can also be an open set.
It is possible to construct a 2D set of points such that each point
simultaneously touches three other connected sets.
A propper class is a collection of things larger than any possible set.
Mathematics is *littered* with utterly counter-intuitive things. ;-)
[And people wonder why mathematicians are so pedantic about everything.
If YOU worked with something so unpredictable, you'd be cautious too...]
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
andrel wrote:
> A couple of remarks:
> - According to that most reliable source of wikipedia, it was Truman
> that fired MacArthur for disagreeing with him. So I would be surprised
> if he did not try to portrait him as an idiot. That is irrespective of
> whether he was right or wrong. Simply the case that a president fires a
> famous general dictates that the president should convince the public
> that he was much better equipped than the general.
Basically, it all came down to the fact that MacArthur wanted to go out,
fight, and win WWIII.
Truman did everything in his power to avoid an actual war - he thought
two World Wars were more than enough, and would rather see the conflict
played out on a smaller scale. The Korean War (and, eventually, the
Vietnam War) were direct results of his policies in that respect, as was
the Cold War in general.
People blame our leadership for those confrontations, but fail to
realize that the alternative was all out war on a scale similar to, if
not larger than, WWII.
...Chambers
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Orchid XP v8 wrote:
> My personal theory is that it *isn't* random - we just can't see it well
> enough to find a pattern. (As in, it's not possible to make the actual
> measurements that would reveal a pattern.) But hey, what do I know?
No, you can actually measure that isn't the case. Look up "Bell's
Inequality."
Basically, if you measure A, you get W or X. If you measure B, you get Y
or Z. If there was some variable C that told you which you got, you'd
get a distribution of W,X,Y,Z when you measured some As and some Bs
that's different from what you really get. Hence, there's no actual
"hidden variable", not even one that you theoretically can't measure.
It's complex and ugly, but if you actually find a decent tutorial, it
makes sense.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> I'm sure if you asked a physicist specialized in quantum mechanics he
> would say that life would probably not be possible without the wild
> uncertainties of quantum phenomena (such as particles physically being
> at multiple locations at the same time).
I imagine that life based on DNA and chemistry and such wouldn't work
the same way. I was talking more about if (say) the universe worked the
way you thought it should, or there really were demons and spirits that
could make fundamental changes to how the world works, etc.
(BTW, you don't get particles being physically present at multiple
locations. If you actually measure where they are, they're only in one
place.)
> Yet, even the counter-intuitive quantum phenomena can be subject to
> mathematical formulation.
Only statistically speaking, tho. Nobody has figured out what causes it
to have the properties they have, even tho (surprisingly enough) it's
the only way you can get a mathematically consistent treatment. In a bit
more detail, QED is based on probabilities. The only probabilities that
work are 1-dimensional probabilities (i.e., real numbers, and =
multiply, or = add), and 2-dimensional probabilities (i.e., complex
numbers as probabilities). I believe it's been mathematically proven
that you can't have something with the properties of "probability" that
has more than 2 dimensions. QED has two-dimensional probabilities for
events, and when you average enough of them you get one-dimensional
probabilities for events.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
andrel wrote:
> exorbitant sums demanded. Yet, in retrospect, these disasters seem
> never to have happened, seem never to have been quite real."
> -- General Douglas MacArthur, 1957
That doesn't really sound like a MacArthur quote. More like something
Truman said to MacArthur. :-)
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Darren New" <dne### [at] sanrrcom> wrote
> Warp wrote:
> > I would say that mathematics can always be used to represent reality
> > when put in the proper context.
> The fascinating thing to wonder about is ... why is this so?
Easy. Mathematics can represent *anything*, since you get to make up your
own axioms.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Orchid XP v8 <voi### [at] devnull> wrote:
> Mathematics is *littered* with utterly counter-intuitive things. ;-)
Ever heard of the Banach-Tarski paradox? A solid ball in 3-dimensional
space can be split into several non-overlapping pieces, which can then be
put back together in a different way to yield two identical copies of
the original ball.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New <dne### [at] sanrrcom> wrote:
> (BTW, you don't get particles being physically present at multiple
> locations. If you actually measure where they are, they're only in one
> place.)
But their simultaneous location in more than one place can be inferred
by other side-effects. For example a single electron can pass through two
slits at the same time, interfering with itself after doing so.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Chambers wrote:
> andrel wrote:
>> A couple of remarks:
>> - According to that most reliable source of wikipedia, it was Truman
>> that fired MacArthur for disagreeing with him. So I would be surprised
>> if he did not try to portrait him as an idiot. That is irrespective of
>> whether he was right or wrong. Simply the case that a president fires
>> a famous general dictates that the president should convince the
>> public that he was much better equipped than the general.
>
> Basically, it all came down to the fact that MacArthur wanted to go out,
> fight, and win WWIII.
>
> Truman did everything in his power to avoid an actual war - he thought
> two World Wars were more than enough, and would rather see the conflict
> played out on a smaller scale.
Indeed, just what Truman would say ;)
> The Korean War (and, eventually, the
> Vietnam War) were direct results of his policies in that respect, as was
> the Cold War in general.
>
> People blame our leadership for those confrontations, but fail to
> realize that the alternative was all out war on a scale similar to, if
> not larger than, WWII.
>
> ...Chambers
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
> Ever heard of the Banach-Tarski paradox? A solid ball in 3-dimensional
> space can be split into several non-overlapping pieces, which can then be
> put back together in a different way to yield two identical copies of
> the original ball.
I hadn't heard of that one, but it makes perfect sense in a topology
context.
In that context "split" really means a 1:2 mapping of spaces.
Cut the ball in half, then in the two hemispheres the new equator plane
is a curve from the lip that follows a 0.5*y scaled sphere, from there
just map the curved planes back to flat to get two spheres.
Since we're talking about a mapping, not a real object, there's no
conservation of volume, a sphere is a sphere, no matter what the size.
The paradox is that the more mathematicians learn,
the less they are able to explain clearly.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Sun, 1 Jun 2008 13:34:22 -0600, "somebody" <x### [at] ycom> wrote:
>"Darren New" <dne### [at] sanrrcom> wrote
>> Warp wrote:
>
>> > I would say that mathematics can always be used to represent reality
>> > when put in the proper context.
>
>> The fascinating thing to wonder about is ... why is this so?
>
>Easy. Mathematics can represent *anything*, since you get to make up your
>own axioms.
>
Oh! You let the secret our :)
--
Regards
Stephen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New wrote:
> Warp wrote:
>> I'm sure if you asked a physicist specialized in quantum mechanics he
>> would say that life would probably not be possible without the wild
>> uncertainties of quantum phenomena (such as particles physically being
>> at multiple locations at the same time).
>
> I imagine that life based on DNA and chemistry and such wouldn't work
> the same way.
It wouldn't work at all. Let's put it this way: if the Universe was as
complicated as the most inventive physicist can image, it would still
not be complex enough for life to develop. Hmm, there might be a good
sig in that for this physicist.
--
Physics is incompatible with life.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
somebody wrote:
> Easy. Mathematics can represent *anything*, since you get to make up your
> own axioms.
Now try inventing a *consistent* set of axioms. ;-)
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Tim Attwood <tim### [at] comcastnet> wrote:
> I hadn't heard of that one, but it makes perfect sense in a topology
> context.
> In that context "split" really means a 1:2 mapping of spaces.
> Cut the ball in half, then in the two hemispheres the new equator plane
> is a curve from the lip that follows a 0.5*y scaled sphere, from there
> just map the curved planes back to flat to get two spheres.
> Since we're talking about a mapping, not a real object, there's no
> conservation of volume, a sphere is a sphere, no matter what the size.
That doesn't work. The volume of the sphere cannot be modified by a
simple change in topology. You cannot simply change the topology and
then calculate the volume as if you hadn't. You have to calculate the
volume using the *new* topology, not the old one.
Besides, if what you say was true, the same trick would work with a
2-dimensional circle, but it has been proven that it doesn't.
And besides, the original setup happens in regular cartesian coordinates,
without any change in topology.
> The paradox is that the more mathematicians learn,
> the less they are able to explain clearly.
You clearly haven't understood the theorem.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> Ever heard of the Banach-Tarski paradox?
There's another cool one, I don't remember what it's called, that proves
you can chop up a filled-in circle (I.e., a 2D slice thru a ball,
whatever you call that) and then put it back together again as a perfect
square, with no overlaps and no gaps.
Personally, I can't imagine how that can be possible, but you can
apparently do it with sufficiently many cuts.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> But their simultaneous location in more than one place can be inferred
> by other side-effects.
Nope. When you actually measure it, it's only going thru one slit.
> For example a single electron can pass through two
> slits at the same time, interfering with itself after doing so.
Not as such. Yes, you get interference patterns. No, as far as I know,
there's no evidence to suggest it goes through both slits. Nobody is
quite sure how it works, but there's no measurement that when you say
"where is the thing" it ever gives you more than one answer.
That's the funky part. It *isn't* intuitive.
Indeed, there are all kinds of experiments (like closing one slit too
close to the photon for it to know that the slit was closed, or
something like that) that indicate that you can't treat the situation
like the photon or electron goes through both slits at once.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
somebody wrote:
> Easy. Mathematics can represent *anything*, since you get to make up your
> own axioms.
Except for two things: all the equations are actually pretty simple,
none of them seem to change.
It's not really the case you can represent *anything* with mathematics.
You cannot represent God (pretty much by definition of God), and you
cannot represent a partially-inconsistent system (one that is
inconsistent sometimes but not other times, or in some places but not
other places). Just as a couple of offhand examples.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Darren New" <dne### [at] sanrrcom> wrote
> somebody wrote:
> > Easy. Mathematics can represent *anything*, since you get to make up
your
> > own axioms.
> Except for two things: all the equations are actually pretty simple,
> none of them seem to change.
Simplicity is in the eye of the beholder.
> It's not really the case you can represent *anything* with mathematics.
> You cannot represent God (pretty much by definition of God), and you
That's because "god(s)" are not anythings. When one shows that
they/he/she/it is, there's no reason why you won't be able to model
they/he/she/it.
> cannot represent a partially-inconsistent system (one that is
> inconsistent sometimes but not other times,
Then you incorporate time into your equations/model.
> or in some places but not
> other places).
Then you incorporate places into your equations/model.
> Just as a couple of offhand examples.
Isotropy/homegeneity of space/time has nothing to do with whether
representation is possible. Since observation can be thought of as a
representation, anything observable automatically has one representation at
least. Whether that model can be simplified, and can have predictive powers
or not is the question, and if it has redundancy, it can. A reality that can
not be expressed with a simplified model, would, in essence, be random in
*all* aspects (again, redundancy leads to prediction). I cannot imagine how
intelligence of any sort can arise in such a reality.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Orchid XP v8" <voi### [at] devnull> wrote in message
news:48431221$1@news.povray.org...
> somebody wrote:
> > Easy. Mathematics can represent *anything*, since you get to make up
your
> > own axioms.
> Now try inventing a *consistent* set of axioms. ;-)
Easy as Pi:
1. Start with some axioms
2. While there are inconsistent axioms, remove a conflicting one.
<g>
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
somebody wrote:
>> Except for two things: all the equations are actually pretty simple,
>> none of them seem to change.
>
> Simplicity is in the eye of the beholder.
While that's true, it's also irrelevant. You *can* compare various
mathematical formalisms for simplicity. That there seem to be only four
non-integer magic constants in the entire universe would seem to
indicate there might be something simpler than expected going on.
>> It's not really the case you can represent *anything* with mathematics.
>> You cannot represent God (pretty much by definition of God), and you
>
> That's because "god(s)" are not anythings.
How do you know?
> When one shows that they/he/she/it is, there's no reason why you won't be able to
model
> they/he/she/it.
How do you know?
I mean, really. First you say "I don't know what it is." Then in the
very next sentence, you assert properties of it.
>> cannot represent a partially-inconsistent system (one that is
>> inconsistent sometimes but not other times,
>
> Then you incorporate time into your equations/model.
Um, no. I mean "inconsistent" in the mathematical sense.
Every once in a while, God comes along and changes the rules so that
nothing makes sense there for a while. Sort of "Tower of Babel" only for
physical laws. I don't think you're going to find a mathematical formula
that models that well enough to predict God's whims.
>> or in some places but not
>> other places).
>
> Then you incorporate places into your equations/model.
Ibid.
>> Just as a couple of offhand examples.
>
> Isotropy/homegeneity of space/time has nothing to do with whether
> representation is possible.
No, it's the inconsistency I'm speaking of. That's what has to do with
representation.
> Since observation can be thought of as a
> representation, anything observable automatically has one representation at
> least.
But that representation might not follow any sort of mathematical model.
For example, there's no known mathematical model to indicate where a
specific electron is, and indeed if I understand correctly, experiments
show there cannot be one.
I strongly suspect there's no possible mathematical model for "free
will" in its usual meaning.
Experiments with gravity show the best theory we have for it is
incompatible with the best theory we have for atomic interactions. What
happens when someone proves that gravity is incompatible with quantum
mechanics? That there cannot be a GUT?
> Whether that model can be simplified, and can have predictive powers
> or not is the question,
If it doesn't have predictive powers, it's not an appropriate model.
It's merely a summary of the past rather than a model of the actual reality.
> A reality that can
> not be expressed with a simplified model, would, in essence, be random in
> *all* aspects
Nah. Your model would just be *wrong*.
> (again, redundancy leads to prediction).
Only redundancy of cause and effect.
> I cannot imagine how
> intelligence of any sort can arise in such a reality.
That's kind of what I was saying. It's hard to imagine that sort of
reality.
--
Darren New / San Diego, CA, USA (PST)
"That's pretty. Where's that?"
"It's the Age of Channelwood."
"We should go there on vacation some time."
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
"Darren New" <dne### [at] sanrrcom> wrote in message
news:484363fb$1@news.povray.org...
> somebody wrote:
> For example, there's no known mathematical model to indicate where a
> specific electron is, and indeed if I understand correctly, experiments
> show there cannot be one.
Some syntatically correct questions can be meaningless. What colour is the
note C#?
> I strongly suspect there's no possible mathematical model for "free
> will" in its usual meaning.
The problem is that the usual meaning isn't. Plus you have to be aware of
and agree on the level of abstraction you are working with. An economical
question becomes practically meaningless at subatomic level of the atoms of
the cells of the human of the masses that create the demand. "Free will" is
at best a crude concept at individual human level, and it goes downhill from
there quickly at any other more fundamental levels.
> Experiments with gravity show the best theory we have for it is
> incompatible with the best theory we have for atomic interactions. What
> happens when someone proves that gravity is incompatible with quantum
> mechanics? That there cannot be a GUT?
Unfortunately (or fortunately), you cannot disprove reality. The question is
not whether or not there's a GUT (reality provides one working model at
least) but when/if we can come up with a manageable and non-ugly one.
> > Whether that model can be simplified, and can have predictive powers
> > or not is the question,
> If it doesn't have predictive powers, it's not an appropriate model.
> It's merely a summary of the past rather than a model of the actual
reality.
Past *is* "actual" reality. More so than future, less so than present.
> > A reality that can
> > not be expressed with a simplified model, would, in essence, be random
in
> > *all* aspects
> Nah. Your model would just be *wrong*.
Modelling randomness is easy (in theory anyway). It just won't have
predictive ability.
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New wrote:
> There's another cool one, I don't remember what it's called, that proves
> you can chop up a filled-in circle (I.e., a 2D slice thru a ball,
> whatever you call that) and then put it back together again as a perfect
> square, with no overlaps and no gaps.
>
> Personally, I can't imagine how that can be possible, but you can
> apparently do it with sufficiently many cuts.
Yes - wasn't that proven only recently?
The remarkable thing, in case anyone didn't glean it from Darren's
description, is that this can be done with a *finite* number of cuts. I
recall it was a huge number, though.
--
Aibohphobia: Fear of palindromes.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Warp wrote:
> But their simultaneous location in more than one place can be inferred
> by other side-effects. For example a single electron can pass through two
> slits at the same time, interfering with itself after doing so.
I have to side with Darren on this. Your assertion that the electron is
passing through two slits at the same time is merely your imposing a
certain belief onto the system. Yet, any attempt to *directly* verify
your theory will fail.
When I learned quantum mechanics, the professors (and probably the
books) tended to be careful not to make statements like these. The
emphasis is always, "I don't really know what's going on, and so we're
not going to waste time pondering over it. We have this abstract
quantity known as the wavefunction, and a formalism about it that
actually does work statistically, and we'll focus on that."
The wavefunction of a particle is nonzero in a whole region - perhaps
in two disconnected regions. They'll all say that. But the (serious)
books don't go from that to saying, "The particle is in two places at once."
--
Aibohphobia: Fear of palindromes.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
John VanSickle wrote:
>> And that theory is simply mathematically invalid (at least with
>> the current state of mathematics).
>
> I'm not sure that "mathematically invalid" means anything here. It
> would be more precise to say that the model described by the mathematics
> in question does not apply to the phenomena described.
I think I was misunderstood. Here are two examples I've seen:
1) Summing a mathematically divergent series and assigning a
non-infinite value to it. I think I saw it only once and there was some
physical rationale, but I've been told this isn't all that rare.
2) Consider the integral of f(x)/(x*x) where the lower limit of
integration is 0. Now the standard way to handle this is to let the
lower limit be p > 0 (assuming the upper limit is positive). Evaluate
the integral, and let the limit of p go to 0.
Except for certain f(x), that limit does not exist, or diverges.
That won't stop the physicists, though. They "solve" the problem by
considering the following integral:
f(x)/(x*x + i*t*t)
t is some positive parameter, and i is the square root of negative 1.
Now the integrand is no longer singular at x=0, because of the t. Great.
Integrate, and get your result in terms of t. Now take the limit as t
goes to 0. It's possible you'll get a finite limit.
The physicists then proceed to take *that* as the answer to the
original integral.
I've seen this "trick" used quite often. To be honest, I don't know how
mathematically invalid it is. I asked a math PhD friend, and he doubted
it was valid - but he's not in analysis, so he wouldn't know for sure.
It's quite possible that it's mathematically valid for a certain domain
of problems, and the physicists never really state them - just
shortcutting to the final result. I should go and study some *real*
analysis (real as in serious, not real vs complex...).
There's the whole issue of "renormalization" to deal with infinities in
physics. I won't go into any detail as I've never formally studied it.
But it's another often cited example of "fishy mathematics".
So by mathematically invalid, I meant that had they tried publishing in
a math journal, it would never get accepted. Within the fields of
mathematics, their results are invalid. Your example of relativity is
not an example of invalid mathematics. The algebra works out whether
you're assuming relativity or not. One of them may not correspond to the
universe, but the algebra is still sane mathwise.
Physicists, however, get away with this often. Mathematical correctness
is a secondary concern. If they can abuse mathematics and get a theory
that better explains the world, then no one cares about the mathematical
irregularities. Physicists are scientists - they're beholden to
different criteria than mathematicians. Consistency is not that important.
So one is left with three possibilities (well, more - but no one
considers those):
1) The theory that works even though it violates rules of mathematics
may actually be false/flawed. It's just fortuitous - an intermediate
theory. It will be replaced by a mathematically consistent theory that
explains the results better.
2) The theory, *and* the mathematics is valid. It's just that current
mathematics is not sufficiently advanced to "explain" the weird
mathematical manipulations in the theory. I wish I could think of a
better example, but it's as if mathematics had no concept of negative
numbers, and a physicist introduced them and better explained the
universe. The mathematicians then finally come up with a system that is
consistent with the old math, but also encompasses negative numbers.
3) The physical world and mathematics, at some fundamental level, are
just inconsistent. It's anathema to some, but at the end of the day, we
have no good reason to insist that the two should be consistent.
--
Aibohphobia: Fear of palindromes.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
On Sun, 01 Jun 2008 23:58:25 -0500, Mueen Nawaz <m.n### [at] ieeeorg>
wrote:
>Darren New wrote:
>> There's another cool one, I don't remember what it's called, that proves
>> you can chop up a filled-in circle (I.e., a 2D slice thru a ball,
>> whatever you call that) and then put it back together again as a perfect
>> square, with no overlaps and no gaps.
>>
>> Personally, I can't imagine how that can be possible, but you can
>> apparently do it with sufficiently many cuts.
>
> Yes - wasn't that proven only recently?
>
> The remarkable thing, in case anyone didn't glean it from Darren's
>description, is that this can be done with a *finite* number of cuts. I
>recall it was a huge number, though.
Do you mean that someone has managed to square the circle?
I thought that it had been proved to be impossible in the 19th century
--
Regards
Stephen
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Stephen <mcavoysAT@aoldotcom> wrote:
> Do you mean that someone has managed to square the circle?
The "squaring the circle" problem imposes some restrictions.
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
| |
|
|
Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > But their simultaneous location in more than one place can be inferred
> > by other side-effects.
> Nope. When you actually measure it, it's only going thru one slit.
So when the electron hits the sensitive film *after* it has passed the
slits, it goes back to the past and changes it so that it goes through
only one of the slits after all?
I knew quantum mechanics were whacky, but I didn't know particles could
travel back in time and change their previous behavior because the effect
of that behavior was measured *after* the fact.
> > For example a single electron can pass through two
> > slits at the same time, interfering with itself after doing so.
> Not as such. Yes, you get interference patterns. No, as far as I know,
> there's no evidence to suggest it goes through both slits. Nobody is
> quite sure how it works, but there's no measurement that when you say
> "where is the thing" it ever gives you more than one answer.
So you are saying that, even though the only possible explanation for
interference patterns is that the electron passed through both slits,
there's still no evidence of that?
If there's "no evidence", what do you call the interference pattern?
"Non-evidence"?
--
- Warp
Post a reply to this message
|
|
| |
| |
|
|
|
|
| |
