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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."
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Darren New <dne### [at] san rrcom> 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
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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*
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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*
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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
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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."
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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."
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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."
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"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.
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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
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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
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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
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> 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.
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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
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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.
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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*
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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
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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."
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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."
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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."
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"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.
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"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>
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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."
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"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.
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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
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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
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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
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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
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Stephen <mcavoysAT@aoldotcom> wrote:
> Do you mean that someone has managed to square the circle?
The "squaring the circle" problem imposes some restrictions.
--
- Warp
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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
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On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:
>Stephen <mcavoysAT@aoldotcom> wrote:
>> Do you mean that someone has managed to square the circle?
>
> The "squaring the circle" problem imposes some restrictions.
Indeed, a straight edge and compass. What more do you need?
--
Regards
Stephen
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>
> If there's "no evidence", what do you call the interference pattern?
> "Non-evidence"?
Don't forget: A single electron doesn't make an interference pattern. It
produces a bright spot on the fluorescence screen saying: Exactly here
and nowhere else the electron hit the screen.
Only if you observe many many events and add up their positions they
converge to an interference pattern.
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Darren New <dne### [at] sanrrcom> 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.
That's a bit like being in the middle of the ocean and saying "there's
no mathematical model which says where the water is", speaking as if the
"water" was a point in space and you'd had to locate it at some specific
coordinates.
Your statement is like that. You are starting from the assumption that
an electron is an extremely small particle with well-defined boundaries,
approximately equal to a mathematical point, and then you ask for a
mathematical model to say where that point is in space. As with the
water example, that's kind of silly.
What the mathematical model *can* do is to give a distribution function
which tells how the electron is distributed in space (a bit like a
function which tells how the water is distributed, except that with
the electron the "density" of the "water" is not constant).
These probability functions may not be infinitely accurate (because they
depend, among other things, on finite measurements which are accurate only
to so many decimals), but they can be used for practical calculations.
It's not like you could shoot an electron to some direction, and then
the electron suddenly hits the other side of the Earth (or the solar
system). It hits a quite accurately calculable place.
--
- Warp
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Stephen <mcavoysAT@aoldotcom> wrote:
> On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:
> >Stephen <mcavoysAT@aoldotcom> wrote:
> >> Do you mean that someone has managed to square the circle?
> >
> > The "squaring the circle" problem imposes some restrictions.
> Indeed, a straight edge and compass. What more do you need?
I assume that dividing the circle into an uncountable set of points.
--
- Warp
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Michael Zier <mic### [at] mirizide> wrote:
> Don't forget: A single electron doesn't make an interference pattern. It
> produces a bright spot on the fluorescence screen saying: Exactly here
> and nowhere else the electron hit the screen.
Wasn't it "impossible" to accurately measure the place and velocity
of a quantum particle? ;)
> Only if you observe many many events and add up their positions they
> converge to an interference pattern.
But I believe it can be done by shooting just one electron at a time,
so the electron indeed interferes only with itself, not with other
electrons.
--
- Warp
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Am Mon, 02 Jun 2008 03:41:22 -0400 schrieb Warp:
> Michael Zier <mic### [at] mirizide> wrote:
>> Don't forget: A single electron doesn't make an interference pattern.
>> It produces a bright spot on the fluorescence screen saying: Exactly
>> here and nowhere else the electron hit the screen.
>
> Wasn't it "impossible" to accurately measure the place and velocity
> of a quantum particle? ;)
Indeed, and that's what I said: It hit the screen *here* and I have no
clue how fast and from what direction :P
>
>> Only if you observe many many events and add up their positions they
>> converge to an interference pattern.
>
> But I believe it can be done by shooting just one electron at a time,
> so the electron indeed interferes only with itself, not with other
> electrons.
Yes, I've seen this experiment. *Single* bright spots lighting up
briefly, no observable pattern if you just look at it. Unless you average
"all the video frames" (which you can do either with real video frames or
"simulated" with a photographic film), an interference pattern emerges.
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On 2 Jun 2008 03:38:58 -0400, Warp <war### [at] tagpovrayorg> wrote:
>Stephen <mcavoysAT@aoldotcom> wrote:
>> On 2 Jun 2008 03:17:17 -0400, Warp <war### [at] tagpovrayorg> wrote:
>
>> >Stephen <mcavoysAT@aoldotcom> wrote:
>> >> Do you mean that someone has managed to square the circle?
>> >
>> > The "squaring the circle" problem imposes some restrictions.
>
>> Indeed, a straight edge and compass. What more do you need?
>
> I assume that dividing the circle into an uncountable set of points.
Invisible ???
:-)
--
Regards
Stephen
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Darren New 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?
>
> 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.)
I wouldn't say that it is truly random, but merely that predicting the
outcome of any interaction requires information that is presently not
available.
For instance, the decay of unstable particles appears to happen
randomly, but at what appears to be a predictable rate for aggregate
amounts of like particles. What is likely is that the particles decay
when they encounter certain conditions (such as a gradient in the
electric or magnetic potential) that is high enough to overcome the weak
internal cohesiveness of the particle, causing it to come apart. Since
the gradient of potential at any place is not (and probably cannot be)
known with sufficient precision (and is certainly in a state of constant
change), it appears random.
Regards,
John
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somebody wrote:
> "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#?
>
It's an octave of blue, if I got the math right. I started from 4435Hz,
though, instead of a more accurate number, so it's probably off by a bit.
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>> Some syntatically correct questions can be meaningless. What colour is
>> the note C#?
>
> It's an octave of blue, if I got the math right. I started from 4435Hz,
> though, instead of a more accurate number, so it's probably off by a bit.
You see the look on my face right now? This look means that you have
just BROKEN MY MIND!
http://www.questionablecontent.net/view.php?comic=165
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Warp wrote:
>
> 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.
>
Am I the only one here, who's waiting for a raytraced animation-example
of this? :)
--
Eero "Aero" Ahonen
http://www.zbxt.net
aer### [at] removethiszbxtnetinvalid
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Eero Ahonen <aer### [at] removethiszbxtnetinvalid> wrote:
> Am I the only one here, who's waiting for a raytraced animation-example
> of this? :)
Visually dividing a sphere into sets with uncountably many infinitely
small points? You wish.
--
- Warp
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Warp wrote:
>
> Visually dividing a sphere into sets with uncountably many infinitely
> small points? You wish.
>
Indeed I do. :p
--
Eero "Aero" Ahonen
http://www.zbxt.net
aer### [at] removethiszbxtnetinvalid
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Warp wrote:
> It's not like you could shoot an electron to some direction, and then
> the electron suddenly hits the other side of the Earth (or the solar
> system). It hits a quite accurately calculable place.
There is a non-zero probability that this can happen.
--
The next war will determine not what is right, but what is left.
/\ /\ /\ /
/ \/ \ u e e n / \/ a w a z
>>>>>>mue### [at] nawazorg<<<<<<
anl
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Mueen Nawaz wrote:
> Yes - wasn't that proven only recently?
I heard about it recently, like in the last couple of years.
> 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.
Something like 10^50 cuts or something? I know it's on Wolfram's
mathworld somewhere, but I don't remember the name of it, so it's hard
to find.
--
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."
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Stephen wrote:
> Indeed, a straight edge and compass. What more do you need?
A ruler?
--
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."
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Warp wrote:
> 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?
No. It either interferes with itself or not. You're assuming the only
way it can interfere with itself is to go through both slits. There's no
evidence that's the case, and much evidence that it isn't.
> 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.
Actually, yes, they can. For example, a photon can emit a
backwards-traveling electron (aka a positron) which cancels with the
electron it emits later, so as to preserve the number of non-virtual
particles around. It's weird.
But there's no evidence that's what's happening in the two-slit experiment.
> 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?
Yes. What makes you think that the only *possible* explanation is that
the electron passed through both slits?
> If there's "no evidence", what do you call the interference pattern?
> "Non-evidence"?
Interference. Nobody knows why, because every time you measure an
electron, there's only one, even when both slits are open. There are
plenty of experiments where both slits are open and you only ever see
the electron go through one or the other and never both. Of course, you
don't get the interference when you actually look, but then the fact
you're looking *after* the electron went through the slits shouldn't
affect which slits it goes through, should it?
--
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."
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Warp wrote:
> Michael Zier <mic### [at] mirizide> wrote:
>> Don't forget: A single electron doesn't make an interference pattern. It
>> produces a bright spot on the fluorescence screen saying: Exactly here
>> and nowhere else the electron hit the screen.
>
> Wasn't it "impossible" to accurately measure the place and velocity
> of a quantum particle? ;)
Only down to Plank's constant. You can easily tell down to the size of
an atom which atom it hit.
>> Only if you observe many many events and add up their positions they
>> converge to an interference pattern.
>
> But I believe it can be done by shooting just one electron at a time,
> so the electron indeed interferes only with itself, not with other
> electrons.
No, it only interferes with other electrons. The electrons it interferes
with are electrons from other times. There's always a possibility that
it lands at any particular place. Why is it any stranger that it
interferes with electrons in the future than it is it interferes with
itself?
That's what I was talking about in the "amazingly, math works" thread.
--
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."
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somebody wrote:
> "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 have no idea what you're trying to say here.
>> 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.
Again, I have no idea what you're trying to say here.
> 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.
Um, yes. That's kind of my point.
I take it you're retracting your statement:
> Easy. Mathematics can represent *anything*, since you get to make up your
> own axioms.
That's what I'm addressing, and nothing else. Mathematics can't
represent "free will", nor can it represent where (say) the tenth
electron to hit the screen will hit it in a particular well-defined
experiment.
>> 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.
Depending on your meaning of "prove", but yes, I think I know what
you're trying to say here.
> The question is
> not whether or not there's a GUT (reality provides one working model at
> least)
That's the assumption I'm challenging. Please provide evidence that
there is one completely describable model of reality possible.
There is reality. Then there's the Grand Unified Theory of reality,
which expresses the behavior of the universe in mathematical terms which
can be symbolically manipulated in a manner isomorphic to how reality
works.
You can't disprove reality. But that doesn't mean there's any formalism
that can express it.
>>> 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.
Yes. But if you can't predict the future based on the past, you don't
have a *model*. You have a mathematical description of the past that may
or may not have anything to do with the future.
If I flip a coin four times in a row and get all heads, it's not a model
of coin flipping to say "it always comes up heads." If I 'predict' in
2008 ever terrorist action for the years 2000-2006 using my mathematical
formula, that doesn't mean it's good for 2010. If my equations match
perfectly with the stock market for the last five years, that doesn't
mean I'll make money next year.
> Modelling randomness is easy (in theory anyway). It just won't have
> predictive ability.
I would claim that if you can't predict, you don't have a model, you
have a history book. If you can't take a model isomorphic to current
reality, perform formal transforms on it, and have a model that is
isomorphic to the reality you get after the modeled transforms are
performed in reality, then you don't have a model.
--
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."
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Sabrina Kilian wrote:
> It's an octave of blue, if I got the math right. I started from 4435Hz,
> though, instead of a more accurate number, so it's probably off by a bit.
That's my giggle of the day, thanks.
--
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."
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