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"Orchid XP v8" <voi### [at] dev null> 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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