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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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>
> 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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Warp wrote:
> 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.
I guess I was kind of sloppy. I was saying that there's no mathematical
model that tells you where you will find a specific electron when you
look for it in a set of places. E.g., if you shoot an electron at a
flourescent screen, there's no model (and *can* be no model) that tells
you where on the screen that electron will hit.
> 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).
No, actually, it tells you the likelihood of finding it at any
particular place, were you to look.
There's another distribution function that tells you the likelihood it's
in a particular place if you *don't* look.
When you put those two together, you get the two-slit experiment.
> 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.
No, it doesn't. The probability of hitting anywhere in particular is an
infinite sum of complex (as in, real+imaginary) probabilities.
Yes, it can actually hit the other side of the Earth. It can also hit a
week before you shoot it. Very unlikely, but possible.
--
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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John VanSickle wrote:
> 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.
You would be incorrect. Google on "Bell's Inequality".
> 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.
That's the "hidden variable" theory. It has been disproven, multiple
times and with hundreds of different experiments. Boggling, isn't 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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Darren New <dne### [at] sanrrcom> wrote:
> 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?
Because time travel doesn't exist?
--
- Warp
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Mueen Nawaz wrote:
> 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".
I understand it enough to explain informally. When you're calculating
the probability of an event, you have to take into account every way
that event could occur, and add them up. So maybe the photon leaves the
candle and hits the film. Or it leaves the candle, splits into an
electron and positron, which then later recombine into a photon, which
hits the screen. Or it splits into an electron and positron, and the
positron goes off to the Sun back in time to combine with an electron
there, which makes it turn into a photon which happens to come back to
Earth which strikes the electron which pushes it into the wall which
emits a photon which hits the film. And so on.
So basically, you're adding up more and more events of lower and lower
probability. And it turns out that if you add them all up, you get
infinite probability everywhere.
But if you stop at, say, 10^-50 probability, and then renormalize
(something like divide by 10^-50), you get a number. And if you stop at
10^-60 and then renormalize (something like divide by 10^-60), you get
the same number. As long as you renormalize to where you stopped, you
get the same number. But nobody knows why you have to stop, and there's
so far no physical reasoning as to where you have to stop.
Speculation is that space is actually quantum, so the mathematics of
"real numbers" breaks down because they can get smaller than reality.
Which is where the Plank's constant seems to come in - speculation that
it's describing the quantum of size.
--
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:
> > 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.
So why does it interfere with itself when there are two slits but not
when there is only one? If it was just one regular physical macroscopical
particle it wouldn't matter how many slits there are: If it goes through
one of them, it just goes through one of them, that's it. It doesn't even
"know" that there are other slits.
However, when there are two slits, the electron passes through and starts
interfering with itself, as if it has passed through both and changed
direction in different ways.
How else can this be explained? How does the electron "know" that there's
another slit so that it "knows" to start interfering with itself, other than
actually going through the other slit as well?
(I believe this has something to do with wave-particle duality: In the
double-slit experiment the wave nature of the electron shows up: The wave
goes through both slits and starts interfering with itself.)
> > 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?
What is the other explanation?
> > If there's "no evidence", what do you call the interference pattern?
> > "Non-evidence"?
> Interference.
The interference can be explained with the electron passing through both
slits at the same time. Ergo the interference is evidence of that happening.
(Note that "evidence" is not the same thing as "proof".)
--
- Warp
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Warp wrote:
> Your statement is like that. You are starting from the assumption that
> an electron is an extremely small particle with well-defined boundaries,
By the way, this is why it's called "quantum" physics. :-) Because it's
*not* a wave - there *is* a well-defined particle in a particular place.
--
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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Mueen Nawaz <m.n### [at] ieeeorg> wrote:
> 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.
I bet the probability is so small that it hits the barrier of some
physical constant (Planck maybe?)
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> > 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).
> No, actually, it tells you the likelihood of finding it at any
> particular place, were you to look.
Assuming the particle *is* at some specific location at any given time
instead of being distributed in space.
> Yes, it can actually hit the other side of the Earth. It can also hit a
> week before you shoot it. Very unlikely, but possible.
I don't believe in the time travelling. As for the location, I assume
the probability of it hitting the other side of the Earth is so small that
some physical constant prevents it.
--
- Warp
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Darren New <dne### [at] sanrrcom> wrote:
> Warp wrote:
> > Your statement is like that. You are starting from the assumption that
> > an electron is an extremely small particle with well-defined boundaries,
> By the way, this is why it's called "quantum" physics. :-) Because it's
> *not* a wave - there *is* a well-defined particle in a particular place.
Actually "quantum physics" means that everything is quantified. That is,
there's a minimum amount of everything (for example electric charge and
mass), and everything is an integer multiple of that amount. You just can't
have eg. half of the electric charge of an electron, for example.
Waves are also quantified for the same reason: There's a minimum amount
of amplitude, for example, and all amplitudes are integer multiples of
that amount.
These "quants" behave oddly. Sometimes they behave like particles,
sometimes they behave like waves, and sometimes they behave like both
at the same time. Different measurements of the exact same quant can
show wildly different behavior in this respect. (One experiment will
clearly show that light behaves like a wave and not like a stream of
particles, while another experiment will show the exact opposite.)
--
- Warp
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On Mon, 02 Jun 2008 09:29:24 -0700, Darren New <dne### [at] sanrrcom>
wrote:
>Stephen wrote:
>> Indeed, a straight edge and compass. What more do you need?
>
>A ruler?
No, I don't think so. ;)
--
Regards
Stephen
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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>> 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.
>
> So why does it interfere with itself when there are two slits but not
> when there is only one? If it was just one regular physical macroscopical
> particle it wouldn't matter how many slits there are: If it goes through
> one of them, it just goes through one of them, that's it. It doesn't even
> "know" that there are other slits.
> However, when there are two slits, the electron passes through and starts
> interfering with itself, as if it has passed through both and changed
> direction in different ways.
>
> How else can this be explained? How does the electron "know" that there's
> another slit so that it "knows" to start interfering with itself, other than
> actually going through the other slit as well?
'It' knows that the second slit is there because an electron has an
infinite size. Part of the problem is that you use 'it', implying that
it is an identifiable object and it has a subconscious connotation of
something finite.
>
> (I believe this has something to do with wave-particle duality: In the
> double-slit experiment the wave nature of the electron shows up: The wave
> goes through both slits and starts interfering with itself.)
Both 'wave' and 'particle' are concepts from classical physics that
don't apply here.
In the double slit experiment you have a source of electrons, a double
slit and a screen. You know that you had an electron at the source and
you can compute the likelihood of the position on the screen that will
light up, enabling you to estimate the pattern if you use a large number
of electrons. Between the source and the screen, the electron passes
through ever point in the universe and you are not even sure that the
same electron hit the screen as the one you started with. Simply because
'same' is not defined here.
A basic rule of quantum mechanics: don't try to visualize what happens.
You can either visualize it or compute it, not both at the same time. ;)
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Warp wrote:
> Darren New <dne### [at] sanrrcom> wrote:
>>> 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).
>
>> No, actually, it tells you the likelihood of finding it at any
>> particular place, were you to look.
>
> Assuming the particle *is* at some specific location at any given time
> instead of being distributed in space.
>
>> Yes, it can actually hit the other side of the Earth. It can also hit a
>> week before you shoot it. Very unlikely, but possible.
>
> I don't believe in the time travelling.
Luckily you don't have to believe it in order for it to exist. BTW I
don't think what Darren proposes can actually happen, though it might be
possible to create a situation that is indistinguishable from it.
> As for the location, I assume
> the probability of it hitting the other side of the Earth is so small that
> some physical constant prevents it.
The only thing that prevents it is the number of electrons you have to
try it. Still even if it will never actually happen, yet the fact that
it could will influence the outcome anyway.
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Darren New wrote:
> Mueen Nawaz wrote:
>> Yes - wasn't that proven only recently?
>
> I heard about it recently, like in the last couple of years.
Actually, I found it - proven in 1990.
> 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.
http://en.wikipedia.org/wiki/Tarski%27s_circle-squaring_problem
--
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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Warp wrote:
>> Indeed, a straight edge and compass. What more do you need?
>
> I assume that dividing the circle into an uncountable set of points.
I posted the link in another message. The set of regions it is cut into
is countably finite.
--
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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Warp wrote:
> However, when there are two slits, the electron passes through and starts
> interfering with itself, as if it has passed through both and changed
> direction in different ways.
>
> How else can this be explained? How does the electron "know" that there's
> another slit so that it "knows" to start interfering with itself, other than
> actually going through the other slit as well?
Your questions are interesting, but the conclusions do not necessarily
follow. If you actually attempt to detect the electron passing through a
slit, you'll detect it passing through only one slit (and you won't get
an interference pattern). When you don't try to detect it, you get an
interference pattern.
You're concluding it passed through two slits when you don't try to
detect it? It knows before passing through the slit that you're trying
to detect it? Such a suggestion is about as weird as an electron
interfering with itself. It may be true, or it may not be. I don't
presume to know.
As you yourself stated elsewhere, you get an interference pattern even
when only one electron is shot at a time. However, the electron strikes
the screen in only one place at a time. Looking at where they struck
individually gives no evidence of any interference - it doesn't "weakly"
strike two places at once. Looking at the whole set of locations the
electron struck, though, does. One could simply explain this by saying
that the presence of two slits causes the electron to act in a
probabilistic manner - resulting in an interference pattern.
And, AFAIK, that's the best explanation there is. I have a formalism
that describes experimental results, and I don't have to resort to
thinking about electrons interfering with themselves.
The reason I don't want to declare self-interference is that there is
no way I can test it (or as Darren would say - any attempt to show this
fails). I can have two slits and put detectors at each slit. When you
detect an electron passing through a slit, interference ceases. Why? If
the electron can pass through both slits, why can't you actually detect
this?
>>> If there's "no evidence", what do you call the interference pattern?
>>> "Non-evidence"?
>
>> Interference.
>
> The interference can be explained with the electron passing through both
> slits at the same time. Ergo the interference is evidence of that happening.
> (Note that "evidence" is not the same thing as "proof".)
And detecting which slit an electron passes through is also evidence
that it isn't passing through both slits.
--
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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Warp wrote:
>> There is a non-zero probability that this can happen.
>
> I bet the probability is so small that it hits the barrier of some
> physical constant (Planck maybe?)
I'm not sure what that means. Probability is a mathematical construct -
not beholden to physical constants. If the probability is 1e-100, you
can't use physics to conclude that it *won't* happen tomorrow.
--
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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Darren New wrote:
> John VanSickle wrote:
>> 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.
>
> You would be incorrect. Google on "Bell's Inequality".
>
>> 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.
>
> That's the "hidden variable" theory. It has been disproven, multiple
> times and with hundreds of different experiments. Boggling, isn't it?
I question the assertion that it's been disproven. I think only a
certain class of hidden variables have been shown not to exist. (Local
vs non-local?)
--
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:
> http://en.wikipedia.org/wiki/Tarski%27s_circle-squaring_problem
Interestingly, following the links from there to
http://en.wikipedia.org/wiki/Non-measurable_subset give an example of
what might be a reality inconsistent with math:
"""
These sets are rich enough to include every conceivable definition of a
set that arises in standard mathematics, but they require a lot of
formalism to prove that sets are measurable.
"""
So if reality actually includes non-measurable sets (something that
wouldn't seem too impossible, given the definition, such as "space where
you can't pick any random position", i.e., quantum space), you already
have a serious problem.
--
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:
> Darren New <dne### [at] sanrrcom> wrote:
>> 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?
>
> Because time travel doesn't exist?
At the quantum level, it most certainly does.
--
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 why does it interfere with itself when there are two slits but not
> when there is only one?
I don't know, offhand. That's actually one of the burning questions of
quantum physics. Are you saying you've figured it out? :-)
Incidentally, it doesn't interfere with itself - I misspoke. It
interferes with other electrons. Sure, they only go through one at a
time. What was that about time travel?
> However, when there are two slits, the electron passes through and starts
> interfering with itself, as if it has passed through both and changed
> direction in different ways.
How do you know? Every time you measure whether it went through both
slits, the answer is "no, there was only one electron." You keep
asserting this, with no evidence other than "I can't think of any other
explanation", along with rejecting both evidence and other explanations.
> How else can this be explained? How does the electron "know" that there's
> another slit so that it "knows" to start interfering with itself, other than
> actually going through the other slit as well?
Your intuition is confusing you. How does it "know" there's a back
surface to the glass and therefore needs to reflect differently? How
does it "know" there's another electron already "on the way" to where
it's going and hence that position needs to be avoided?
Why is it a wave going through both slits but a particle by the time it
gets to the detector?
> (I believe this has something to do with wave-particle duality: In the
> double-slit experiment the wave nature of the electron shows up: The wave
> goes through both slits and starts interfering with itself.)
That's the older explanation from when physicists thought like you're
thinking, yes. The math works like a wave function, so people thought it
was a wave. It's not.
>>> 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?
>
> What is the other explanation?
I don't know, and as far as I understand, nobody else does either. But
all of the evidence so far suggests your interpretation is incorrect.
For example, if you do the same thing with photons, wait for them to go
thru the slits, and after they've already passed through, you either
turn on or off the detector that says which slit they went through, you
always see them only go through one slit when the detector is on, and
always generate interference probabilities when the detector is off. How
do you explain that?
> The interference can be explained with the electron passing through both
> slits at the same time.
Yes. But that's also at odds with many other experiments. If the
electron goes through both slits, why is it that you never see it go
through both slits when you put a detector behind each slit? It's one
possible explanation with reams of experimental evidence against it.
The sun rising can be explained by angels pushing it along, as well, but
that too is at odds with many other experiments. "I can't think of a
better explanation" isn't the same as "the one I thought of must be
true", *particularly* when evidence from other measurements is
consistently at odds with one's explanation. (True regardless who "I" is
in there.)
--
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 bet the probability is so small that it hits the barrier of some
> physical constant (Planck maybe?)
Possibly. Renormalization works, but I don't think anyone yet knows why.
--
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
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