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Eero Ahonen <aer### [at] removethis zbxtnetinvalid> 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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