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Date Posted: 13:02:54 04/10/02 Wed
Author: Chris
Subject: Re: IC notes about magic 04/10/2002
In reply to: Jess 's message, "Re: IC notes about magic 04/10/2002" on 12:29:34 04/10/02 Wed

>The obvious two candidates are chaos math and quantum
>physics. Both of those systems of thought can be used
>to imply that as long as something is possible - no
>matter how improbable - then there's some chance that
>it could happen. If you think about it chaotically,
>that would imply that what we call "magic" is really
>the ability to sense, predict and control impossibly
>complex systems. Quantum physics would posit that we
>have some innate ability to control the apparently
>random actions of atoms at the very smallest levels.

Interesting, but I think this is flawed. Chaos Theory and Quantum Mechanics both predict outcomes with in a certian range of possible outcomes.

The bending of light we have seen is far too extreme to be acounted for by either of these theories. Remember that there are a very limited number of things that can shift the cource of light: An electro magnetic interaction (like reflection of a solid body or a density constant change ("n")) and gravity. Remember that we were able to put our face through the bent light and feel the fabric on the other side. This would rule out an electro magnetic interaction as we would have felt the substance inquestion rather than the fabric. As for the other mechanism, gravity can't be (conventionally) dampened, and if we were in the precense of a strong enough gravitational field to bend the light like that, well, we would have known it. That all pretty much rules out Chaos Theory, that some microsopic cause created a macroscopic solution.

As for Quantum Mechanics, lets examine things as if the photons were "jumping" past Jessie rather than bending around him. That would be the natural QM soultion based on Uncertanty. The maximum jump length would have been at least a quarter of a meter, which is at least five orders of maginitude more than we can reasonably expect. Of course, anything is possible, and there is a small but finite chance of a single photon making such a jump. Recall now that we are talking about millions of photons that are not jumping randomly but are specifically hugging the outline of Jessie's body (otherwise we would have only seen "static" behind him rather than a clear image). So the odds are astronomical. Possible, but stageringly unlikely. I think its more reasonable to assume that there is a non-conventional explanation.

>But that doesn't account for things that are simply
>impossible. But there's the Banach-Tarski hypothesis
>- a mathematical principle that states that a sphere
>can be decomposed into parts and reassembled to make
>TWO spheres of the same radius - it seems impossible
>but it's mathematically provable. Maybe this is all
>just a manifestation of transfinite mathematics? I
>know that sounds crazy ... oh well.

Hmm, I'm interested to hear more. Is that in a conventional Eucliean universe?

>There should be a way to analyze and understand the
>logical principles involved without just trying to
>taxonomize the things we've seen - especially as we're
>of limited experience. I'm a theoretician, not an
>experimentalist! :)

We have to start with taxonomy, otherwise we are just making hypothesis with no grounding! I'm an experimentalist, not a theoretician! :)

>Though you know, Chris, I think I've just come up with
>a way to determine whether this is magic or some weird
>other kind of ability - I've got your falsifiability
>test right here. Consider problems that are provably
>unsolvable in a mathematical rather than an
>experimental sense. For example, the most obvious one
>would be the Halting Problem. (For those not familiar
>with theoretical computer science, that's the question
>of whether a series of operations done on a particular
>input will ever terminate - it's kind of like asking
>whether a program will finish or loop endlessly, but
>in a mathematical rather than a computer-based sense.)
> We KNOW that this problem MUST be unsolvable
>according to any existing way of thinking about the
>world. If we could develop a solution to the Halting
>Problem using this stuff - maybe building a machine to
>determine it? - then I at least would be convinced
>that there is no possible conventional explanation for
>all the things we've been able to do, even if they
>might still be based on natural effects of various
>sorts.

Now, I never did take 121, but doesn't the Halting Problem state that halting can be determined for *some* programs, just not for *all* programs?

ie:
while (true) {
printf("I don't halt!");
}

So, if you are proposing to build a machine that can determine halting for programs that isn't good enough, because we can set it to work on random programs for ever and not know that it can show halting for *all* programs.

On the other hand, if there are programs whose halting status is provably unknown and we can show the halting status of one of those then we are in good shape. This is an excellent avenue of approach, if you know of such a provably unknown program.

Or you could be proposing to build a machine that will write a disproof of the Halting problem (ie, up one "meta" level if you will). This is a valid approach, but it might be very hard. Its relatively easy to get a machine to test all cases of the 4 colored map problem, but difficult to get a machine to create all cases of the 4 colored map problem and prove that those are all the cases.

I might also be making no sence.

--Chris

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