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Date Posted: 13:32:25 04/10/02 Wed
Author: Jess
Subject: Re: IC notes about magic 04/10/2002
In reply to: Chris 's message, "Re: IC notes about magic 04/10/2002" on 13:02:54 04/10/02 Wed

>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.

[snip]

>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.

Ah, but what if that non-conventional explanation is that we can CONTROL those apparently random actions? If there's some imposed control from above, it's not just a random set of photons that are making the jump. I'm not suggesting that it was some sort of hugely improbable accident, especially because he could do it on demand. I'm suggesting that it's possible that he (and we, maybe) can control the probabilities of things on a quantum level and increase the probability that those photons - and ONLY those - would make the jump.

As for your point about chaos theory - you're forgetting that another solution might be the air polarizing - effectively becoming a mirror and bouncing the light around him so he doesn't appear. That's something that could happen through random interactions between air particles - like the effects you get with mirages in the desert, a layer of heated air reflecting the sky. That effect could be duplicated by some sort of kinetic motion - speeding up the local air molecules while others nearby remain relatively still - which is definitely a chaotic effect.

I'd like to look at him through a diffraction grating while he's trying that invisibility trick - that should give us more information.

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

Yup. The only "weird" thing it requires as an assumption is the Axiom of Choice - the principle that it is possible to arbitrarily choose a number from each of an infinite number of sets - in other words, that there is some way to randomly choose an item from a set, even if we can't enumerate the properties of every set we're choosing from. Most mathematicians accept this principle, from what I've read, but not all.

>>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! :)

Sigh. :)

>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?

What the Halting Problem states is that given a program (and you WOULD think about it in practical programming terms, wouldn't you? -g-) and an input, it is impossible to tell whether that program will or will not terminate its operation. If it will terminate, you can know it because it DOES terminate; but if it won't terminate you can't know it because it might terminate in just one ... more ... minute ....

>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.

Ah, but the way to do it would be to have it determine halting for an arbitrary problem M and an arbitrary string w. Or, actually, you could even use the empty string as a subject, since the two problems are reducible to each other.

>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.

I don't off the top of my head, but I can look it up. I imagine there are many.

>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 understand what you mean, but the point is not to write a disproof. If we could make something that would work for an ARBITRARY Turing machine M then that would effectively be a disproof. It's the "black box" solution - the proof doesn't matter, but if it's accurate on any given M then it must be accurate.

The point is that given ANY M it should be able to tell whether or not M halts on e. If we just run it on enough M, we can tell whether or not it is accurate. Hell, the problem of whether or not the machine is accurate is actually a halting problem in and of itself. So what if we ran the machine on the question of whether the machine is accurate? Ooh, that makes my head hurt. -g-

>I might also be making no sence.

Some sense. At least as much as I do. :)

Jess

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