Re: Is reality unknowable?

From: Matt King <m.domain.name.hidden>
Date: Sat, 25 Oct 2003 13:22:30 +0100

Hey all,

    Nice to see some activity on this list again.

    I think the filament's blown, but then again I'm a physicist :-)

            Matt.

Norman Samish wrote:

>"Perhaps you've heard of Thompson's Lamp. This is an ideal lamp, capable of
>infinite switching speed and using electricity that travels at infinite
>speed. At time zero it is on. After one minute it is turned off. After
>1/2 minute it is turned back on. After 1/4 minute it is turned off. And so
>on, with each interval one-half the preceding interval. Question: What is
>the status of the lamp at two minutes, on or off? (I know the answer can't
>be calculated by conventional arithmetic. Yet the clock runs, so there must
>be an answer. Is there any way of calculating the answer?)"
>
>
>I've been greatly intrigued by your responses - thank you.
>
>Marcelo Rinesi, after analysis, thinks that the "problem has no solution".
>
>Bruno Marchal thinks that the "Church thesis . . . makes consistent the
>'large Pythagorean view, according to which everything emerges from the
>integers and their relations.'"
>
>George Levy, after reading Marchal, thinks there may be a solution if there
>is a new state for the lamp besides ON and OFF, namely ONF.
>
>Stathis Papaioannou thinks the lamp is simultaneously on and off at 2
>minutes. He thinks the problem is equivalent to "asking whether infinity is
>an odd or an even integer". He shows that there are two sequences at work,
>one of which culminates in the lamp being on, while the other culminates in
>the lamp being off. Both sequences can be rigorously shown to be valid.
>
>Now Joao Leao paraphrases Hardy to say that "'mathematical reality' is
>something entirely more precisely known and accessed than 'physical
>reality'"
>
>So I'm to understand that "mathematical reality" is paramount, and "physical
>reality" is subservient to it. Yet mathematics is unable to determine the
>on-or-off state of Thompson's Lamp after 2 minutes.
>
>What are the philosophical implications of unsolvable mathematical problems?
>Does this mean that mathematical reality, hence physical reality, is
>ultimately unknowable?
>
>
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When God plays dice with the Universe, He throws every number at once...

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Received on Sat Oct 25 2003 - 09:09:08 PDT