The "lamp" is a translated version of the Achilles - Turtle race.
My (non-physicist) tupence to the topic:
Reality is a tricky concept. WE know the part of it that is interpreted by
the mind for our limited appreciation. Tis is OUR "reality" and we know
'that' - only that. It constitutes the (common sense) world.
This pertinent to 'physical reality'.
Mathematical 'reality' is IMO an oxymoron, since mathematics is a virtual
domain with (Hilbert's) reality of a piece of paper and a pencil (now:

My added question:
since math is the domain of our internal mental functions - generated within
the mind and our knowledge of reality is restricted to the domain of
mind-representation upon "not mind generated" impacts we receive, is
"mathematical knowledge" also an oxymoron?
(This is not a phyicistic question)

John Mikes

----- Original Message -----
From: "Matt King" <[EMAIL PROTECTED]>
Sent: Saturday, October 25, 2003 8:22 AM
Subject: Re: Is reality unknowable?

> 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
> >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
> >on, with each interval one-half the preceding interval.  Question:  What
> >the status of the lamp at two minutes, on or off?  (I know the answer
> >be calculated by conventional arithmetic.  Yet the clock runs, so there
> >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
> >
> >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
> >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
> >an odd or an even integer".  He shows that there are two sequences at
> >one of which culminates in the lamp being on, while the other culminates
> >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
> >reality" is subservient to it.  Yet mathematics is unable to determine
> >on-or-off state of Thompson's Lamp after 2 minutes.
> >
> >What are the philosophical implications of unsolvable mathematical
> >Does this mean that mathematical reality, hence physical reality, is
> >ultimately unknowable?
> >
> >
> ------------------------------------------------------------------------
> When God plays dice with the Universe, He throws every number at once...
> ------------------------------------------------------------------------

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