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: computer).
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]> To: <[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 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? > > > > > ------------------------------------------------------------------------ > > When God plays dice with the Universe, He throws every number at once... > > ------------------------------------------------------------------------ > >
