----- Original Message ----- From: "Eric Hawthorne" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Saturday, October 25, 2003 2:50 PM Subject: Re: Ideal lamps
> "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." > > Is it pedantic of me to point out that this is an IDEAL lamp, i.e. one which only > exists as an idea, and one which, because of its transcendence of the speed of > light, can never exist in our universe? > > Therefore, there are probably many fanciful or mathematical answers which work within > one ideal, abstract, mathematical model of the situation or another. These models > must all be incorrect models of known reality however. > > I'm with Hal. The question doesn't mean anything about the real world. > > This just means I'm too lazy to try to figure it out, but sometimes that's the > right answer. > > Eric I don't know why anyone thought the speed of light had anything to do with this problem. The lamp can be at a single point and so can its switch. Since nothing has to travel between switching events the speed of light is not relevant. By present theories the shortest meaningful time interval is on the order of the Planck time ~10^-43 sec which depends on the gravitational constant and Planck's constant as well as the speed of light. I agree with Hal that, being an ideal problem, it doesn't necessarily have an answer. You can more clearly pose the problem as Tompson's function, which is one on intervals (0.5^2n, 0.5^2n+1] and zero on (0.5^2n+1, 0.5^2n+2] - so, as someone else noted, the problem is the same as asking whether infinity is odd or even. However, not having an answer isn't the same as being self-contradictory. It's the opposite. It means you can choose to add an axiom to your ideal system that defines the answer. I don't know if anyone has ever bothered, but I suppose you could add as an axiom of arithemetic that infinity is even (or odd). So long as this didn't produce any contradictions, one axiom is as good as another. Brent Meeker There are 10 kinds of people. Those who think in binary and those who don't.
