Re: Ideal lamps

From: Brent Meeker <meekerdb.domain.name.hidden>
Date: Sat, 25 Oct 2003 15:15:57 -0700

----- Original Message -----
From: "Eric Hawthorne" <egh.domain.name.hidden>
To: <everything-list.domain.name.hidden>
Cc: <everything-list.domain.name.hidden>
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.
Received on Sat Oct 25 2003 - 18:16:42 PDT