I'd say the lamp is simultaneously on and off at 2 minutes. Take the two
sequences independently, (a) "time at which the lamp turns on" and (b) "time
at which the lamp turns off".
(a) goes: 0, 1+1/2 min, 1+7/8 min, 1+31/32 min, 1+127/128 min, ...
1+(2^i-1)/(2^i) min where i is all the odd integers.
(b) goes: 1, 1+3/4 min, 1+15/16 min, 1+63/64 min, ... 1+(2^i-1)/(2^i) min
where i is all the even integers.
You can see that the limit in both cases as i approaches infinity is 2
minutes. This means that at 2 minutes the lamp will turn on according to
sequence (a) and off according to sequence (b). The problem is equivalent to
asking whether infinity is an odd or an even integer, the usual answer to
which is (I think) that infinity is neither - in fact, is not an integer at
all. You may be disatisfied with this and say that "2 minutes" is a
definite, measurable interval in the real world, and that there must be an
actual, observable, on-or-off state of the lamp at this time. The problem
is, of course, that no such ideal lamp could exist in the real world. If it
did, aside from any other considerations, instantaneous switching on would
mean infinite current, and hence infinite power in a finite volume, which
would probably cause a big explosion putting an end to your experiment, and
possibly putting an end to your universe as well! Big explosions, infinite
power densities, end-of the-universe... where have I heard all this before?
Stathis Papaioannou
Melbourne, Australia
-----Original Message-----
From: Norman Samish [mailto:ncsamish.domain.name.hidden]
Sent: Monday, 20 October 2003 5:07 PM
To: everything-list.domain.name.hidden
Subject: Thompson's Lamp
Welcome,
I've been looking for an idiot savant to answer this question: 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?)
Norman
----- Original Message -----
From: incarn81
To: everything-list.domain.name.hidden
Sent: Saturday, October 18, 2003 11:36 PM
Subject: Joining
Hello
I'm mainly an idoit, sometimes a savant. I get most of the references that
I've read so far, but don't really have a deep technical background in any
one area.
Can't wait to catch up on the archives!
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Received on Tue Oct 21 2003 - 09:24:02 PDT