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From: Stathis Papaioannou <stathispapaioannou.domain.name.hidden>

Date: Tue, 21 Oct 2003 23:20:04 +1000

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!

_________________________________________________________________

Get less junk mail with ninemsn Premium. Click here

http://ninemsn.com.au/premium/landing.asp

Received on Tue Oct 21 2003 - 09:24:02 PDT

Date: Tue, 21 Oct 2003 23:20:04 +1000

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!

_________________________________________________________________

Get less junk mail with ninemsn Premium. Click here

http://ninemsn.com.au/premium/landing.asp

Received on Tue Oct 21 2003 - 09:24:02 PDT

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