Talk:Thomson's lamp

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How can this quote be true? "The sum of all these progressively smaller times is exactly two minutes." The sum of an infinite progression of intervals that are halved would never reach 2 minutes. But maybe that's the crux of the paradox and I'm just not getting it. :-) If so, seems more like a koan to me.

Just like there's a formula to quickly find the sum of all integers to 10,000 there's one for an infinite series that converges. Click on the word sum in the article (or below) --JimWae 2005 July 3 23:25 (UTC)

The sum of all these progressively smaller times is exactly two minutes



--RickO5 The idea is that 2 minutes will eventually come, the error is in the phrasing. Eventually, the intravles will become infinately tiny, and the bulb will remain in a state of ifinately tiny state changes. The idea behind the argument is that you can not divide by infinity bassically, but 2 minutes will eventually occur anyway.

The state of the bulb would bassically be whether or not the number of times it is switched is even or odd, but scince the number of times must become infinate, because one is infinately dividing by 2, it is neither odd nor even. one could assume that the bulb is neither on nor off after a certain period of time. (In reality the bulb stops flickering because of the lack of cool down time for the filliment.)

So, the biggest problem with the argument is the inability of time to be divided by the infinite.

  • the biggest problem is that within any physical reality, after a while you bump up against quantum consideration and limits of measurement. My conclusion: Time is not a thing that can be divided, time IS a measurement --JimWae 05:38, 3 January 2006 (UTC)
  • Good point, time increments for change can be devided but not time itself. I think thats a problem left unresolved on some of the other paradox pages. --RickO5

[edit] Mathematical proof...

I'm marking this stuff as original research. I doubt that the mathematical theory of convergent series is really capable of "proving" anything about the ill-posed metaphysical question at hand. And I find it hard to believe that a reputable source has made this assertion. Melchoir 04:50, 2 January 2007 (UTC)

I've finally skimmed Thomson's original paper. He says the opposite of this article: that the divergence of the series has nothing to do with the impossibility of the supertask. I'll be rewriting the section soon. Melchoir 11:00, 13 January 2007 (UTC)

Done! Melchoir 19:46, 13 January 2007 (UTC)

I think this question is the same as asking: what is the limit of sin(1/x) when x goes to 0? The answer is: it doesn't exist. See this link: http://www.math.washington.edu/~conroy/general/sin1overx/ —Preceding unsigned comment added by 201.53.83.199 (talk • contribs) 19:33, 12 September 2007
It's certainly related, but not the same. Again, the metaphysical problem does not so easily reduce to mathematics. Melchoir 20:23, 12 September 2007 (UTC)

[edit] Incorrect

The reasoning that S = ½ is a non proof:

"Another way of illustrating this problem is to let the series look like this:

S = 1 - 1 + 1 - 1 + 1 - 1 + \cdots

The series can be rearranged as:

S = 1 - (1 - 1 + 1 - 1 + 1 - 1 + \cdots)

The unending series in the brackets is exactly the same as the original series S. This means S = 1 - S which implies S = ½."

Assigning S as it has been assumes that the sequence converges. In fact, it can be shown using the fact that there exist two subsequences of the partial sums (namely partial sums up to an even number and partial sums up to an odd number)--that converge to different limits--that the sum does not converge and so this algebra of S = 1 - S cannot be performed. —Preceding unsigned comment added by 163.1.62.24 (talk • contribs) 00:46, 19 January 2008

You should read the rest of the paragraph you just quoted: "In fact, this manipulation can be rigorously justified: there are generalized definitions for the sums of series that do assign Grandi's series the value ½. On the other hand, according to other definitions for the sum of a series this series has no defined sum (the limit does not exist)." Do you disagree? Melchoir (talk) 00:56, 19 January 2008 (UTC)


I disagree with the use of this series as a "solution" to the problem. Why sum the results? This is not explained, and makes no sense. I think it's a discredit to mathematics to have this "mathematical" solution to the problem on this page. —Preceding unsigned comment added by 70.150.87.29 (talk) 21:18, 16 April 2008 (UTC)