Comments by "" (@TheDavidlloydjones) on "The mystery of 0.577 - Numberphile" video.

  1. How far the ant has walked in the past is irrelevant. If the question is "Will the ant get to the end," then the only relevant question is, "How far is the ant from the end?" At the end of the first second the ant is 99cm. from the end. At the end of the second second it is 198 cm.s from the end. After three second it is 297 cm. from the end. The distance from the end is increasing monotonically. The ant loses. Q.E.D. The fallacy in the presentation is one of misdirection, and there are at last two ways of looking at this. The first is, "How is it relevant how far the ant has travelled?" Answer: it is not relevant at all. It might have just walked over from Spain. So what? A second way of looking at the fallacy is "What is the denominator of this percentage being thrown out at us?" The answer is, it's not a quantity in the sense that percentages deal with quantities. It is an algorithm, a way of making up an amount that changes all the time. Thus the 1% presented at the beginning of the chatter is not comparable to the 2% presented later: they're one and two over two different denominators*. They are not percentages of the same thing. This means the series written down on his brown paper does not apply, since it is fractions of "a whole," the same whole, i.e. the number one. -dlj. *After one second the distance left is 99% of one meter. After two seconds it is 99% of two meters. The ant will always be 1% of the way to the finish line.
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