Zeno's Bisection Paradox - A New Angle

Apropos of my last posting - in my latest lectures I have found a much better tool to convey the idea of time bisection so crucial to CTF. Up until recently I have applied the analogy of half life (possibly now invalidated by Mr MacIntyre) or Zeno's bisection paradox. This is called Thomson's Lamp in honour of James Thomson, Professor of Philosophy at the Massachusetts Institute of Technology who first suggested it back in 1954. It goes like this:

Consider a lamp, with a switch. Hit the switch once, it turns it on. Hit it again, it turns it off. Let us imagine there is a being with supernatural powers who likes to play with this lamp as follows. First, he turns it on. At the end of one minute, he turns it off. At the end of half a minute, he turns it on again. At the end of a quarter of a minute, he turns it off. In one eighth of a minute, he turns it on again. And so on, hitting the switch each time after waiting exactly one-half the time he waited before hitting it the last time.

QUESTION: At the end of two minutes, is the lamp on, or off?

The answer is rather startling. If we represent the successive states of the lamp by the series of increasingly short periods in which it is on and off, we obtain something that has no last member: 60, 30, 15, 7.5, 3.75, 1.875 .... The series, in other words, is infinite. So at the end of two minutes, the lamp has been switched on (and off) an infinite number of times. Now in my opinion there is nothing mathematically incoherent in the description of the experiment (unlike, possibly my analogy of half-life discussed in the last post). The sum of all the series of periods is not infinite: it approaches without quite reaching, 120 seconds.

This, I argue, is exactly what happens to the dying person as they approach death. Let us assume that I am a skydiver and in 120 milliseconds I will hit the ground and be killed. At 120 milliseconds before I do so the glutamate flood in the brain slows down my perception of time by increasing my metaboloic rate. Each subjective millisecond takes twice as long to pass in my perception as the one before. Exactly the same situation as Thomson's Lamp applies. I will never hit the ground because I will always be a fraction away from it - just like the lamp's switch I am trapped in an eternity of subdivisions. As such I never die.

Max Payne of the Scientific & Medical Network suggested at a recent presentation I did for the SMN that this bisection of time would come to an end when no more space and time was available for a further subdivision. He cited Cantor's Infinity Argument in support of this position. I am unaware of this and it is my intention to check this out when I have time (subjective or objective).

Of course I am hopeful that somebody out there can clarify this argument once and for all.

If you are interested in the source of my Thomson Lamp material it can be found in a wonderful book called Travels In Four Dimensions - The Enigma of Space & Time by Robin Le Poidevin, Professor of Metaphysics at Leeds University (ISBN 0-19-875255-5)

New Review on Amazon USA & Zeno's Bisection Paradox vs Radioactive Half-Life

I am pleased to write that reviews are still appearing on Amazon UK and Amazon USA. The latest one on Amazon USA is, in general terms, a fairly positive one. Unfortunately Mr(?) B MacIntyre has ruined my sequence of five star reviews but his comments are still valid ones - after all not everybody will rate the book highly. I think that his comments with regard to me being a 'crank theorist' to be a little unfair but on the face of it CTF could be seen as such.

One of his points is particularly interesting. In ITLAD I give the analogy that my theory on the bisection of time is similar to that of the radioactive decay of a substance - i.e. that in any given time period a substance loses half its quantity. I apply Zeno's bisection paradox to this. Mr McIntyre points out that this is in error. He writes:

"For instance, he says that a radioactive half life implies that there will always be a quantity of a given radioactive substance - not so, a billion atoms of cobalt 60 will eventually be reduced to one, and then none."

Now I think that it is a little unfair and somewhat disingenuous of him to criticise me for using this because radioactive half life is not, in any way a component of CTF so as such my misunderstanding of this is irrelevant. Indeed I only use it as an analogy for something else. However that is not the point of this posting. I am of the opinion that he is right in that what is happening in half life is that numbers of atoms are being reduced and their will be a point, as he says, when it will decrease from 2 to 1 and then to zero - because an atom cannot be split into half an atom (after all is that not what atom means - Greek atomos (indivisible).

Is he, as I suspect, right on this point?