# RE: Anything goes?

John E. Rylander (rylander@prolexia.com)
Thu, 11 Jun 1998 20:44:54 -0500

Thanks for the article, Steve. Interesting.

I'm more of a philosopher than a physicist (by some margin, in fact :^> ),
so I can only point out -one- mistake he makes, in his numerical example:

> Another difficulty with the ultimate ensemble theory is that it appears
> very wasteful. However, Tegmark has an extraordinary argument
> with which to counter his critics. He says there is actually less
> information in the multiverse than in an individual universe..
>
> To illustrate his argument, Tegmark gives the example of the
> numbers between 0 and 1. A useful definition of something's
> complexity is the length of a computer program needed to generate it.
> Imagine trying to generate a single number between 0 and 1, specified
> by an infinite number of decimal places. Expressing it would take an
> infinitely long computer program. But to generate all numbers
> between 0 and 1, all you would have to do is start at 0, step through
> 0œ1, 0œ2 and so on, then 0œ01, 0œ11, 0œ21 and so on--an easy program
> to write. In other words, creating all possibilities is much simpler than
> creating one very specific one..

But of course the algorithm he describes doesn't come even remotely close to
listing all the numbers there are, which task is per se impossible even with
an infinitely long list. E.g., where on the list would "1/3" be spelled
out? Answer: using his algorithm, it would not appear on the list. And so
on, for uncountably many numbers between zero and one: no number with
infinitely many digits, leaving out infinitely many rationals, and
uncountably infinitely many irrationals (i.e., all of them).

If this is really the example he gives, I suspect his theories are much more
profound to those without philosophical training than those with. Seems
pretty sloppy for one trying to start a revolution.

And even if his example did work, his conclusion wouldn't follow.

Yikes.