Re: White Rabbit vs. Tegmark

From: Patrick Leahy <jpl.domain.name.hidden>
Date: Tue, 24 May 2005 00:10:17 +0100 (BST)

On Mon, 23 May 2005, Hal Finney wrote:

>> I've overlooked until now the fact that mathematical physics restricts
>> itself to (almost-everywhere) differentiable functions of the continuum.
>> What is the cardinality of the set of such functions? I rather suspect
>> that they are denumerable, hence exactly representable by UTM programs.
>> Perhaps this is what Russell Standish meant.
>
> The cardinality of such functions is c, the same as the continuum.
> The existence of the constant functions alone shows that it is at least c,
> and my understanding is that continuous, let alone differentiable, functions
> have cardinality no more than c.
>

Oops, mea culpa. I said that wrong. What I meant was, what is the
cardinality of the data needed to specify *one* continuous function of the
continuum. E.g. for constant functions it is blatantly aleph-null.
Similarly for any function expressible as a finite-length formula in which
some terms stand for reals.
Received on Mon May 23 2005 - 19:17:34 PDT