George Levy writes:
> <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
> <html>
> <head>

Oh, sorry, I'm supposed to ignore that, aren't I?  I guess you had
some neat graphics in your message that made all that HTML necessary,
along with requiring two copies of the text.  Unfortunately for me, I
didn't see the special effects, since I am using a text-based mail system.

> Discreteness may be important in our world for the development of 
> consciousness, but it is certainly not necessary across worlds. I 
> believe therefore that the differences between the simulations is 
> infinitesimal - not discrete - and therefore that the number of 
> simulations is infinite like the continuum.

The last part doesn't follow.  It could be that the number of simulations
is infinite like the rational numbers, which would still allow for the
differences between simulations to be infinitesimal.  In that case the
number of simulations is countably infinite rather than uncountable.

Personally I am uncomfortable with the infinity of the continuum, it
seems to be a much more troublesome concept than is generally recognized.
I would not want to invoke it unless absolutely necessary.

I think the rest of your argument works just as well with a countable
infinity as an uncountable one.

Hal Finney

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