# RE: Anything goes?

John E. Rylander (rylander@prolexia.com)
Sat, 20 Jun 1998 16:52:31 -0500

> -----Original Message-----
> From: Stephen Jones [mailto:sejones@ibm.net]
[snip]
> >SJ> 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...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 0þ1, 0þ2 and so on, then 0þ01, 0þ11, 0þ21 and so on--an
> >>easy program to write. In other words, creating all possibilities is
> >>much simpler than creating one very specific one...
>
> JR>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)..
>
> I don't even understand what the connection is between the ensemble
> theory appearing very wasteful and there being less information in
> the multiverse than in an individual universe..

His (flawed) train of thought seems to be this:

(1) Picking any one rational or irrational number to specify the one
existing universe implies a very large amount of arbitrary information,
which is puzzling and may lead people to infer design.

(2) His proposed solution to this puzzle: -all possible- universes are
instantiated -- hence there's no longer a puzzle as to why -our- universe in
particular exists.

(3) An obvious objection: if -one- universe contains a large amount of
information, -infinitely many- universes must contain even more, making even
more of a puzzle, and being a very wasteful way to get a universe suited for
life.

(4) His response to that: Infinitely many universes are -in a deep sense-
simpler than just picking one, in that a very simple low-info process leads
to the infinity in question.
(4.1) His analogy: Does a list of all the numbers have more information than
any one infinitely-long real number? So it may -seem-, but in fact, this is
false: these infinitely many numbers can all be generated by a very simple
algorithm (given above), whereas storing just that one infinitely long
number would take an infinitely large program/data bank.

My point was that his analogy fails, because there is no simple algorithm
that generates all the real numbers. He's just shockingly wrong about that.
(One can, however, generate all the rationals and an infinitely large proper
subset of the irrationals. But his algorithm doesn't even do this!)

> But there seems to be a logical flaw in Tegmark's claim for multiple
> universes but only one algorithm. In an infinite ensemble of universes,
> wouldn't Tegmark's algorithm be run in each?

No -- the algorithm is just an analogy to show how a comprehensive infinity
can spring from a simple source, not an actual component in his theory that
must be instantiated in each universe. The utter weakness of his analogy
doesn't reflect well on his intellectual precision (and so undercuts his
authority as a clear thinker), but it doesn't itself refute his actual
theory. (Am I understanding your question properly?)

>
> Also, I have read somewhere that the infinite universe answer to the
> fine-tuning of the universe would defeat all science, because it would
> destroy cause-and-effect. In a truly infinite set of universes,
> everything would happen an infinite number of times. Thus any effect
> following a cause could just be because we happened to live in that
> universe where that effect just happened to follow that cause..

I don't know if natural laws are allowed to change within these universes --
I'd think not. Even so, you're right that in at least one universe (if
really -all- of them are created), the otherwise least probable outcome
would occur in every case. I suspect it'd be better to say that in a
minority of the universes natural phenomena would be too unpredictable to
make science feasible, but this wouldn't be the general case. (The biggest
obstacle to practical science would be that the vast majority of universes
couldn't sustain life.)
One aside: it's tricky to apply things like "minority" and "majority" to
infinite subsets of infinite sets of universes [if each set is of the same
cardinality] -- one needs some non-counting-based way to define such. E.g.,
it seems natural to say that only a minority of the natural numbers are
powers of 1000, but since there are infinitely many of each [and the same
"order" of infinity], one can't say there are more of one than the other,
merely quantitatively! similarly: are there more points in a 5x5 square of
Euclidean space than a 1x1 square? No, even though the area of the 5x5
square is 25 times larger. But that isn't determined by counting points.

> JR>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..
>
> Indeed. But then if there is not an infinite number of universes, then
> the materialist has no other way of explaining the design of this one..

Well, there are other theories too, of course, as Loren and David have been
thoughtfully discussing of late.

> JR>And even if his example did work, his conclusion wouldn't
> follow..
>
> Agreed. It just goes to show the failure of methodological naturalism
> when it is applied to origins!

Or, more precisely, the failure (we're supposing; this guy could
still -conceivably- turn out to be right) of a particular scientific
hypothesis.

--John