```X-Message-Number: 24951
From: "Michael C Price" < var s1 = "michaelprice"; var s2 = "ntlworld.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
References: < var s1 = "20041027090000.25328.qmail"; var s2 = "rho.pair.com"; var s3 = s1 + "@" + s2; document.write("<a href='mailto:" + s3 + "'>" + s3 + "</a>"); >
Subject: Re: Forever Friendly versus Techno-Hell
Date: Sun, 31 Oct 2004 03:30:23 -0000

I am grateful that Mike Perry has focussed on the nub of my
argument :
> The thrust of Mike Price's argument for the existence of techno-
> Hells alongside of Heavens seems to be contained in the
> following.
>
>> It doesn't matter how likely you imagine the group selection
>> pressures will be against the construction of techno-Hells by
>> sadistic superbeings, [.] some will still exist.  Your arguments,
>> as I have repeatedly tried to point out, will only reduce
>> the ratio of Hells: Heavens, not eliminate them.  In an infinite
>> multiverse any non-zero ratio implies an infinite number of
>> Hells.
>
> I agree that any nonzero ratio implies an infinite number of
> various types of places that actually exist.

Okay

Mike goes on to argue that the ratio of Hells:Heavens is actually
zero and uses an analogy:

> First it will be instructive to consider an analogous but simpler issue:
> the coin toss sequence. Assuming a coin is fair, we have an equal
> probability of heads or tails on each toss. For a given sequence of
> tosses, let h be the fraction of tosses that show heads. For a finite
> sequence, however long, h can assume values between 0 and 1,
> and there will be infinitely many coin toss sequences (in more than
> one sense) with the given value h. However, for an infinite sequence,
> the only allowable value of h is 0.5 corresponding to a "balanced"
> sequence having an equal frequency of heads and tails-all other
> outcomes have probability zero, as should be clear by considering
> the probabilities. So logically we can imagine an infinite sequence of
> tosses where h, say, is 0.6 rather than 0.5. And it's true that there are
> finite sequences of arbitrary length where this is so, and they must
> occur infinitely often in an infinite multiverse. Yet again, the infinite
> but unbalanced sequence with h=0.6 (or any other value besides
> 0.5) never occurs. It is logically possible but physically impossible.

First, I accept that we never see such an unbalanced sequence.
As Mike Perry knows, such a demonstration is used, by some
people, to derive Max Born's quantum statistics, which are amply
confirmed by countless experiments.

Second, I am not persuaded that techno-hell's existence is as
improbable as an infinite unbalanced sequence of coin-tosses.
(i.e. I do not accept that the ratio of Hells: Heavens is zero.)

But rather than try to demonstrate the falsity of the analogy (which
would take a lot of iterations between Mike Perry and myself) I shall
merely demonstrate the internal inconsistency of the analogy; every
logically possible outcome (h not near 0.5 for infinite sequences) is in
fact physically realised, even though the ratios of such outcomes,
relative to more probable outcomes, may be zero.  Thus techno-Hells
exist in any reasonably plausible infinite multiverse if I can demonstrate
the physical reality of every logical possible outcome.  (Note though,
that the converse is not true; even if my demonstration is flawed that
this does not disprove the existence of any techno-Hells.)

The demonstration of the physical reality of every logically possible
outcome follows when we realise that (in the coin tossing example)
these proofs all rely on the *ratios* of the number of outcomes as the
number of tosses go to infinity.  If instead we were to ask what are
the *absolute number* of logically possible outcomes where h was
between, say, 0.6 and 0.7, we would find that this number diverges
as the number of tosses diverges; the reason why we never see such
outcomes (and why quantum statistics doesn't break down) is not
because such outcomes don't happen, but simply because they are
increasingly out-numbered in the infinite limit by outcomes that
conform to the usual statistics (with h close to 0.5, in the coin
example).

Cheers,
Michael C Price

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