----- Original Message -----
From: "Nick Bostrom" <nick@nickbostrom.com>
> Suppose we know that the true theory of everything is of the form T, and
> that it has one free parameter, a physical constant k that, on theoretical
> grounds, can take on any integer value between 1 and 1,000,000. But there
> is no a priori ground, let's assume, why k should have one of these values
> rather than another. So by a principle of indifference, we assign each of
> these possibilities an equal probability. Now consider the specific
> hypotheses Tn:="T and k=n" for n=1, ..., 1,000,000. Probability calculus
> then implies that the probability of Tn <= 1/1,000,000. In other words,
> each of these specific hypotheses must be highly a priori improbable since
> they are mutually exclusive and their combined probability cannot exceed
1.
But, again, why should we reason this way at all? Why should we be of the
belief that since we are able to attach a numerical value to a property of
the universe, it is therefore a 'variable'? On what sort of theoretical
grounds can you presume to assign a particular set of integer values to
physical constants?
There's a little bit of devil's advocacy going on here-- I admit to being a
proponent of multiverse theories of reality (ALL things happened is as
logically consistent in my mind and NO things happened,) but even in the
context of many worlds theorems, I wonder why we should consider 'alternate
numbers' as being logical possible place-holders for physical constants.
This is one step beyond what I imagine the human mind is capable of
attaching much significance to, but can we hypothesize about a
non-mathematical template for reality? Attaching numbers to processes as a
means of measuring fundamental building blocks and relative ratios of values
seems to reference the intrinsic fabric of our existence-- but I wonder if
our adherence to numbers as the ultimate rules of reality doesn't put us
into arbitrary mindsets with regards to possible existence scenarios.
> Even if it was in some sense physically necessary that
> k=42925, so that the physical chance of k=42925 is 1, this is compatible
> with our prior epistemic probability of k=42925 being very small.
Not following you here. Again: why should we reason that since other
numbers exist, they are (even a priori cognitively) available to said
constant?
Thanks.
--::jason.joel.thompson:: ::founder::
www.wildghost.com
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