In a previous post I launched a kamizake assault on UDA which was
justly cut to shreds on the basis of a number of misunderstandings on
my part, perhaps most crucially my conflation of information and
computation. I claimed that the UD cannot be distinguished from the
set of all possible information states and therefore from an infinite
field of static, within which all possible realities can be found,
none of which, however, have the slightest coherence. I also
mistakenly used the word 'random' to describe this bit field, which of
course is wrong. I should instead have used the word 'incoherent'.
Bruno and others quickly put me straight on these errors.

I am still troubled however by the suspicion that UDA, by explaining
'everything' (except itself - there is always that lacuna in any
explanatory framework) also explains nothing. Because the UD executes
every computation, it cannot explain why certain computations (say
Schroedinger's equation, or those of general relativity) are preferred
within our presenting reality. This very universality also insulates
it against disproof, since although it allows everything we see, it is
hard to conceive of something it would disallow. David Deutsch's idea
of a good explanation is one that closely matches the structure of the
thing it describes, allowing for little variation. The vast variation
in the possible worlds where UDA could be invoked makes it a bad
explanation, in those terms.

Of course the objection that nobody has yet found an application for
UDA, a concrete example of its usefulness, is more of an objection to
it as a scientific theory than a philosophical one. Still, I believe
there is an argument against it at the philosophical level. The UDA
invokes the notion of probability in relation to 1-p states on the
basis of the "infinite union of all finite portions of the UD in which
correct emulation occurs". Thus the indeterminacy of 1-p experience is
a function of the distribution of states within the observer’s
consistent histories. For instance, there’s a 20% chance of x
happening, if it happens within 20% of my consistent histories. Please
Bruno correct me if this is a misunderstanding.

Now we know from QT there is a finite, if absurdly remote, probability
of my turning into a giraffe in the next minute. So the UD, if not to
contradict science as it stands, must allow this too. And indeed there
is no reason for it not to, since there must be computational pathways
that lead from human to giraffe - a sort of deep version of the
morphing algorithms used in CGI - or a simple arbitrary transform. In
fact there must be infinite such pathways leading to slight variations
on the giraffe theme, as well as to all other animals, inanimate
objects and so on - okay let’s leave out the inanimate objects since
they possess no consciousness as far as we know, therefore no 1-p
experience.

Of course, these pathways are an extreme minority compared to the ones
in which I retain my present form, behaving as we would expect on the
basis of the past. But here’s where I see the problem. In a
mathematical platonia we cannot make such a statement. The notion of
probability within an infinite set is untenable. It is analogous to
expecting that a number selected at random from the set of natural
numbers is more likely to be divisible by 2 than by, say, a million.
This is only the case of the set is ordered to appear this way, eg
1,2,3,4... If we write the set thusly: 1, 1 million, 2 million, 3
million, 2, 4 million, 5  million, 6 million, 3, 7 million.... etc
then our expectation breaks down.

So if there are infinite pathways where I turn into a giraffe, as
there must be, there is no way for my 1-p experience to select
probabilistically among these pathways. I can no longer say, if the
set of calculation pathways is infinite, that giraffe transformation
occurs in, say .000000001% of them, or 5%, or 99% of them.

This is not a problem for an Everett -type multiverse, in which the
universes are bound together by consistent physical laws which allow
one to speak of a proportion of universes in which event x occurs.
However, in a mathematical platonia where all possible calculations
occur, and nothing outside of them, there can be no such ordering
principle.

I believe this same principle can be used to show that the
calculations of the UD must be disorderly. Consider some calculation c
which employs number n. In the UD there will also be a calculation
which instead uses the number n+1, another which uses n+2 etc. There
will also be calculations in which the ordering of the natural numbers
is rearranged in arbitrary ways such as my example above. Instead of
using simple n, the calculation will employ someFunction(n), where
someFunction() transforms the number as per my example, i.e. (in
pseudocode):

if n modulo 4 = 0
        return n
else
        return (n-1) * 1,000,000

Thus the UD cannot rely even on the ordering of natural numbers to
‘prefer’ certain calculations, since the set of variants such as the
above will be infinite, and overwhelm calculations involving simple n.

Bruno?

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