Since there is a distinct possibility that readers of Russell's 'Theory of
Nothing' book will be left with the wrong impression that my approach to the
White Rabbit problem is essentially the same as that of the author, I feel I
should at least record here a brief summary of the relevant part of my own
ideas, which are in essence very simple and straightforward.
My starting point is a consideration of the potentially fatal 'failure of
induction' (WR) challenge to the 'all logically possible universes' (alpu)
solution to the question of our existence (a solution that general
arbitrariness and abstract symmetry arguments appear more-or-less to ultimately
require): even if the world happened to be ordered up to now, why should we
happen to be in that world that continues in an ordered way, if all logically
possible futures do in fact occur, as alpu requires.
The solution to this challenge that is outlined here also explains why we live
in a relatively simple world, and is arrived at by a general consideration of
the most compressed fully accurate representation of our (past/present/future)
world (which in that most compressed form may well need to include other
worlds, for example those of (what would be the rest of) an Everett
multiverse), conceptually in the form of Tegmark's 'bird view'; whether the
form of this representation is some standard interpretation of a bit string, or
an axiom list (under some common theorem-generating inference rules), the two
key points are the same: first, there is nothing logically to prevent some
worlds themselves (including ours) being more 'compressed' than as we would
perceive them to be, and second, any difference from the world to be
represented (which must also exist under alpu) has to be reflected in a
difference in that representation - it then follows that in any comparison of
all possible combinations of bit/axiom strings up to any equal finite (long)
length (many representing not only a world but also (using 'spare' string
segments inside the total length) extraneous features such as other worlds,
nothing in particular, or perhaps 'invisible' intra-world entities), it is
reasonable to suppose that the simplest worlds (ie those with the shortest
representing string segments) will occur most often across all strings, since
they will have more 'spare' irrelevant bit/axiom combinations up to that equal
comparison length, than those of more complex worlds (and so similarly for all
long finite comparison lengths).
Thus out of all worlds inhabitable by SAS's, we are most likely to be in one of
the simplest (other things being equal) - any physics-violating events like
flying rabbits or dragons would require more bits/axioms to (minimally) specify
their worlds, and so we should not expect to find ourselves in such a world, at
any time in its history.
(It also seems to me that for at least some of the scenarios where the above
analysis could conceivably be considered inaccurate/incorrect (eg in comparing
uncountably infinite quantities), the necessary assumptions for these scenarios
render the White Rabbit problem void anyway.)
These ideas are fleshed out in:
www.physica.freeserve.co.uk/pa01.htm (which enlarges on the 'compressed'
objective reality that corresponds to the more compressed representations), and
www.physica.freeserve.co.uk/pb01.htm (a more general and informal read).
(Comments welcome - particularly if any problems are spotted in the above.)
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