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:
(Comments welcome - particularly if any problems are
spotted in the above.)
Alastair Malcolm