One of my references did not 'HTMLize' properly for some reason. This one 
  ----- Original Message ----- 
  From: Alastair Malcolm 
  Sent: Saturday, April 19, 2008 9:48 AM
  Subject: 'White Rabbit' solution summary (+ simplicity explanation)

  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: (which enlarges on the 'compressed' 
objective reality that corresponds to the more compressed representations), and (a more general and informal read).

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

  Alastair Malcolm


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