Juergen wrote (on 12th Oct): > . . . In most possible futures your computer will > vanish within the next second. But it does not. This indicates that our > future is _not_ sampled from a uniform prior.
I don't wish to comment directly on the computer-vanishing problem as it applies to Juergen's scheme (my own problem with this laudable scheme is that it appears to be vulnerable to the same 'turtle-itis' criticism as for all theistic religions - the (literal or abstract GP) 'turtle' responsible for the world seems to need another turtle to support it and so on - there is no full explanation), but I would like to say that certain other proposed solutions don't suffer from this computer-vanishing problem (also known as the WR/dragon problem), if one thinks of infinite length bit strings / formal system descriptions via Limit n -> infinity, where n is the relevant string/description length (see appendix below). It seems to me that in thinking in simple infinity terms one can lose essential information (for example integers cannot be determined to be more numerous than the odd numbers - both are of the lowest order of infinity - not a problem for limit analysis). Alastair Malcolm APPENDIX One might naively think that as there are at least hundreds of possible states (call them V1, V2... ) where some part of our computer clearly vanishes (and only one (N), where normality prevails), then even if one considers bit string or other types of formal description involving other variations in our universe or indeed other universes, one could still 'divide through' to find that we are most likely to be in a universe where our computer vanishes in whole or part. However, we note that in any minimal description of our universe (and the following argument does not depend on there having to *only* be a minimal description), deviations from the actual physical laws causing V1, V2... will involve additional ad-hoc rules/events, so we can say that in complexity terms (whether as a bit string or formal system description) we will have V1 = N + VE1, V2 = N + VE2 etc, where VE1, VE2 etc are the extra segments of description required to cater for the part-vanishings (strictly: Length(V1) = Length(N) + Length(VE1) etc, but hopefully this is clear). Moreover, if we are considering all possible descriptions, we also have to allow for extra descriptions corresponding to entities beyond our observability. For each V = N + VE we will have many DC = N + DCE, where DC is a 'don't care' description - it is a universe (or set of universes) indistinguishable by us from N (our own, non-computer-vanishing one), yet objectively different. Now, the key point is that in any objective descriptive framework (whether by bit string or formal system), one should take the Limit as the description length increases to infinity, not as our (humanly biassed) visible universe is progressively and unobservably added to (say by other universes). As we do this, we are far more likely to be in a DC (= N + DCE) universe than a V (= N + VE) universe: computers don't normally vanish, in whole or in part. More details at: http://www.physica.freeserve.co.uk/p105.htm linking to: http://www.physica.freeserve.co.uk/p111.htm http://www.physica.freeserve.co.uk/p112.htm