On Thu, Mar 05, 2020 at 11:34:55AM +1100, Bruce Kellett wrote: > On Thu, Mar 5, 2020 at 10:39 AM Russell Standish <[email protected]> > wrote: > > On Thu, Mar 05, 2020 at 09:46:34AM +1100, Bruce Kellett wrote: > > > The greater problem is that any idea of probability founders when all > outcomes > > occur for any measurement. Or have you not followed the arguments I have > been > > making that shows this to be the case? > > > > I must admit I haven't followed the arguments either - admittedly, I > haven't read your cited material. > > ISTM - probability is all about what an observer observes. Since the > observer cannot see all outcomes, an objection based on all outcomes > occurring seems moot to me. > > > The fact that the observer cannot see all outcomes is actually central to the > argument. If, in the person-duplication scenario, the participant naively > assumes a probability p = 0.5 for each outcome, such an intuition can only be > tested by repeating the duplication a number of times and inferring a > probability value from the observed outcomes. Since each observer can see only > the outcomes along his or her particular branch (and, ipso facto, is unaware > of > the outcomes on other branches), as the number of trials N becomes very large, > only a vanishingly small proportion of observers will confirm their 50/50 > prediction . This is a trivial calculation involving only the binomial > coefficient -- Brent and I discussed this a while ago, and Brent could not > fault the maths.
But a very large proportion of them (→1 as N→∞) will report being within ε (called a confidence interval) of 50% for any given ε>0 chosen at the outset of the experiment. This is simply the law of large numbers theorem. You can't focus on the vanishingly small population that lie outside the confidence interval. > > The crux of the matter is that all branches are equivalent when both outcomes > occur on every trial, so all observers will infer that their observed relative > frequencies reflect the actual probabilities. Since there are observers for > all > possibilities for p in the range [0,1], and not all can be correct, no > sensible > probability value can be assigned to such duplication experiments. I don't see why not. Faced with a coin flip toss, I would assume a 50/50 chance of seeing heads or tails. Faced with a history of 100 heads, I might start to investigate the coin for bias, and perhaps by Bayesian arguments give the biased coin theory greater weight than the theory that I've just experience a 1 in 2^100 event, but in any case it is just statistics, and it is the same whether all oputcomes have been realised or not. > > The problem is even worse in quantum mechanics, where you measure a state such > as > > |psi> = a|0> + b|1>. > > When both outcomes occur on every trial, the result of a sequence of N trials > is all possible binary strings of length N, (all 2^N of them). You then notice > that this set of all possible strings is obtained whatever non-zero values of > a > and b you assume. The assignment of some propbability relation to the > coefficients is thus seen to be meaningless -- all probabilities occur equal > for any non-zero choices of a and b. > For the outcome of any particular binary string, sure. But if we classify the outcome strings - say ones with a recognisable pattern, or when replayed through a CD player reproduce the sounds of Beethoven's ninth, we find that the overwhelming majority are simply gobbledegook, random data. And the overwhelming majority of those will have a roughly equal number of 0s and 1s. For each of these categories, there will be a definite probability value, and not all will be 2^-N. For instance, with Beethoven's ninth, that the tenor has a cold in the 4th movement doesn't render the music not the ninth. So there will be set of bitstrings that are recognisably the ninth symphony, and a quite definite probability value. > > > > You may counter that the assumption that an observer cannot see all > outcomes is an extra thing "put in by hand", and you would be right, > of course. It is not part of the Schroedinger equation. But I would > strongly suspect that this assumption will be a natural outcome of a > proper theory of consciousness, if/when we have one. Indeed, I > highlight it in my book with the name "PROJECTION postulate". > > This is, of course, at the heart of the 1p/3p distinction - and of > course the classic taunts and misunderstandings between BM and JC > (1p-3p confusion). > > > I know that it is a factor of the 1p/3p distinction. My complaint has > frequently been that advocates of the "p = 0.5 is obvious" school are often > guilty of this confusion. > > > Incidently, I've started reading Colin Hales's "Revolution of > Scientific Structure", a fellow Melburnian and member of this > list. The interesting proposition about this is Colin is proposing > we're on the verge of a Kuhnian paradigm shift in relation to the role > of the observer in science, and the that this sort of misunderstanding > is a classic symptom of such a shift. > > > > Elimination of the observer from physics was one of the prime motivations for > Everett's 'relative state' idea. Given that 'measurement' and 'the observer' > play central roles in variants of the 'Copenhagen' interpretation. > Yes - but not everyone is pure Everett, even if they're many worlds. I have often argued publicly that the observer needs to be front and centre in ensemble theories. It is also true of Bruno's computationalism - the observer is front and centre, and characterised by being a computation. Maybe it's so, maybe it ain't, but at least the idea gets us out of the morass that science of conscioussness is in. -- ---------------------------------------------------------------------------- Dr Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders [email protected] http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/20200305062552.GP2903%40zen.
