On Wed, Apr 27, 2022 at 10:32 AM smitra <smi...@zonnet.nl> wrote:

> On 27-04-2022 01:37, Bruce Kellett wrote:
> > I think you
> > should pay more attention to the mathematics of the binomial
> > distribution. Let me explain it once more: If every outcome is
> > realized on every trial of a binary process, then after the first
> > trial, we have a branch with result 0 and a branch with result 1.
> > After two trials we have four branches, with results 00, 01, 10,and
> > 11; after 3 trials, we have branches registering 000, 001, 011, 010,
> > 100, 101, 110, and 111. Notice that these branches represent all
> > possible binary strings of length 3.
> >
> > After N trials, there are 2^N distinct branches, representing all
> > possible binary sequences of length N. (This is just like Pascal's
> > triangle) As N becomes very large, we can approximate the binomial
> > distribution with the normal distribution, with mean 0.5 and standard
> > deviation that decreases as 1/sqrt(N). In other words, the majority of
> > trials will have equal, or approximately equal, numbers of 0s and 1s.
> > Observers in these branches will naturally take the probability to be
> > approximated by the relative frequencies of 0s and 1s. In other words,
> > they will take the probability of each outcome to be 0.5.
> >
> The problem with this is that you just assume that all branches are
> equally probable. You don't make that explicit, it's implicitly assumed,
> but it's just an assumption. You are simply doing branch counting.

The distinctive feature of Everettian Many worlds theory is that every
possible outcome is realized on every trial. I don't think that you have
absorbed the full significance of this revolutionary idea. There is no
classical analogue of this behaviour, which is why your lottery example is
irrelevant.  I spelled out the sequences that Everett implies in my earlier
response. These clearly must have equal probability -- that is what the
theory requires. It is not an assumption on my part -- it is a
consequence of Everett's basic idea. So there is no branch counting
involved. That is just another red herring that you have thrown up to
distract yourself from the cold hard logic of the situation.


> The important point to notice is that this result of all possible
> > binary sequences for N trials is independent of the coefficients in
> > the binary expansion of the state:
> >
> >       |psi> = a|0> + b|1>.
> >
> > Changing the weights of the components in the superposition does not
> > change the conclusion of most observers that the actual probabilities
> > are 0.5 for each result. This is simple mathematics, and I am amazed
> > that even after all these years, and all the times I have spelled this
> > out, you still seek to deny the obvious result. Your logical and
> > mathematical skill are on a par with those of John Clark.

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