On 2/15/2020 10:03 PM, Bruce Kellett wrote:
On Sat, Feb 15, 2020 at 3:17 PM 'Brent Meeker' via Everything List
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On 2/14/2020 2:17 PM, Bruce Kellett wrote:
I attach an extract from Kent's paper. Take up your argument with
him if you think he has got the statistics wrong.
I don't find it very convincing
Whether you are convinced or not does not really affect the logic of
Kent's argument. I think, as I have thought for some time, that your
intuitions are too conditioned by the probabilities of coin tosses in
a single world. You slip single word intuitions into your criticisms
of the many-worlds picture.
He asserts “After N trials, the multiverse contains 2 N branches,
corresponding to all 2 N possible binary string
outcomes." which is not true if pushing the red button produces 0
or 1 with some fixed probability p0 (which isn't made clear).
It is true, whatever the probability associated with pushing the red
button. And, in the case I consider, there simply is no matter-of-fact
about such probabilities.
I took, " Suppose too that the inhabitants believe (correctly) that this
is a series of independent identical experiments," to mean there there
is some unknown, but fixed probability of writing a 0 or 1. Otherwise I
don't know what "independent identical" means? Those are commonly
statistical terms.
When the button is pushed, two new worlds are created, one with a 0
written on its tape and the other with a 1.
Which implies that number of 0's and 1's will be equal, though not along
a give tape.
The button is pushed afresh in each of the created worlds, so in each
world, two new worlds are created. This give 2^N branches or worlds
for N trials. And these worlds will contain tapes, one in each world,
on which is written the binary string corresponding to the history of
results for that world. So there are 2^N different binary strings;
that exhausts the space of possible binary strings of length N. Unless
you get hold of this fact, the rest probably will not make sense.
Translate the red button into a Stern-Gerlach magnet measuring the
x-spin of an ensemble of particles all prepared in a z-spin up
eigenstate. If we record x-spin up as 0, and x-spin down as 1, we get
exactly the same set of 2^N binary sequences after N trials, all
sequences different, as we got from pushing the red button. The crunch
comes when we rotate the S-G magnet by 10 degrees and repeat. We still
get all possible 2^N binary strings -- the same set of strings as we
found before, because this set of exhausts the space of N binary
strings. If If you are still not convinced, rotate your S-G magnet by
a further 20 degrees and repeat the N trials. Do you get any new
binary strings? Of course not, the space of possible strings has
already been exhausted.
The message is clear, the data that any observer in any world can get
is independent of the coefficients in the original expansion of the
prepared state in an appropriate basis. The Born rule can have no
relevance in many-worlds -- whether Everettian or not.
There is nothing which guarantees that all sequences will occur
in any finite sample.
Think again, all 2^N sequences will occur in any set of N trials.
OK, each time the button is pushed and two new worlds created, which are
identical in their records up to the current writing and in one world 0
is added to the tape and in the other 1 is added to the tape. I
understand that is not consistent with observation. And that there is
no mechanism described in Everett's evolution to deviate from this.
That's why I said that in order to get the Born rule there must be
many-worlds before the experiment which are then divided, possibly
unevenly, to produce the Born rule.
But I suppose we can pass over this noting that for large enough
N it is highly probable, though not certain.
He's right that the citizens of different branches of the
multiverse will infer different values of p from their
experiments. But isn't it also true that most of them will infer
a value close to the true value.
Close to the true value? Have you not grasped the point that in the
red button case, there is no "true value". And whatever the
coefficients in the original state, the majority of binary strings
will have close to equal number of 0s and 1s -- that is just a fact
about the binomial expansion. It says nothing about the "true value",
because no such true value may exist.
That's just metaphysical angst. 1/2 is as "true" a value as science can
ever infer. That's why I find these two paragraphs misleading:
/ “Let’s consider further the perspective of inhabitants on a branch
with pN zero outcomes and//
//(1 − p)N one outcomes. They do not have the delusion that all observed
strings have the same//
//relative frequency as theirs: they understand that, given the
hypothesis that they live in a multiverse,//
//every binary string, and hence every relative frequency, will have
been observed by someone. So how//
//do they conclude that the theory that the weights are (p,1 − p) has
nonetheless been confirmed?.//
//Because they have concluded that the weights measure the importance of
the branches for theory//
//confimation. Since they believe they have learned that the weights are
(p,1−p), they conclude that a//
//branch with r zeros and (N −r) ones has importance p r (1−p) N−r .
Summing over all branches with//
//pN zeros and (1 − p)N ones, or very close to those frequencies, thus
gives a set of total importance//
//very close to 1; the remaining branches have total importance very
close to zero. So, on the set//
//of branches that dominate the importance measure, the theory that the
weights are (very close to)//
//(p,1 − p) is indeed correct. All is well! By definition, the important
branches are the ones that//
//matter for theory confimation. The theory is inded confirmed!//
// “The problem, of course, is that this reasoning applies equally
well for all the inhabitants, whatever//
//relative frequency p they see on their branch. All of them conclude
that their relative frequencies//
//represent (to very good approximation) the branching weights. All of
them conclude that their own//
//branches, together with those with identical or similar relative
frequencies, are the important ones//
//for theory confirmation. All of them thus happily conclude that their
theories have been confirmed.//
//And, recall, all of them are wrong: there are actually no branching
weights.”/
The "all of them" who conclude a branch weighting very different from
0.5 will be a vanishingly small fraction. The whole argument is "There
will necessarily be outliers and they can't tell they are outliers.
Therefore science is impossible because we can never be certain we are
not misled into seeing patterns were none exist."
And the fact that 50/50 seems to be obtained on the majority of
branches is true, even if the true probabilities are 0.99 and 0.01.
But you postulated that every time a 0 is printed on a tape, a 1 is
printed of the other world's tape. So every tape will be a branching
graph with 0 and 1 at each branch point. Almost all paths thru this
tree will have approximately equal numbers of 0s and 1s per the binomial
theorem. Each path corresponds to an experimenter. So almost all
experimenters will estimate P(0)=P(1)=0.5 or nearly so.
And the larger is N, the greater the percentage of branches
within a small interval around the true value. Are there some
branches in which the citizen infer values very different from the
true value p0? Sure. But in a single world where N experiments
have been performed to use in estimating p, there is a probability
that some value far from p0 will be observed.
This is where you fall back on your single-world intuitions about
probability. You have to get away from this, those intuitions fail in
the many-worlds case.
This is untrue: "In the many-worlds case, recall, all observers
are aware that other observers with other data must exist, but
each is led to construct a spurious measure of importance that
favours their own observations against the others" If they have
any understanding of statistics they will infer that it is highly
probable that most other universes obtained a value close to theirs.
That is rather like Bruno's "frequency operator". Sure, they infer
that it is highly probable that most other universes obtained a value
close to theirs -- that is another simple property of the binomial
expansion. But everyone infers this -- even those with widely
disparate observed relative frequencies. They can't all be right, so
the inference along these lines that any individual makes is clearly
wrong.
Of course some of them will be wrong about that...some of them
will be outliers.
How do they know that they are outliers? Or how can you even define an
"outlier" when there is no underlying probability -- as in Bruno's WM
duplication scenario.
So Kent's argument is really that in a universe with randomness we
can never be sure we're not an outlier. But as Ring Lardner would
say, "But that's the way to bet."
You are basing probabilities on a one-world model again. You can't
really mean that everyone in the two-outcome case should bet 50/50,
regardless of the data?
No. I'm arguing they should bet p/(1-p) for whatever p they observe.
It's inductive inference.
Note that this exact same argument could be made in which there is a
"true value" p=0.5. Would you then conclude that it is impossible to
experimentally infer p=0.5?
That is not to say I don't agree with the point that for MWI to work the
value of p must depend on the prepared system; which brings me back to
the idea there must be many (infinitely many) branches or weights which
just get divided proportionately at measurement. It must be MW+Born.
Brent
Bruce
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