On 2/7/2020 6:04 PM, Bruce Kellett wrote:
On Sat, Feb 8, 2020 at 12:48 PM 'Brent Meeker' via Everything List
<[email protected]
<mailto:[email protected]>> wrote:
On 2/7/2020 2:36 PM, Bruce Kellett wrote:
You certainly have. The argument that output strings that give
results inconsistent with your observations have vanishing
measure overall -- an argument based on the Pascal Binomial and
the law of large numbers -- applies equally to all observers,
whatever output string they observe. So whatever data you
observe, you conclude that the theory that is consistent with
that data is confirmed by the data. Which is useless, because you
reach that conclusion whatever data you observe. The law of large
numbers fails you when all possible outcomes are observed by
someone or the other.
So if the experiment is to toss a coin six times, there will be a
branch of the MW where HTHHTHHHHH is observed
If you observe that result on six tosses, then something is seriously
wrong :-).
and this will confirm the theory that H's are four times as
probable as T's. But there will be many more branches where it is
found that P(H)=P(T) (252 vs 45). And in the limit of large
experiments almost all experimenters (in the MW) will find
P(H)~P(T). Hence almost all experimenters will conclude something
close to the presumed true value.
But experiments are not conducted by polling all possible observers.
One cannot communicate with those on other branches, so this is just
silly. The experimenter has only his own data to work with, and he
must make whatever deductions he can using only that data.
Right. So he may, depending on the branch, infer the wrong conclusion.
But such observers are small in number in the limit of many experiments
and longer experiments. So we too make our deductions based on the data
we observe. And the above analysis gives us reason to think we will be
among those getting the data that supports the right theory.
Brent
This however depends on the assumption that each sequence of H and
T occurs in one branch of the MW. Other probability values, like
1/pi, are going to require very large numbers of branches to
approximate.
Irrelevant.
Bruce
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