On Fri, Feb 21, 2025 at 07:22:38PM +1100, Bruce Kellett wrote:
> On Fri, Feb 21, 2025 at 5:16 PM Brent Meeker <[email protected]> wrote:
> 
> Brent,
> 
> This is beginning to sound like an argument we had with someone on another
> list. His final position in that case was that, although he could not give
> comprehensive arguments for his contentions, it had to be that way if his
> theory was correct.
> 
> This is precisely where Quentin is currently. He keeps making extrordinary
> claims without any shred of justification -- because if these claimds are not
> so then his theory is in trouble.
> 
> The simplest conclusion is that his theory is not correct.
> 
> Bruce

Bruce - the ony way you can do branch counting to get measure is if
the branches obey a physically symmetry. Then you can apply the
indifference principle - just as you say the probability of a die
outcome is 1/6th, you can say the probability of up or down is
1/2. But by construction, your "counter example" does not have
symmetric branches, therefore branch counting does not apply. All we
can say is that there will be some probability of each outcome. Just
like slicing a cake, you can slice the Multiverse in many different
ways, with different effects on the measure.

Quentin is not claiming to be able to generate the Born rule from all
of this, just that it is an open problem. Some say the Gleason theorem
is sufficient for this. My own derivation sort of goes the other
way. Starting with a probability measure attached to each branch, you
can construct an inner product space (and prove it is a Hilbert space)
that gives you the Born rule. Is this the only way of constructing an
inner product space? The Gleason theorem suggests it is.

What would be nice is to have all of that arise naturally from
information processing considerations. I don't know if that is
possible. It might be we need to augment our theory of computation
with something like quantum computation, for example.

-- 

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Dr Russell Standish                    Phone 0425 253119 (mobile)
Principal, High Performance Coders     [email protected]
                      http://www.hpcoders.com.au
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