Le 28-août-07, à 18:26, David Nyman a écrit :
>
> On 28/08/07, Bruno Marchal <marchal.domain.name.hidden> wrote:
>
>>>> If you drop a pen, to
>>>> compute EXACTLY what will happen in principle, you have to consider
>>>> all
>>>> comp histories in UD* (the complete development of the UD) going
>>>> through your actual state (the higher level description of it, which
>>>> exists by comp, but which is actually not knowable by you. Of course
>>>> this cannot be used in practice, but has to be used to derive the
>>>> more
>>>> usable laws of physics.
>>>
>>> I hope this will become clearer as we proceed.
>>
>>
>> I hope too. Perhaps it would help us if you could tell me which step
>> of
>> the UDA you find unclear.
>
> I'm sorry, I should have been clearer myself. It isn't the UDA per se
> that I don't find clear, but some of your specific statements and
> language above. For example, what specifically enables us to 'derive
> the usable laws of physics'?
I'm afraid "usable" is a fatal typo mistake. I dont see what I was
trying to say! My fault. Do you understand that to predict the exact
behavior of the pen, you have to take into account all computations
going through your state? (your state = your third person comp state
when you are looking at the pen before you drop it, which exists by
comp.
Of course nobody are interested in something as exact as that in any
application, for the same reason nobody will use Schroedinger equation
to study the trajectory of a satellite, nor will anybody use string
theory for doing a pizza. Even if we succeed in deriving physics from
the comp hyp, it could be that such a physics would be always too much
exact for any practical use. Still, it could give general idea, like
the existence of interfering many worlds, the refutation of
in-exploitability of sub-level comp computation (the comp-"quantum"
computing ability, etc.
> But perhaps I'm anticipating. I'm also
> not sure exactly what you mean by 'comp histories going through your
> actual state'.
I mean the set of computations which are going through your third
person state (in the UD*), but as seen from your first person pov.
> I think you mean that an 'actual state' (i.e. first
> person OM) that I'm experiencing can be attributed to any of these
> histories - yes?
OK. A bit more exact would be .... can be attributed to some 3-state
occurring in those histories/computations. Let us be more specific
later, when we will have a bit more vocabulary to put the right
nuances.
>
>> Remember that we *assume* the comp hyp. Sometimes some people does not
>> understand because they (more or less unconsciously believe that I am
>> arguing for comp, but that is something I am never doing since a very
>> long time: I really take it as a working hypothesis with no
>> (conscious)
>> prejudice about where this can lead us.
>
> Yes, I accepted this a while back.
OK. (I knew, but sometimes I add little things for the benefice of some
others so that they doesn't miss the train, just in case ...).
>
>> By linearity the cat
>> will be in the superposition state. What prevent us of seeing the cat
>> in that superposition state is not that the cat is macroscopic but
>> comes from the fact that we cannot isolate the cat sufficiently well
>> from us, so that, very quickly we will find ourselves in a
>> superposition seeing the cat in such state + seeing the cat in the
>> orthe state. The "quickly" here is not due to some magical quick wave
>> collapse, but is due to the rapidity of the decoherence process, which
>> mainly describes the (linear) way superposition are contagiopus to
>> their neighborhood.
>
> OK, so 'the cat' quickly becomes us + the cat in two orthogonal
> states? BTW, I've never seen the cat referred to as a 'contagio-puss'
> before, but it might catch on!
OK.
>
>> Now with comp, it is the same. You cannot known, by the first person
>> indeterminacy, which computations support your conscious state among
>> all computations that you cannot discerned. To make this clearer, I
>> will wait you telling me where exactly you have some trouble in the
>> UDA. OK?
>
> I think this is what I intended above - i.e. the UD* entails
> computations that support both versions of 'me' + the cat; which one
> "I" experience in a given OM is indeterminate.
OK (I think).
>
>> A state by itself cannot change the probabilities. It is the relative
>> number of possible continuations of a state, relative to the "number"
>> of comp histories going through that state which counts, up to some
>> (extraordinarily complex) equivalence relation.
>
> Are you still talking about the equivalence relation between the mind
> and the brain? I'm sorry to be so picky, but I'm really trying to be
> sure I understand each sentence.
I'm not sure I have ever talk about an equivalence relation between the
mind and the brain, unless you mean the relation between one mind (one
person) and the infinity of computation going through indiscernible (by
that person) states. Probably this includes "brain states", but such a
thing is, and has to be, problematic (bu UDA).
>
>> Can you compute how many functions from A to B there are, in case A
>> has
>> n elements and B has m elements? Answer: m^n. Can you see that?
>
> Yes, I can see it now I understand the notation better.
I'm glad! It is really sad when someone miss math due to a notation
problem. Always be sure you got the right interpretation of the
notation before thinking something mysterious is at play. (This is also
addressed to some others ...).
Did you read the first five pages by Cutland on prerequisites and
notations?
>
>> By "proof" here, I mean an argument which convinces you,
>> or better, an argument which you have the feeling that it can be used
>> to convince your "little sister" (which I suppose not to be a
>> mathematician).
>
> In fact I have two little sisters (and one little brother), and none
> are mathematicians.
You are more lucky than me. I have only a big sister and a big
brother, and there is no question I explain them math. Ah, but then I
am training myself explaining math to the children of my colleagues
those days.
Teaching to others is the key path to understand that you understand
... or not.
I must go. Tomorrow I begin to explain the idea of a computable
function. To let you think in advance I give you a problem: have you an
idea why NON computable functions have to exist?
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Wed Aug 29 2007 - 11:23:30 PDT