Ricardo,

On 19 Nov 2011, at 16:33, R AM wrote:

Has Eric Vandenbush written a paper about how complex numbers are derived from UDA?

He has some health problem, and rarely finish papers. Sorry. I work hard to encourage him to finish a paper on those complex numbers. I will let you know if he succeeds in that task.

Bruno




Ricardo

El nov 19, 2011 9:49 a.m., "Bruno Marchal" <marc...@ulb.ac.be> escribió:

On 19 Nov 2011, at 03:02, Pierz wrote:

In a previous post I launched a kamizake assault on UDA which was
justly cut to shreds on the basis of a number of misunderstandings on
my part, perhaps most crucially my conflation of information and
computation. I claimed that the UD cannot be distinguished from the
set of all possible information states and therefore from an infinite
field of static, within which all possible realities can be found,
none of which, however, have the slightest coherence. I also
mistakenly used the word 'random' to describe this bit field, which of
course is wrong. I should instead have used the word 'incoherent'.
Bruno and others quickly put me straight on these errors.

I am still troubled however by the suspicion that UDA, by explaining
'everything' (except itself - there is always that lacuna in any
explanatory framework) also explains nothing.

The UD is not proposed as an explanation per se. On the contrary UDA shows that it is a problem we met when we assume that the brain (or generalized brain) is Turing emulable.





Because the UD executes
every computation, it cannot explain why certain computations (say
Schroedinger's equation, or those of general relativity) are preferred
within our presenting reality.

That is basically my critics of Schmidhuber I have made on this list.

I'm afraid that you miss the role of the first person indeterminacy.
I will add explanation here asap. You have to follow UDA step by step: it is a proof (in the theory "mechanism"), so to refute UDA you have to say where it goes wrong. I insist: UDA is a problem, not a solution. Indeed it is a subproblem of the mind-body problem in the mechanist theory.
AUDA will be the solution, or the embryo of the solution.





This very universality also insulates
it against disproof, since although it allows everything we see, it is
hard to conceive of something it would disallow.

Not at all. A priori it predicts everything *at once*. That is the "white rabbit problem". We don't see white rabbits, or everything at once, so mechanism seems to be disproved by UDA. The point will be that such a quick disprove does not work, and when we do the math we see mechanism is not yet disproved, but that it predicts or explain the quantum weirdness.



David Deutsch's idea
of a good explanation is one that closely matches the structure of the
thing it describes, allowing for little variation. The vast variation
in the possible worlds where UDA could be invoked makes it a bad
explanation, in those terms.

You have just not (yet) understood the role of the 1/3 person pov distinction in the reasoning. UDA shows that physics is determined by a relative measure on computations. If this leads to predict that electron weight one ton then mechanism is disproved. UDA shows that physics is entirely reduce to computer science/number theory in a very specific and unique way (modulo a variation on the arithmetical definition of knowledge).




Of course the objection that nobody has yet found an application for
UDA, a concrete example of its usefulness, is more of an objection to
it as a scientific theory than a philosophical one.


UDA is a proof. Unless wrong, it is done. Asking for the use of the UDA is like asking for the use of the theorem saying that no numbers n and m are such that (n/m)^2 = 2. UDA shows a fact to be true and that we have to live with it. UDA shows that mechanism and materialism are (epistemologically) incompatible.



Still, I believe
there is an argument against it at the philosophical level. The UDA
invokes the notion of probability in relation to 1-p states on the
basis of the "infinite union of all finite portions of the UD in which
correct emulation occurs". Thus the indeterminacy of 1-p experience is
a function of the distribution of states within the observer’s
consistent histories. For instance, there’s a 20% chance of x
happening, if it happens within 20% of my consistent histories. Please
Bruno correct me if this is a misunderstanding.

No, here I mainly agree with you.




Now we know from QT there is a finite, if absurdly remote, probability
of my turning into a giraffe in the next minute. So the UD, if not to
contradict science as it stands, must allow this too. And indeed there
is no reason for it not to, since there must be computational pathways
that lead from human to giraffe - a sort of deep version of the
morphing algorithms used in CGI - or a simple arbitrary transform. In
fact there must be infinite such pathways leading to slight variations
on the giraffe theme, as well as to all other animals, inanimate
objects and so on - okay let’s leave out the inanimate objects since
they possess no consciousness as far as we know, therefore no 1-p
experience.

Of course, these pathways are an extreme minority compared to the ones
in which I retain my present form, behaving as we would expect on the
basis of the past.

"Of course"?
No, what UDA shows is that it is not obvious, and that computer science can show it false, and so refute mechanism. But the math shows that such a refutation, if it exists, is not trivial at all, and the logic of self-reference shows that we are led to absurdities, not contradiction (yet), and the absurdities are quite similar to the quantum weirdness that we can "observe" (non locality, indeterminacy, many worlds/dreams/states, symmetry at the bottom, etc.)



But here’s where I see the problem. In a
mathematical platonia we cannot make such a statement. The notion of
probability within an infinite set is untenable.

On the contrary. Probability calculus and measure theory have been invented to put measure on infinite spaces.




It is analogous to
expecting that a number selected at random from the set of natural
numbers is more likely to be divisible by 2 than by, say, a million.
This is only the case of the set is ordered to appear this way, eg
1,2,3,4... If we write the set thusly: 1, 1 million, 2 million, 3
million, 2, 4 million, 5  million, 6 million, 3, 7 million.... etc
then our expectation breaks down.

You can use the usual Lebesgue measure on the real.
http://en.wikipedia.org/wiki/Lebesgue_measure

Think about the repeated self-duplication. It shows that self- duplication is a Bernouilli experience, so that in the limit (which define the uncertainty domain for the first person experience), we can use the usual normal distribution based on e^(- x^2) with the normalisation factor.





So if there are infinite pathways where I turn into a giraffe, as
there must be, there is no way for my 1-p experience to select
probabilistically among these pathways. I can no longer say, if the
set of calculation pathways is infinite, that giraffe transformation
occurs in, say .000000001% of them, or 5%, or 99% of them.

Yes, you can. The problem is that the UD does not just iterate self- multiplication (random noise), but it mixes it in a highly non trivial way with infinitely many computations.




This is not a problem for an Everett -type multiverse, in which the
universes are bound together by consistent physical laws which allow
one to speak of a proportion of universes in which event x occurs.
However, in a mathematical platonia where all possible calculations
occur, and nothing outside of them, there can be no such ordering
principle.

If the Everett idea works, and is the solution, (which has not yet been completely proved) then the UDA conclusion is that the Everett simultion in the UD wins the "measure battle", and we HAVE to justify this from computer science alone.

It would mean that the quantum computation are statistically more frequent than the non quantum computations. But this must be shown, or we miss the explanation of the origin of the physical laws, together with the distinction quanta/qualia that digital mechanism already explained (by the Solovay split between truth and proof).




I believe this same principle can be used to show that the
calculations of the UD must be disorderly. Consider some calculation c
which employs number n. In the UD there will also be a calculation
which instead uses the number n+1, another which uses n+2 etc. There
will also be calculations in which the ordering of the natural numbers
is rearranged in arbitrary ways such as my example above. Instead of
using simple n, the calculation will employ someFunction(n), where
someFunction() transforms the number as per my example, i.e. (in
pseudocode):

if n modulo 4 = 0
       return n
else
       return (n-1) * 1,000,000

Thus the UD cannot rely even on the ordering of natural numbers to
‘prefer’ certain calculations, since the set of variants such as the
above will be infinite, and overwhelm calculations involving simple n.

This shows that the extraction of physics from numbers is not an easy task, but again, you have to take into account the non triviality of the 1 and 3 pov relation, and of computer science and mathematical self-reference (G, G*, S4Grz, etc.) Then the shadows of why quanta and qualia already appear.

Recently Eric Vandenbush (a guy who solved the first open problem in my thesis) has found an explanation why the UD leads necessarily to complex numbers for the measure problem (that's new! but I have yet to be entirely convinced).

Pierz, I insist that the UD is not proposed as a solution, but as a problem for DM. It is shown to be an unavoidable problem we have to solve if we keep digital mechanism in cognitive science. I am open that it will lead to a refutation of mechanism, but the contraidiction has not yet appear, and on the contrary, what we get is a similar "many-world" problem that the physicists encounter too. This confirms Digital Mechanism (DM) instead of refuting it. UDA just transforms the mind body problem into a mathematical body appearances problem.

Bruno

PS have you see that edot has become enet? I will come back on the UDA there too! Here is the link:
http://www.entheogen-network.com/forums/


http://iridia.ulb.ac.be/~marchal/



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