On 27 Dec 2009, at 18:13, Nick Prince wrote:

> Ok so I have come up with an argument to try and convince myself of
> step 8 but it still has some catches to it. If anyone sees that I am
> using incorrect thinking at any time please correct me.
> Misunderstanding means bad foundations.
> Up to step 7 all seems well and you begin step 8 by saying “but what
> if we don’t grant a concrete robust physical universe?”
> Some people have attempted to suggest the possibility of a Universe
> which is sufficiently robust.  For example in Frank Tipler “The
> physics of Immortality “ he explains how the universe could be
> utilised to act as a computational engine in order to generate
> consistent extensions of sentient beings.  His claims have been
> heavily criticised, but I do think he has made a brave and ingenious
> try at explaining how a reductionist approach along with a belief in
> strong AI can yield interesting speculations.  If he had written his
> book in a more modest and understated manner his ideas would have been
> much better received.  Incidentally, the fact that, because the
> universe has been shown to be expanding at an accelerating rate does
> not invalidate his theory because there is currently no clear
> understanding of the nature of dark energy – for example it may be a
> decaying scalar field ( we understand theoretically this type of
> mechanism because it is one of the best candidate mechanisms for
> understanding the (temporary) inflation in the early universe.  If it
> is like this, then re-collapse might provide the physics necessary for
> high computational capability.
> But let’s suppose things are as you say and that the universe is not
> robust enough in any circumstances.

Careful. If the universe contains a real UD, we don't need step 8 to  
conclude that physics is derivable from computer science. I don't  
assume that the universe is not robust enough, I was just considering  
that move as an objection to the UDA seventh first steps. The 8th step  
is an independent step showing that the physical supervenience thesis  
is incoherent with the mechanist assumption.

> I want to understand the assertion that platonic realism underpins my
> ist person reality.  If I dispense with Schmidhuber’s great  
> programmer
> (and his hardware) then rather than infinite regress, I assume there
> exists a platonic UD.

Well, it is better to assume just the axiom of, say, Robinson  
arithmetic. You assume 0, the successors, s(0), s(s(0)), etc.
You assume some laws, like s(x) = s(y) -> x = y, 0 ≠ s(x), the laws  
of addition, and multiplication. Then the existence of the universal  
machine and the UD follows as consequences.
I am not assuming more, with respect to math, than any mathematicians  
(on the contrary, given that the ontology is provided by a tiny part  
of arithmetic). Platonism or realism means here that we explicitly  
allow non constructive proof of existence, that is we allow the  
excluded-middle principle: we accept the idea that a closed  
arithmetical sentences is either true, or false.

> Now, since (I also assume) platonic reality is
> somehow timeless,

You don't have to assume arithmetic is timeless! To do that you have  
to first assume there is a time, and then say that arithmetic is true  
at all the times. But arithmetical proposition, by definition or  
construction are not conceive as being time dependent,  at the start.  
Theories of time will on the contrary depend on the assumption of some  
mathematical structures.

> then  the UD algorithm must surely exist  in this
> timeless “place”.

Better not to conceive them as living in some place. "where" and  
"when" are not arithmetical predicate. The UD exists like PI or the  
square root of 2.
(Assuming CT of course, to pretend the "U" in the UD is really  
universal, with respect to computability).

I have implemented and run a UD in 1991, for about six days. I mean, a  
UD is a very concrete object. Here is the PDF of the code and example  
of executions (but it is badly commented):

> Now it gets interesting.  I have assumed the
> algorithm is there too just like I assume that a perfect scalene
> triangle is in a more general platonia.  However this triangle is made
> of perfect line segments combined together to make it - and in turn
> the segments were made up of a sum of ideal points (lets not go into
> details about the reals and integers at this stage).  Clearly though
> the triangle does not have to be fully represented in this reality if
> everything can be made of points. As long as an algorithm exists in
> the platonic realm which enables lines and combinations of them to be
> combined as triangles.  But such an algorithm would be made up of
> numbers anyway and hence it’s all numbers.  Indeed the numbers  
> hardly
> need to be grouped in an list as we are familiar with seeing programs
> in because ordering is hardly important.
> Now I’ve almost convinced myself that I’m on the right track but  
> then
> come the niggles.   The static timeless platonic reality  has to
> somehow generate my seemingly dynamic existence and we are back to the
> same problem. Where is the spotlight which shines on each platonic
> number in the right order to give the experience of succession?
> Russell’s theory of nothing idea springs to mind here.  The
> arithmetical reality I am supposing underpins my existence has no
> meaning without the spotlight that some observer would have to give
> to it to make it feel like our existence feels (somehow intuition
> calls out for a sequential map from N to N with some notion of time/
> order).  Indeed there is also the idea of an “instruction set”.  A
> jumble of bit strings make up a program but the physical hardware has
> to react to these numbers in a well defined way in order to know how
> to shuffle other numbers around. In other words the function mapping
> the numbers has to be represented in the platonic reality somehow and
> I am not sure it can be done with just more numbers.

There is a "time order". The most basic one, after the successor law,  
is the computational steps of a Universal Dovetailer.
Then you have a (different) time order for each individual  
computations generated by the UD, like

phi_24 (7)^1,   phi_24 (7)^2,   phi_24 (7)^3,   phi_24 (7)^4, ...

where    "phi_i (j)^s" denotes the sth steps of the computation (by  
the UD) of the ith programs on input j.

Then there will be the time generated by first person learning and  
which relies eventually on a statistical view on infinities of  

Time is not difficult. It is right in the successor axioms of  
arithmetic. And all universal numbers reinvent it. What is most  
intriguing is the appearance of time symmetry at the bottom. It is the  
lack of appearance of time, in the physical world, which intrigues me  
the most. If "nature" happens to be a bit too much symmetrical, it may  
be bad news for comp. Subjective time may appear when you relate  
"proof" and "truth", for technical reasons, and is not directly  
related to any digital time, it is a first person continuum.

We don't need an external spotlight, because we conceive time in the  
indexical way, like personal identity. This is hardly new. I mean many  
physicists, like Einstein, conceived that time could be an illusion.  
Assuming comp I argue that the whole of physicalness is an indexical,  
but the "we" is larger than usual: "we" = "the universal machines".

It would be like you need a spotlight to be the one chosen in  
Washington, but with comp we put a spotlight, in that sense to all  
"reasonable" universal machine state, be it the one in Washington than  
the one in Moscow, be it today, tomorrow, or yesterday. From the first  
person point of view, it is always here and now.



> On Dec 25, 2:56 pm, Bruno Marchal <marc...@ulb.ac.be> wrote:
>> Hi Nick, hi Quentin,
>> On 25 Dec 2009, at 04:13, Quentin Anciaux wrote:
>> Nick Prince wrote
>>>> I can understand that numbers and arithmetic operations (as well  
>>>> as a
>>>> whole lot of other stuff) exist as some kind of objective reality
>>>> (called a platonic reality).  These archetypal “things” are to  
>>>> me
>>>> clearly discovered by us rather than invented.  But that our  
>>>> dynamic
>>>> world emerges somehow from this static ethereal repository seems  
>>>> very
>>>> difficult to see.
>> And Quentin commented:
>>> Would it be easier if I said that all of this came from bouncing
>>> particle of matter (whatever that is) ?
>> That is a good point, which I find rather convincing. To attribute
>> consciousness to arithmetical (static, ethereal) relations is not  
>> more
>> intriguing than to attribute it to continuous particle 4D line
>> universe in any block universe conception.
>> But remember the "Peter Jones" type of move. He understands comp as a
>> material form of comp. He posits that to be conscious, you need a
>> physical primary universe in which the computations are executed. Of
>> course this moves seems completely ad hoc. he has to invoke some  
>> magic
>> in both mind and matter, which is already against the comp idea. But
>> unfortunately, with only the first seven steps, you can still believe
>> in such "ad hoc" theory. It is enough to believe that the seven steps
>> just show that we are living in a small primary physical universe
>> (small = not enough big to run the UD),  and that is why the 8th step
>> is needed to prevent that type of move, and to conclude the proof.
>> Nick Prince wrote
>>> This must be difficult. How can any theory be interpreted without  
>>> the
>>> formalisms or some model.
>> Remember that logicians use the word "model" like the painters. The
>> model (the naked person) is the reality. The theory (the painting) is
>> the finite piece of crap trying to capture or represent that reality.
>> A theory is on the side of the machine. It is a finite or finitely
>> representable things, like a program. It has a sort of operational
>> syntactical "interpretation": it generates mechanically theorems or
>> numbers, and it can (and usually have) a (mathematical )meaning  
>> called
>> model, and which is the thing it compute or prove statements about.
>> If you want, a brain is already a theory (with reality as intended
>> model). The brain is supposed to interpret reality, or to implement
>> some higher level interpreter (you, actually) of reality. for  
>> example:
>> reality = a bird flies in the sky (let us assume).
>> You look at it, and this makes your eyes sending a (giant) bitstring
>> to your brain, which, through many (parallel) computations makes your
>> self interpreting the bitstring as  (strong evidence that) a bird
>> flies in the sky.
>> Who interpret the working of the brain itself? Well the answer is
>> certainly *some reality*. Aristotelian would say it is nature, or the
>> physical reality, but by the cartesian dream argument, a
>> computationalist will say "some universal machine", but then he will
>> eventually understand that below his level of substitution an  
>> infinity
>> of universal machines have to compete.
>>> It is often said that with the many worlds
>>> interpretation it is the mathematics which tends to give us the lead
>>> on how to interpret Quantum Mechanics.  It was this that made me  
>>> tend
>>> to agree with the many worlders.
>> Then you should love comp :)
>> Comp forces us to do, in arithmetic, exactly what Everett has done in
>> the quantum theory.
>> I do agree with Bryce deWitt (and Everett) that the "(statistical)
>> interpretation of quantum mechanics" is given by the theory itself
>> (QM). And this in some precise sense. By QM I mean the high
>> dimensional Hilbert space, the tensor product rule, and the unitary
>> evolution of states (or observables). I mean, no collapse.
>> Then you could define the interpretation of QM by the normal average
>> talk of the memory-machine described by the wave. This makes really
>> the universal wave explanatively close.
>> But you need comp to do that, as most Everettian accept. But then the
>> uda should make understand that this has to  be done for any  
>> universal
>> machine (not just the universal QM wave), and even that the
>> "appearance" of the universal wave has to be explained by the
>> competition between all universal machines below some level.
>> Arithmetic generates its own interpretation, exactly like Everett
>> showed for the universal wave. The universal wave can justify the
>> "appearance of the collapse" in most observer's mind, and uda shows
>> that if QM and comp are correct, then the appearance of the universal
>> wave can be explained by the average universal machine intepretation
>> of what they observe.
>> Monist theories, which embed the subject in the object, have to do a
>> trick of that kind, in a way or in another.
>> Note that this is not standard. What I am doing for arithmetic is as
>> original for a logician, than what Everett has done for QM is for a
>> physicist (or the layman).
>> To sum up roughly: an interpretation is the doing of a universal
>> number, as defined by its additive and multiplicative structure with
>> other numbers.
>>> A map is a kind of (mathematical) model of reality so although there
>>> is a one to one correspondence between the points on the map to
>>> reality I still can’t see the trick of how to get through your  
>>> step
>>> 8.  Sorry if I am seeming stupid.
>> Ah ah! Should I deduce you are OK with the seven first steps?
>> I don't see the relevance of the bijection between the map and the
>> territory. The key here is that if the map is embedded in the
>> territory (or the subject in the object) there will be a fixed point.
>> There will be a point of the map which is superposed to the "real"
>> point of the territory. We don't confuse the map and the territory,
>> but we do confuse a point of the map with a point iof the territory.
>> Same with the painting: if the painters describe all what he sees, at
>> some point he will paint the brushes itself, and the end point of the
>> brush on the paper will, for a moment, be superposed to its painted
>> description (at least infinitesimally).
>> It is the same in computer science, even with "weakly
>> representational" theory of mind. Consciousness is a good candidate
>> for a universal invariant in self-observing universal machine/number.
>> But this is just tangentially related to the step 8, and is exploited
>> only in auda. Except that some familiarity with some amount of
>> theoretical computer science can help to get the "computational
>> supervenience thesis". You need to understand here what is a
>> computation, mathematically. Church thesis is needed here, to
>> legitimate the "universal" character of the universal dovetailer
>> (universal in respect to computability). Auda needs provability  
>> logic,
>> which is something quite different from computability (but they have
>> important connections).
>> UDA is simple, because the concept of universal machine is not to  
>> hard
>> to grasp. The base of computability theory is simple. You need only a
>> few bit of naive set theory, numbers, and the technic of
>> diagonalization. AUDA is more difficult because it needs mathematical
>> logic, which is a field where the beginning is hard. It is long and
>> boring to even give the little examples of formal theories. The
>> difficulty consists in understanding that we have to NOT understand,
>> nor even give sense, to the formalism. We have to abstract us from  
>> the
>> meaning, to be able to tackle it mathematically after. I will have
>> some opportunity to illustrate this. I have already done this with  
>> the
>> modal logics.
>>>> To understand this well, it is necessary to NOT confuse a theory,
>>>> with
>>>> his mathematical interpretation, and to NOT confuse a mathematical
>>>> interpretation with an interpretation in some reality. Physicists
>>>> have
>>>> not yet this level of sophistication. They usually confuse a theory
>>>> (the SWE for example) with the mathematical (standard)  
>>>> interpretation
>>>> (the wave function).  This can lead to many misunderstanding of  
>>>> what
>>>> the logicians are doing, especially in applied logic.
>>> I’m struggling with this one as stated above.
>> If you are interested enough you may think to study a good book in
>> mathematical logic, like Boolos and Jeffery, or Mendelson, or Epstein
>> and Carnielli. Then you could take a look at some  textbook in the
>> logic of self-reference (Boolos 1979, 1993),  Smorynski 1985.
>> But you don't need to do that to understand the necessity of the
>> reversal, that is UDA.
>> For UDA you need only to understand the math needed to understand
>> Church thesis, I would say. A good simple book is the book by N.J.
>> Cutland.
>> Mathematical logic is exploited only in the mathematical AUDA. Yet,
>> for some mathematicians, AUDA provides at least a consistent
>> arithmetical interpretation of the kind of "reality" the UDA forces  
>> us
>> (if I am correct) to envisage.
>> Hope this helped a bit,
>> Happy Xmas, and happy new year,
>> Bruno
>> http://iridia.ulb.ac.be/~marchal/
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