A question for Bruno

[Charles Goodwin]

Hi everyone and everything, I was discussing comp and similar things with Liz the other day and we came across a sticking point in what I think (from memory) is step 7 of the UDA. Maybe you can help?

I'm assuming AR, "Yes, Doctor" and so on. At step 7 we reach the point where we assume that a physical Universal Dovetailer can be created and that it runs forever, and ask what is the probability that my observer moments are generated by it, rather than by my brain.

Now ISTM that the UD will have an infinite number of possible programmes to run, so even if it runs forever, how does it get on to the second step in any of them?

[Telmo Menezes]

Every program can be mapped to a natural number (intuitively, imagine
the binary encoding of a program in any Turing-complete language).
With something akin to the binary encoding (more abstractly, you can
do this to the state table of a Universal Turing Machine), program
size increases with their numbers.

Then the dovetailer proceeds like so:

- execute step 1 of program 1
- execute step 2 of program 1
- execute step 1 of program 2
- execute step 3 of program 1
- execute step 2 of program 2
- execute step 1 of program 3
...

So it will only take finite time for all the computable programs of up
to a certain size to finish.

Telmo.

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[Russell Standish]

By dovetailing. Consider programs p[0], p[1], ... whose steps are
p[i][0], p[i][1], etc

Then run the steps as

p[0][0], p[1][0], p[0][1], p[1][1], p[2][0], p[2][1], p[0][2],
p[1][2], p[2][2], p[3][0], p[3][1], p[3][2], p[0][3], p[1][3],
p[2][3], p[3][3], ...


Other schemes are of course possible. Net result is that all steps of
all programs are eventually executed.

Cheers

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[Charles Goodwin]

Thank you, we should have remembered that zig-zag approach!

[Bruno Marchal]

Hi Charles,

On 28 Aug 2016, at 04:37, Charles Goodwin wrote (to Telmo and Russell):

Thank you, we should have remembered that zig-zag approach!

Yes, that's the dovetailing, and we cannot avoid it because there is no algorithmic procedure to decide if a program (with or without input) will stop or not (the logical price of Turing completeness). So we zig-zag among them indeed, and as the others said, this ensures that all accessible computational states will be generated soon or later. Obviously, there will be greater and greater delays (measured in some UD-step "time") between the states of each computation, but as you can guess, this does not change the first person indeterminacy, as it explain in step 2 and 4.

Note that if the universe was a one-branch universe, the probability is near-zero that we are not generated by the UD, as it contains (generates) the infinitely many computations going through our states infinitely many times. Indeed the physics has to be retrieved from that statistic on the UD* (the work of the UD). Same with a concrete multiverse, although this is less obvious, and perhaps more debatable a priori (as Russell remarked once).

Nice to hear from you and Liz,

Bruno

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[Stephen Paul King]

Hi,

   Is there any consideration of the duration of the period of time of the moment? Are they assumed to have vanishingly small durations?

[Brent Meeker]

In the UD model of the world, time as we perceive it, is emergent.  The "execution" of the program is timeless and exists in Platonia.  So the steps of the UD have no duration, they are logically prior to time and duration.  On the other hand, I think so called "observer moments" must have duration in the emergent sense and must overlap.  But their relation to the UD threads is more aspirational than proven.

Brent

[Bruno Marchal]

On 10 Sep 2016, at 16:22, Stephen Paul King wrote:

Hi,

   Is there any consideration of the duration of the period of time of the moment? Are they assumed to have vanishingly small durations?

Duration and moment are more like Bergson-Brouwer 1p notion. It emerges in the 1p statistics on all relative computations. 

I guess a moment might be well approximated there by an open set in some topological space, probably through the semantics of the machine first person theories (S4Grz(1), X1*).

To have the notion of computation, and the computations per se, we need only the digital clock given by the successor operation, and (at a different level) from the induction axioms (for the machine who want prove things about the computations).

Bruno

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

[agrays...@gmail.com]

On Sunday, September 11, 2016 at 10:50:17 AM UTC-6, Bruno Marchal wrote:

On 10 Sep 2016, at 16:22, Stephen Paul King wrote:

Hi,

   Is there any consideration of the duration of the period of time of the moment? Are they assumed to have vanishingly small durations?

Duration and moment are more like Bergson-Brouwer 1p notion. It emerges in the 1p statistics on all relative computations. 

I guess a moment might be well approximated there by an open set in some topological space, probably through the semantics of the machine first person theories (S4Grz(1), X1*).

To have the notion of computation, and the computations per se, we need only the digital clock given by the successor operation, and (at a different level) from the induction axioms (for the machine who want prove things about the computations).

Bruno

 Ahaa! So it is the monkey typing randomly that creates everything. But where does he/it get the clock and the notion of a successor element? God given? AG

[Bruno Marchal]

On 11 Sep 2016, at 19:23, agrays...@gmail.com wrote:

On Sunday, September 11, 2016 at 10:50:17 AM UTC-6, Bruno Marchal wrote:

On 10 Sep 2016, at 16:22, Stephen Paul King wrote:

Hi,

   Is there any consideration of the duration of the period of time of the moment? Are they assumed to have vanishingly small durations?

Duration and moment are more like Bergson-Brouwer 1p notion. It emerges in the 1p statistics on all relative computations. 

I guess a moment might be well approximated there by an open set in some topological space, probably through the semantics of the machine first person theories (S4Grz(1), X1*).

To have the notion of computation, and the computations per se, we need only the digital clock given by the successor operation, and (at a different level) from the induction axioms (for the machine who want prove things about the computations).

Bruno

 Ahaa! So it is the monkey typing randomly that creates everything. But where does he/it get the clock and the notion of a successor element? God given? AG

It follows from the assumption, which are part of what all scientists assume. Precisely, everything follows from the following axioms (with digital mechanism assumed at the metalevel---that *is* the result):

0 ≠ (x + 1)

((x + 1) = (y + 1))  -> x = y

x = 0 v Ey(x = y + 1)

x + 0 = x

x + (y + 1) = (x + y) + 1

x * 0 = 0

x * (y + 1) = (x * y) + x

That is not obvious, note. But, I insist, the UD has nothing to do with the typing monkey. You get the Monkey already with

0 ≠ (x + 1)

((x + 1) = (y + 1))  -> x = y

which is not Turing Universal. To get the computations, you need addition and multiplication. The rest is elementary theoretical computer science. See the book by Davis, or Boolos-and-Jeffrey.

If you can explain how a Turing universal machine/number can distinguish introspectively (without doing measurement) the arithmetical reality from any reality invoking a transcendent notion (like Primary Matter), it is up to you to solve the paradoxes of being both Turing emulable, and using something not Turing emulable. The step 8 shows that this is logically impossible. This is not done in the sane04 paper, see:

Bruno Marchal. The computationalist reformulation of the mind-body problem, Progress in Biophysics and Molecular Biology, Volume 113, Issue 1, September 2013, Pages 127–140

Bruno

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

[Stathis Papaioannou]

On Monday, 12 September 2016, <agrays...@gmail.com> wrote:

 Ahaa! So it is the monkey typing randomly that creates everything. But where does he/it get the clock and the notion of a successor element? God given? AG

Ordering by an external clock is unnecessary for a subjective sense of order. You remember yesterday as occurring in the past, but assuming there is an objective past, it might not have. You would still feel that yesterday occurred in the past if there was no objective yesterday at all.

--
Stathis Papaioannou

[Stathis Papaioannou]

On Sunday, 11 September 2016, Brent Meeker <meek...@verizon.net> wrote:

In the UD model of the world, time as we perceive it, is emergent.  The "execution" of the program is timeless and exists in Platonia.  So the steps of the UD have no duration, they are logically prior to time and duration.  On the other hand, I think so called "observer moments" must have duration in the emergent sense and must overlap.  But their relation to the UD threads is more aspirational than proven.

I think it should be possible to pause and restart at any point a process underpinning consciousness and leave the stream of consciousness unchanged; otherwise there would be a radical decoupling of the mental from the physical. At the limit, this means the process underpinning consciousness can be cut up into infinitesimals.

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[Stephen Paul King]

Not to rehash an old chestnut, but can a bit dance on an infinitesimal?

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[Bruno Marchal]

On 13 Sep 2016, at 16:22, Stathis Papaioannou wrote:

On Sunday, 11 September 2016, Brent Meeker <meek...@verizon.net> wrote:

In the UD model of the world, time as we perceive it, is emergent.  The "execution" of the program is timeless and exists in Platonia.  So the steps of the UD have no duration, they are logically prior to time and duration.  On the other hand, I think so called "observer moments" must have duration in the emergent sense and must overlap.  But their relation to the UD threads is more aspirational than proven.

I think it should be possible to pause and restart at any point a process underpinning consciousness and leave the stream of consciousness unchanged;

Yes. That is the invariance of the 1p discourse for the delays, if I get you right. It is a consequence of computationalism.

Consciousness is the most typical 1p notion. It is 1p per excellence.

otherwise there would be a radical decoupling of the mental from the physical.

But there is one, anyway, in the sense that there is always an infinity of computations (the doing of some universal program, in the UD, that is a tiny part of arithmetic) going through your consciousness, and the physical can only be a statistical sum on all those relative computations. Well, OK, that is more a coupling than a decoupling.

At the limit, this means the process underpinning consciousness can be cut up into infinitesimals.

I think something like that occurs. For all universal program, there is a notion of elementary step, and there is an infinity of universal machine having less coarse grained computations. Just imagine the smoker machine, which in between two steps of a computation make a pause café and smoke a cigarette before coming back at work! The UD can't miss it, even if we can bet it lives only in negligible (measure null) consistent histories.

Bruno

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[Brent Meeker]

Infinitesimals, I think not, at least not in Bruno's model.  Each thread of the UD's computation can be cut and restarted, but underlying an "observer moment" or a "thought" are infinitely many threads and there is no reference by which you can define cutting them all at "the same time".  So they make the "time" of consciousness essentially real valued.

Brent

[Stephen Paul King]

"...an "observer moment" or a "thought" are infinitely many threads and there is no reference by which you can define cutting them all at "the same time"."

   I agree that there is no natural preference for a basis of the threads, but ISTM that each Intelligence has its very own basis of biases which it "determines" as its optimal preference in a moment by moment adaptation on surfaces of constant time. There is some merit in the capacity to "look ahead" over multiple moves, but from what I have studied so far, there are rapidly diminishing returns when one is considering environments that are not fixed - as real world environments tend to be.

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[Bruce Kellett]

That understanding of an "observer moment" appears to undermine the "Yes Doctor" scenario. The point of YD, it seems to me, is that one can replace oneself with a computer running some program -- the digital simulation at the basis of mechanism. Such a simulation, being a single computation, can be stopped and restarted at will without the observer being conscious of anything. If consciousness, or "observer moments", are intrinsically made up of an infinite number of threads, then this is not possible, and YD fails.

Bruce

[Bruce Kellett]

On 14/09/2016 11:24 am, Stephen Paul King wrote:

"...an "observer moment" or a "thought" are infinitely many threads and there is no reference by which you can define cutting them all at "the same time"."

   I agree that there is no natural preference for a basis of the threads, but ISTM that each Intelligence has its very own basis of biases which it "determines" as its optimal preference in a moment by moment adaptation on surfaces of constant time.

I don't think "surfaces of constant time" are defined in the dovetailer.

Bruce

[Brent Meeker]

Right, except I take the other fork.  I think you can stop and restart a consciousness - with a small gap; and if you can it contradicts Bruno's model of a single consciousness being a kind of statistical mechanics over UD threads.  That model is motivated by Everett in which there are many possible evolutions of the wave function which are equivalent at the classical level (where thoughts are instantiated).  But Everett and all QM assume a background time in which evolution takes place.  Bruno intends that physical time emerge from the model.

Brent

[Stephen Paul King]

Speaking of time: https://arxiv.org/abs/1606.04759

A minimalist approach to conceptualization of time in quantum theory

H. Kitada, J. Jeknic-Dugic, M. Arsenijevic, M. Dugic

(Submitted on 15 Jun 2016 (v1), last revised 4 Sep 2016 (this version, v2))

Ever since Schrodinger, Time in quantum theory is postulated Newtonian for every reference frame. With mathematical rigor, we show that the concept of the so-called Local Time allows avoiding the postulate. In effect, time appears as neither fundamental nor universal on the quantum-mechanical level while being consistently attributable to every, at least approximately, closed quantum system as well as to every of its (conservative or not) subsystems.

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[Bruno Marchal]

That's a reasonable short rendering of the UDA, except that you are far to quick to conclude. 

It looks like YD fails indeed (too much white rabbits a priori), but when you translated the argument in arithmetic, you get a non trivial propositional logic for the observable and to see if it fails or not becomes experimentally testable, and tested partially assuming Everett QM is the correct empirical theory. Computationalism makes Arithmetic and QM share in the limit the same internal renormalization problem. 

Eventually I conceived that what makes the physical reality and consciousness possible relies in subtle property of the number 24, with the help of the total computable functions known as e, pi, gamma, etc. But here it is just an end of hot summer speculation due to my contemplation of Moonshine(*).

Bruno

(*) https://en.wikipedia.org/wiki/Monstrous_moonshine

Bruce

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[Stathis Papaioannou]

The question of whether you should replace your brain with a machine is a starting point, not a conclusion. The conclusion is that if you can, then there are neither physical brims nor physical machines.

[Stathis Papaioannou]

The starting point of computationalism is that you can replace your brain with a machine. If you can, then consciousness supervenes on a physical process of the machine. Thought A supervenes on process a and thought B supervenes on process B. A and B are unaffected if the timing, order or duration of a and b are changed. A and B are unaffected if there are copies of processes a and b up to an infinite number, as long as there is at least one of each. A and B are unaffected if a and b are paused and restarted at arbitrary points; we have then a1, a2, b1, b2 and A1, A2, B1, B2, but there is no subjective consequence to splitting A and B. 

If A and B are the observer moments and they can be rearranged and split up any way without changing the stream of subjective experience, then in a sense their being rearranged and split up is only meaningful because it can be defined for the physical processes on which they supervene. 

[Stephen Paul King]

Hi Stathis,

   I really like this explanation of supervenience. I only worry that we need a lot more detail, of how exactly "A and B are unaffected if the timing, order or duration of a and b are changed." works. AFAIK, this requirement looks a lot like mutual independence, but it clearly can not be. There must be a non-zero probability of transitions within the processes at each level of the tower, something like a 'time' at each. 

   That brings me to my next question: Where do we get the inequality of entropy when it is NOT at equilibrium for a system. Deriving an arrow of time is not just a matter of figuring out how to chain labels in observer moments, we need an actual transition from one state to another in our theory.

   Does anyone here have a nice explanation of Markov Processes that they could point me to?

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[Bruno Marchal]

Good point. 

But that is where the "infinitesimal" comes in, I would say, be them in terms of Cauchy sequences or in term of Non Standard analysis, that's not important at this stage. It depends on the mathematics of the arithmetical measure on 1p experiences (we get them trough the math of self-reference, but are still a long way from an arithmetical Gleason theorem).

Bruno

PS wrote this mail yesterday, seems to not have gone through. Sorry if sent in double exemplars.

Brent

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[Stathis Papaioannou]

On 15 September 2016 at 05:25, Stephen Paul King <Step...@provensecure.com> wrote:

Hi Stathis,

   I really like this explanation of supervenience. I only worry that we need a lot more detail, of how exactly "A and B are unaffected if the timing, order or duration of a and b are changed." works. AFAIK, this requirement looks a lot like mutual independence, but it clearly can not be. There must be a non-zero probability of transitions within the processes at each level of the tower, something like a 'time' at each.

Information about timing, order or duration of a and b that does not change a and b cannot change A and B either. This follows from the definition of supervenience.

 

 

   That brings me to my next question: Where do we get the inequality of entropy when it is NOT at equilibrium for a system. Deriving an arrow of time is not just a matter of figuring out how to chain labels in observer moments, we need an actual transition from one state to another in our theory.

   Does anyone here have a nice explanation of Markov Processes that they could point me to?

If there are real processes occurring in real time, this is not necessarily relevant to the supervenient mental processes. A future mental state could be computed in real time before a past mental state; it could have happened to you right now, and you wouldn't know. Thus, even if there is a real world, with real time and an arrow of time, the subjective world is timeless.

--

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[Brent Meeker]

On 9/15/2016 12:44 AM, Bruno Marchal wrote:

On 14 Sep 2016, at 02:13, Brent Meeker wrote:

On 9/13/2016 7:22 AM, Stathis Papaioannou wrote:

On Sunday, 11 September 2016, Brent Meeker <meek...@verizon.net> wrote:

In the UD model of the world, time as we perceive it, is emergent.  The "execution" of the program is timeless and exists in Platonia.  So the steps of the UD have no duration, they are logically prior to time and duration.  On the other hand, I think so called "observer moments" must have duration in the emergent sense and must overlap.  But their relation to the UD threads is more aspirational than proven.

I think it should be possible to pause and restart at any point a process underpinning consciousness and leave the stream of consciousness unchanged; otherwise there would be a radical decoupling of the mental from the physical. At the limit, this means the process underpinning consciousness can be cut up into infinitesimals.

Infinitesimals, I think not, at least not in Bruno's model.  Each thread of the UD's computation can be cut and restarted, but underlying an "observer moment" or a "thought" are infinitely many threads and there is no reference by which you can define cutting them all at "the same time".  So they make the "time" of consciousness essentially real valued.

Good point. 

But that is where the "infinitesimal" comes in, I would say, be them in terms of Cauchy sequences or in term of Non Standard analysis, that's not important at this stage. It depends on the mathematics of the arithmetical measure on 1p experiences (we get them trough the math of self-reference, but are still a long way from an arithmetical Gleason theorem).

Bruno

PS wrote this mail yesterday, seems to not have gone through. Sorry if sent in double exemplars.

But the 'time' is only a real number if you can order the events in the different threads relative to one another.  In the materialist theory of mind that is provided by physical time, the evolution parameter of the wave function.  I think that means that in your theory you have to derive time in order to locate 'thoughts' or 'observer moments'; they are no givens that you can assume.

Brent

[Stephen Paul King]

There is "time is a measure of change" concept, which lines up with what you're saying: "... 'time' is only a real number..." The numbers are labels, not the change itself.

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[Brent Meeker]

Yet one subjective experiences duration and order.

I think you've misplaced the concrete.

Brent

[Stephen Paul King]

Could it be that the concrete is the subjective reflection of the abstract?

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[Brent Meeker]

In this case we have a lot of threads and along each thread there is an implicit order (the execution of the UD), but there is no inherent relative order of the threads. 

Brent

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[Stephen Paul King]

OK, but where is the "motivation" that pushes the execution of the UD coming from? Where is the "go!" in the numbers?

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[Bruno Marchal]

OK. In the 3-1 picture, where we look at the cloud of true (and prouvable) sigma_1 sentences, that seems quite reasonable.

Before smoking salvia, I would have added: but *only* in the 3-1 picture. I would have defended the idea that in the 1p picture, the (1p) subjective experience is bounded to get some duration/subjective-time aspects, like Brouwer, Bergson, Dogen and other Heracliteans seemed to claim, and even like the universal machine seems to claim ([]p & p, the 1p,  leads to a logic of intuitionist time) but salvia succeeded in making me doubt about this. Salvia can be *quite* dissociative. 

Still today, I doubt that consciousness without time makes subjective sense, but I believe there might be an altered consciousness state where we feel to live the contrary.  Coming back from that state is a highly surprising and highly confusing experience. We can memorize only a piece of that coming back.

Bruno

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[Stephen Paul King]

I think that time (and physicality) within 1p is sufficient, if there have a large enough plurality of interacting finite minds. What I have trouble with DM is that it is not obvious where we get that plurality. I still suspect that a weak version of Tennenbaum's theorem could solve this problem, but we may lose Turing completeness. I would happily trade completeness for correctness.

http://mathoverflow.net/questions/38160/computable-nonstandard-models-for-weak-systems-of-arithemtic/121252

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[Brent Meeker]

According to Bruno it's in Platonia.  It's timeless and doesn't "go", it just IS, like 2+2 IS 4.

Brent

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[Stephen Paul King]

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly. 

   This seems to be an attack on the UD, which requires computational universality, but I assure you that it is very Digital Mechanism friendly. I am after Correct computers, not Universal computers. An example of such is the TauChain.

[Brent Meeker]

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

Brent

[Stathis Papaioannou]

What I meant was that the subjective experience of time would be the same whether there was a material universe with real time, a material block universe without time, or no material universe.

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[Stephen Paul King]

On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meek...@verizon.net> wrote:

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

​Yes, sorta.​

 

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

​It has itself as an input. :-P​

 

Brent

   This seems to be an attack on the UD, which requires computational universality, but I assure you that it is very Digital Mechanism friendly. I am after Correct computers, not Universal computers. An example of such is the TauChain.

On Thu, Sep 15, 2016 at 1:54 PM, Brent Meeker <meek...@verizon.net> wrote:

According to Bruno it's in Platonia.  It's timeless and doesn't "go", it just IS, like 2+2 IS 4.

Brent

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[Brent Meeker]

On 9/15/2016 4:29 PM, Stephen Paul King wrote:

On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meek...@verizon.net> wrote:

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

​Yes, sorta.​

 

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

​It has itself as an input. :-P​

I suppose you can think of it as a null input.  But it also has not output.  It doesn't halt.  So I'm not sure what you mean by computing one algorithm efficiently and correctly.

Brent

[Stephen Paul King]

The idea is to think of computations as discrete, they do one thing: process one algorithm and halt. Obviously I am not talking about Turing machines...

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[Brent Meeker]

Can you give an example?  What I'm led to think of is something like:

% Add two and two
    print "4"
    halt

Brent

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[Stephen Paul King]

That's a good example, actually!

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[Bruno Marchal]

On 15 Sep 2016, at 19:38, Stephen Paul King wrote:

I think that time (and physicality) within 1p is sufficient, if there have a large enough plurality of interacting finite minds. What I have trouble with DM is that it is not obvious where we get that plurality. I still suspect that a weak version of Tennenbaum's theorem could solve this problem, but we may lose Turing completeness. I would happily trade completeness for correctness.

http://mathoverflow.net/questions/38160/computable-nonstandard-models-for-weak-systems-of-arithemtic/121252

Tennenbaum theorem does not make us losing Turing-completeness. Quite the contrary, we escape the bound of the computable, which belongs to all intepretation of arithmetic, standard and non standard as well.

We would loose computationalism, in some sense.

Bruno

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[Bruno Marchal]

OK, but it does not work, as we lost all connection between physicalness and consciousness (by UDA).

I think that means that in your theory you have to derive time in order to locate 'thoughts' or 'observer moments'; they are no givens that you can assume.

Indeed. But we already got it through the logics of the first person (S4Grz1, X1*).

Note that the physical time is also not well explained in "materialist physics". In the DeWitt-Wheeler equation, it disappears, and reappears as a local indexical/modal notion. Strictly speaking, physicists have not yet an account of reality coherent with both QM and GR, so that is an problem in physics too. Anyway, we can't invoke a primitive physicalness to explain the conscious appearance of physicalness in the digital mechanist frame.

Bruno

Brent

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[Bruno Marchal]

On 15 Sep 2016, at 20:03, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly. 

   This seems to be an attack on the UD, which requires computational universality, but I assure you that it is very Digital Mechanism friendly. I am after Correct computers, not Universal computers. An example of such is the TauChain.

Robinson Arithmetic (which is basically only the succession, addition and multiplication laws) is *essentially undecidable*. It means that it is Turing complete (and thus undecidable and arithmetically incomplete) and, and that is what Tarski meant by *essentially undecidable, all its consistent extensions are (even those non computable).

Bruno

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[Bruno Marchal]

On 16 Sep 2016, at 01:29, Stephen Paul King wrote:

On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meek...@verizon.net> wrote:

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

​Yes, sorta.​

 

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

​It has itself as an input. :-P​

?

Possibly in a quite novel non standard sense, but I'm afarid this could lead to confusion, especially with beginners.

The UD is typically a program without input. You enter its code in the language of some universal machine, without giving it any input, and it runs forever, meaning it has no output. 

Extensionally, it is equivalent with the empty function from the empty set to the empty set (the unique element of 0^0 in set theoretical term, with 0 identified with the empty set). 

Intensionally, assuming computationalism it is all activities of all machines in all locally consistent context.

Some would like to add, all thoughts, but the thoughts remain stable and make possibly sense only on the infinities on which the First Person Indeterminacy operates.

In the 3-1 picture, we can attach a consciousness to a program/machine/3-p-representation..., it is often polite, but in the 1-p picture, that is, from the first person perspective "you" are related to an infinity (2^aleph_0) of computational histories. The UD "runs" you on all real oracles, notably.

Bruno

 

Brent

   This seems to be an attack on the UD, which requires computational universality, but I assure you that it is very Digital Mechanism friendly. I am after Correct computers, not Universal computers. An example of such is the TauChain.

On Thu, Sep 15, 2016 at 1:54 PM, Brent Meeker <meek...@verizon.net> wrote:

According to Bruno it's in Platonia.  It's timeless and doesn't "go", it just IS, like 2+2 IS 4.

Brent

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[Bruno Marchal]

On 16 Sep 2016, at 03:27, Stephen Paul King wrote:

The idea is to think of computations as discrete, they do one thing: process one algorithm and halt.

or not halt. You limit yourself to halting computation.

If each halting computation is simpler than arbitrary computations, it happens that the notion of halting computations is more complex than the notion of arbitrary computations.

For example, there is no universal halting machine, and there is no UD computting all and only all halting computations.

The only way to generate all halting computations necessitate the generations of all computations, the halting one and the non halting. There is no algorithmic means to separate the halting machine from the non halting one.

yet, the halting computations, when you get them all, is what structure the "measure space", and that is exploited to get the measure one case by the intensional ("material") variant of the self-reference logic, restricted to the "halting computations", modeled by the true sigma_1 sentences.

Obviously I am not talking about Turing machines...

?

We seem to miss a precise idea of what you are talking about, I'm afraid. 

Bruno

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[Stephen Paul King]

On Fri, Sep 16, 2016 at 11:16 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 16 Sep 2016, at 01:29, Stephen Paul King wrote:

On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meek...@verizon.net> wrote:

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

​Yes, sorta.​

 

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

​It has itself as an input. :-P​

?

Possibly in a quite novel non standard sense, but I'm afarid this could lead to confusion, especially with beginners.

The UD is typically a program without input. You enter its code in the language of some universal machine, without giving it any input, and it runs forever, meaning it has no output. 

Extensionally, it is equivalent with the empty function from the empty set to the empty set (the unique element of 0^0 in set theoretical term, with 0 identified with the empty set). 

Intensionally, assuming computationalism it is all activities of all machines in all locally consistent context.

Some would like to add, all thoughts, but the thoughts remain stable and make possibly sense only on the infinities on which the First Person Indeterminacy operates.

In the 3-1 picture, we can attach a consciousness to a program/machine/3-p-representation..., it is often polite, but in the 1-p picture, that is, from the first person perspective "you" are related to an infinity (2^aleph_0) of computational histories. The UD "runs" you on all real oracles, notably.

Bruno

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

Can the UD diagonalize with almost all possible versions of itself? I have forgotten some details...

[Stephen Paul King]

I apologize but it seems that none of us has time to explain other people's ideas to each other or to read their papers for ourselves. 

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[Bruno Marchal]

On 16 Sep 2016, at 17:40, Stephen Paul King wrote:

On Fri, Sep 16, 2016 at 11:16 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:

On 16 Sep 2016, at 01:29, Stephen Paul King wrote:

On Thu, Sep 15, 2016 at 6:47 PM, Brent Meeker <meek...@verizon.net> wrote:

On 9/15/2016 11:03 AM, Stephen Paul King wrote:

I get that and buy it too, Brent. Platonia is the "flat" Complete version, I am looking for the infinite tower of incomplete yet consistent theories

I don't understand what you mean by that.  I assume "theories" refers to axiomatic systems.  If I take one such system, like arithmetic, I can keep adding the unprovable Godel sentences as axioms and so create an unbounded "tower" of systems.  Is that what you mean?

​Yes, sorta.​

 

and trying to make sense of computational languages that could use those theories. Remember that computers do not need to be Turing Complete if they only need to compute one algorithm efficiently and correctly.

That's the view of an algorithm as computing a function; so given an input there is a certain correct output.  But the UD doesn't have any input.

​It has itself as an input. :-P​

?

Possibly in a quite novel non standard sense, but I'm afarid this could lead to confusion, especially with beginners.

The UD is typically a program without input. You enter its code in the language of some universal machine, without giving it any input, and it runs forever, meaning it has no output. 

Extensionally, it is equivalent with the empty function from the empty set to the empty set (the unique element of 0^0 in set theoretical term, with 0 identified with the empty set). 

Intensionally, assuming computationalism it is all activities of all machines in all locally consistent context.

Some would like to add, all thoughts, but the thoughts remain stable and make possibly sense only on the infinities on which the First Person Indeterminacy operates.

In the 3-1 picture, we can attach a consciousness to a program/machine/3-p-representation..., it is often polite, but in the 1-p picture, that is, from the first person perspective "you" are related to an infinity (2^aleph_0) of computational histories. The UD "runs" you on all real oracles, notably.

Bruno

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

Can the UD diagonalize with almost all possible versions of itself? I have forgotten some details...

The giant miracle here is that the class of all programs is immune to diagonalization, unlike any class of always stopping programs. So, to get all stopping programs, we must generate all programs, and to get all stopping executions, there is no choice other than dovetailing on all executions, the stopping and non stopping one.

The closure of the set of partial recursive function for diagonalization is the main conceptual argument in favor of Church thesis, and it is what make the universal machines/numbers, truly universal, so to speak.

So yes, the UD can be said to diagonalize itself, but it changes nothing: the UD remains invariant for the application of the diagonal.

Best regards Stephen,

Bruno

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[Bruno Marchal]

I realise I did not answer this post. As the step 7 is crucial, I will make some remark, and try to answer the question. Sorry for the delay Charles.

On 28 Aug 2016, at 00:38, Charles Goodwin wrote:

Hi everyone and everything, I was discussing comp and similar things with Liz the other day and we came across a sticking point in what I think (from memory) is step 7 of the UDA. Maybe you can help?

I'm assuming AR, "Yes, Doctor" and so on. At step 7 we reach the point where we assume that a physical Universal Dovetailer can be created

Actually, we don't need to assume that. It is a consequence of the fact that the physical universe is Turing-complete, like the existence of the physical implementation of the universal number (the general purpose computer) illustrates. So we can write the code of a Universal Dovetailer, and run it.

The infinite tape is not part of the universal Turing machine. It is his environment. A number u is universal with respect to an acceptable enumaration of partial computable function if phi_u(<x, y>) = phi_x(y). (<x, y> is coding of a couple of numbers into a number).

and that it runs forever,

Yes, that is the important assumption in step 7, and normally discharged in step 8.

and ask what is the probability that my observer moments are generated by it, rather than by my brain.

Well, this is simple to compute or evaluate intuitively in a mono-universe, there is no chance that your experience remains "out of the UD*".

With a multiverse, it is less easy, but there is also no chance, to remain in the level zero of the physical reality.

Now ISTM that the UD will have an infinite number of possible programmes to run, so even if it runs forever, how does it get on to the second step in any of them?

Now I remember why I did not answer, someone else did. And the answer was: that is why we have to dovetail, and run all programs little piece by little pieces.

All the best to you and Liz,

Bruno

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