Hi Russell, Hi Stephen,

I comment the two (now three!) posts in one mail.

On 14 Apr 2011, at 04:12, Stephen Paul King wrote:

-----Original Message-----
From: Russell Standish
Sent: Wednesday, April 13, 2011 8:07 PM
To: everything-list@googlegroups.com
Subject: Re: A possible flaw un UDA?

I confess I got lost too with your presentation. My gut feeling is your
discomfort stems from an "almost magical" insertion of the subjective
(ie a knower) into the UDA. Another way of putting it is "what runs
the UD?".

However, the knower is introduced explicitly with the "yes, doctor"
assumption - that I survive with my "brain" substituted by a digital
device. What is this "I" if it isn't the knower? What possible meaning
can "survive" have, without there being a sense of "being"?

Yes. And for the UDA (UD Argument), the knower is sufficiently defined by his/her personal memory, like the sequence of self-localization in its duplication history written in his diary (WWWMWMMWMWMMWMWWMMMW...). In AUDA, the definition is more subtle, and is due to Theaetetus (or Plato), it is the believer in some truth (by definition), and is handled by the Bp & p translation. Remember that, by the second incompleteness theorem, Bf is not equivalent with Bf & f, from the point of view of the machine. G* (the 'divine intellect') proves that Bf is equivalent with Bf & f, but the machine itself cannot.

Externally, a UD just exists as a static program (just a number that
exists platonically). However, once you have a knower, you can run the
UD, albeit viewed from the inside. In my book I make this explicit
with the TIME postulate, but I don't see anything hugely controversial
about it. It is not referring to any external time, just that the
knower cannot experience all experiences at once.

Which makes sense in the "block arithmetical universe" with TIME given by the UD-steps. The *execution* of the UD is also static in Platonia. It is static not through one static number, but through infinite (and bifurcating/branching) sequence of numbers.

Here, physicists accepting even just special relativity have no problem with that. Subjective time (re)appears in the static discourse made by the machine inside that block statical mindscape.

I suspect that Stephen, in the manner of Prigogine, wants some basic fundamental time. I suspect him also to be under the charm of some mathematical mermaids!

I answer Stephen below.

Have I put my finger on it, or is this just wide of the mark?

[SPK] Hi Russell,

Yes, that is part of the discomfort. Another is a feeling that the UDA is the semantic equivalent of building a beautiful castle in midair. One first erects is a brilliant scaffolding then inserts the castle high up on top of the scaffolding. We then are invited to think that the castle will stay in place after the scaffolding is removed. Let me be clear, I find Bruno's idea to be work of pure genius. I delight in it and I deeply admire Bruno and his tenacity. I just was to remove these nagging doubts I have about it. I want to be absolutely sure that it can stand up to ferocious and diligent attacks before I will commit to it.

Remember: if COMP is true, we will never know it for sure. We will never be sure about it, and we might even be at risk if we take it for granted. And that might happen.

If you are using each day a (classical) teleporting device, you might find hard to doubt comp, yet you can't still not be sure. You might suffer an 'agnosologic" disease, like that poor first pionneer of teleportation: after being reconstituted, he was blind, deaf, paralysed, and when after years of effort he succeed to communicate something it was "great, the experience was successful, I feel healthy, with all my capacities, and I am willing to do it again!".

That is one of the reason I insist that COMP belongs to theology, you need an act of faith, and you need to reiterate it all the time. I do think plausible that nature has already bet on it, in some way, and that we do those reiteration bets, all the time, instinctively, but that is a theory, and to believe and to apply a theory to yourself, you need an unavoidable act of faith.

Let us consider in detail an idea that emerged here in my post and Bruno's response:

start cut/paste
From: Bruno Marchal
Sent: Wednesday, April 13, 2011 7:02 AM
To: everything-list@googlegroups.com
Subject: Re: A possible flaw un UDA?
Hi Stephen,

On 13 Apr 2011, at 02:35, Stephen Paul King wrote:

AR must be expressible as some belief in each 1p (modulo coherent and soundness):

[BM] Why? It is true, but I don't see the relevance.

for AR to exist

[BM]What do you mean by "AR exists"? That is ambiguous. And what you are saying begin to look like "archeology is needed for dinosaur to exist". The very idea of AR is that 1+1=2 does not need a human for being true. Of course, a human or some alien is needed to say that "1+1=2" is believed.

then it is necessary that a 1p believe that AR exists and the statement “AR exists” is true. If the belief that AR exists cannot be expressed by a CUD then AR cannot be said to exist since it would be impossible to express the statement “AR exists”. Diagonalizations require some form of CU support or else they all collapse into Nothing.

[BM] Why does diagonalization need a CU?

For AR to exist as distinct from Nothing then there must exist a concrete structure, a CU,

[BM] I doubt this.

 end cut/paste

Why does diagonalization need a concrete universe? So that it can represent something other than itself to some thing other than itself. Does not more than one 1p exist? If only one 1p can exist then we have a perfect example of a solipsism, no? If the 1p are purely relations between numbers “as seen from the inside” (an idea that I find to be wonderful and useful and expressed in the myth of the Net of Indra), does this not lead to a duality between the numbers and the representations that the multiple 1p have of themselves, a duality exactly like what we see in the representation theorems that I have referenced previously? What I am thinking is that the sum of the inside views of the 1p is a CU that cannot be removed or reduced to just the existence of the numbers themselves so long as the numbers are collection of entities that have some differences between themselves. In other words the numbers are not Nothing.

Exactly. That is why they are postulated in the theory. But they are postulated in all theories. Even Hartree Field in "science without numbers" postulates them implicitly. It is nothing more than the axiom: 0 is a number, and if x is a number, then s(x) is a number, and if s(x) =s(y) then x = y.
+ the usual recursive axioms of addition and multiplication.
And to understand this, we have to use the intuitive informal numbers we live with since we are born.

They are “something to something else” and that ‘somethingness’ is concrete and irreducible even if it is the “inside looking out” aspect of the numbers. The fact that there is an ‘inside’ that is different from an ‘outside’ demands the kind of duality that I am proposing.

OK. And here the numbers, when they introspect themselves relatively to some local universal numbers, get better than a duality, they get an octo-lity. They get four dualities. I have already compared yours to the duality between Bp and Bp &p.

We talk a lot about Gödel's brilliant idea of representing propositions of a theory that includes arithmetic using arithmetic statements so that we can consider the theory to be able to “make statements about itself”. We go on and consider Turing and others that showed how this can be done in wider settings. All well and good. But do these “theories” or “abstract machines” actually have the property that we are ascribing to them absent a “knower”, to use your word and implied definition? What does it means to claim that something has such and such properties when it is in principle impossible to determine if indeed that claim is true? That sounds a bit too much like the idea of blind faith that we chastise religious fanatics for!

You need faith to build a plane, and you will need even more faith to use it. The religious fanatics are dangerous only when they pretend to know. In science, and in "real religion" it is exactly the same. We might encounter some certainties, but they are private and incommunicable, like already consciousness.

Sure, we can go thru a long litany of reasonings and tangential evidence and analogies, but if we remove the very ability to determine truth as we know it,

Careful Stephen. The power of the Theaetetus's idea, is that we know the truth, by *definition*. The price is that we never know the truth- for-sure, except for consciousness and other private incommunicable effects.

how can we continue to claim that truth exists unsupported (in the sense of supervenience) by any representation of it that is not the entity itself? Please help me figure this out. Can truth exist if all that exists is Nothing without an Everything that is its dual (as per your and Hal Ruhl’s definition) and capable of manifesting concreteness?

I would say that you can't have a notion of nothing, without some notion of everything going with it. We don't start from nothing in comp. UDA, as Russell mentioned, even start from accepting some amount of consensual reality (we believe in brain and doctors). Then a reasoning shows that numbers and addition+multiplication put already all the mess we need (and don't need) in Platonia, and explains why from inside, that Platonia has a border/shadow which acts like a physical reality. But like in Plato, the physical reality emerges from something else (number theoretical truth).

The failure of logicism is that we cannot get the numbers from less than the numbers, so all theories postulates the numbers, (or equivalent) either at the level of objects, or at the metalevel.

I think that “the knower cannot experience all experiences at once” is telling us something very important about what a knower is, something not obvious!

It is basic with Mechanism. A knower needs a brain, and a brain is a local structure. Personal memories are disconnected. No telepathy, but as much axons, mobile phones, radio waves, TV, computers and interacting devices as you need.


Oops... I was about sending this message, but I see you send a new one. I will answer it here too:

Did you see my response to Russell’s comment on this thread? I was using his definition of Nothing that is defined in his book.

See above.

I have more questions that puzzle me from your responses. You wrote: “ The reason I assumed explicitly AR was for reason of clarity, but AR is redundant, given that you need it to make sense of Church thesis. As it is written in sane04, and in the text you quote AR is just the idea that classical logic can be applied to arithmetic. “

    What is the status of AR now in your thinking?

AR is arithmetical realism. It is the statement that propositions like "24 is even" are true independently of me, you, the humans, the aliens, etc. It is the idea that such truth are absolute, atemporal, aspatial, and that they would be true, but perhaps unknown, in case the life did not appear here or anywhere.

More precisely, AR is the statement that all arithmetical statement obeys classical logic. You need it to make sense of statements of the kind 'machine i on input j does stop, or does not stop'. You need this to get an understanding of Church thesis and of the notion of partial computable functions and the possibility (and necessity) of universal digital machine. In fact, without AR, a word like "digital machines" loses its meaning, or becomes vague, or restricted in appearance.

Everyone believes in it, when it is not made explicit. Making it explicit attracts the Sunday philosophers, or the ultrafinitist (which are either mute, or do believe in it for being able to say that they don't believe in it).

AR is the part of math where all mathematicians agree, in practice. By a subtle result of Gödel, arithmetical intuitionism is basically equivalent with arithmetical classical realism. Intuitionism becomes sensibly different only when handling the real numbers, and with comp, we don't need them at the ontological level. At the epistemological level, we need more and will always need more than the 'existing mathematics', due to incompleteness. Arithmetic seen from inside is *much* more big than arithmetic seen from outside. It is a form of Skolem paradox.

“AR gives all you need to have a concrete (even if immaterial) implementation of the UD. In a sense, it arguable that AR is more concrete than anything suggested by physical experiments and physical theories.”

Does not AR require a 1p, such that we cannot say that one can exist without the other?

The word "requires" is ambiguous. Accepting comp, AR *implies* the existence of 1p. AR implies that all numbers developing correct discourses about themselves (and that exists by AR) will be befuddled by the apparent discrepancy between what they know (Bp & p) and what they believes/proves (Bp).

Comp implies that numbers have unavoidable difficulties in betting that they are relative numbers. Numbers will instinctively say NO to the doctor, but, once 120 years old, and still wanting to see their grand-grand-grand-children, or just to see the next soccer cup, they might change their mind. The social pressure will even push them to do that, if only because the society likes tax payers.



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