On 14 Feb 2012, at 06:57, Stephen P. King wrote:

acw:Yet the problem is decidable in finite amount of steps, even ifthat amount may be very large indeed. It would be unfeasible forsomeone with bounded resources, but not a problem for any abstractTM or a physical system (are they one and the same, at leastlocally?).## Advertising

Hi ACW, WARNING WARNING WARNING DANGER DANGER! Overload is Eminent!OK, please help me understand how we can speak of computationsfor situations where I have just laid out how computations can'texist.

In which theory? The concept of "existence" is theory dependent.

If we take CTT at face value, then it requires some form ofimplementation. Some kind of machine must be run. Are you sure thatyou are not substituting your ability to imagine the solution of acomputation as an intuitive proof that computations exist as purelyabstract entities, independent from all things physical? Mydifficulty may just be a simple failure of imagination but how canit make any sense to believe in something in whose very definitionis the requirement that it cannot be known or imagined?

If we assume this:

`Ax ~(0 = s(x)) (For all number x the successor of x is different from`

`zero).`

`AxAy ~(x = y) -> ~(s(x) = s(y)) (different numbers have different`

`successors)`

Ax x + 0 = x (0 adds nothing) AxAy x + s(y) = s(x + y) ( meaning x + (y +1) = (x + y) +1) Ax x *0 = 0 AxAy x*s(y) = x*y + x Then we can define "computations" and we can prove them to exist.

`It is not more difficult that to prove the existence of an even`

`number, or of a prime number. It is just much more longer, but`

`conceptually without any new difficulty.`

Knowing and imagining are, at least, computations running inour brain hardware. If your brained stopped, the knowing, imaginingand even dreaming that is "you" continues?

`Not relatively to those sharing the reality where your brain stop. But`

`from your own point of view, it will continue.`

So you do believe in disembodies spirits,

`No. If your brain stop here and now, from your point of view, it`

`continue in the most normal near computational histories. In those`

`histories you will still feel as locally and relatively embodied.`

`Globally you are not, even in this local reality, given that there a`

`re no bodies at all. Bodies are appearances.`

you are just not calling them that. I apologize, but this is a bithard to take. The inconsistency that runs rampant here is making mea bit depressed.

You have to find the inconsistency.

Now, given all of that, in the concept of Platonia we have theidea of"ideal forms", be they "the Good", or some particular infinitestring ofnumbers. How exactly are they determined to be the "best possible bysome standard". Whatever the standard, all that matters is thatthereare multiple possible options of The Forms with the stipulationthat itis "the best" or "most consistent" or whatever. It is still anoptimization problem with N variables that are required to becomparedto each other according to some standard. Therefore, in most casesthereis an Np-complete problem to be solved. How can it be computed ifit hasto exist as perfect "from the beginning"?The problem is that you're considering a "from the beginning" atall, as in, you're imagining math as existing in time. Instead ofthinking it along the lines of specific Forms, try thinking of alimited version along the lines of: "is this problem decidable in afinite amount of steps, no matter how large, as in: if a truesolution exists, it's there."And what exactly partitions it away from all the other "truesolutions"? This idea seems to only work if there is "One TrueTheory of Mathematics"....

`Not at all. Comp needs only one true conception of arithmetic. The`

`evidence is that it exists, even if we cannot define it in arithmetic.`

`We need the intuition to understand the difference between finite and`

`non finite.`

But we know that that is not the case, there are many differentArithmetics. How exactly do you know that yours is the "truestandard" one?

`It does not matter as long as we reason in first order logic, or if we`

`are enough cautious with higher logic. The consequence are the same in`

`all models, standard or non standard. IF PA proves S, S is true in all`

`models of arithmetic, and we don't need more than that.`

I'm not entirely sure if we can include uncomputable values there,such as if a specific program halts or not, but I'm leaning towardsthat it might be possible.OK, there is no beginning. Recursively enumerable functionsexist eternally. OK. Why not Little Ponies? My daughters tells meall about How Princess Celestia rules the sky... This entire theoryreminds me of the elaborated Pascal's Gamble... How do we know thatour "god" is the true god? OK. So we Bet on Bp&p. OK... Then what?How do I know what "Bp&p" means?

`Because for all arithmetical p, Bp & p is an arithmetical formula. You`

`need just to understand predicate logic, and the standard`

`interpretation of elementary arithmetic. You refer to papers which`

`assumes that understanding, and much more.`

I figured this out when I was trying to wrap my head aroundLeindniz'idea of a "Pre-Established Harmony". It was supposed to have beencreated by God to synchronize all of the Monads with each other sothatthey appeared to interact with each other without actually "havingtoexchange substances" - which was forbidden to happen as Monads"have nowindows". For God to have created such a PEH, it would have tosolve anNP-Complete problem on the configuration space of all possibleworlds.Try all possible solutions for a problem, ignore invalid ones.And how exactly do we distinguish valid from invalid ones? Bywhat process do we "try all possible solutions"? Process andtimelessness do not mix.

`Validity, unlike soundness is Turing verifiable. Even unconscious`

`zombie or robot can make the checking for us. That is why we make`

`proof, to let other people checking them.`

If the number of possible worlds is infinite then the computationwillrequire infinite computational resources. Given that God has tohave thesolution "before" the Universe is created,"before", what is this "before", it makes no sense to talk of timewhen dealing with timeless structures. A structure either exists invirtue of its consistence/soundness, or it doesn't (it can exist assomething considered by someone within some other structure, whichdoes happen to be consistent, thus it only exists as a(n incorrect)thought). Introducing a ``God'' agent to actually do creation ordestruction will only lead to confusion, because creation ordestruction implies time or causality. Platonia only implies localconsistency. On the other hand, I'm not even asking for any fullPlatonia, just recursively enumerable sets should be enough...How does the existence on an entity determine its properties?Please answer this question.

`Please define existence. Normally properties depends on the initial`

`assumption making possible to something to exist in the frame of some`

`theory.`

What do "soundness" and "consistency" even mean when there does notexist an unassailable way of defining what they are? Look carefullyat what is required for a proof, don't ignore the need to be able tocommunicate the proof.

This is the subject of any elementary textbook in logic.

It cannot use the timecomponent of "God's Ultimate Digital computer". Since there is nospacefull of distinguishable stuff, there isn't any memory resourceseitherfor the computation. So guess what? The PEH cannot be computed andthusthe universe cannot be created with a PEH as Leibniz proposed.You can encode computation in arithmetic or other timeless systemsjust as well.Encode computation? How does it even makes sense to juxtapose aprocess that requires time in a situation that is timeless? Wecannot have our computational cake and eat it (eliminate itstemporality) too.

So you assume "time", and abandon your neutral monism.

Time is merely a relation between states, it's always possible toexpress such a relation timelessly.Is it? So there is no such thing as change? Then why is theillusion of it so damned persistent?

`By the nature of the arithmetical indexicals. Both physical time and`

`experiential duration are recovered (and are quite different).`

Surely we can start in a environment that is transitory and changeladen and think up systems of ideas that seem to be timeless, but dothey really have these properties? Did you see my argument about howinvariants require a set and transformations on the set to bedefined. Take away the transformations and what you have? A set withnothing like an invariance to be seen anywhere. We can eliminatemeasure of Change, but we cannot eliminate Change itself.

`Comp votes for the contrary. We can eliminate the metaphysical`

`"Change" and explain the appearance of the measure and feeling of`

`change.`

To be fair, I'm not sure how even a single computation can beperformed without there existing a consistent definition of thatcomputation (thus the existence of that sentence in Platonia).Does my no-brand name Desktop that I built myself, with its harddrives, mother board, power supply, etc, depend on its running thiscrappy Windows 7 OS only if someone has defined what a computationsis?

The definition and the object are arithmetical.

Of course not! Again, how exactly does the existence of an entity,be it a computation, Pony, UD or whatever, determine the particularset of properties that make that computation a computation, the Ponyand Pony and the UD a UD? This is like the Randians chanting "A isA" over and over never minding questions like what the <expletivedeleted> is A?

`Not at all. Well, I don't know for the pony, because you don't give a`

`theory.`

You cannot even compute 1+1 without it, much less NP-completeproblems. I don't see how a in-time universe solves the problemsyou ascribe to Platonia - same problems are present in both andthey can only be avoided by giving some consistent systemexistence. As for space? why would space be needed for deciding ifsome recursive relations hold. Space is itself an abstraction and Idon't see how introducing it would solve anything about suchabstract recursive relations, except maybe making it simpler toreason for those that like to imagine physical machines instead ofpurely abstract ones.Without space or time the operation of "copying" is impossible.

Prove this.

`or study computer science, where you can see that programs copying`

`themselves exists in arithmetic, and their running exists in arithmetic.`

Try it some time. How can you over come the identity ofindiscernibles without space or time?The idea of a measure that Bruno talks about is just another way oftalking about this same kind of optimization problem withouttipping hishand that it implicitly requires a computation to be performed to"find"it. I do not blame him as this problem has been glossed over forhundredof years in math and thus we have to play with nonsense like theAxiomof Choice (or Zorn's Lemma) to "prove" that a solution exists,never-mind trying to actually find the solution. This so called'proof"come at a very steep price, it allows for all kinds of paradox <http://en.wikipedia.org/wiki/Banach-Tarski_paradox>.All possible OM-chains/histories do exist and one just happens tolive in one of them.Sure.A measure is useful for predicting how likely some next OM wouldbe, but that doesn't mean that our inability of listing allpossible OMs and deciding their probabilities means that no next OMwill exist - we all inductively expect that it will.No! You are neglecting the fact that there are not just a set ofconnected OMs floating out in Platonic NowhereLand. You have toconsider all possible OMs and show how the continuation works.

`Sure. That's part of the problem. But what about the initial solution`

`of it? Comp just makes it clear, and show tha solution of the machine`

`in the context of the usual classical theory of knowledge, which up to`

`know works very well.`

You at least have to have something like a fixed point and thatrequires a space with closure and compactness and *a transformation*on that space. You cannot define continuation without meeting thisrequirement.

Arithmetic provides all that.

Unfortunately the measure itself is likely to be uncomputable,unlike finding some next OM (actually, I'm not so sure about thisbeing entirely computable as well, it might prove that it's onlycomputable in specific cases, just never in general; within COMP,finding a next OM means finding a machine which implements theinner machine('you'), that should always exist as UMs exist,however what if the inner machine crashes? a slightly modifiedinner machine might not, yet that machine would still identifymostly as 'you' - whatever this measure thing is, it's way toosubjective and self-referential, yet this is complicated becausethe inner machine doesn't typically know their own godel number,nor can they always trust their inputs to be exactly what they'expect')."Know its own Godel number"? How exactly does that happen?Please remember, all of this is *occurring*, (dammit, we cannot evenuse that word consistently) in the Timelessness of Platonia. Thereis no Occurring at all there. There isn't even any "there" there!

`There is, once you understand that "here and there", "now and`

`sometimes", are indexical relative concept.`

A possible solution to this problem, proposed by many even back asfaras Heraclitus, is to avoid the requirement of a solution at thebeginning. Just let the universe compute its least actionconfigurationas it evolves in time, but to accept this possibility we have tooverturn many preciously held, but wrong, ideas and replace themwithbetter ideas.In a way, you could avoid thinking of Platonia and just considerthe case of a machine's 1p always finding its next OM. As long asfinding one next OM doesn't take infinite steps, you could considerit alive. What if no next step OM exists for it, but it exists in aversion where a single bit was changed?Here is the problem, given the measure of a single number in aninfinite set is zero, The possibility of defining a continuance thisway is also zero.

`OK. This shows that you have to define continuance in another way.`

`(The machine already know this).`

Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.