On 09 Jan 2012, at 19:36, acw wrote:

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On 1/9/2012 19:54, Craig Weinberg wrote:On Jan 9, 12:00 pm, Bruno Marchal<marc...@ulb.ac.be> wrote:On 09 Jan 2012, at 14:50, Craig Weinberg wrote:On Jan 9, 6:06 am, Bruno Marchal<marc...@ulb.ac.be> wrote:I agree with your general reply to Craig, but I disagree that computations are physical. That's the revisionist conception of computation, defended by Deustch, Landauer, etc. Computations have been discovered by mathematicians when trying to expalin some foundational difficulties in pure mathematics.Mathematicians aren't physical? Computations are discoveredthrough aliving nervous system, one that has been highly developed and conditioned specifically for that purpose.Computation and mechanism have been discovered by many people sincehumans are there. It is related to the understanding of thedifferencebetween "finite" and "infinite". The modern notion has beendiscoveredindependently by many mathematicians, notably Emil Post, AlanTuring,Alonzo Church, Andrzei Markov, etc. With the comp. hyp., this is easily explainable, given that we are somehow "made of" (in some not completely Aristotelian sense to be sure) computations.They are making those discoveries by using their physical brain though.Sure, but that requires one to better understand what a physicalbrain is. In the case of COMP(given some basic assumptions), matteris explained as appearing from simpler abstract mathematicalrelations, in which case, a brain would be an inevitable consequenceof such relations.We can implement computation in the physical worlds, but that means only that thephysical reality is (at least) Turing universal. Theoreticalcomputerscience is a branch of pure mathematics, even completelyembeddablein arithmetical truth.And pure mathematics is a branch of anthropology.I thought you already agreed that the arithmetical truth are independent of the existence of humans, from old posts you write. Explain me, please, how the truth or falsity of the Riemann hypothesis, or of Goldbach conjecture depend(s) on anthropology. Please, explain me how the convergence or divergence of phi_(j) depends on the existence of humans (with phi_i = the ith computable function in an enumeration based on some universal system).The whole idea of truth or falsity in the first place depends onhumans capacities to interpret experiences in those terms. We canreadthis quality of truth or falsity into many aspects of our direct and indirect experience, but that doesn't mean that the quality itself is external to us. If you look at a starfish, you can see it has five arms, but the starfish doesn't necessarily know it had five arms.Yet that the fact the starfish has 5 arms is a fact, regardless ofthe starfish's awareness of it. It will have many consequences withregards of how the starfish interacts with the rest of the world orhow any other system perceives it.If you see something colored red, you will know that you saw red andthat is 'true', and that it will be false that you didn't see 'red',assuming you recognize 'red' the same as everyone else and that yournervous system isn't wired too strangely or if your sensory systemsaren't defective or function differently than average.Consequences of mathematical truths will be everywhere, regardlessif you understand them or not. A circle's length will depend on itsradius regardless if you understand the relation or not.Any system, be they human, computer or alien, regardless of the lawsof physics in play should also be able to compute (Church-TuringThesis shows that computation comes very cheap and all it takes isability of some simple abstract finite rules being followed andalways yielding the same result, although specific proofs forshowing Turing-universality would depend on each system - some maybe too simple to have such a property, but then, it's questionableif they would be powerful enough to support intelligence or evenmore trivial behavior such as life/replicators or evolution), and ifthey can, they will always get the same results if they asked thesame computational or mathematical question (in this case,mathematical truths, or even yet unknown truths such as Riemannhypothesis, Goldbach conjecture, and so on). Most physics shouldsupport computation, and I conjecture that any physics that isn'tstrong enough to at least support computation isn't strong enough tosupport intelligence or consciousness (and computation comes verycheap!). Support computation and you get any mathematical truth thathumans can reach/talk about. Don't support it, and you probablywon't have any intelligence in it.To put it more simply: if Church Turing Thesis(CTT) is correct,mathematics is the same for any system or being you can imagine.

`I am not sure why. "Sigma_1 arithmetic" would be the same; but higher`

`mathematics (set theory, analysis) might still be different.`

If it's wrong, maybe stuff like concrete infinities,hypercomputation and infinite minds could exist and that wouldfalsify COMP, however there is zero evidence for any of that beingpossible.

`Not sure, if CT is wrong, there would be finite machines, working in`

`finite time, with well defined instructions, which would be NOT Turing`

`emulable. Hypercomputation and infinite (human) minds would contradict`

`comp, not CT. On the contrary, they need CT to claim that they compute`

`more than any programmable machines. CT is part of comp, but comp is`

`not part of CT.`

Beyond this, I agree with your reply to Craig.

`BTW, acw, you might try to write a shorter and clearer version of your`

`joining post argument. It is hard to follow. If not, I might take much`

`more time.`

Bruno

If any intelligent system capable of interpreting the same idea willalways reach the same conclusions about it (if they followed thesame steps), I'd call that an external truth, it's about as externalas it can get. If your consciousness or physics were a direct resultof such abstract relations, it would also be both an internal andexternal truth.What about arabic numerals? Seeing how popular their spread has been on Earth after humans, shouldn't we ask why those numerals, given an arithmetic universal primitive, are not present in nature independently of literate humans? If indeed all qualia, feeling, color, sounds, etc are a consequence of arithmetic, why not the numerals themselves? Why should they be limited to human minds and writings?I think you're confusing numerals with numbers. Numeral systems arejust an encoding we have for talking about numbers. Numeralencodings are a matter of history, which is a matter of physics, andin case of COMP, is a matter of arithmetic (or any other universalcomputational system - they're all equivalent by the Church TuringThesis). In that sense, numeral systems(encodings) are a consequenceof arithmetic.The encoding itself is irrelevant, you could use tally notation(such as ||| + || = |||||) and it wouldn't matter. Nor is the choiceof the universal system - all that matters is the ability offollowing simple finite rules and getting the same result each timeyou do.Us finding about the CTT or any other mathematical truth is alsosuch a consequence of arithmetic. In a less serious way, you couldsay: "It's turtles all the way down!". In a more serious way, youcould think of quines and Kleene's recursion theorems about fixedpoints.Craig--You received this message because you are subscribed to the GoogleGroups "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.

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