Polymorphism sucks [Was: Paradigms which way to go?]
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From: Dmitry A. Kazakov on 16 Aug 2005 06:33 On Mon, 15 Aug 2005 11:35:35 -0500, Chris Sonnack wrote: > Dmitry A. Kazakov writes: > >> Hmm, was Shannon aware of Hilbert's program? I think he was. >> Anyway in the times after Goedel, we know that there is no >> way to "break" everything down to 1s and 0s. > > Are we possibly talking about two different things here? Yes, > Goedel showed we can't fully analyse any non-trivial system, > but I believe Shannon hasn't been superceded in the sense that > anything that *can* be expressed or computed can be expressed > or computed in binary. Which contains a hidden tautology, of course. Everything = anything computable in 1s and 0s? (:-)) >> And even if there were one, neither fuzziness nor randomness >> can be expressed in a deterministic system without some >> incomputable elements. > > But they are incomputable by *any* means, right? That's an interesting question. It depends on the hardware. We don't know if the Universe can offer us anything beyond Turing machine. In particular, can our biological "hardware" compute incomputable? Nobody knows it for sure. Then there is quantum computing. So far people are busy trying to make 1/0s computing out of it. But let's look in another direction. What if quantum computing is more than that? Purely fictitious, let you can compute random distributions, rather than their realizations (the only thing we can do now), then this class of computing will be incomputable for any Turing machine. -- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.de
From: Mark Nicholls on 18 Aug 2005 07:32 > > >> And even if there were one, neither fuzziness nor randomness > >> can be expressed in a deterministic system without some > >> incomputable elements. > > > > But they are incomputable by *any* means, right? > > That's an interesting question. It depends on the hardware. We don't know > if the Universe can offer us anything beyond Turing machine. But the turing machine is a theoretical machine, it is not the universe that constrains it (in terms of physics) but the maths, and that is only constrained by the wit of man. > In particular, > can our biological "hardware" compute incomputable? Isn't this the point about 'belief', i.e. that human rational is not constrained by formal logic, it cannot be inconsistent with formal logic (well it can be, but provability is a subset of 'truth'), but we believe we can deduce the correctness of some assertions that are beyond the scope of formal logic....(thus our previous discussion about god, and aethiesm as a belief system, rather than within the scope of a logical or scientific discussion). > Nobody knows it for > sure. Then there is quantum computing. So far people are busy trying to > make 1/0s computing out of it. But let's look in another direction. What if > quantum computing is more than that? Purely fictitious, let you can compute > random distributions, rather than their realizations (the only thing we can > do now), then this class of computing will be incomputable for any Turing > machine. > I haven't got a clue what quantum computing is, but you should be able to model it, even if it doesn't exist....as long as it obeys the axioms. Would it be capable of belief in the absence of formal proof? Could it discern the truth?
From: Dmitry A. Kazakov on 18 Aug 2005 13:23 On 18 Aug 2005 04:32:05 -0700, Mark Nicholls wrote: >>>> And even if there were one, neither fuzziness nor randomness >>>> can be expressed in a deterministic system without some >>>> incomputable elements. >>> >>> But they are incomputable by *any* means, right? >> >> That's an interesting question. It depends on the hardware. We don't know >> if the Universe can offer us anything beyond Turing machine. > > But the turing machine is a theoretical machine, it is not the universe > that constrains it (in terms of physics) but the maths, and that is > only constrained by the wit of man. But computer is a physical object. You can build it of atoms, you cannot do it out of thoughts. Many people strongly believe that the physical world is equivalent to a giant FSM, which is even weaker than a TM. >> In particular, >> can our biological "hardware" compute incomputable? > > Isn't this the point about 'belief', That could be that sort of questions Goedel's incompleteness is about. > i.e. that human rational is not > constrained by formal logic, it cannot be inconsistent with formal > logic (well it can be, but provability is a subset of 'truth'), but we > believe we can deduce the correctness of some assertions that are > beyond the scope of formal logic....(thus our previous discussion about > god, and aethiesm as a belief system, rather than within the scope of a > logical or scientific discussion). > >> Nobody knows it for >> sure. Then there is quantum computing. So far people are busy trying to >> make 1/0s computing out of it. But let's look in another direction. What if >> quantum computing is more than that? Purely fictitious, let you can compute >> random distributions, rather than their realizations (the only thing we can >> do now), then this class of computing will be incomputable for any Turing >> machine. >> > > I haven't got a clue what quantum computing is, but you should be able > to model it, even if it doesn't exist....as long as it obeys the > axioms. There are two objections to this: 1. You cannot say what follows from the axioms (Goedel.) 2. Not that I would insist on it, but it is thinkable that the minimal set of axioms required to adequately describe what's going on [by means of our logic] could be bigger than the number of the states of all our brains. > Would it be capable of belief in the absence of formal proof? Could it > discern the truth? An extended Turing test, a capability to believe in irrational as a criterion of intelligence? (:-)) -- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.de
From: Mark Nicholls on 19 Aug 2005 06:22 Dmitry A. Kazakov wrote: > On 18 Aug 2005 04:32:05 -0700, Mark Nicholls wrote: > > >>>> And even if there were one, neither fuzziness nor randomness > >>>> can be expressed in a deterministic system without some > >>>> incomputable elements. > >>> > >>> But they are incomputable by *any* means, right? > >> > >> That's an interesting question. It depends on the hardware. We don't know > >> if the Universe can offer us anything beyond Turing machine. > > > > But the turing machine is a theoretical machine, it is not the universe > > that constrains it (in terms of physics) but the maths, and that is > > only constrained by the wit of man. > > But computer is a physical object. You can build it of atoms, you cannot do > it out of thoughts. A turing machine is not. > Many people strongly believe that the physical world is > equivalent to a giant FSM, which is even weaker than a TM. TM? > > >> In particular, > >> can our biological "hardware" compute incomputable? > > > > Isn't this the point about 'belief', > > That could be that sort of questions Goedel's incompleteness is about. That was really my point about the god discussion, science is limited by maths, and that is limited, belief needs to be consistent with the maths, but can live in the gaps. > > > i.e. that human rational is not > > constrained by formal logic, it cannot be inconsistent with formal > > logic (well it can be, but provability is a subset of 'truth'), but we > > believe we can deduce the correctness of some assertions that are > > beyond the scope of formal logic....(thus our previous discussion about > > god, and aethiesm as a belief system, rather than within the scope of a > > logical or scientific discussion). > > > >> Nobody knows it for > >> sure. Then there is quantum computing. So far people are busy trying to > >> make 1/0s computing out of it. But let's look in another direction. What if > >> quantum computing is more than that? Purely fictitious, let you can compute > >> random distributions, rather than their realizations (the only thing we can > >> do now), then this class of computing will be incomputable for any Turing > >> machine. > >> > > > > I haven't got a clue what quantum computing is, but you should be able > > to model it, even if it doesn't exist....as long as it obeys the > > axioms. > > There are two objections to this: > > 1. You cannot say what follows from the axioms (Goedel.) you can say a lot, but not everything. > > 2. Not that I would insist on it, but it is thinkable that the minimal set > of axioms required to adequately describe what's going on [by means of our > logic] could be bigger than the number of the states of all our brains. Goedel would imply that the set of axioms required for the system to be complete is unbounded, if the states of our brains are finite, then we cannot 'know' everything. > > > Would it be capable of belief in the absence of formal proof? Could it > > discern the truth? > > An extended Turing test, a capability to believe in irrational as a > criterion of intelligence? (:-)) > irrational may be strong....though people often believe irrational things.....unprovable certainly. so it is reasonable to believe in god it is reasonable to not believe in god it is irrational to assert that you know the answer......it would be harsh on the proponent of aethiesm as a fact to assert that that made him unintelligent!
From: Dmitry A. Kazakov on 19 Aug 2005 08:28
On 19 Aug 2005 03:22:13 -0700, Mark Nicholls wrote: > Dmitry A. Kazakov wrote: >> On 18 Aug 2005 04:32:05 -0700, Mark Nicholls wrote: >> >>>>>> And even if there were one, neither fuzziness nor randomness >>>>>> can be expressed in a deterministic system without some >>>>>> incomputable elements. >>>>> >>>>> But they are incomputable by *any* means, right? >>>> >>>> That's an interesting question. It depends on the hardware. We don't know >>>> if the Universe can offer us anything beyond Turing machine. >>> >>> But the turing machine is a theoretical machine, it is not the universe >>> that constrains it (in terms of physics) but the maths, and that is >>> only constrained by the wit of man. >> >> But computer is a physical object. You can build it of atoms, you cannot do >> it out of thoughts. > > A turing machine is not. Do you mean infinite band? >> Many people strongly believe that the physical world is >> equivalent to a giant FSM, which is even weaker than a TM. > > TM? Turing Machine >> 2. Not that I would insist on it, but it is thinkable that the minimal set >> of axioms required to adequately describe what's going on [by means of our >> logic] could be bigger than the number of the states of all our brains. > > Goedel would imply that the set of axioms required for the system to be > complete is unbounded, if the states of our brains are finite, then we > cannot 'know' everything. That is not required. The question is whether we could "know" physical world and ourselves there. Provided that somebody would define what does it mean to "know". (:-)) >>> Would it be capable of belief in the absence of formal proof? Could it >>> discern the truth? >> >> An extended Turing test, a capability to believe in irrational as a >> criterion of intelligence? (:-)) > > irrational may be strong....though people often believe irrational > things.....unprovable certainly. > > so it is reasonable to believe in god > it is reasonable to not believe in god > it is irrational to assert that you know the answer......it would be > harsh on the proponent of aethiesm as a fact to assert that that made > him unintelligent! Atheism is a religion, as irrational as any other! (:-)) -- Regards, Dmitry A. Kazakov http://www.dmitry-kazakov.de |