Can the Mind Be Modeled by Mathematics? Classic ID-related Paper Now Available Online

_{Jonathan Bartlett

January 15, 2012

Intelligent Design}

Share: Facebook; Twitter; LinkedIn; Flipboard; Print; Email

I don’t know how long this has been available (I have looked before, but was unable to find it), but I just noticed that Douglas Robertson’s “Algorithmic information theory, free will, and the Turing test” is available online. This paper has been highly influential in ID circles, as can be attested by its citation list.

The main thrust of the paper is that, solely on the basis of mathematics, any mathematical physical theory is incapable of producing consciousness as we know it. The reason for this is that mathematics are incapable of producing mathematical axioms. Therefore, a mathematical physical theory is incapable of producing the mathematical axioms on which it is based.

The paper is a fantastic read, and anyone who is interested in ID or in the relationship of mind to matter should give it a read. It is definitely both readable and worthwhile.

Robertson’s conclusion is this:

The existence of free will and the associated ability of mathematicians to devise new axioms strongly suggest that the ability of both physics and mathematics to model the physical universe may be more sharply limited than anyone has believed since the time of Newton.

Now, I actually disagree with this, at least in a way. I think we will continue to advance in our models of the universe, but I think we will have to rethink the *types* of models we come up with. The models we have looked at so far are deterministic, past-determines-future models. I think we will need to be looking at non-deterministic, future-influences-present models in order to accurately model the universe as we find it.

For those interested in these kinds of topics, remember that there is a conference this summer covering these things and their practical applications – The Engineering and Metaphysics 2012 Conference. I hope to see you there!

Comments

Oops misread your post. Yes, unequivocally, information transfer (from parent to offspring) must have preceded Darwinian evolution. Darwinian evolution cannot occur in the absence of replication, and replication necessarily involves information transfer.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
12:09 PM
12
12
09
PM
PDT}

Well, I'm not sure what "Darwinian information" is, but clearly, no Darwinian evolution could begin to take place until something managed to copy itself with variance that reflected itself in reproductive success. Copying is an information transfer process, so that, clearly, preceded any information reflecting genotypes that maximise reproductive success in the current environment (which may be what you mean by "Darwinian information". If so, then, of course, non-Darwinian information preceded Darwinian information. I'm not going to say "unequivocally" though, until I know what you mean by each term. Certainly information transfer between parent and offspring must have preceded the accumulation of information regarding optimal adaptation of the population.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
12:07 PM
12
12
07
PM
PDT}

So without equivocation, which came first, information or Darwinian evolution?Upright BiPed_{January 16, 2012
January
01
Jan
16
16
2012
11:58 AM
11
11
58
AM
PDT}

The key thing, though, Upright BiPed, is that once you have a self-replicating system (which, as you say, requires some kind of information transfer process, so that the offspring has information transferred from the parent) we have the potential for bootstrapping in further information. This is true whether you are talking about a neural learning system, or the evolution of robots, or brains, or organisms. The hard part is that first bit of information transfer from "parent" to "offspring" (with a little variance of course). That's the part Darwinian evolution can't explain, because the prerequisites for Darwinian evolution are not yet present.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
11:57 AM
11
11
57
AM
PDT}

No, it doesn't! Darwinian evolution doesn't explain the origin of life! You are absolutely correct.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
11:49 AM
11
11
49
AM
PDT}

7.2.1.1.8 Then it doesn't explain the rise of the very thing that organizes inanimate matter into functioning organic systems, does it?Upright BiPed_{January 16, 2012
January
01
Jan
16
16
2012
11:47 AM
11
11
47
AM
PDT}

So you are asking about the origin of life?Petrushka_{January 16, 2012
January
01
Jan
16
16
2012
11:43 AM
11
11
43
AM
PDT}

How many robots gave rise to their own organizational control systems by means of evolution?Upright BiPed_{January 16, 2012
January
01
Jan
16
16
2012
11:41 AM
11
11
41
AM
PDT}

You know, Upright BiPed, you are absolutely right! Darwinian evolution doesn't explain how replication with heritable variation in reproductive success first came into being!Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
11:39 AM
11
11
39
AM
PDT}

That's a nice paper! Of course there are two levels of evolution going on there - "between generation" evolution, and "within robot" evolution. Both are learning, but the second is learning by an individual, and the first is learning by a population.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
11:33 AM
11
11
33
AM
PDT}

Ever since Cicero's De Natura Deorum ii.34., humans have been intrigued by the origin and mechanisms underlying complexity in nature. Darwin suggested that adaptation and complexity could evolve by natural selection acting successively on numerous small, heritable modifications.
uh oh. Sounds like recorded information. Now you'll need a source of symbollic representations and transfer protocols operating in a coordinated system. The rise of formalism doesn't come cheap.Upright BiPed_{January 16, 2012
January
01
Jan
16
16
2012
11:30 AM
11
11
30
AM
PDT}

No, let's not start with complex language output. What is wrong with my SVM output? It's an algorithm. Its output is new (and therefore original). Its output digital. Its output is highly complex - the chances of getting that output from some comparable random data generator are tiny. Its output specified - it is one of a much smaller set of coherent sensible outputs. And its output is information. It tells me something I didn't know before.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
11:27 AM
11
11
27
AM
PDT}

http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.1000292 I know nothing on this topic will ever satisfy you, but this kind of computation is in it's infancy.Petrushka_{January 16, 2012
January
01
Jan
16
16
2012
11:22 AM
11
11
22
AM
PDT}

Petrushka: You know, I understand that algorithms can compute different results, if the input is different. I am not completely stupid, you know. Algorithms compute the same result if the inputs are the same. You can well write an algorithm to compute interisting results from random seeds. These things are well known, and do not change a comma of what I have said. Show me an algorithm that can output new original dFSCI, such as complex language output, and we will discuss.gpuccio_{January 16, 2012
January
01
Jan
16
16
2012
11:19 AM
11
11
19
AM
PDT}

GAs are algorithmic, but do not compute the same result on each run. I know you find this difficult, but a GA can construct objects that have not previously existed.Petrushka_{January 16, 2012
January
01
Jan
16
16
2012
11:16 AM
11
11
16
AM
PDT}

Elizabeth: No, thank you, my razor is sharp enough anyway :) The point is, huamns can create algorithms that can apprently "learn" (please, note the quotation marks :) ). But those algorithms just process and compute information that is given them, according to what they have been programmed to do. There is no need of understanding meanings for that. There is no need for consciousness to do that. I repeat that all forms of algorithmic computing are independnt from the hardware, and can be implemented on any computing machine, starting with an abacus. The computation is an abstract form. However you perform it, the results will be the same, because computation is a necessity procedure. In essence, there is no difference between computing 2 + 2 and computing the movement of a robot. It is still computing. The movement of a robot is computed by adding 2 + 2, or similar operation, many times in some sequence. What in that should generate a subjective consciousness is really beyond my understanding. The machine computes bits, and does nothing else. Bits are all the same for the machine that computes. They mean nothing, just a long series of 2 + 2.gpuccio_{January 16, 2012
January
01
Jan
16
16
2012
11:05 AM
11
11
05
AM
PDT}

Well, sure, but my example still rather blunts your razor, doesn't it?Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
10:51 AM
10
10
51
AM
PDT}

Elizabeth: I was referring more to new theoretical perspectives, such as relativity, quantum mechanics, godel theorem, and similar. Approaches that cannot come from previously programmed algorithms, and require creativity and understanding. Like Hamlet.gpuccio_{January 16, 2012
January
01
Jan
16
16
2012
10:49 AM
10
10
49
AM
PDT}

Actually, the halting problem (which is essentially isomorphic to Godel incompleteness) uses an infinite tape, so if the universe is not finitely specifiable, as long as it is quantized (as quantum physics suggests), the same results would hold.
That the Turing machine uses an infinite tape is not actually relevant to this particular discussion. The computation begins with only a finite amount of data on the tape. So the computation has to be finitely specifiable for that. At any time during a computation, only a finite part of the tape has ever been used. All computation is inherently finite. The point of the infinite tape is to make it clear that there is no a priori limit on how much memory is used. There's no implication that more than a finite amount will ever be used in any computation. Gödel's theorem is not about physics. It isn't even about mathematics. It is about logic, and the limitations of logic. It has significance for mathematics if your philosophy of mathematics is logicism - the thesis that mathematics arises purely from the use of logic. Russell and Whitehead's Principia was based on logicism. Most mathematicians are platonists, not logicists, and many of them consider Gödel's incompleteness results to be mildly interesting but of no particular significance to their work. Gödel, himself, was a mathematical platonist.Neil Rickert_{January 16, 2012
January
01
Jan
16
16
2012
10:06 AM
10
10
06
AM
PDT}

johnnyb, yeah Chaitin made some fairly huge concessions to make his program work, but when looked at objectively, free of any Darwinian bias, and even though he himself probably does not like the conclusion of his work, the fact is that his work is entirely supportive of intelligent design principles.bornagain77_{January 16, 2012
January
01
Jan
16
16
2012
10:04 AM
10
10
04
AM
PDT}

Human minds have generate new and unexpected scientific models of reality. Formal mathemathical systems cannot do that.
Unexpected by whom? Support Vector Machines can generate new and unexpected (by the researchers) models of reality that turn out to be rather good.Elizabeth Liddle_{January 16, 2012
January
01
Jan
16
16
2012
09:48 AM
9
09
48
AM
PDT}

bornagain - Thanks for the link! I was aware of Chaitin's paper (Chaitin had emailed me the paper when it came out). I was not aware of Vincent's critique. It looks well-thought-out, but I'll have to dive into it later. The one thing that I noticed in Chaitin's paper was that it had no room for extinction - that is, all his organisms were minimally survivable no matter what the mutation.johnnyb_{January 16, 2012
January
01
Jan
16
16
2012
09:42 AM
9
09
42
AM
PDT}

johnnyb, this article may interest you:
At last, a Darwinist mathematician tells the truth about evolution - November 2011 Excerpt: 7. Chaitin looks at three kinds of evolution in his toy model: exhaustive search (which stupidly performs a search of all possibilities in its search for a mutation that would make the organism fitter, without even looking at what the organism has already accomplished), Darwinian evolution (which is random but also cumulative, building on what has been accomplished to date) and Intelligent Design (where an Intelligent Being selects the best possible mutation at each step in the evolution of life). All of these – even exhaustive search – require a Turing oracle for them to work – in other words, outside direction by an Intelligent Being. In Chaitin’s own words, “You’re allowed to ask God or someone to give you the answer to some question where you can’t compute the answer, and the oracle will immediately give you the answer, and you go on ahead.” 8. Of the three kinds of evolution examined by Turing (Chaitin), Intelligent Design is the only one guaranteed to get the job done on time. Darwinian evolution is much better than performing an exhaustive search of all possibilities, but it still seems to take too long to come up with an improved mutation. https://uncommondescent.com/intelligent-design/at-last-a-darwinist-mathematician-tells-the-truth-about-evolution/ Also Per Chaitin; Oracle must possess infinite information for ‘unlimited evolution’ of a evolutionary algorithm; i.e. The Oracle must be God! https://uncommondescent.com/intelligent-design/at-last-a-darwinist-mathematician-tells-the-truth-about-evolution/comment-page-1/#comment-408176
bornagain77_{January 16, 2012
January
01
Jan
16
16
2012
09:21 AM
9
09
21
AM
PDT}

If you don't regard mathematical physics as true, then I don't see where you would have any real problem with Robertson. In fact, his conclusion is precisely yours, with a slight philosophical twist. He states,
The possibility that phenomena exist that cannot be modeled with mathematics may throw an interesting light on Weinberg’s famous comment: “The more the universe seems comprehensible, the more it seems pointless.” It might turn out that only that portion of the universe that happens to be comprehensible is also pointless.
I don't see how that differs dramatically from your stance. If mathematical physics is simply a methodological point, and not a metaphysical one, then what follows is that there shouldn't be any requirement for nature to behave in a mathematically-specifiable way. Robertson's (and mine) only objection is to the people who think that mathematical-physics-like phenomena is descriptive of total reality. However, I (and not Robertson as far as I am aware), think that we can extend modeling to include other types of phenomena, if we remove some of the historically-assumed requirements. On an similar note, I have argued elsewhere that physics has progressed not by squeezing out theological notions, but by incorporating more and more of them.
No, this does not follow. It requires mathematically modeling the entire universe. And that requires that the entire universe be finitely specifiable. This is very unlikely.
Actually, the halting problem (which is essentially isomorphic to Godel incompleteness) uses an infinite tape, so if the universe is not finitely specifiable, as long as it is quantized (as quantum physics suggests), the same results would hold.johnnyb_{January 16, 2012
January
01
Jan
16
16
2012
08:40 AM
8
08
40
AM
PDT}

Well, I applaud anyone who digs deep into the internals of sendmail. It was an amazing system especially for the days when mail was not so standardized. I use Postfix myself, but the long tradition started by sendmail and its administrators can still be seen by the fact that the standard command to invoke the mail system, even in the most feverishly anti-sendmail mail systems, is still /usr/sbin/sendmail.johnnyb_{January 16, 2012
January
01
Jan
16
16
2012
08:26 AM
8
08
26
AM
PDT}

if mathematical physics is true ...
My personal view is that scientific laws, such as the laws of physics, are neither true nor false. Their role in science is methodological, not descriptive.
... then one can construct an equation for which there is no new information possible – it is all just axioms and initial conditions.
No, this does not follow. It requires mathematically modeling the entire universe. And that requires that the entire universe be finitely specifiable. This is very unlikely.Neil Rickert_{January 16, 2012
January
01
Jan
16
16
2012
08:17 AM
8
08
17
AM
PDT}

Neil - I think you will understand a lot more of Robertson's arguments if you familiarize yourself better with the state of Mathematics at the time of Hilbert, and specifically his plan to make a universal formal axiomatic system. Indeed Godel did put an end to formalization in the Hilbert sense. And, indeed, as this was known as "Hilbert's Program", is falsification is indeed a fundamental and embarrassing error for Hilbert. And, as gpuccio noted, your criticism that "typing on the keyboard" is new information completely ignores the point - if mathematical physics is true, then one can construct an equation for which there is no new information possible - it is all just axioms and initial conditions. It is only if mathematical physics is not true that things such as "typing on a keyboard" become additional information. So, your point actually proves Robertson's, rather than detracting from it.johnnyb_{January 16, 2012
January
01
Jan
16
16
2012
07:39 AM
7
07
39
AM
PDT}

To be clear myself, I have been and still am a critic of AI. I doubt that it can work, though I don't claim to be able to prove that it cannot work. The available evidence strongly suggests that biological systems are more creative than silicon systems.Neil Rickert_{January 16, 2012
January
01
Jan
16
16
2012
07:37 AM
7
07
37
AM
PDT}

Neil: I don't think it is too hard, but I really have not the time now. I apologize...gpuccio_{January 16, 2012
January
01
Jan
16
16
2012
07:35 AM
7
07
35
AM
PDT}

That looks fine to me. It is hard to come up with implication for free will from such a statement.Neil Rickert_{January 16, 2012
January
01
Jan
16
16
2012
07:33 AM
7
07
33
AM
PDT}

Prev 1 2 3 Next

You must be logged in to post a comment.

Leave a Reply