Lumpy's Contribution : Part 2 - A Reply (rev II)

This post is the second in a series. The last post dealt with my writing goals and my regard for feedback to refocus the discussion. In this one, I reorient the topic to deal with comments that Lumpy Pea Coat made.

Although I write this page to give an answer to Lumpy’s points of dispute, I have to give him his due. You’ll find Lumpy quite accurate in what he says (here and here). Plus, at the time of that exchange, I read some posts on Lumpy’s blog that lead me to think that he might be a graduate student in a related field. It adds to it that I really cannot find fault with the facts as he represents them.

So how I can I answer him? Well, I knew quite a bit of what he gave as the factual basis. He wrongly assumed that I did not. I get that because I used shorthand, he assumed that I thought in shorthand. While, I don’t think I know Turing Machine Theory, the Church-Turing Thesis, and Rice’s Theorem to the level that a graduate student in this field would, I do have some basis for my case.

At least, I think I have a case. But if that be so, it should become clear here.

More than Facts

At first, he took me to task about the lack of precision I used to describe the Turing Machine (TM) and the Halting Problem. His seems to point out that the brain is not a TM (here), as I may have implied. But, in theory, we have a method to show that it is like one. The limits of the brain, as concerns the Halting Problem, didn’t spring from its being a TM. Instead, Halting (short for “The Halting Problem”) imposes a basic limit on every kind of computation, even human.

As I stated last time, I wrote the portions about TM theory in Black Box Brain (BBB1 and BBB2) posts because I hadn’t seen signs that people knew about what Computability Theory (CT) implied. I wanted to cursorily mention it and move onto my main concept which continues on the theme started here.

To BBB1, Lumpy wrote, “The brain is no better than a universal TM as far as computation ability goes.” So were this true, what was the brain no better than? A “Universal TM”? What the heck is that?

And how was it no better than whatever that is? What did that say about the limit of “computation ability” in the human brain?

More to my reason for mentioning it: Did the wide public know that viewing the brain as a computer gave it limits? Did they know that the brain had limits—regardless of what they were!

It is my witness that the public does not talk about the limits of brains or computers. I’ve never heard the Halting Problem talked about other than in my Computer Science classes (with the possible exception of Roger Penrose’s book, The Emperor’s New Mind.) Yet I’ve heard the idea that the brain is just some kind of computer from throngs of materialists. So I thought to discuss, on the same level of the simple model of brain-as-computer, what that implies.

As I noted, Lumpy’s objection contained the charge that brain was limited via the Halting Problem. If this is so, wouldn’t it be nice to know what the “Halting Problem” is? Has anybody ever told you that computation is limited? If you think it would be nice to know and nobody has ever told you, then you are the reader that I am talking about.

But Lumpy’s charge of gloss rings a bit hollow: I gave links to more in-depth treatments on these things in case somebody wanted to learn a little more about these terms. When I had drafted pages on this kind of topic for my former site, I had usually inserted my own expansions of the details in them, but since I have discovered Wikipedia, I can reuse work that has already been done there.

But by and large, most people are just not going to want to read those texts. Does that mean that they should be kept in the dark about the matter? Does that mean that nobody should add these facts to the materialist narrative?

Lay or initiate, we tend to discern the meaning of the phrase “the brain is a computer.” It seems to paint a clear enough picture. And as such, it seems to have a layman’s level of detail in mind. Why is it then wrong to mention Halting Problem in lay terms? We’ve already used “computer”. If there is a problem it must come in fitting some joins.

Does the Halting Problem not apply to computers? “Indeed,” Lumpy seems to say, “Even brains”. So is the lack of fitness the brain-as-computer? Perhaps. In that case, that is the model I object to. If the problem with the fit is not that the Halting Problem vexes every type of computer—which, as both I and Lumpy understand it, it does—it is in the method by which we equate the brain with the computer?

Imagine that experts should keep people in the dark because a general sense of TMs and the Halting Problem could never be captured because of inner intricacies. Can a computer be any more widely used—if the concept of a computer is first formed and then ruled by TM theory?

The computer is not its singular architecture. It is not a vacuum-tube machine. It is not a silicon machine. Mathematicians first devised it as a theoretical machine which did computations step by step. Because we define it by its purpose and function, it remains linked to its role. And its role is heavily defined by TM theory.

The idea of the brain as a computer seems to be the source of confusion and error—NOT my plea to submit Halting into the public record. I said that in that the brain is a computer if suffers from Halting just the same. Thus if we can take a “not in front of the kids” approach to TM theory, why are we calling the brain a computer in the first place? And shouldn’t that claim be the one subjected to the same scrutiny that Lumpy gave a possible misstatement of the halting theory?

It seems that most of Lumpy’s objection was to the relation that brains have to TMs. He said, “I don't know anybody who genuinely holds that the brain just is a Turing machine….” (here) But let’s say that to comply with the sense of the term “computer”, the thing called such a thing must be a device that proceeds by steps to process recursive functions. As such it is bound by Halting. It is quite in the definition, subject to the Halting Problem.

If I could have said it this simply, I would have. But if you didn’t know any of the subject matter, you don’t know why I’m saying what I’m saying. Nor would you get a sense of how well these concepts fit when applied to the brain. So I went over a smattering of TM theory, so that I can say that not all logical processes end.

Thus although verifying the correctness of how someone else processes input from the world seems like a logical process, we have no proof that such a process ever ends. And had I been able to say that as simply as I did right there, I would have just kept it to that. Thus Halting suggests that despite that a process seems to be exact and have well-defined steps to compute intermediate products, you cannot say that the whole enterprise is not fraught with a never ending cycle until you are done. And as this has to do with brains, it has a recursive application to the question itself, when considered by brains.

Close Enough…

That said, we still have reasons to consider it a computer or “alike” in any case.

First, we know some part about how computers “think”. As I have said, before we had computers, we had mathematical of them. So we’ve always had more definite things to say about these devices than whatever brains are.

The brain also, fixed in the material world, has mechanisms. Chemical reactions and electrical reactions propagate causing a change of state in the brain and leave us with the material surmise that those changes in the brain cause what we think.

Now, I didn’t say that it doesn’t work that way (And Lumpy was wrong to infer that). I only doubted that it does. And I don’t doubt it as a personal conviction, I intellectually doubt it.

Materialists and atheists often make the claim (as I discussed here) that positive claims must be backed up with evidence. (see “Other uses”) When I make the claim that God exists, they charge me to prove that claim (as if I ever said, “it is clearly evident that God exists”). They claim—as a general strategy—that the party with the positive claim must give evidence (as if there were some tribunal for personal opinions—but that is another war.)

Thus, I should not receive the burden to prove that the brain and computer are dissimilar (a negative) if atheists and materialists are being at all consistent with their rules. Are rules only to be imposed for the hobble of the opposition?

What we call computers fall into two types: one is a mathematical conception of algorithm and the other is a designed machine to meet that specification. Neither is an evolved, undesigned protoplasmic thingy which dreamt up both.

We have a difference. The other side makes the charge that the organ fits the specification where every other evident case presents a machine designed to meet the definition of computation. This instance was not designed to fit this model. And we know how the other examples function so we know to what extent they do.

Appeals to future knowledge aside, we do not now know how the brain works. Thus whether the functions that we do not now know help or hinder the brain as a kind of computer, we do not know. Thus we cannot say now (because that’s when we are saying it, right?) that the brain conforms to the design, because we do not know to what respects it does or does not conform.

Besides, the whole appeal to future knowledge 1) breaks the burden of proof on the claimant, but greater than that 2) is never dealt with inside of the whole computational model. If we will know something, brains and computers will know it. And thus, such a thing depends upon what brains and computers are.

Future knowledge claims are often softened into a statement that we “may know”. Seldom if ever does the writer deal with the fact that we “may not”. They tend to leverage future knowledge as evidence in current debates. They tend to cow you with a shared faith in technology, despite whether or not they can prove the positive claim “it is possible to know x.” But the full discourse on the problems with “Positive Claim” rule is yet to come.

hat is more important to me is the second. I repeat, Lumpy said that endless recursion is a problem in 1) the human brain and 2) the machines we build to think for us. The most general statement of this is: a problem is only computable, if it is computable.

Thus Halting (short for “The Halting Problem”) gives real challenge to claims of future knowledge. If our brains are computers and the physics of the brain are not computable, we will never get how it does what it does. We can only form a rough model, ruled by a different set of special case rules than how the brain actually functions.

How close will they be? Rice (short for “Rice’s Theorem”) tells us. If the brain is a computer and we create TM B to compute near-brain function, unless “brain-like” property is trivial (which it is not) the idea of having an algorithm than can prove that various submitted TMs produce “brain-like” behavior is impossible to determine. Arguably, by Rice, we can never tell if a brain-simulation is more or less “brain-like”.

The most we can get is a strong correspondence between the output of the brain and the output of the computer. But how computable is “strong correspondence.” How strong? What is our threshold? How will we measure it? How will we encode similarities? Is it close enough that the computer predicts that Joe wants an ice-cream cone, if Joe wants an Eskimo Pie? What is “close enough”? How is it encoded?

Do we decide? I would say that we do. But, in process of creating software that I know, we decide based on what we want the computer to do. We decide on the basis of our preference. Therefore “close enough” would depend on what we wanted it to do. (Odd that this has a meta-application on how a treated TM theory according to my purpose in writing.)

Is there then a precise specification of what is “close enough”?

Let’s say that every verdict of “close enough” has a mathematical definition of distance (and so “closeness”) and a mathematical definition of tolerance (but why this line and no other?) within that distance. Suppose we needed to find the TM that solves the problem.

Again Rice messes us up here, because there is no sure way of finding which TM this is. Thus there may be a TM which solves this type of question for each and every instance, but unless we know what it is, we cannot find it by picking TMs off of a conveyor belt and examining each one as they come by.

Therefore, if we do not already know how to do this, we find many questions in the notion of computing an algorithm to arrive there. Is the problem computable? What kind of shortcuts will we need to make? How “close” can we come with a simulation? How do we verify “closeness”?

In fact these questions produce an endless regress, in my mind. The TM that would solve Halting also answers the question whether something is computable. If the brain holds to the TM model and thus subject to Halting, you could never answer whether a problem was computable. Thus, the notion of a minimum distance between model and the problem depends on whether there is a “zero-distance” solution—or an exact computation, should it happened to be computable.

See the problem with “future knowledge” is on the level of a TM, we know that a TM encodes a computable function only if it has stopped. Any TM grinding away at its answer out there can possibly stop and possibly arrive an answer. But if we break this whole concept down to the machines computing, then having spent time computing a given verdict, is no guarantor of an answer. Only having spit out an answer is.

This is why in my exchange with Lumpy, I specified what we know. It is not good enough that we have made “progress’ in figuring out the brain, finding that the brain is a computer—by agency of the brain—means that the brain must run an algorithm to determine that the brain is a computer.

Lumpy’s worst mistake was to tell me that “Turing machines do not compute functions representing interpreted predicates like 'is useful'.” (here) I can only wonder what our brain-machine do by saying that then. Is nothing actually “useful”? Is the brain ill fit for that task? Is there an embarrassing gaucheness buried within our notion of “useful”? What does it mean when our brain gets a sense that something is “useful”? Does our conviction that something is useful have little to do with whether it is or is not?

We can then wonder about “is close enough”? Is it really “close enough” when we say it is? Well, I said above we do arrive at the verdict that something is close enough to our purposes in developing software. But if the “interpreted predicate” is just a by-product of real algorithmic processes going on in our brains, where does that leave “interpreted predicates”?

And where does that leave the link between what our brain thinks and what our language says? Can we accept that something we say can be “right” if it is naturally incorrect by the lack of an exact algorithm to compute these predicates? Can we interpret if TMs cannot? And how can we if our computation faculty has the same bounds as TMs?

And on we go…