Years ago, a colleague of limited intellectual powers accosted me with the charge that I had been telling students that the ‘mind was meat’. This was my colleague’s way of putting things. I then fell for the question which the charge led up to: ‘So you’re a materialist?’ ‘Yes,’ I answered. To which my normally witless interlocutor responded: ‘Pray tell, what is the nature of the material world?’
Witless was right. We naturalists don’t remotely understand what makes up the world, let alone the world itself. Our materialism is promissory. If the world can be explained, it can be done without introducing non-natural or supernatural properties, phenomena or processes. But what principles demarcate natural properties, phenomena and processes from those too weird to be natural is not something that is much discussed, let alone agreed on. Whoever calls for a ‘deeper physicalism’, whether it be Witless or a leading mathematical physicist like Roger Penrose has got to be right. Deep physicalists look to biology, chemistry and physics for depth. They are sceptics – and rightly – about the resources of both a priori philosophy of mind and computer science to explain nature and mind.
Computationalism continues to grip the academic and popular imaginations, however. A recent issue of the New York Times led its science section with an article called ‘The Brain Manages Happiness and Sadness in Different Centres.’ Immediately beneath the first paragraphs of text were pictures of PET scans showing the different areas of the brain that are active when people are happy or sad. The pictures were introduced in large, boldface type with this headline: ‘How the Brain Computes Tears and Laughter.’
This might seem innocuous, but if so, it can only be because talk of the brain computing things is the dominant way of speaking about the mind. But in this case, at least, the pictures decidedly did not show the brain computing anything, let alone tears and laughter. What PET scans show are blood-flow patterns. So what the pictures showed were areas where blood flows; and thus oxygen, and thus, we presume, activity, were increased or decreased. The maps were correlated with phenomenological reports of the relevant feelings, and the plausible inference that such and such areas of the brain are importantly implicated in the relevant emotions is made. Nothing was revealed, however, about how anything was being computed.
Why do we speak this way? The simple answer is because the computer is the dominant metaphor for mind. For Penrose it is a metaphor which has overstepped its bounds. We forget that it is a metaphor, and take the claim literally, so that the mind/brain is a computer. Colin McGinn calls this view ‘pan-computationalism’. In its most extreme version the universe becomes a computer, whose parts run their own particular programs or sub-routines.
Penrose defines computation as the action of a Turing machine, a perfectly idealised computer, and takes ‘algorithm’ to be completely synonymous with ‘computation’. The appeal of ‘pan-computationalism’ comes both from the success of computer modelling across disciplines and from the construction of machines which display ‘intelligence’. But just because we can model chemical reactions, photosynthesis, genetic transmissions, the weather and so on, computationally, it seems absurd to say that any of these things are computers or the computational children of the mother of all computers, the universe.
Penrose has, I think, just the right targets here: overconfidence that our current explanatory apparatus can give an account of reality – hence the need for a deeper physicalism; and a metaphorical model that is taken literally and thereby obstructs progress in the science of the mind. Model, metaphor and simile are relations of likeness, not of identity. The mind may function like a computer, but so do I function like other land-based mammals. But I am not a computer, nor am I a chimp, an orang-utan, or a deer.
Penrose rejects both the idea that the brain is a computer and the idea that it can be adequately modelled computationally. Why? Because certain things we humans do we do non-computationally. Since the brain is not a computer, its causal powers cannot be duplicated by one. So much for the program of strong Artificial Intelligence. And since the brain cannot be adequately modelled computationally, so much for the program of weak Artificial Intelligence. Computers will never pass the Turing test because we cannot even in theory build one that will simulate or mimic the input-output relations normally mediated by the human brain.
What is it that humans can do that computers can’t, and why think that ‘some, at least, of conscious activity, must be non-computational’ (his italics)? Penrose’s answer is simple and direct. Mathematicians can ‘see’ the truth of certain mathematical statements that we know, thanks to Gödel and Turing, cannot be proven by procedures known to be sound. This shows that our awareness of these truths is ‘demonstrably noncomputational’.
Penrose here responds to twenty earlier criticisms of his initial argument. But I still don’t see that his arguments succeed. The reasons are pretty straightforward. Take first the limitative results of Turing, establishing that we cannot guarantee that for every problem within arithmetic we can ascertain whether the program dedicated to its solution will come to a halt and tell us what the solution is, or even whether the problem has a solution. Imagine a primitive program designed to do whatever it is told – call it ‘Dopey’. Imagine we tell Dopey to find an odd number that is the sum of two even numbers. Now suppose that mathematicians just ‘see’ that this problem is a non-starter – there simply is no odd number that is the sum of two even numbers. Dopey, however, keeps searching for all eternity. What does this show? It establishes that when we ‘see’ there is no such number, we are not simply using whatever algorithm Dopey uses. Does this show we’re not using an algorithm? No. Penrose allows that connectionist systems, which learn as they go, are algorithmic. So imagine that we are not Dopey but a system like Dopey that will do what it is told, but only up to a point. Once we have tried the best known solution strategy, failed to find a solution and discerned a pattern of failure, we stabilise into a state of ‘high confidence’ that the problem is a non-starter. The most this example shows is that the human who discerns the relevant truth is not computationally equivalent, as far as the solution to this problem goes, to Dopey.
The same point applies in Gödel’s case. Gödel tells us that for any formal system as complex as simple (Peano) arithmetic (P), if that system is consistent, there will be a true sentence that expresses P’s consistency which the system cannot prove. Suppose world-class human mathematicians agree that arithmetic is consistent; even suppose they ‘know’ this and are right. Does this show that ‘human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth’? I think not. What it shows is that if the human is using a formal system to ‘see’ that P is consistent he is not using P. But Gödel’s theorem, as developed by Gentzen, shows that the consistency of P can be proved using axioms different from P; call them P1. So one possibility is that the mathematical insight displayed in the first case is due to the fact that we are not operating with a Dopey equivalent, and in the second case that we are not operating with P, but that in both cases we are operating with some formal system or other, with some Turing-computable apparatus.
Penrose opens himself up to this sort of response by his own expansive notion of computability. As long as you can get a computer to do it, it is computable. But surely you can program a computer to make guesses about a pattern, including the consistency of its own productions, based on assessment of its accrued knowledge base. Correct guessing in such cases would be computable because a computer does it, but it would not be computable in the sense that what the computer or person asserts with confidence, sees, or knows, is deductively derived from the axioms and transformation rules. Penrose never eliminates either the possibility that what mathematicians see, they see because they are in fact using some formal system with which they unconsciously prove what they see, or the possibility that they run a program whose heuristic principles cause them to assert or see things a certain way. Computational systems include ‘top-down’ systems that come with a pre-specified program and a store of knowledge, and ‘bottom-up’ systems like the artificial neural networks that learn from experience.
Penrose has another argumentative ploy up his sleeve. Mathematicians don’t think they are following any type of unconscious algorithms when they discern mathematical truth. Either they consciously use computable principles or they just consciously see the truth of those statements that are (or might be) noncomputable in some formal system or other. Penrose admits that mathematicians might be wrong in thinking that the insight they display is noncomputable insight pure and simple, but I don’t see that he takes this possibility seriously enough. Mathematical reality exists independently of us and mathematicians are sometimes able to detect it by noncomputable insight or intuition. Penrose’s Platonism runs deep, too deep.
His ultimate target is consciousness. What mathematicians consciously understand is key to the entire argument. It is a truism of contemporary mind science, however, that only certain mental states are conscious, and that more often than not what we are conscious of is product, not process. Indeed, almost all progress in the science of the mind to date has resulted from abandoning the assumption that people are capable of giving reliable reports on, let alone knowing, how the mind works.
Penrose lacks the warrant to say that humans demonstrably use noncomputational procedures in ascertaining mathematical truth, and without this conclusion in place the rest of his project, which involves speculation about brain structures that might support noncomputable thought, is unmotivated. Penrose’s tactic is first to secure the conclusion that we humans use noncomputable techniques or skills, then to locate brain structures that could do the job. But we don’t need what we don’t need. And something not worth doing is not worth doing well.
Still Penrose persists. Where might we find noncomputable processes? Quantum physics is queer enough to have promise. The trouble is that Penrose thinks that quantum physics, as we now know it, is computable. So we will need some new noncomputable quantum phenomena. Where might we find these? Certainly not in any structure as large as a neuron. He speculates that quantum gravitational effects – quantum gravity is not known to exist anywhere in the universe – might exist in the very tiny structures called microtubules inside the skeletal structures that hold all cells together – the non-neuronal cells of single-cell paramecia as well as the neurons of mammalian brains.
The next move, and it is key, is to claim that there is direct evidence that consciousness is related to activity in the microtubules of the cytoskeleton of neurons. This evidence comes from the fact that all general anaesthetics, their different chemical structures notwithstanding, interrupt action in the microtubules and render patients unconscious. Noncomputable quantum gravity to one side, this is not a very good argument for attributing a significant causal role in generating consciousness to the microtubules. First, the argument is hardly direct. Remove a spark plug and my car won’t start. Spark plugs are causally relevant, even necessary for a car to start, but they are not sufficient; they are one among a multitude of things that need to be working properly for my car to start. Second, it is not at all clear that people under general anaesthesia are unconscious in the relevant sense. We say of the person clubbed over the head that he was rendered unconscious; and we say of people in deep sleep that they are unconscious; and we speak of people under general anaesthesia as unconscious. But saying these things doesn’t make them true.
The fellow knocked unconscious might claim to have seen stars and heard voices and had strange dreams. And it is true, but not widely known, that people are mentating in non-REM (Rapid Eye Movement) sleep as well as in REM sleep. Finally, I have attended conferences, including a splendid one in Tucson, Arizona last spring organised by Stuart Hameroff, Mr Microtubules himself, in which anaesthesiologists worried aloud about whether their patients are conscious while anaesthetised. Despite the fact that patients don’t seem to be experiencing pain, and despite the fact that under general anaesthesia, more so even than in normal sleep, memory is lousy, there are reports of dreamlike states, and even of memories of occurrences in operating rooms. The point is that if patients under general anaesthesia are unconscious in the sense that they can’t experience pain, this hardly establishes that they are not having experiences of other sorts, even if these are difficult to remember. Penrose admits that quantum gravitational effects in the microtubules are not sufficient when he acknowledges that nothing he says requires that we attribute consciousness to other animals: ‘there may well be a great deal, in addition to properly functioning cytoskeletons, that is needed to evoke a conscious state.’ Indeed, there must be more to consciousness than properly functioning cytoskeletons since zombie-like paramecia, too, have these.
In the end, Penrose’s deep Platonism leads to a physicalism that is, as I’ve said, too deep. In the excited rush to solve the problem of consciousness Penrose passes over vast and promising terrain. It is called ‘the brain’. The right sort of deep physicalism involves paying attention to the whole brain, not just to neural connectivity but to connectivity plus the exciting new discoveries being made each day about the wash of neurochemicals that are implicated in different states of mind and consciousness.
The main problem with the computational model of the mind is that it makes doing neuroscience seem less important than getting at the abstract programs that allegedly support various aspects of mentality. Ironically, Penrose’s excessive enthusiasm about quantum level phenomena lands him in the same place. It makes solving the whole mind/brain problem seem less important than getting at noncomputable quantum effects in tiny portions of brain tissue, effects that we have no overwhelming reason to think exist, and which, even if they do, shed no light whatsoever on why some systems are conscious and some not.
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