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January 7 - January 20, 2019
There is also the question of what one means by the term ‘intelligence’. This, after all, is what the AI people are concerned with, rather than the perhaps more nebulous issue of ‘consciousness’. Alan Turing (1950), in his famous paper (cf. Chapter 1, p. 7) did not refer so much directly to ‘consciousness’, but to ‘thinking’, and the word ‘intelligence’ was in the title.
In my own way of looking at things, the question of intelligence is a subsidiary one to that of consciousness. I do not think that I would believe that true intelligence could be actually present unless accompanied by consciousness. On the other hand, if it does turn out that the AI people are eventually able to simulate intelligence without consciousness being present, then it might be regarded as unsatisfactory not to define the term ‘intelligence’ to include such simulated intelligence. In that case the issue of ‘intelligence’ would not be my real concern here. I am primarily concerned with
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When I assert my own belief that true intelligence requires consciousness, I am implicitly suggesting (since I do not believe the strong-AI contention that the mere enaction of an algorithm would evoke consciousness) that intelligence cannot be properly simulated by algorit...
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For I shall shortly argue strongly (see, particularly, the discussion of mathematical thought given three sections hence, on p. 538) that there must be an essentially non-algorithmic ingredient in the action of consciousness.
Second, consider the ruthless process of natural selection. View this process in the light of the fact that, as we have seen in the last chapter, not all of the activity of the brain is directly accessible to consciousness. Indeed, the ‘older’ cerebellum – with its vast superiority in local density of neurons – seems to carry out very complex actions without consciousness being directly involved at all. Yet Nature has chosen to evolve sentient beings like ourselves, rather than to remain content with creatures that might carry on under the direction of totally unconscious control mechanisms.
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Of course there would be no problem about deliberately programming a computer to seem to behave in this ridiculous way (e.g. it could be programmed to go around muttering ‘Oh dear, what is the meaning of life? Why am I here? What on earth is this “self” that I feel?’). But why should natural selection bother to favour such a race of individuals, when surely the relentless free market of the jungle should have rooted out such useless nonsense long ago!
Let us accept that the presence of consciousness in a creature is actually of some selective advantage to that creature. What, specifically, might that advantage be? One view that I have heard expressed is that awareness might be of an advantage to a predator in trying to guess what its prey would be likely to do next by ‘putting itself in the place’ of that prey. By imagining itself to be the prey, it could gain an advantage over it.
Of course, it is difficult to see how the random procedures of natural selection could have been clever enough to give an automaton predator a complete copy of the prey’s program. This would sound more like espionage than natural selection! And a partial program (in the sense of a piece of Turing machine ‘tape’, or something approximating a Turing machine tape) would hardly be of much selective advantage to the predator. The unlikely possession of the whole tape, or at least some entire self-contained part of it would seem to be necessary.
I therefore suggest that, whereas unconscious actions of the brain are ones that proceed according to algorithmic processes, the action of consciousness is quite different, and it proceeds in a way that cannot be described by any algorithm.
My own line of reasoning has been that unconscious processes could well be algorithmic, but at a very complicated level that is monstrously difficult to disentangle in detail. The fully conscious thinking that can be rationalized as something entirely logical can again (often) be formalized as something algorithmic, but this is at an entirely different level.
Indeed, algorithms, in themselves, never ascertain truth! It would be as easy to make an algorithm produce nothing but falsehoods as it would be to make it produce truths. One needs external insights in order to decide the validity or otherwise of an algorithm (more about this later). I am putting forward the argument here that it is this ability to divine (or ‘intuit’) truth from falsity (and beauty from ugliness!), in appropriate circumstances, that is the hallmark of consciousness.
Why do I say that the hallmark of consciousness is a non-algorithmic forming of judgements? Part of the reason comes from my experiences as a mathematician. I simply do not trust my unconscious algorithmic actions when they are inadequately paid attention to by my awareness.
The same sort of thing is continually happening at all levels of mathematical thought. One often strives for algorithms, when one does mathematics, but the striving itself does not seem to be an algorithmic procedure. Once an appropriate algorithm is found, the problem is, in a sense, solved.
NATURAL SELECTION OF ALGORITHMS?
If we suppose that the action of the human brain, conscious or otherwise, is merely the acting out of some very complicated algorithm, then we must ask how such an extraordinarily effective algorithm actually came about. The standard answer, of course, would be ‘natural selection’.
As creatures with brains evolved, those with the more effective algorithms would have a better tendency to survive and therefore, on the whole, had more progeny. These progeny also tended to carry more effective algorithms than their cousins, since they inherited the ingredients of these better algorithms from their parents; so gradually the algorithms improved – not necessarily steadily, since there could have been considerable fits and starts in their evoluti...
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But I do not see how natural selection, in itself, can evolve algorithms which could have the kind of conscious judgements of the validity of other algorithms that we seem to have.
The products of natural selection are indeed astonishing. The little knowledge that I have myself acquired about how the human brain works – and, indeed, any other living thing – leaves me almost dumbfounded with awe and admiration.
One could imagine that these objects could have a tremendous advantage over us, since they could be designed specifically for the task at hand, namely to achieve consciousness. They would not have to grow from a single cell. They would not have to carry around the ‘baggage’ of their ancestry (the old and ‘useless’ parts of the brain or body that survive in ourselves only because of the ‘accidents’ of our remote ancestry).
One might imagine that, in view of these advantages, such objects could succeed in actually superseding human beings, where (in the opinions of such as myself) the algorithmic computers are doomed to subservience.
If we can see that the role of consciousness is non-algorithmic when forming mathematical judgements, where calculation and rigorous proof constitute such an important factor, then surely we may be persuaded that such a non-algorithmic ingredient could be crucial also for the role of consciousness in more general (non-mathematical) circumstances.
Thus, we are driven to the conclusion that the algorithm that mathematicians actually use to decide mathematical truth is so complicated or obscure that its very validity can never be known to us.
But this flies in the face of what mathematics is all about! The whole point of our mathematical heritage and training is that we do not bow down to the authority of some obscure rules that we can never hope to understand.
As a mathematician, I am especially concerned with inspirational and original thought in others who are mathematicians, but I imagine that there is a great deal in common between mathematics and the other sciences and arts.
It seems clear to me that the importance of aesthetic criteria applies not only to the instantaneous judgements of inspiration, but also to the much more frequent judgements that we make all the time in mathematical (or scientific) work. Rigorous argument is usually the last step! Before that, one has to make many guesses, and for these, aesthetic convictions are enormously important -always constrained by logical argument and known facts.
The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements of thought are certain signs and more or less clear images which can be ‘voluntarily’ reproduced and combined . . . The above mentioned elements are, in my case, of visual and some muscular type. Conventional words or other signs have to be sought for laboriously only in a second stage, when the mentioned associative play is sufficiently established and can be reproduced at will.
It is a serious drawback to me in writing, and still more in explaining myself, that I do not think as easily in words as otherwise. It often happens that after being hard at work, and having arrived at results that are perfectly clear and satisfactory to myself, when I try to express them in language I feel that I must begin by putting myself upon quite another intellectual plane. I have to translate my thoughts into a language that does not run very evenly with them. I therefore waste a vast deal of time in seeking appropriate words and phrases, and am conscious, when required to speak on a
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I insist that words are totally absent from my mind when I really think and I shall completely align my case with Galton’s in the sense that even after reading or hearing a question, every word disappears the very moment that I am beginning to think it over; and I fully agree with Schopenhauer when he writes, ‘thoughts die the moment they are embodied by words’.
I quote these examples because they very much accord with my own thought-modes. Almost all my mathematical thinking is done visually and in terms of non-verbal concepts, although the thoughts are quite often accompanied by inane and almost useless verbal commentary, such a...
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Before leaving the topic of the importance of verbalization to consciousness, I should address the question, raised briefly earlier, of whether non-human animals can be conscious. It seems to me that people sometimes rely on animals’ inability to speak as an argument against their having any appreciable consciousness – and, by implication, against their having any ‘rights’.
The matter gave him no peace, and he returned to it again. Then, suddenly – and there is no other way to describe it – his previously gloomy face ‘lit up’. His eyes now moved from the banana to the empty space beneath it on the ground, from this to the box, then back to the space, and from there to the banana. The next moment he gave a cry of joy, and somersaulted over to the box in sheer high spirits.
Note that, just as with Poincaré’s experience as he boarded the omnibus, the chimpanzee was ‘completely assured of his success’ before he had verified his idea. If I am right that such judgements require consciousness, then there is evidence here, also, that non-human animals can indeed be conscious.
My own viewpoint is different from this, since I believe that (conscious) minds are not algorithmic entities. But I am somewhat disconcerted to find that there are a good many points in common between the strong-AI viewpoint and my own.
The good ones are simply much too good to be the survivors of ideas that have arisen in that random way. There must, indeed, be some deep underlying reason for the accord between mathematics and physics, i.e. between Plato’s world and the physical world.
I have been attempting to expound, that non-algorithmic action ought to have a role within the physical world of very considerable importance. I am suggesting that this role is intimately bound up with the very concept of ‘mind’.
So far I have said little about the question of ‘free will’ which is normally taken to be the fundamental issue of the active part of the mind–body problem. Instead, I have concentrated on my suggestion that there is an essential non-algorithmic aspect to the role of conscious action. Normally, the issue of free will is discussed in relation to determinism in physics.
This would imply that the future would not be computable from the present, even though it might be determined by it. I have tried to be clear in distinguishing the issue of computability from that of determinism,
However, it is very hard to believe that this kind of classical uncertainty can be what allows us our (illusion of?) free will. The future behaviour would still be determined, right from the big bang, even though we would be unable to calculate it (cf. p. 225
According to strong determinism, it is not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time.
‘What I’m really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all!’ (letter to Ernst Strauss; see Kuznetsov 1977, p. 285).
How important is consciousness for the universe as a whole? Could a universe exist without any conscious inhabitants whatever? Are the laws of physics specially designed in order to allow the existence of conscious life? Is there something special about our particular location in the universe, either in space or in time? These are the kinds of question that are addressed by what has become known as the anthropic principle.
Normally, when Nature seeks out a crystalline configuration, she is searching for a configuration of lowest energy (taking the background temperature to be zero).
Let me now carry these speculations further, and ask whether they might have any relevance to the question of brain functioning. The most likely possibility, as far as I can see, is in the phenomenon of brain plasticity.
Recall that the brain is not really quite like a computer, but it is more like a computer which is continually changing.
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The growth of a crystal or quasicrystal is strongly influenced by the concentrations of the appropriate atoms and ions that are in its neighbourhood. Similarly, one might envisage that the growth or contraction of families of dendritic spines could well be as much influenced by the concentrations of the various neurotransmitter substances that might be around (such as might be affected by emotions).
Listen to the quadruple fugue in the final part of J. S. Bach’s Art of Fugue. No-one with a feeling for Bach’s music can help being moved as the music stops after ten minutes of performance, just after the third theme enters. The composition as a whole still seems somehow to be ‘there’, but now it has faded from us in an instant.
Would he have needed to play it over to himself in its entirety in his mind, at the normal pace of a performance, trying it again and again, and yet again, as various different improvements came to him?
People might suppose that a mathematical proof is conceived as a logical progression, where each step follows upon the ones that have preceded it. Yet the conception of a new argument is hardly likely actually to proceed in this way.
In this book I have presented many arguments intending to show the untenability of the viewpoint – apparently rather prevalent in current philosophizing – that our thinking is basically the same as the action of some very complicated computer.
Is it not ‘obvious’ that mere computation cannot evoke pleasure or pain; that it cannot perceive poetry or the beauty of an evening sky or the magic of sounds; that it cannot hope or love or despair; that it cannot have a genuine autonomous purpose?
