The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Oxford Landmark Science)

by Roger Penrose

Perhaps the reader is familiar with the concept of escape velocity. This is the speed which an object must attain in order to escape from some massive body. Suppose that body were the earth; then the escape velocity from it would be approximately 40 000 kilometres per hour, which is about 25 000 miles per hour. A stone which is hurled from the earth’s surface (in any direction away from the ground), with a speed exceeding this value, will escape from the earth completely (assuming that we may ignore the effects of air resistance). If thrown with less than this speed, then it will fall back to the earth. (Thus, it is not true that ‘everything that goes up must come down’; an object returns only if it is thrown with less than the escape velocity!) For Jupiter, the escape velocity is 220000 kilometres per hour, i.e. about 140000 miles per hour; and for the sun it is 2 200 000 kilometres per hour, or about 1400000 miles per hour. Now suppose we imagine that the sun’s mass were concentrated in a sphere of just one quarter of its present radius, then we should obtain an escape velocity which is twice as great as its present value; if the sun were even more concentrated, say in a sphere of one-hundredth of its present radius, then the velocity would be ten times as great. We can imagine that for a sufficiently massive and concentrated body, the escape velocity could exceed even the velocity of light! When this happens, we have a black hole.9

A black hole is when the escape velocity required is fastee than light. If we refer to light as the constant of the universe no object can go faster than light

Fig. 7.18. If the constraint WEYL = 0 is removed, then we have a high-entropy big bang also, with WEYL → ∞ there. Such a universe would be riddled with white holes, and there would be no second law of thermodynamics, in gross contradiction with experience.

White holes

Weyl curvature hypothesis.

U and R of quantum mechanics (U obeys the completely deterministic Schrödinger’s equation – called unitary evolution – and R was the probabilistic state-vector reduction that one must apply whenever an ‘observation’ is deemed to have been made).

U and R

possible type of initial singularity other than that of the big bang would be the singularity in a white hole – which, as we recall from Chapter 7, is the time-reverse of a black hole (refer back to Fig. 7.14). But we have seen that the singularities inside black holes satisfy WEYL → ∞, so for a white hole, also, we must have WEYL → ∞. But the singularity is now an initial singularity, for which WCH requires WEYL = 0. Thus WCH rules out the occurrence of white holes in our universe! (Fortunately, this is not only desirable on thermodynamic grounds – for white holes would violently disobey the second law of thermodynamics – but it is also consistent with observations! From time to time, various astrophysicists have postulated the existence of white holes in order to attempt to explain certain phenomena, but this always raises many more issues than it solves.) Note that I am not calling the big bang itself a ‘white hole’. A white hole would possess a localized initial singularity which would not be able to satisfy WEYL = 0; but the all-embracing big bang can have WEYL = 0 and is allowed to exist by WCH provided that it is so constrained.

Why white holes haven't been observed

WHEN DOES THE STATE-VECTOR REDUCE?

Skipped

The right somatosensory cortex deals with sensations from the left-hand side of the body, and the left, with the right-hand side. There is a corresponding region of the frontal lobe, lying just in front of the divison between the frontal and parietal lobes, known as the motor cortex. This is concerned with activating the movement of different parts of the body and again there is a very specific correspondence between the various muscles of the body and the regions of the motor cortex. We now have a ‘motor homunculus’ to depict this correspondence, as given in Fig. 9.4. The right motor cortex controls the left-hand side of the body, and the left motor cortex, the right-hand side. Fig. 9.2. The left-hand field of vision of both eyes is mapped to the right visual cortex and the right-hand field of vision to the left visual cortex. (View from below; note that the images on the retina are inverted.) Fig. 9.3. The ‘somatosensory homunculus’ graphically illustrates the portions of the cerebrum – just behind the division between frontal and parietal lobes – which, for various parts of the body, are most immediately concerned with the sense of touch.

It is not left eye to right cortex, it is the left field of vision in both eyes that match to the right cortex

Broca’s area is concerned with the formulation of sentences, and Wernicke’s area with the comprehension of language.

Perhaps I have minor damage to broca's area- see if its related to modafinil and inflammation

A nerve bundle called the arcuate fasciculus connects the two areas. When this is damaged, comprehension is not impaired and speech remains fluent, but comprehension cannot be vocalized.

Or, possibly this mechanism has been damaged.

Many differing views have been expressed with regard to the relation of the state of the brain to the phenomenon of consciousness. There is remarkably little consensus of opinion for a phenomenon of such obvious importance. It is clear, however, that all parts of the brain are not equally involved in its manifestation. For example, as hinted above, the cerebellum seems to be much more of an ‘automaton’ than the cerebrum. Actions under cerebellar control seem almost to take place ‘by themselves’ without one having to ‘think about’ them. While one may consciously decide to walk from one place to another, one does not often become aware of the elaborate plan of detailed muscle movements that would be necessary for controlled motion. The same may be said of unconscious reflex actions, such as the removal of one’s hand from a hot stove, which might be mediated not by the brain at all but by the upper part of the spinal column. From this, at least, one may be well inclined to infer that the phenomenon of consciousness is likely to have more to do with the action of the cerebrum than with the cerebellum or the spinal cord. On the other hand, it is very far from clear that the activity of the cerebrum must itself always impinge upon our awareness. For

Cerebellum isn't related to consciousness

as in Peter Sellers’s well-known cinema portrayal of Dr Strangelove!)

Images received by the retina are also processed in certain regions of the brain other than just the visual cortex, one of the more obscure regions involved lying in the lower temporal lobe. It seems that D. B. may have been basing his ‘guesses’ on information gained by this lower temporal region. Nothing was directly perceived consciously by the activation of these regions, yet the information was there, to be revealed only in the correctness of D. B. ’s ‘guesses’. In fact, after some training, D. B. was able to obtain a limited amount of actual awareness in respect of these regions.

An important feature of nerve transmission is that the signals are (for the most part) entirely ‘all-or-nothing’ phenomena. The strength of the signal does not vary: it is either there or it is not. This gives the action of the nervous system a digital computer-like aspect. In fact there are quite a lot of similarities between the action of a great number of interconnected neurons and the internal workings of a digital computer, with its current-carrying wires and logic gates (more about these in a moment). It would not be hard, in principle, to set up a computer simulation of the action of a given such system of neurons. A natural question arises: does this not mean that whatever the detailed wiring of the brain may be, it can always be modelled by the action of a computer?

Utterances like ‘How can you expect me to think of more than one thing at a time?’ are commonplace. Is it possible at all to keep separate things going on in one’s consciousness simultaneously? Perhaps one can keep a few things going on at once, but this seems to be more like continual flitting backwards and forwards between the various topics than actually thinking about them simultaneously, consciously, and independently. If one were to think consciously about two things quite independently it would be more like having two separate consciousnesses, even if only for a temporary period, while what seems to be experienced (in a normal person, at least) is a single consciousness which may be vaguely aware of a number of things, but which is concentrated at any one time on only one particular thing.

In line with the considerations touched upon at the end of the previous chapter, we should ask whether enough matter is disturbed by the passage of the signal that the one-graviton criterion of that chapter is met. While it is true that an impressively enormous magnification is achieved by the retina in converting the photon’s energy into a movement of mass in the actual signal – perhaps by a factor of as much as 1020 in mass moved – this mass still falls short of the Planck mass mp by a very large figure (say about 108). However, a nerve signal creates a detectable changing electric field in its surroundings (a toroidal field, with the nerve as axis, and moving along the nerve). This field could disturb the surroundings significantly, and the one-graviton criterion might be easily met within these surroundings. Thus, according to the viewpoint I have been putting forward, the procedure R could have been already effected well before we perceive the flash of light, or not, as the case may be. On this viewpoint, our consciousness is not needed in order to reduce the state-vector!

Moreover, there is a simple ‘bottom line’ reason for believing that consciousness must have some active effect, even if this effect is not one of selective advantage. For why is it that beings like ourselves should sometimes be troubled – especially when probed on the matter – by questions about ‘self? (I could almost say: ‘Why are you reading this chapter?’ or ‘Why did I feel a strong desire to write a book on this topic in the first place?’) It is hard to imagine that an entirely unconscious automaton should waste its time with such matters. Since conscious beings, on the other hand, do seem to act in this funny way from time to time, they are thereby behaving in a way that is different from the way that they would if not conscious – so consciousness has some active effect! 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! It

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.

This is me with programming trying to find recursive components

Imagine an ordinary computer program. How would it have come into being? Clearly not (directly) by natural selection! Some human computer programmer would have conceived of it and would have ascertained that it correctly carries out the actions that it is supposed to. (Actually, most complicated computer programs contain errors – usually minor, but often subtle ones that do not come to light except under unusual circumstances. The presence of such errors does not substantially affect my argument.) Sometimes a computer program might itself have been ‘written’ by another, say a ‘master’ computer program, but then the master program itself would have been the product of human ingenuity and insight; or the program might well be pieced together from ingredients some of which were the products of other computer programs. But in all cases the validity and the very conception of the program would have ultimately been the responsibility of (at least) one human consciousness.

We consciously determine the relvancy and propogation of algorithmic procedures which is perhaps encoded in genes or memes.

If we ever do discover in detail what quality it is that allows a physical object to become conscious, then, conceivably, we might be able to construct such objects for ourselves–though they might not qualify as ‘machines’ in the sense of the word that we mean it now. 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. But there may well be more to the issue of consciousness than this. Perhaps, in some way, our consciousness does depend on our heritage, and the thousands of millions of years of actual evolution that lie behind us. To my way of thinking, there is still something mysterious about evolution, with its apparent ’groping’ towards some future purpose. Things at least seem to organize themselves somewhat better than they ‘Ought’ to, just on the basis of blind-chance evolution and natural selection. It may well be that such appearances are quite deceptive. There seems to be something abou...

Let us recall the arguments given in Chapter 4 establishing Gödel’s theorem and its relation to computability. It was shown there that whatever (sufficiently extensive) algorithm a mathematician might use to establish mathematical truth – or, what amounts to the same thing,1 whatever formal system he* might adopt as providing his criterion of truth – there will always be mathematical propositions, such as the explicit Gödel proposition Pk (k) of the system (cf. p. 140), that his algorithm cannot provide an answer for. If the workings of the mathematician’s mind are entirely algorithmic, then the algorithm (or formal system) that he actually uses to form his judgements is not capable of dealing with the proposition Pk (k) constructed from his personal algorithm. Nevertheless, we can (in principle) see that Pk(k) is actually true! This would seem to provide him with a contradiction, since he ought to be able to see that also. Perhaps this indicates that the mathematician was not using an algorithm at all!

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. We must see–at least in principle – that each step in an argument can be reduced to something simple and obvious. Mathematical truth is not a horrendously complicated dogma whose validity is beyond our comprehension. It is something built up from such simple and obvious ingredients -and when we comprehend them, their truth is clear and agreed by all.

Fuck math purists

For a very fine account, I refer the reader to the slim volume The Psychology of Invention in the Mathematical Field, a classic by the very distinguished French mathematician Jacques Hadamard.

Pick this up as slim read regarding inventions

What is striking about this example (and numerous others cited by Hadamard) is that this complicated and profound idea apparently came to Poincaré in a flash, while his conscious thoughts seemed to be quite elsewhere, and that they were accompanied by this feeling of certainty that they were correct – as, indeed, later calculation proved them to be. It should be made clear that the idea itself would not be something at all easy to explain in words. I imagine that it would have taken him something like an hour-long seminar, given to experts, to get the idea properly across. Clearly it could enter Poincaré’s consciousness, fully formed, only because of the many long previous hours of deliberate conscious activity, familiarizing him with many different aspects of the problem at hand. Yet, in a sense, the idea that Poincaré had while boarding the bus was a ‘single’ idea, able to be fully comprehended in one moment! Even more remarkable was Poincaré’s conviction of the truth of the idea, so that his subsequent detailed verification of it seemed almost superfluous.

I must agree, also, that it cannot be that the unconscious mind is simply throwing up ideas at random. There must be a powerfully impressive selection process that allows the conscious mind to be disturbed only by ideas that ‘have a chance’. I would suggest that these criteria for selection – largely ‘aesthetic’ ones, of some sort – have been already strongly influenced by conscious desiderata (like the feeling of ugliness that would accompany mathematical thoughts that are inconsistent with already established general principles).

In relation to this, the question of what constitutes genuine originality should be raised. It seems to me that there are two factors involved, namely a ‘putting-up’ and a ‘shooting-down’ process. I imagine that the putting-up could be largely unconscious and the shooting-down largely conscious.

A vivid quote (Hadamard 1945, p. 16), as by Mozart, though now believed fake, nevertheless well illustrates contemporary views of his thinking: When I feel well and in a good humour, or when I am taking a drive or walking after a good meal, or in the night when I cannot sleep, thoughts crowd into my mind as easily as you could wish. Whence and how do they come? I do not know and I have nothing to do with it. Those which please me I keep in my head and hum them; at least others have told me that I do so. Once I have my theme, another melody comes, linking itself with the first one, in accordance with the needs of the composition as a whole: the counterpoint, the part of each instrument and all the melodic fragments at last produce the complete work. Then my soul is on fire with inspiration. The work grows; I keep expanding it, conceiving it more and more clearly until I have the entire composition finished in my head though it may be long. Then my mind seizes it as a glance of my eye a beautiful picture or a handsome youth. It does not come to me successively, with various parts worked out in detail, as they will later on, but in its entirety that my imagination lets me hear it.

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.

I have, myself, noticed occasions such as watching helplessly as my hand closes the car door a moment after I have noticed something within the car that I had wished to retrieve, and my willed command to stop the motion of my hand acts disturbingly slowly – too slowly to stop the closing of the door. But does this take a whole second or two? It seems unlikely to me that such a long timescale was involved. Of course, my conscious awareness of the object within the car together with my imagined ‘free willing’ of the command to stop my hand could all have occurred well after both events.

Consciousness is, after all, the one phenomenon that we know of, according to which time needs to ‘flow’ at all! The way in which time is treated in modern physics is not essentially different from the way in which space is treated* and the ‘time’ of physical descriptions does not really ‘flow’ at all; we just have a static-looking fixed ‘space–time’ in which the events of our universe are laid out!

Recall your thought of how time was measured when you were a kid: How could time be encoded in atoms