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Consciousness. Inspiration and Invention. Penrose, Emperor’s New Mind, page 418 Poincar é ’s experience:

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Penrose, Emperor’s New Mind, page 418

  • Poincaré’s experience:
  • … I left Caen, where I was living, to go on a geologic excursion under the auspices of the School of Mines. The incidents of the travel made me forget my mathematical work. Having reached Coutances, we entered an omnibus to go to some place or other. At the moment when I put my foot on the step, the idea came to me, without anything in my former thoughts seeming to have paved the way for it, that the transformations I had used to define the Fuchsian functions were identical with those of non-Euclidean geometry. I did not verify the idea; I should not have had time, as upon taking my seat in the omnibus, I went on with a conversation already commenced, but I felt a perfect certainty. On my return to Caen, for convenience sake, I verified the result at my leisure.

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 subsequent detailed verification of it seemed almost superfluous.


Penrose page 423, speaking of Mozart:

  • When I feel well and in a good humor, 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.

Penrose: It seems to me that this accords with a putting-up/shooting-down scheme of things. The putting-up seems to be unconscious (‘I have nothing to do with it’) though, no doubt, highly selective, while the shooting-down is the conscious arbiter of taste (‘those which please me I keep …’). The globality of inspirational thought is particularly remarkable in Mozart’s quotation (‘it does not come to me successively … but in its entirety’) and also in Poincaré’s (‘I did not verify the idea; I should not have had time’).

non verbality of thought
Non-verbality of thought
  • Letter from Einstein: 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.

Quoting Francis Galton, the geneticist:

  • 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 sudden, of being often very obscure through mere verbal maladriotness, and not through want of clearness of perception.

Quoting Hadamard:

  • 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 in words’.
inspiration in animals
Inspiration in animals
  • Lorenz describes a chimpanzee in a room which contains a banana suspended from the ceiling just out of reach, and a box elsewhere in the room:
  • The matter gave him no peace, and he returned to it again and 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. Completely assured of his success, he pushed the box below the banana. No man watching him could doubt the existence of a genuine ‘Aha’ experience in anthropoid apes.
consciousness and language
Consciousness and Language
  • Penrose 383-4:
  • Many philosophers and psychologists seem to take the view that human consciousness is very much bound up with human language. Accordingly, it is only by virtue of our linguistic abilities that we can attain a subtlety of thinking that is the very hallmark of our humanity ... From this viewpoint, our language is taken to be the key ingredient of our possession of consciousness.
Now we must recall that our language centres are (in the vast majority of people) just on the left-hand sides of our brains … The viewpoint just expressed would seem to imply that consciousness is something to be associated only with the left cerebral cortex and not with the right! Indeed, this appears to be the opinion of a number of neurophysiologists….
Penrose, page 425: It should be clear to the reader … why I find that viewpoint totally unacceptable. … there can be no doubt of the high level of consciousness required for mathematical thought. Whereas analytical thinking seems to be mainly the province of the left side of the brain, geometrical thinking is often argued to be the right side’s, so it is a very reasonable guess that a good deal of conscious mathematical activity actually does take place on the right!
split brain experiments
Split Brain Experiments
  • Penrose, p. 384: In relation to this, I should mention a remarkable collection of observations concerning human subjects (and animals) who have had their corpus callosums completely severed, so that the left and right hemispheres of the cerebral cortex are unable to communicate with one another.
Penrose, p. 385: What is most striking about these split-brain subjects is that the two sides seem to behave as virtually independent individuals, each of which may be communicated with separately by the experimenter – although communication is more difficult, and on a more primitive level, with the right hemisphere than with the left, owing to the right’s lack of verbal ability.
One is tempted to raise the issue: do we have two separately conscious individuals both inhabiting the same body? This question has been the subject of much controversy. …Donald Wilson and his coworkers examined a split-brain subject, referred to as ‘P.S.’. After the splitting operation, only the left hemisphere could speak but both hemispheres could comprehend speech; later the right hemisphere learned to speak also! Evidently both hemispheres were conscious. Moreover, they appeared to be separately conscious, because they had different likes and desires. For example, the left hemisphere described that its wish was to be a draughtsman and the right, a racing driver!
Pages 385-386: I, myself, simply cannot believe the common claim that ordinary human language is necessary for thought or for consciousness. … I therefore side with those who believe, generally, that the two halves of a split-brain subject can be independently conscious.
  • Presumably, before the operation each split-brain subject possessed only a single consciousness; but afterwards there are two! In some way, the original single consciousness has bifurcated.
  • The puzzle would be further exacerbated if somehow the two consciousnesses could later be brought together again.
consciousness and time
Consciousness and Time
  • Penrose pp. 439-442: A number of human subjects volunteered to have electrical signals recorded at a point on their heads, and they were asked to flex the index fingers of their right hands suddenly at various times entirely of their own choosing. … there is a gradual build-up of recorded electric potential for a full second, or perhaps even up to a second and a half, before the finger is actually flexed. This seems to indicate that the conscious decision process takes over a second in order to act!
This may be contrasted with the much shorter time that it takes to respond to an external signal if the mode of response has been laid down beforehand. For example, instead of it being ‘freely willed’, the finger flexing might be in response to the flash of a light signal. In that case a reaction time of about one-fifth of a second is normal, which is about five times faster than the ‘willed’ action ….
In the second experiment, Benjamin Libet … with Bertram Feinstein …tested subjects who had to have brain surgery for some reason unconnected with the experiment and who consented to having electrodes placed at points in the brain … . When a stimulus was applied to the skin of these patients, it took about half a second before they were consciously aware of that stimulus, despite the fact that the brain itself would have received the signal of the stimulus in only about a hundredth of a second, and a pre-programmed ‘reflex’ response to such a stimulus could be achieved by the brain in about a tenth of a second. Moreover, … there would be the subjective impression by the patients themselves that no delay had taken place at all in their becoming aware of the stimulus!
Conscious perception of a stimulus can be masked by an event about a quarter of a second later.
  • However, one does not seem to be ‘aware’ of such a long time-delay in one’s perceptions. [Perhaps] the ‘time’ of all one’s perceptions is actually delayed by about a half a second from the ‘actual time’ …. The subject does appear to refer the perception of the skin touching backwards in time by about half a second. The cortical stimulation … seems not to be referred back in this way.
The apparent implication of these two experiments taken together is that consciousness cannot even be called into play at all in response to an external event, if that response is to take place within a couple of seconds or so!
  • … we appear to be driven to the conclusion that we act entirely as ‘automatons’ when we carry out any action that would take less than a second or two in which to modify a response.
Page 443: I suggest that we may actually be going badly wrong when we apply the usual physical rules for time when we consider consciousness!
  • Page 445: Suppose that there is even something vaguely teleological about the effects of consciousness, so that a future impression might affect a past action.
  • Recall my proposal that consciousness, in essence, is the ‘seeing’ of a necessary truth; and that it may represent some kind of actual contact with Plato’s world of ideal mathematical concepts.