In the last chapter of his book “The Emperor’s New Mind”, Roger Penrose draws on his scientific career to offer insights into the spontaneous, aesthetic and non-algorithmic nature of mathematical insight, the non-verbal thought process of the scientist, and other topics related to what he calls the “physics of the mind”. Many of his remarks chime quite well with corresponding observations made by Sri Aurobindo and the Mother on the nature of the thought process, as we see in this article.
New Ideas occur during mental silence
It has been the experience of many scientists that flashes of new insight occur when the mind has stopped thinking about the difficult problem and is either silent or dwelling on mundane issues. They have also found that the flash of insight often carries an unmistakable sign of certitude which is confirmed by later proof and calculation. In the book, Penrose relates an anecdote from his professional career regarding this phenomenon:
…Probably I would be just beginning to think about a problem that I had set aside for a while. The many hard hours of deliberate conscious activity would certainly be necessary, and sometimes it would take a while to re-acquaint myself with the problem. But the experience of an idea coming ‘in a flash’, under such circumstances- together with a strong feeling of conviction as to its validity- is not unknown to me.
It is perhaps worth relating a particular example of this, which has an additional curious point of interest. In the autumn of 1964, I had been worrying about the problem of black-hole singularities.
[…] A colleague (Ivor Robinson) had been visiting from the USA and he was engaging me in voluble conversation on a quite different topic as we walked down the street approaching my office in Birkbeck College in London. The conversation stopped momentarily as we crossed a side road, and resumed again at the other side. Evidently, during those few moments, an idea occurred to me, but then the ensuing conversation blotted it from my mind!
Later in the day, after my colleague had left, I returned to my office. I remember having an odd feeling of elation that I could not account for. I began going through in my mind all the various things that had happened to me during the day, in an attempt to find what it was that had caused this elation. After eliminating numerous inadequate possibilities, I finally brought to mind the thought that I had had while crossing the street- a thought which had momentarily elated me by providing the solution to the problem that had been milling around at the back of my head! Apparently, it was the needed criterion that I subsequently called a ‘trapped surface’ and then it did not take me long to form the outline of a proof of the theorem that I had been looking for. Even so, it was some while before the proof was formulated in a completely rigorous way, but the idea that I had had while crossing the street had been the key. 
Penrose’s experience of receiving a flash of insight when the conversation had stopped aligns well with Sri Aurobindo’s observation that inspiration is an “external thought” which slips into the human mind when it has fallen silent. We seldom realize that all thoughts come from outside, out of which we retain only the ideas which are in congruence with our personality.
As a disciple, Satprem, elucidated in his book, the Adventures of Consciousness:
Satprem: …The intellect is an absurdly overactive part of the nature; it always thinks that nothing can be well done unless it puts its finger into the pie and therefore it instinctively interferes with the inspiration, blocks half or more than half of it and labours to substitute its own inferior and toilsome productions for the true speech and rhythm that ought to have come. The poet labours in anguish to get the one true word, the authentic rhythm, the real divine substance of what he has to say, while all the time it is waiting complete and ready behind.
But effort helps, the disciple protested again, and by dint of beating one’s brains, the inspiration comes. Exactly! When any real effect is produced, it is not because of the beating and the hammering, but because an inspiration slips down between the raising of the hammer and the falling and gets in under cover of the beastly noise .
In another conversation, Sri Aurobindo explained that (subtle thought) images are all around us, but we can’t tell the difference because they get imperceptibly appropriated by the mind:
Pavitra: If the images are all around us, how is it that they do not come in our mind?
Sri Aurobindo: They come often in man’s mind but he believes them to be his own thoughts. Moreover one must have something that corresponds to them, otherwise they make no impression and do not come out of the subconscient. But once you begin to open, images arise more frequently and you need to discriminate among them .
Global and Aesthetic nature of inspired thought
Further on, Penrose relates that the flashes of illumination that lead to the right solution usually display a preternatural sense of beauty and universality. The scientist finds beauty, albeit of a more austere kind, when he or she chances upon a simple new law or an enigmatic equation which displays a striking symmetry and unites disparate and unrelated phenomena. Let us hear in the words of Penrose himself:
…The above anecdote brings me to another issue concerning inspiration and insight, namely that aesthetic criteria are enormously valuable in forming our judgements. In the arts, one might say that it is aesthetic criteria that are paramount. Aesthetics in the arts is a sophisticated subject, and philosophers have devoted lifetimes to its study. It could be argued that in mathematics and the sciences, such criteria are merely incidental, the criterion of truth being paramount.
However, it seems to be impossible to separate one from the other when one considers the issues of inspiration and insight.
My impression is that the strong conviction of the validity of a flash of inspiration (not 100 per cent reliable, I should add, but at least far more reliable than just chance) is very closely bound up with its aesthetic qualities. A beautiful idea has a much greater chance of being a correct idea than an ugly one. At least that has been my own experience, and similar sentiments have been expressed by others (of. Chandrasekhar 1987). For example, Hadamard (1945, p. 31) writes: it is clear that no significant discovery or invention can take place without the will of finding. But with Poincare, we see something else, the intervention of the sense of beauty playing its part as an indispensable means of finding.
We have reached the double conclusion: that invention is choice that this choice is imperatively governed by the sense of scientific beauty.
Dirac (1982), for example, is unabashed in his claim that it was his keen sense of beauty that enabled him to divine his equation for the electron (the “Dirac equation’ alluded to on p. 373), while others had searched in vain.
I should mention another striking feature of inspirational thought, namely its global character. Poincare’s anecdote above (omitted from this excerpt) was a striking example, since the idea that came into his mind in a fleeting moment would have encompassed a huge area of mathematical thought. Perhaps more immediately accessible to the nonmathematical reader (though no more comprehensible, no doubt) is the way that (some) artists can keep the totality of their creations in mind all at once.
[The musician Mozart said]…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’s remarks on the beauty and universality of scientific insight are in accord with the gradations of the universal mind lucubrated by Sri Aurobindo in considerable detail in his writings. While Penrose believes that these flashes of inspiration emerge from the subconscious, Sri Aurobindo explained that they actually descend from the universal planes of the Superconscient which are also touched by Yogis during heightened periods of meditation. In his works, Sri Aurobindo delineated the following planes of the mind: ordinary mind, higher mind, illumined mind, intuitive mind, overmind and supermind, each representing a higher “frequency” of consciousness. As we become capable of greater degrees of mental silence, our mind comes into contact with these higher planes of consciousness and imbibes their greater global and aesthetic character. The scientist unwittingly rises to these planes during deep contemplation, while the Yogi attains and unites with them through meditation.
A brief exposition of these planes of the universal mind will be useful in clarifying their scientific application.
The ordinary mind operates in a sequential manner, plodding through the thought images one at a time, engaging in a process of inference, deduction, discrimination and abstraction until it settles on a new conclusion. In its memory, it holds an image of the world which was formed via the senses. People whose minds operate at this level rarely get any breakthrough idea or scientific insight because they just can’t “see” deeper or far enough.
The Higher mind is the first step out of this ignorance. It is a mind whose “most characteristic movement is a mass ideation, a system or totality of truth-seeing at a single view; the relations of idea with idea, of truth with truth are not established by logic but pre-exist and emerge already self-seen in the integral whole.” . At this level, one is capable of holding many ideas in the mind and seeing their relative linkages and discerning their universal application.
The Illumined Mind is a plane not of higher thought but of spiritual light. The individual mind which has ascended to this level works not by thought but by vision. As Sri Aurobindo wrote, “The human mind, which relies mainly on thought, conceives that to be the highest or the main process of knowledge, but in the spiritual order thought is a secondary and a not indispensable process… A consciousness that proceeds by sight, the consciousness of the seer, is a greater power for knowledge than the consciousness of the thinker.” .
One step higher is the Intuitive Mind, where there is contact between the consciousness of the subject and the object. The mind which reaches this plane gains new knowledge through a “revealing flash”. This close perception is neither sight nor conception, writes Sri Aurobindo, but the result of a “penetrating and revealing touch which carries in it sight and conception as part of itself or as its natural consequence” . In scientific terms, this is the ray of light which brings the oft-startling breakthrough idea.
It is not necessary in this article to expound on the Overmind and the Supermind, because scientists rarely ascend to that level. The aesthetic and global character of scientific insight is sufficiently represented by the action of the Higher Mind, the Illumined Mind and the Intuitive Mind.
The scientist thinks in non-verbal fashion
Penrose also muses on the non-verbal nature of the scientist’s thought process. Scientists, he observes, rarely think in words; they contemplate by creating and manipulating images in their mind. Some scientists are highly visual while others think more analytically. They do not hold the same image of a problem in their minds, yet they are capable of understanding each other. Penrose writes:
One of the major points that Hadamard makes in his study of creative thinking is an impressive refutation of the thesis, so often still expressed, that verbalization is necessary for thought. One could hardly do better than repeat a quotation from a letter he received from Albeit Einstein on the matter:
“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.”
The eminent geneticist Francis Galton is also worth quoting:
“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.”
No doubt different people think in very different ways as has certainly been my own experience, even just amongst mathematicians. The main polarity in mathematical thinking seems to be analytical versus geometric. It is interesting that Hadamard considered himself to be on the analytical side, even though he used visual rather than verbal images for his mathematical thinking. As for myself, I am very much on the geometrical end of things, but the spectrum amongst mathematicians generally is a very broad one.
A common experience, when some colleague would try to explain some piece of mathematics to me, would be that I should listen attentively, but almost totally uncomprehending of the logical connections between one set of words and the next. However, some guessed image would form in my mind as to the ideas that he was trying to convey formed entirely on my own terms and seemingly with very little connection with the mental images that had been the basis of my colleague’s own understanding -and I would reply. Rather to my astonishment, my own remarks would usually be accepted as appropriate, and the conversation would proceed to and fro in this way. It would be clear, at the end of it, that some genuine and positive communication had taken place.
How is it that mathematical ideas can be communicated in this way? I imagine that whenever the mind perceives a mathematical idea, it makes contact with Plato’s world of mathematical concepts. (Recall that according to the Platonic viewpoint, mathematical ideas have an existence of their own, and inhabit an ideal Platonic world, which is accessible via the intellect only; of. pp. 127, 205. ) When one ‘sees’ a mathematical truth, one’s consciousness breaks through into this world of ideas, and makes direct contact with it (‘accessible via the intellect’). I have described this ‘seeing’ in relation to Godel’s theorem, but it is the essence of mathematical understanding. When mathematicians communicate, this is made possible by each one having a direct route to truth, the consciousness of each being in a position to perceive mathematical truths directly, through this process of ‘seeing’.
(Indeed, often this act of perception is accompanied by words like “Oh, I see’!) Since each can make contact with Plato’s world directly, they can more readily communicate with each other than one might have expected. The mental images that each one has, when making this Platonic contact, might be rather different in each case, but communication is possible because each is directly in contact with the same externally existing Platonic world! .
Roger Penrose is what they call a “Platonist”. Platonism is a philosophy which believes that all objective knowledge pre-exists in a higher external realm. This concept was first articulated by Plato and variations of the idea have been enunciated by the Greek Stoics (via “lekton”), Bernard Bolzano (via his “Wahrheiten an sich” or “truth in itself”), Gottlob Frege (through his Drittes Reich or third realm) and Karl Popper (with his three worlds theory).
Sri Aurobindo’s theory of the mind is different. It is based on the Vedantic model of consciousness. According to this worldview, the Universe consists of seven planes of varying gradations of consciousness. A human being is not just a physical body but actually consists of five concentric sheaths of consciousness much like the rings of an onion which are held together by the central psychic being. Man is said to be the microcosm of the Universe because for every universal plane of consciousness, there is a corresponding sheath in the human being. It is through this one-to-one correspondence that the commerce of thoughts, desires and cells occurs between the individual and the Universe at the mental, vital and physical level.
Despite these differences, we find that Penrose’s musings on the non-verbal nature of thought and the variations through which the individual mind imbibes abstract ideas concur felicitously with insights offered by Sri Aurobindo and the Mother on the same topics.
Penrose said above that “When one ‘sees’ a mathematical truth, one’s consciousness breaks through into this world of ideas, and makes direct contact with it (‘accessible via the intellect’).” The Mother said something similar:
Question, Sweet Mother, how are our thoughts created by the forces of the universal Mind?
Mother: Because the forces of the universal Mind enter into our heads. We are bathed in forces, we are not aware of it. We are not something enclosed in a bag and independent from the rest: all forces, all vibrations, all movements enter into us and pass through us. And so we have a certain mental force held in, that is to say, ready to be used by the formative or creative mental power. These are, as it were, free forces. As soon as a thought coming from outside or a force or movement enters our consciousness, we give it a concrete form, a logical appearance and all kinds of precise details; but in fact all this belongs to a domain one is rarely conscious of.
But this is not a special instance which occurs only from time to time: it is something constant. If a current of force is passing, with a particular thought formation, one sees it passing from one into another, and in each one it forms a kind of centre of light or force which keeps the imprint — more or less pure, more or less clear, more or less mixed — of the initial current; and the result is what we call “our” thought.
But our thought is something which hardly exists. It can be “our” thought only if, instead of being like a public place as we generally are in our normal state — we are like a public place and all the forces pass there, come and go, enter, depart, jostle each other and even quarrel — if instead of being like that, we are a concentrated consciousness, turned upwards in an aspiration, and open beyond the limits of the human mind to something higher; then, being open like this brings down that higher something across all the layers of reality, and this something may enter into contact with our conscious brain and take a form there which is no longer the creation of a universal force or a personal mind stronger than ours, but the direct expression and creation of a light which is above us, and which may be a light of the highest kind if our aspiration and opening allow it. That is the only case in which one can say that the thought is our own. Otherwise, all the rest is simply a passing notation: we note down, we invest a force with words, a force that’s altogether universal and collective, which enters, goes out, moves and passes freely from one person to another .
Penrose also said with reference to differences in individual minds that the “main polarity in mathematical thinking seems to be analytical versus geometric”. In the Adventures of Consciousness, Satprem describes how the same thought form can get imbibed differently by individuals based on differences in their mental makeup:
…But then, asked a disciple, if it is not our own mind that thinks, if thoughts come from outside, how is it that there is such a difference between one person’s thoughts and another‘s? First of all, replied Sri Aurobindo, these thought-waves, thought-seeds or thought-forms or whatever they are, are of different values and come from different planes of consciousness. And the same thought substance can take higher or lower vibrations according to the plane of consciousness through which the thoughts come in (e.g. thinking mind, vital mind, physical mind, subconscient mind) or the power of consciousness which catches them and pushes them into one man or another. Moreoever there is a stuff of mind in each man and the incoming thought uses that for shaping itself or translating itself (transcribing we usually call it), but the stuff is finer or coarser, stronger or weaker, etc., etc., in one mind than in another. Also there is a mind-energy actual or potential in each which differs and this mind-energy in its recipience of the thought can be luminous or obscure, sattwic (serene), rajasic (impassioned) or tamasic (inert) with consequences which vary in each case .
The value of mathematical effort
If all new ideas are the result of some higher inspiration, what is the point in labouring hard and investigating alternative approaches to a problem? Why not just wait for the inspiration to strike? Penrose observes that the goal of mathematical discovery is to broaden the mind so as to enhance the contact with the Platonic realm where mathematical truth pre-exists :
… the mind is always capable of this direct contact (with the Platonic world of abstract ideas). But only a little may come through at a time. Mathematical discovery consists of broadening the area of contact. Because of the fact that mathematical truths are necessary truths, no actual ‘information’, in the technical sense, passes to the discoverer. All the information was there all the time. It was just a matter of putting things together and ‘seeing’ the answer! This is very much in accordance with Plato’s own idea that (say mathematical) discovery is just a form’ of remembering’. Indeed, I have often been struck by the similarity between just not being able to remember someone’s name, and just not being able to find the right mathematical concept. In each case, the sought-for concept is in a sense already present in the mind, though this is a less usual form of words in the case of an undiscovered mathematical idea .
Penrose’s remarks are in congruence with the advice that the Mother gave once to a child. She told him that the real value of mathematical work lies in its ability to crystallise the mental power so as to make the mind adept at receiving higher inspiration.
Question: (Another child) For a mathematical problem, sometimes the solution comes quickly, sometimes it takes too long.
Mother: Yes, it is exactly that: it depends on the degree of concentration. If you observe yourself, you will notice this quite well: when it does not come, it is because of a kind of haziness in the brain, something cloudy, like a fog somewhere, and then you are there as in a dream. You push forward trying to find it, and it is as though you were pushing into cotton-wool, you do not see clearly there; and so nothing comes. You may remain in that state for hours.
Concentration consists precisely in removing the cloud. You gather together all the elements of your intelligence and fix them on one point, and then you do not even try actively to find the thing. All that you do is to concentrate in such a way as to see only the problem – but seeing not only its surface, seeing it in its depth, what it conceals. If you are able to gather together all your mental energies, bringing them to a point which is fixed on the enunciation of the problem, and you stay there, fixed, as though you were about to drill a hole in the wall, all of a sudden it will come. And this is the only way. If you try: Is it this, is it that, is it this, is it that?.. You will never find anything or else you will need hours. You must get your mental forces to a point with strength enough to pierce through the words and strike upon the thing that is behind. There is a thing to be found – find it. […]
The usefulness of work is nothing else but that: to crystallise this mental power. For, what you learn (unless you put it in practice by some work or deeper studies), half of what you learn, at least, will vanish, disappear with time. But it will leave behind one thing: the capacity of crystallising your thought, making something clear out of it, something precise, exact and organised. And that is the true usefulness of work: to organise your cerebral capacity .
As we can see, the practical observations on the human mind made by a distinguished scientist like Roger Penrose can be used to illustrate and illumine the insights obtained through Yoga by Sri Aurobindo and the Mother.
Check out the article How does the brain absorb new ideas? which juxtaposes anecdotes from the lives of scientists like Richard and Joan Feynman, Stanislav Ulam and Sofia Kovalevskaya with corresponding insights of the Mother.
The article All thoughts come from outside dwells further on commerce between the individual and the universal mind as expounded by Sri Aurobindo and the Mother.
For further details on the planes of the mind that I briefly touched upon above, see Satprem’s Adventures of Consciousness (Chapter 12) or Sri Aurobindo’s Life Divine (chapter on “The Ascent to the Supermind”).
Other related articles are listed in the “Related Posts” section below
- Roger Penrose. The Emperor’s New Mind, Oxford ; New York : Oxford University Press, 1989. pp. 523-583
- Satprem, Adventures of Consciousness, Chap 16, Man A Transitional Being.
- Pavitra, Conversation with Sri Aurobindo, Monday, July 26, 1926
- Sri Aurobindo. The Life Divine, CWSA vol. 21-22, p 975
- Ibid., pp. 978-981.
- Collected Works of the Mother, vol. 8, pp. 344-345.
- Satprem, Adventures of Consciousness, Chap 16, Man A Transitional Being.
- Collected Works of the Mother, vol. 5, 126-127
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- Four Powers of Intuition
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- Syncretism in Sri Aurobindo’s thought – part 2
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