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On Inspiration

Whenever there was a post on this forum about the "mental blockages" of going about designing a particular task, or about God and Godel, if my recollection is to be creditable, I've always wanted to share this piece with you friends.

This essay on Inspiration, written by an ardent fellow-member of ISKCON (International Society for Krishna Consciousness), formerly a scientist, rechristened as Sadaputa Dasa into the Swami Order of the fraternity, now of course a tonsured monk, makes a point about Inspiration. In a nutshell, he says that any attempt to give a mechanical explanation of inspiration based on the known principles of physics meets with two fundamental difficulties.

First, the process of inspiration can be explained mechanically only if we posit the existence of an elaborate algorithm embodied in the neural circuitary of the brain. However, it is as hard to account for such an algorithm as it is to account for the inspirations themselves.

Second, even if we accept the existence of such an algorithm, the mechanical picture provides us with no understanding of the subjective experience of inspiration, in which a person obtains the solution to a problem by sudden revealation, without any awareness of the intermediate steps.

Those of you who might have read Joseph Murphy's "The Power of your Sub-conscious Mind" or Jose' Silva's Mind Power techniques would collate the pieces.

I'd love to reproduce some excerpts out of his essay, but cannot do so right away for paucity of time.

Sathyaish Chakravarthy
Thursday, February 19, 2004

Arthur Koestler took the idea of Inspiration to the Nth degree in his book On Creativity. I felt the book, while it had it's inpspired moments, was on the whole bland. I'd tend towards an A Priori view of Inspiration, or at least writing about it - You have to be inspired to come up with a theory of it, it's not something you can tackle through market research and board meetings.

Blondie24 is a computer program that taught itself how to play Checkers. Using a generational and natural selection based process it created different algorithms for play until it reached a certain level, and ranked very highly on Yahoo! games.

By feeding the raw information of the current state of the chess board into the program, Blondie24 would spit out a move, yet the programmer didn't even know exactly how it arrived at the choice it made, and - if concious - I doubt Blondie24 could explain the process.

If you're a fan of Chaos Theory, you could think of life and of the mind as a fractal pattern, where minor variations at one point could lead to stunningly different and beautiful patterns after a short while.

That is, if you insist on thinking of any of these things in mechanical terms.
Thursday, February 19, 2004

I don't know; sounds pretty wishy-washy to me.

The human brain is the most sophisticated pattern matching machine in existance, but that function occurs at a level below our consious mind, so we don't realize it's happening. Perhaps "inspiration" is just the brain finally getting that last piece of data to trigger a pattern match on something?

Chris Tavares
Thursday, February 19, 2004

> I don't know; sounds pretty wishy-washy to me.

Shhhh. ;-) You can't sell your book/talk show/audio cassette series/lectures/religion based on "the brain is the most sophisticated pattern matching machine..."

No wait, I think there is a lecture series based on that.
Thursday, February 19, 2004

Um, isn't the term "rechristened" spectacularly inappropriate for a Hare Krishna dedication ceremony?

It seems to me that the two arguments against mechanistic explanations for inspiration are both a bit dubious.

The trouble with the first is that it amounts to "If X is true then Y must be true; I don't find Y plausible; so X must be false", which is only any use when addressing other people who don't find Y plausible. In this case Y is "The brain's workings involve sophisticated algorithms embodied in neural circuitry", and anyone who's at all inclined to believe in a mechanistic explanation for inspiration will have absolutely no trouble believing Y. So unless argument #1 is accompanied by a separate argument against Y, it's not going to convince the people you want it to convince.

The trouble with the second is that it's not true. In other words, I bet that any half-plausible mechanistic explanation for inspiration *will* (at least purport to) explain how it is that inspiration tends to feel like it arrives as a sudden revelation.

Gareth McCaughan
Thursday, February 19, 2004

I apologize for sounding a bit rude with the use of an inappropriate word; I am more often subject to lapses of anomia, and so I couldn’t resist the tickling a while longer. I’ll be a little more careful in the future.

You’re right when you nitpick a subjective disinclination against a mechanistic explanation in the “summary” I posted. However, reading the relevant excerpts from the essay would dismiss the suggestion.

I bet that any half-plausible mechanistic explanation for inspiration *will* (at least purport to) explain how it is that inspiration tends to feel like it arrives as a sudden revelation.”

While the author does quote a rudimentary analysis of the mechanical interactions in the brain that could be thought of as leading to inspiration, what he irradiates is the inadequacy of such a materialistic explanation to explain the “subjective experience” involved.

Let’s hear it from him.


Modern day scientists acquire knowledge, at least in principle, by what is called the hypothetico-deductive method. Using this method, they formulate hypotheses, and then test them by experimental observation. Investigators consider the hypothesis valid only insofar as they are consistent with the data obtained by observation, and they must in principal reject any hypotheses that disagrees with the observation. Much analysis has been directed toward the deductive side of the hypothetico-deductive method, but the equally important process of hypothesis formation has been largely neglected. So we ask, “Where do the hypotheses come from?”

It is clear that scientists cannot use any direct step-by-step process to derive hypothesis from raw observational data. To deal with such data at all, they must already have some working hypotheses, for otherwise the data amounts to nothing more than a bewildering array of symbols or sights and sounds, which is no more meaningful than a table of random numbers. In this connection Albert Einstein once said, “It may be heuristically useful to keep in mind what one has observed. But in principle it is quite wrong to try grounding a theory on observable magnitudes alone. In reality the very opposite happens. It is the theory which determines what we can observe.” (Reference: S.G. Brush, “Should the History of Science be rated X?” Science, Vol. 183, p. 1167)

Pure mathematics contains an equivalent of the hypothetico-deductive method. In this case, instead of hypotheses there are proposed systems of mathematical reasoning intended to answer specific mathematical questions. And instead of experimental testing of a hypotheses, there is a step-by-step process of verifying that a particular proof, or line of mathematical reasoning is correct. This verification process is straight-forward and could, in principle, by carried out by a computer. However, there is no systematic, step-by-step method of generating mathematical proofs and systems of ideas, such as group theory or the theory of Labesque integration.

If the hypotheses in science and systems of reasoning in mathematics are not generated by any systematic procedure then what is their source? We find that they are almost universally arise within the mind of the investigator by sudden inspiration. The classic example is Archimedes’s discovery of the princple of specific gravity. The Greek mathematician was faced with the task of determining whether a king’s crown was solid gold without drilling any holes in it. After a long period of fruitless endeavour, he received the answer to the problem by sudden inspiration while taking a bath.

Such inspirations generally occur suddenly and unexpectedly to persons who had previously made some unsuccessful conscious effort to solve the problem in question. They usually occur when one is not consciously thinking about the problem, and they often indicate an entirely new ay of looking at it – a way the investigator had never even considered during his conscious efforts to find a solution. Generally, an inspiration appears by a sudden awareness of the problem’s solution, accompanied by the conviction that the solution is correct and final. One perceives the solution in its entirety, though it may be quite long and complicated when written out in full.

Inspiration plays a striking and essential role in the solution of difficult problems in science and mathematics. Generally, investigators can successfully tackle only routine problems by conscious endeavour alone. Significant advances in science almost always involve sudden inspiration, as the lives of great scientists and mathematicians amply attest. A typical example is the life of the nineteenth-century mathematician Karl Gauss. After trying unsuccessfully for years to prove a certain theorem about numbers, Gauss suddenly became aware of the solution. He described his experience as follows, “Finally, two days ago, I succeeded. Like a sudden flash of lightening, the riddle happened to be solved. I myself cannot say what was the conducting thread which connected what I previously knew with what made my success possible.” (Reference: J. Hadamard, The Psychology of Invention in the Mathematical Field, Princeton: Princeton University Press, 1949, p. 15.)

We can easily cite many similar examples of sudden inspiration. Here is another example given by Henry Poincare, a famous French mathematician of the late nineteenth century. After working for some time on certain problems on the theory of functions, Poincare had occasion to go on a geological field trip, during which he set aside his mathematical work. While on the trip, he received a sudden inspiration involving his researches, which he described as follows: “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 were identical with those of Euclidean geometry.” Later on, after some fruitless work on an apparently unrelated question, he suddenly realized, “with just the same characteristics of brevity, suddenness, and immediate uncertainty,” that his work could be combined with his previous inspiration to provide a significant advance in his research on the theory of functions. Then a third sudden inspiration provided him with the final argument he needed to complete that work. (Reference: Henry Poincare, The Foundations of Science, Lancaster, Pa.: The Science Press, 1946, pp 387-88)

Although inspirations generally occur after a considerable period of intense but unsuccessful effort to consciously solve a problem, this is not always the case. Here is an example from another field of endeavour. Wolfgang Mozart once…


From these two instances, we discover two significant features of the phenomenon of inspiration: first, its source lies beyond the subject’s conscious perception, and second, it provides the subject with information unobtainable by any conscious effort. These features led Poincare and his follower Hadamard to attribute inspiration to the action of an entity Poincare called “the subliminal self”, and that he identified with the subconscious or unconscious self of the psychoanalysts. Poincare came to the following interesting conclusions about the subliminal self: “The subliminal self is in no way inferior to the conscious self; it is not purely automatic; it is capable of discernment, it has tact, delicacy; it knows how to choose, to divine. What do I say? It knows better how to divine than the conscious self, since it succeeds where that has failed. In a word, is not the subliminal self superior to the conscious self?” Having raised the question, Poincare turns back away from it: “Is this affirmative answer forced upon us by the facts I have just given? I confess that for my part, I should hate to accept it.” He then offers a mechanical explanation of how the subliminal self viewed as an automation, could account for the observed phenomenon of inspiration.


Let us carefully examine the arguments for such a mechanical explanation of inspiration. This question is of particular importance at the present time, because the prevailing materialistic philosophy of modern science holds that mind is nothing more than a machine, and that all mental phenomena, including consciousness, are nothing more than the products of mechanical interactions. The mental machine is specifically taken to be the brain, and its basic functional elements are believed to be the nerve cells and possibly some systems of interacting macromolecules within these cells. Many modern scientists believe that all brain activity results simply from the interaction of these elements according to the known laws of physics.

No one, as far as we are aware, has yet formulated an adequate explanation of the difference between a conscious and an unconscious machine, or even indicated how a machine could be conscious at all. In fact, investigators attempting to describe the self in mechanistic terms concentrate exclusively on the duplication of external behaviour by mechanical means: they total disregard each individual person’s subjective experience of conscious self-awareness. This approach to the self is characteristic of modern behavioural psychology. It was formally set forth by British mathematician A.M.Turing, who argued that since whatever a human being can do a computer can imitate, a human being is merely a machine.

For the moment, we will follow this behavioural approach and simply consider the question of how the phenomenon of inspiration could be duplicated by a machine. Poincare proposed that the subliminal self must put together many combinations of mathematical symbols by chance until at last it finds a combination satisfying the desire of the conscious mind for a certain kind of mathematical result. He proposed that the conscious mind would remain unaware of the many useless and illogical combinations running through the subconscious, but that it would immediately become aware of the satisfactory combination as soon as it was formed. He therefore proposed that the subliminal self must be able to form enormous numbers of combinations in a short time and that these could be evaluated subconsciously as they were formed, in accordance with the criteria for a satisfactory solution determined by the conscious mind.

As a first step in evaluating this model, let us estimate the number of combination symbols that could be generated within the brain within a reasonable period of time. A very generous upper limit on this number is given by the figure 3.2 X (10^16). We obtain this figure by assuming that in each cubic Angstrom unit of the brain, a separate combination is formed and evaluated once during each billionth of a second over a period of one hundred years. Although this figure is an enormous overestimate of what the brain could possibly do within the bounds of our present understanding of the laws of nature, it is still infinitesimal compared to the total number of possible combinations of symbols one would have to form to have any chance of hitting a proof for a particular mathematical theorem of moderate difficulty.

If we attempt to elaborate a line of mathematical reasoning, we find that at each step there are many possible combinations of symbols we can write down, and thus we can think of a particular mathematical argument as a path through a tree possessing many successive levels of sub-dividing branches.


The number of branches in such a tree grows exponentially with the number of successive choices and the number of choices is roughly proportional to the length of the argument. Thus as the length of the argument increases, the number of branches will very quickly pass such limits as 10^16 and 10^100 (1 followed by a 100 zeros).

Even a brief mathematical argument will often expand to great length when written out in full, and many mathematical proofs require pages and pages of highly condensed exposition, in which many essential steps are left for the reader to fill in. Thus there is only an extremely remote chance that an appropriate argument would appear as a random combination in Poincare’s mechanical model of the process of inspiration.

Clearly the phenomenon of inspiration requires a process of choice capable of going more or less directly to the solution, without even considering the vast majority of possible combinations of arguments.

If the process underlying inspiration is not one of extensive trail and error, as Poincare suggested, but rather one that depends mainly on direct choice, then we can explain it in terms of current mechanistic ideas only by positing the existence of a very powerful algorithm built into the neural circuitry of the brain. However, it is not at all clear that we can satisfactorily explain inspiration by reference to such an algorithm. Here we will only briefly consider this hypotheses before going on to outline an alternative theoretical basis for the understanding of inspiration.

The brain algorithm hypotheses gives rise to the following basic questions:

(1)    Origins
If mathematical, scientific and artistic inspirations result from the workings of a neural algorithm, then how does the pattern of nerve connections embodying this algorithm arise? We know that the algorithm cannot be a simple one when we consider the complexity if automatic theorem proving algorithms that have been produced thus far by worker in the field of artificial intelligence. (Reference: Joseph Weizenbaum, Computer Power and Human Reason, San Fransisco: W.H. Freeman and Company, 1976, ch.9.)

These algorithms cannot even approach the performance of advanced human minds, yet they are extremely elaborate. But if our hypothetical brain algorithm is extremely complex, how did it come into being? It can hardly be accounted for by extensive random genetic mutation or recombination in a single generation, for then the problem of random choice amoung vast numbers of possible combinations would again arise. One would therefore have to suppose that only a few relatively probable genetic transformations separated the genotype of Mozart (THERE WAS A MOZART EXAMPLE THE AUTHOR QUOTED THAT I DIDN’T INCLUDE) from those of his parents, who though talented, did not possess comparable musical ability.

(2)    Subjective Experience
If the phenomenon of inspiration is caused by the working of a neural algorithm, then why is it that an inspiration tends to occur as an abrupt realization of a complete solution, without the subject’s conscious awareness of intermediate steps? The examples of Riemann and Galosis (THAT I DID NOT INCLUDE IN THESE EXCERPTS) show that some persons have obtained results in an apparently direct way, while others were able to verify these results only through a laborious process involving many intermediate stages. Normally we solve relatively easy problems by a conscious, step-by-step process. Why then, should inspired scientists, mathematicians and artists remain unaware of important intermediate steps in the process of solving difficult problems or producing intricate works of art, and then become aware of the final solution or creation only during a brief experience of realization?

Sathyaish Chakravarthy
Friday, February 20, 2004

Deepak Chopra, a California based Indian author and a medical doctor by profession, writes in one of his books, that features Merlin, the wizard, his connotation of the Poincare’s “subliminal self”, Joseph Murphy’s “Subconscious mind” and Jose Silva’s “Alpha Level” or “Higher Intelligence”, the para-psycholoanalyst’s “Super-consciousness”, and a boy Arthur (the conscious or the objective mind).

A wizard can turn fear to joy, frustration to fulfillment.

A wizard can turn the time bound into the timeless.

A wizard can carry you beyond limitations into the boundless.

A wizard exists in all of us

The wizard sees and knows everything.

Everything the wizard sees has its roots in the unseen world.

The body and the mind may sleep but the wizard is always awake.

The wizard possesses the secret of immortality.

Deepak Chopra often quotes the word Quantum as resembling “a packet of information and energy”, the energy that is also the fabric of the universe, since the whole of the universe is born of this quantum, the very essence of the neural thought, the universe itself is thought: it is energy vibrating at a certain level. Our thought influences the anatomy of the universe.

Sathyaish Chakravarthy
Friday, February 20, 2004

I'm sorry if you thought I was saying it was *rude* to use the word "rechristened". I don't think it was rude at all. I just thought it was a very strange word to use, since it refers quite specifically to a religion quite different from the one ISKCON is all about.

I think the author you quote goes too far when he claims that "almost universally" scientific hypotheses arise from sudden mysterious inspiration. It certainly happens sometimes, but not always.

Let's go back to the alleged difficulty of explaining sophisticated algorithms in the brain. There are at least two weak points in the author's argument. Firstly, the vast amount of computational power available to the brain. Although the human brain (considered as a computer) is not a *fast* computer, it is a very *big* one. We have an enormous number of neurons, with an enormous number of connections between them, and computation (of sorts) happening in each neuron and at each connection. Our computers are a long way away from having the level of resources we have, still. So it's possible that the brain can get by with less sophisticated algorithms than a computer would need; the fact that computer programs to do things like playing chess require what seem to us to be complicated programs and plentiful resources may be misleading.

Secondly, he says "One would therefore have to suppose that only a few relatively probable genetic transformations separated the genotype of Mozart from those of his parents, who though talented, did not possess comparable musical ability" and clearly considers that this is somehow a fatal objection to any claim that the brain's algorithms got there by genetic variation. There are several different things wrong here. (1) The brain isn't composed of independent subsystems each controlled by one gene. So there's no reason at all why someone's brain shouldn't have capabilities quite different from those of his or her parents; genes interact. (2) As he admits, Mozart's parents were pretty good musically. (I hadn't known that his mother was, but I'm wiling to believe it.) I don't buy the idea of Mozart as towering superhuman; sure, he was better than his parents, but I don't see any miracles here. (3) Environment matters too. Mozart's whole upbringing was unusually musical, and that has to make a difference.

The author claims that normally we solve easy problems by a conscious step-by-step process. I think that's entirely false. We often solve easy problems "unconsciously"; it's just that the level of cleverness required isn't so great that we're struck by it afterwards.

The author also implies that "inspiration" provides the *final* stage of a scientific discovery. Just as often it's the first, or one somewhere in the middle. I don't think this is terribly important, but it doesn't give me much confidence in the author's understanding of the phenomena he's writing about.

Gareth McCaughan
Friday, February 20, 2004

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