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Creativity:  Mathematical genius Ramanujan

Posted on 22 October 2013, 8:58

“For Einstein… music and physics were closely linked. He imagined Mozart plucking melodies out of the air as if they were ever present in the universe, and he thought of himself as working like Mozart, not merely spinning theories but responding to Nature, in tune with the cosmos..He thought of both musical and physical truths as Platonic forms that mind must intuit.

Great music cannot be ‘created’ any more than great physics can be deduced strictly from experimental data. Some aesthetic sense of the universe is necessary for both.”

In my previous blog I was quoting freely from Irreducible Mind, a Psychology for the 21st Century.2006.  I would like to continue to do so, in the hopes that many will buy and study this book as a whole.

There are popular sayings linking genius to madness, and it is true that some of history’s most celebrated creative geniuses were mentally ill, from renowned artists Vincent van Gogh and Frida Kahlo to literary giants Virginia Woolf and Edgar Allan Poe.

Today, the fabled connection between genius and madness is no longer merely anecdotal. Mounting research shows these two extremes of the human mind really are linked. A Swedish study found that people who excelled when they were 16 years old were four times as likely to go on to develop bipolar disorder.

Statistically this may be true, but at page 371 in Irreducible Mind  it is remarked that genius can master its subliminal uprushes whereas the insane are overwhelmed by theirs. There come to mind such very un-insane geniuses as Schiller, Browning, George Sand, Emerson, Longfellow, Lowell, Whittier and Olive Wendall Holmes.  We don’t hear too much of the “insanity” of Einstein or of Mozart either.

Einstein felt that some aesthetic sense of the universe is necessary for both the scientist and the musician (or other artist). Polymath Johann Wolfgang von Goethe wanted totality, he fought the mutual extravagances of reason, senses, feeling and will.. he disciplined himself to wholeness, he created himself.”

Art as transformative. [p.483]

“For Jung..art provides more than aesthetic pleasure, indeed, to the extent that we can imaginatively involve ourselves in a great work of art we can vicariously participate in the transformative, integrative process effected by its creator, and are in some measure transformed and integrated ourselves.”

John Stuart Mill felt himself spiritually healed by reading Wordsworth’s poetry.. Shakespeare augments not just his consciousness but ours as well when we experience performances of his plays. Are we not uplifted by great works of art, sculpture, architecture, by great music? Of course we are – the great geniuses of many kinds help uplift us from grey self-centredness. They give us visions of the creative order of things.       

Genius and mysticism [p.484]

“Wordsworth.. is typical in experiencing his moments of inspiration as moments of entrance or insight into a normally hidden spiritual environment that somehow undergirds or interpenetrates the everyday, observable world.”

“Love … is the foundation both of genius and religion, religion being conceived in its essence as genius of the spiritual world.” We could describe Jesus, Paul, and Buddha (not to mention some of the great Old Testament prophets) as religious geniuses, through whom poured an aesthetic sense of the universe, a deep insight into the basic order of things, in which love reigned supreme.

Geniuses of all kind intuit great things, and remind us all of who we actually are, namely products of a great, and holy, unfathomable mind.

[p.487] “The products of cognitive intuition are often anything but vague. We refer here especially to pure mathematicians and mathematical physicists, nearly all of whom are Platonists of some description. Further examples can readily be found in the realm of pure mathematics. Hadamard (1949) briefly discusses some cases of paradoxical intuition including in discoveries by Permat, Risemann, and Galois of correct mathematical results that were not obvious and were far beyond the possibility of proof by means of mathematics available at the time. Indeed some of the proofs were only possible after the development of whole new areas of mathematics over periods ranging from decades to centuries. Hadamard. himself specifically suggests… that such intuitions arise from unusually deep strata of the psyche, and that they sometimes emerge as automatisms.” [p.488]

“These properties are also found in the extra ordinary and well documented life of the mathematical genius Srinivas Ramanujan’s (below) family, and he received only a patchy form of training in the course of a generally unhappy educational experience in the schools of his childhood in south India.

Nevertheless, between the ages of 16 and 26, ignited by what amounted to little more than a dry compendium of some 5000 known mathematical equations, this largely self-taught prodigy managed not only to recapitulate single-handedly a sizeable fraction of the history of Western mathematics but to generate an astonishing volume and variety of novel results in number theory as well.

raman

Discovered in 1913 by the distinguished British mathematician G.H. Hardy, Ramanujan continued this prodigious outpouring until his untimely death in 1920 at the age of 33. Some of his most important theorems have already taken decades to prove, and his crammed notebooks will continue to occupy mathematicians for generations to come. As workers found application in areas as diverse as blast furnace design, manufacture of plastics and telephone cables, cancer research, statistical mechanics, and computer science. On Hardy’s informal scale of natural mathematical ability, on which most of us would rate close to 0 and Hardy placed himself only at 25, the magnificent David Hilbert ranks in at 80, and Ramanujan stands all by himself at 100. All the main ingredients of genius are conspicuously present in this case. First there is extraordinary memory. Hardy recounts, for example, that upon informing Ramanujan of the number of the taxi in which he had just arrived for a visit, Ramanujan exclaimed at once that this number, 1729, is the smallest integer expressible as the sum of two cubes in two different ways. Second and more important, his biography is replete with signs of automatism. Some examples: It was to the goddess Namagiri, he would tell his friends, to whom he owed his mathematical gifts. Namagiri would write the equations on his tongue. Namagiri would give him mathematical insight in his dreams… Another time, in a dream, he saw a hand write across a screen made red by flowing blood, tracing out elliptic integrals.

This appearance of drops of blood in his dreams signified the presence of the god Narahimsa, then scrolls containing the most complicated mathematics used to unfold before his eyes.

Unfortunately, neither Hardy nor apparently Ramanujan himself took much interest in observing or reporting these psychological phenomena. Ramanujan’s were elegant, unexpected, and deep. Mathematicians of great ability, including Hardy among others, were enraptured by his work, and specifically by its richness, beauty and mystery – its sheer mathematical loveliness. He was not often wrong, and when he was wrong (as in his early work on the distribution of prime numbers), the incorrect results still exude id this peculiar atmosphere of mathematical beauty. Yet, as Hardy himself observed, ‘all his results, new or old, right or wrong, had been arrived at by a process of mingled argument, intuition, and induction, of which he was entirely unable to give any coherent account.’

Ramanujan was also an overt Platonist, Indian style. He pictured equations as products of the mind of God. Mathematical reality exists independently of us, and is discovered, not made; for him, numbers and their mathematical relationships fairly threw off clues to how the universe fits together. Each new theorem was one more piece of the Infinite unfathomed. In this matter at least, Ramanujan, the apotheosis of intuition, was in complete accord with his colleague and mentor Hardy.” [pp. 488-9. NOTE: because this is a blog, some scholarly references have been omitted. The original text should be consulted.]

The “Patience Worth” books and poems come to mind, as exhibiting creativity that can be compared, to some degree, to that of Ramaanujan. These can be explored in the following links.

Remembering Patience Worth 100 Years Later —An Interview with Her Foremost Fan

The mystery of Patience Worth

Patience Worth: A Psychic Mystery

Michael Cocks edits the journal, Ground of Faith.

Afterlife Teaching From Stephen the Martyr by Michael Cocks is published by White Crow Books and available from Amazon and other bookstores.

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Afterlife Teaching from Stephen the Martyr - Michael Cocks

 


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Genius

Posted on 08 October 2013, 15:21

Lord Kelvin, the eminent scientist, is reputed to have said, “There is nothing new to be discovered in physics now, All that remains is more and more precise measurement.” But then an anomaly was found: the result was quantum physics. It is through the study of anomalies, that science advances.  The phenomenon of Genius, is such an anomaly. Genius seems to be much more than superior intelligence. It is much more than the rearrangement of supposed memory traces in the brain, as some modern psychologists maintain. From the minds of geniuses entirely new creations emerge exciting the wonder and admiration of humankind. Their creativity suggests that they are drawing on a much wider and deeper dimension of Spirit, and that they provide a window of understanding of Spirit every bit as evidential as that provided by spirit communications through mediumship.

Consider the genius of Leonardo da Vinci, (below) and the wealth of scientific discoveries, mechanical inventions, and works of art that he brought into being. He very much believed that his creativity drew on the resources of such a wider and deeper dimension of Spirit.  He wrote: ‘Nature is full of infinite causes which were never set forth in experience! Every part is disposed to unite with the whole, that it may thereby escape from its own incompleteness.’  [An excerpt from The Notebooks of Leonardo da Vinci (15th April, 1452 – 2nd May, 1519)] I understand him to be affirming the interconnection of all things in heaven and earth, and   that causes and effect are largely hidden; that his creativity had something to do with a kind a revelation from the realm of Spirit.

leonardo

The genius Albert Einstein wrote, “Nature shows us only the tail of the lion. But there is no doubt in my mind that the lion belongs with it even if he cannot reveal himself to the eye all at once because of his huge dimension.” [Einstein, 1910]

In the ancient world, especially in “Rome, the rational powers and abilities of every human being were attributed to their soul, which was a genius. Each individual place had a genius (genius loci) and so did powerful objects, such as volcanoes. The concept extended to some specifics: the genius of the theatre, of vineyards, and of festivals, which made performances successful, grapes grow, and celebrations succeed, respectively.

It was extremely important in the Roman mind to propitiate the appropriate genii for the major undertakings and events of their lives.” [Wikipedia article]  So, in thinking of da Vinci and Einstein as geniuses, we may perhaps claim that their creativity was a kind of inrush from the realm of Spirit, from their souls which in turn were connected to all else.

The landmark book Irreducible Mind, a Psychology for the 21st Century [800pp. 2006] devotes 70 pages to the study of genius.

On page 426 F.W.H. Myers (whom his friend William James thought of as a near genius,) is recorded as saying, “Genius…should rather be regarded as a power of utilising a wider range of subliminal mentation to subserve the supraliminal stream of thought”. We can associate “subliminal mentation” with what we call the world of Spirit. Myers (below) writes that genius, “… must involve something original, spontaneous unteachable, and it must win for itself in some way the admiration of mankind.” [p..427]

myers

Myers affirmed that there was indeed continuity between mind of a genius and the ordinary mind. Geniuses and ordinary people are all human, and have their connections to the spiritual dimension. But whereas ordinary people have flashes of inspiration, in the case of the genius there is a burning fire.

Then he changes the analogy: “There are bubbles that break on the surface, but every now and then there is a stir among them.

There is a rush upwards as of a subaqueous spring, an inspiration flashes into the mind for which our conscious effort has not prepared us. This so-called inspiration may in itself be trivial or worthless….”  [deep within us is rubbish heap as well as a treasure house]

At page 450 Myers is quoted: “We all can have flashes of inspiration, but.. “in more extreme cases of real genius the subliminal uprush becomes more intense and protracted, and arises from deeper subliminal strata that utilize different modes of operation and may have access to additional sources of information.” 

At pages 444-5 we read the following: A.E.Houseman described how inspiration came to him in afternoon walks, and absent-mindedly looking about…”there would flow into my mind, with sudden and accountable emotion, sometimes a line or two of verse, sometimes a whole stanza at once, accompanied but not preceded, by a vague notion of the poem which they were destined to be part of. Then there would be a full hour or so, and then the spring would bubble again,…. I happen to remember distinctly the genesis of a piece which stands last in my first volume. Two of the stanzas, I do not say which, came into my head, just as they are printed, while I was crossing the corner of Hampstead Heath between Spaniard’s Inn and the foot path in Temple Fortune. A third stanza came with a little coaxing after tea, but it did not come. I had to turn to and compose it for myself, and that was a laborious. I wrote it thirteen times , and it was more than a twelvemonth before I got it right.” 

Another poetic genius, William Blake, ... wrote to his friend Butts that his prophetic poem Milton was written from “immediate dictation”, “twelve or sometimes twenty or thirty lines at a time, without premeditation, and even against my will.”

Turning to the realm of music, we discover that Mozart’s first biographer, in collaboration with Mozart’s wife, related a congruent account of how Mozart composed: “Mozart wrote everything with a facility and rapidity, which perhaps at first sight could appear as carelessness or haste; and while writing he never came to the klavier. His imagination presented the whole work, when it came to him, clearly and vividly. …. In the quiet repose of the night, when no obstacle hindered his soul, the power of his imagination became incandescent with the most animated activity, and unfolded all the wealth of tone which nature had placed in his spirit …. Only the person who heard Mozart at such times knows the depth and the whole range of his musical genius: free and independent of all concern his spirit could soar in daring flight to the highest regions of art.”

In the realm of philosophy, Friedrich Nietzsche wrote: “The notion of revelation describes the condition most simply, by which I mean something profoundly convulsive and disturbing suddenly becomes visible and audible with indescribable definiteness and exactness. One hears – one does not seek; one takes – one does not ask who gives: a thought flashes out like lightning, inevitably without hesitation – I have never had any choice about it. There is ecstasy whose terrible tension is sometimes released by a flood of tears.” Irreducible Mind pp. 445-446

This is how geniuses describe the uprush of creativity as they experience it.  What can else can be said about such uprushes?                               

Perhaps the most intriguing is a séance message purportedly originating from psychical pioneer Sir William Barrett, author of the ground-breaking book Deathbed Visions:

“When I come into the conditions of a sitting I then know that I can only carry with me – contain in me – a small portion of my consciousness. The easiest things to lay hold of are what we may call ideas; a detached word, a proper name, has no link with a train of thought except in the detached sense; that is far more difficult than any other feat of memory or association of ideas.” [p.73]

In a session with Mrs. Leonard, a communicator purporting to be the same William Barrett elaborated on this idea:

“Sometimes I lose some memory of things from coming here [i.e., coming to the sitting]; I know it in my own state but not here. In dreams you do not know everything; you only get parts in a dream. A sitting is similar; when I go back to the spirit world after a sitting like this I know I have not got everything through that I wanted to say. That is due to my mind separating again, the consciousness separating again. In the earth body we have the separation of subconscious and conscious.

Consciousness only holds a certain number of memories at a time. When we pass over they join, make a complete mind that knows and remembers everything; but when one comes here to a sitting the limitation of the physical sphere affects one’s mind, and only a portion of one’s mind can function for the time being. When I withdraw from this condition one’s whole mind becomes again both subconscious and conscious; my subconscious mind encloses my conscious one and I become whole again mentally… I cannot come as my whole self. I cannot.” [pp. 191, 192]

“William Barrett” speaks of the separating of the conscious and the subconscious, or the subliminal of Myers. This can be equated with the unconscious of Carl Jung, the unconscious which is Collective.  I consider that the voice of Jung should be heard here. For in the Universal Mind we are non-separate, we are all interconnected more or less conscious participants in a Whole. Language, knowledge, experience, belongs to the Whole.

Each of us can be regarded as organs of action, creativity, feeling, and learning for this Whole. In the words of the languages we use, are recorded countless experiences of this Whole, and in this respect at least, we are non-separate. We are each other, as organs of one whole. So, with the genius, we can be thankful for the bursts of creativity and understanding of the nature of things, that they bring about. But it would be hard to define how the creativity of a particular genius was peculiar to that person.

Accounting for the genius of Leonardo da Vinci, or Mozart, as supposedly separate from this Whole might thus be a challenge.

Michael Cocks edits the journal, Ground of Faith.

Afterlife Teaching From Stephen the Martyr by Michael Cocks is published by White Crow Books and available from Amazon and other bookstores.

Paperback               Kindle

Afterlife Teaching from Stephen the Martyr - Michael Cocks


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“Life After Death – The Communicator” by Paul Beard – If the telephone rings, naturally the caller is expected to identify himself. In post-mortem communication, necessitating something far more complex than a telephone, it is not enough to seek the speakers identity. One needs to estimate also as far as is possible his present status and stature. This involves a number of factors, overlapping and hard to keep separate, each bringing its own kind of difficulty. Four such factors can readily be named. Read here
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