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.
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.