Mathematicians and Dreams

Some time ago I wrote about "Cybernetics and Dreams" and how the cipher to John Wesley's coded journal was revealed to Nehemiah Curnock in a dream.

One of the most extraordinary stories about mathematical revelations through dreams was celebrated recently at the 125th anniversary of the birth of the Indian mathematician, Srinivasa Ramanujan. Ramanujan, a mathematical genius and prodigy.

Photo: Wikipedia

Wikipedia says...

Srinivasa Ramanujan FRS (22 December 1887 - 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. ...
Born at Erode, Madras Presidency (now Tamil Nadu) in a poor Hindu Brahmin family, Ramanujan's introduction to formal mathematics began at age 10. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of 12; he even discovered theorems of his own, and re-discovered Euler's identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By 17, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler-Mascheroni constant.

This remarkable man died at the age of 32. A Daily Mail article,  reported...

While on his death-bed in 1920, Ramanujan wrote a letter to his mentor, English mathematician G. H. Hardy, outlining several new mathematical functions never before heard of, along with a hunch about how they worked. 

Decades later, researchers say they've proved he was right - and that the formula could explain the behaviour of black holes.
....
Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.

The Durban Sunday Tribune elaborated, crediting the Daily Mail report...

Genius saw formulas in dreams 

Researchers have finally solved the cryptic deathbed puzzle renowned Indian mathematician Srinivasa Ramanujan claimed came to him in dreams...outlining several new mathematical functions never before heard of... Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.
...
Emory University mathematician said..... "No one was talking about black holes back in the 1920s when Ramanujan first came up with mock modular forms, and yet, his work may unlock secrets about them,"
...
The findings were presented... at the Ramanajun 125 conference at the University of Florida, ahead of the 125th anniversary of the mathematician's birth on December 22.

- Tribune Herald, 6 January 2013

Hinduism Today featured an article posted by Dr Jai Maharaj in which he wrote:

.... Ramanujan possessed supernatural intelligence, a well of genius that leaves even brilliant men dumb-founded.  Ramanujan was a meteor in the mathematics world of the World War I era.  Quiet, with dharmic sensibilities, yet his mind blazed with such intuitive improvisation that British colleagues at Cambridge -- the best math brains in England -- could not even guess where his ideas originated.  It irked them a bit that Ramanujan told friends the Hindu Goddess Namagiri whispered equations into his ear.  Today's mathematicians -- armed with supercomputers -- are still star-struck, and unable to solve many theorems the young man from India proved quickly by pencil and paper.   

Ramanujan spawned a zoo of mathematical creatures that delight, confound and humble his peers.  They call them "beautiful," "humble," "transcendent," and marvel how he reduced very complex terrain to simple shapes.   

In his day these equations were mainly pure mathematics, abstract computations that math sages often feel describe God's precise design for the cosmos.  While much of Ramanujan's work remains abstract, many of his theorems are now the mathematical power behind several 1990's disciplines in astrophysics, artificial intelligence and gas physics.

Who is Namagiri?

In Hindu mythology Namagiri is the consort of Narasimha, the lionman avatar of Vishnu. Narasimha symbolises the omnipresence of God. Like the Sphynx of Giza, he is the everpresent guardian, an Aslan figure.

Srinivasa Ramanujan attributed his mathematical findings to the goddess Namagiri. According to Ramanujan, she appeared in his dreams, proposing mathematical formulae, which Ramanujan would then have to verify. One such event was described by him as follows:

"While asleep, I had an unusual experience. There was a red screen formed by flowing blood, as it were. I was observing it. Suddenly a hand began to write on the screen. I became all attention. That hand wrote a number of elliptic integrals. They stuck to my mind. As soon as I woke up, I committed them to writing."

Dr. Jai Maharaj wrote:

"Debate still lingers as to the origins of Ramanujan's edifice of unique ideas.  Mathematicians eagerly acknowledge surprise states of intuition as the real breakthroughs, not logical deduction.  There is reticence to accept mystical overtones, though.... many can appreciate intuition “in the guise” of a Goddess.  But we have Ramanujan's own testimony of feminine whisperings from a Devi and there is the sheer power of his achievements.  Hindus cognize this reality."

Namagiri, the goddess of creativity, is akin to the Greek Muse, Urania, the muse of astronomy, science, and mathematics. As such she is an Anima figure inspiring, revealing, and unveling the mysteries of nature. Namagiri would be the feminine, guiding aspect, who can be thought of as a counterpart of the Jewish Hokmah or the Christian Sophia.

The genius of  dreams....let us pay attention to our dreams!

Also see: http://www.legacyoframanujan.com/index.html and http://www.hinduwisdom.info/quotes321_340.htm

Picture Credits: Wikipedia and Gustave Moreau, Hésiode_et_la_Muse

©Colin G Garvie HomePage: http://www.garvies.co.za

Cybernetics and Dreams

...build belief in yourself and as you do this, you reactivate the success mechanism -- the servo-mechanism -- within you. This implies that your eyes are open to opportunities that arise because you want to see them and reach them -- without stepping on other people's toes, but also without tripping over your own toes. 

-Maxwell Maltz, Psycho-Cybernetics and Self-Fulfillment, p.8

The term cybernetics stems from the Greek κυβερνήτης (kybernētēs, steersman, governor, pilot, or rudder — the same root as government). In 1 Corinthians 12:28 (cf Prov 1.5; 11.14 Septuagint) κυβέρνησις is one of the gifts of the Holy Spirit. Today the word is generally used in the context of Information Systems.

The significance of cybernetics to anthropology, sociology, physiology, and psychology was appreciated by the father of modern cybernetics, Norbert Wiener  and others. He wrote, "Drs McCulloch and Fremont-Smith have rightly seen the psychological and sociological implications of the subject.... The need of including psychologists had indeed  been obvious from the beginning. He who studies the nervous system cannot forget the mind, and he who studies the mind cannot forget the nervous system. (Wiener, Cybernetics, p.26). Thus the relevance of cybernetics to dreaming and dreams.

Over the years I have come to experience and think of dreams as an inner guidance system, a rudder or steering mechanism to help one navigate through life's difficulties. Dreams can be a useful problem-solving resource.

A little while ago I had been reading John Kehoe (Quantum Warrior, p.120f) explaining how one can consciously dream solutions to problems through a process he calls "dream incubation". Top of my mind at the time was an awful conflict situation I had had at work. It was an accounting environment and the problem was one of financial accountability. I was a programmer and a technician but not an accountant so felt inadequate to deal with it. The problem was a complex legal-forensic one and a very serious one at that. It affected me deeply.  Kehoe led me to think differently about the problem by  reactivating the "servo-system" within myself.

So, on going to bed I kept repeating the question that was running through my mind, "What must I do about this situation at work? Do I continue working at it or do I just resign from it, throw in the towel, and not get involved?" With this concern on my heart I went to sleep.

I woke early the next morning dreaming that I was at a radio observatory of sorts like the one at Hartebeesthoek where I had previously worked. In a mysterious way my dream had latched on to a context I could easily relate to as a technician and programmer. In the dream we weren't getting a clear "picture" of a critical deep space object that we were looking at. I suggested the noise level was anomalously high, distorting the picture, and that we should check the signal to noise ratio (SNR is a standard measurement in radio telecommunication). We needed to take corrective action in order to see the big picture by reducing internally generated dissonance . (See Gestalt and Cybernetics.) And so it happened.

Mariner 6 photo enhancement.

First panel is the original picture. The top-right panel

is the system noise pattern which when digitally

applied to the original clarifies it as in the lower pictures.

Photo Credit: NASA

It was quite some dream! As a direct response to my question, the the dream seemed to be advising me that the problem should not simply be ignored but that it had to be addressed. It also indicated the kind of contribution I could make.

Remarkable as my dream was, dreams of this nature are not unusual. Indeed, one of the most significant instances comes from my own Methodist tradition. John Wesley wrote parts of his Journal in code, intentionally guarding its contents deliberately hiding it by means of a cipher. Sometimes there is good reason for encoding transmissions. In this case, it was not noise that hid the true content but encoding.

John Wesley had left behind a Journal much of it written in an indecipherable code. In 1909, the Rev. Nehemiah Curnock was poking around through a secondhand bookstore when he came across a treasure - John Wesley's personal Bible, with marginal handwritten notes in the same mysterious code. Curnock bought the Bible, studied it, and then forgot about it. One night, shortly thereafter, while deep in sleep, Reverend Curnock had a dream - he saw Wesley's Journal, and on one page the code was deciphered. Waking, he had the key. Remembering his dream, he examined Wesley's code in the Bible, and unlocked the mystery. Curnock alludes to the dream in his introduction to his edition of the Journal of John Wesley. His dream was cybernetic, it had guided and directed him to the key that would help unlock the mysterious cipher John Wesley had used.

Dreams do that for us! They open us to new possibilities helping us to see the underlying issues and get the  "bigger picture".

oOo

Further Reading:
Two interesting articles by George Butler:
"Minister's Remarkable Dream", http://news.google.com/newspapers?nid=1891&dat=19761010&id=-6QfAAAAIBAJ&sjid=OtYEAAAAIBAJ&pg=1360,1216912
"Dreams often provide key to many of world's mysteries", http://news.google.com/newspapers?nid=1891&dat=19750816&id=wKcfAAAAIBAJ&sjid=VtYEAAAAIBAJ&pg=811,2666820

Recent Wesleyan research has built on the earlier work of Nehemiah Curnock. Richard Heitzenrater has devoted much of his time decoding the diaries of John Wesley http://divinity.duke.edu/publications/2008.10/features/code/index.htm. Charles Wesley also coded large sections of his Journal which has been cracked by Professor Kenneth Newport http://www.dailymail.co.uk/news/article-1049285/Coded-diary-reveals-secret-sex-scandal-haunted-Methodist-founder-Charles-Wesley.html


©Colin G Garvie HomePage: http://www.garvies.co.za