Staring Into the Abyss……

11 Nov

It is often said that there exists a fine line between genius and madness but is there any truth in that statement and, if so, why…..?

History is littered with examples numbering into the hundreds of famous academics who have struggled with their mental health.  Many spent time in asylums or committed suicide which raises an interesting question; why have so many highly intelligent and successful people been driven insane or to the point at which they felt such despair that suicide was the only option to escape their torment?  I feel that I to have stood at the precipice, staring into the abyss and very close to that line……

Case Histories – The Mathematicians……


Georg Cantor: Born 3 March 1845, Georg Cantor was a brilliant German mathematician best known for his work on set theory and infinity.  Cantor’s work on set theory is now one of the fundamental theories of contemporary mathematics but it is his work with infinity and ‘The Continuum Hypothesis’ which probably contributed the most to his struggle with his mental health.

Georg Cantor

Infinity had been known about for millennia and even school children are able to grasp the concept that one can start counting 1, 2, 3, 4 and continue forever.  However, it was Cantor who was the first mathematician to delve deeper into infinity and discover some of its paradoxical implications.  The paradoxes Cantor discovered raised many philosophical questions and can get pretty complicated so follow this link to Wikipedia to find out more but as a simple demonstration here is one example:

If you write down a list of whole numbers starting 1, 2, 3, 4, 5, 6, 7, 8, 9 (and on to infinity), then write a corresponding list below of only the odd whole numbers, matching 1 with 1, 3 with 2, 5 with 3, 7 with 4, 9 with 5 (and on to infinity).  You end up with two sets of numbers which contain no gaps, however, intuitively the second set contains half of the numbers in the first, yet both are infinite.  This is a very simple example but demonstrates that you can have infinities of differing sizes.  Cantor went much further in order to prove his theorem and, although now accepted, at the time he was attacked by his contemporaries such as Leopold Kronecker and Henri Poincaré and even by Christian theologians who saw his work as ‘a challenge to the uniqueness of the absolute infinity in the nature of God’.

Georg Cantor later began work on what became known as The Continuum Hypothesis’, the proof of which was to consume the rest of his life and led to him spending long periods in an asylum where he died in 1918.  The decline in Cantor’s mental health can be seen in his personal correspondence.  He feels he is on the verge of proving ‘The Continuum Hypothesis’, then stating he was wrong; changing his opinion with ever increasing frequency……

Kurt Godel: Born 28 April 1906, Godel was an Austrian mathematician whose most famous achievement was ‘The Incompleteness Theorem’, a form of logic.  Godel’s work is extremely complicated and difficult even to summarise so again follow this link for a detailed explanation of The Incompleteness Theorem’.  However, what Godel’s work showed was that there are some mathematical problems which cannot be proved by the use of logic and, to exacerbate an already difficult problem, there is no way of knowing which of these problems can and cannot be proved using mathematical axioms of logic.

Kurt Gödel

In 1938 Godel moved to America to work at the Institute for Advanced Studies at Princeton, New Jersey.  There he became close friends with Albert Einstein and helped elucidate many features of the general theory of relativity.  However, like Cantor his mental health began to deteriorate, he was a hypochondriac and was convinced his food was being poisoned.  Kurt Godel died of malnutrition in 1978 in a New Jersey Hospital…….

The Physicist……

Ludwig Boltzmann: Born 20 February 1844, Boltzmann is most famous for his work on statistical thermodynamics and the concept of entropy.  However, it is partly due to his work on thermodynamics that led him to be an early exponent of atomic theory.

Ludwig Boltzmann

Boltzmann proposed that all matter was made up of fundamental atomic particles for which he was berated by many in the scientific community.

Feeling isolated and probably suffering from bi-polar disorder he hung himself whilst on a family holiday in Italy.  He is buried in Vienna.  His grave stone bears the inscription ‘S=k*logW’, the equation which defines the entropy of a system.  Sadly, unknown to Boltzmann, Albert Einstein had just written a paper on ‘Brownian Motion’ which proved the existence of the atoms Boltzmann had proposed……

‘So what links these people, their discoveries and many others like them and, why is the balance between genius and madness so close?’……

I believe that the nature of the enquiring minds of the people who become scientists can be one which is seeking answers to the fundamental questions about our existence.  What they seek is certainty and definitive answers to deeply philosophical questions.  The problems arise when the answers offer only uncertainty or are paradoxical.  Albert Einstein once reportedly said “God doesn’t play dice with the world”.  When one sets out to find answers and discovers a paradox, or worse, that there is no definitive answer or more than one, it can lead an enquiring mind to go into overdrive desperately trying to resolve the issues.  One can become convinced that there must be a mistake in the results of an experiment or equation.  It is then that a person’s mental health may be adversely affected as they start to question themselves on a deeper level.  Clearly, this does not affect everybody and some can work on subjects such as Quantum Mechanics, accepting that the uncertainty and paradoxes may never be resolved.  Providing that the mathematics enables them to further their research they continue where others are unable to move on……

From a personal perspective, I have sometimes felt close to the line and am troubled by the gaps in our knowledge which have yet to be filled.  Fortunately, I can wait for answers without being driven insane, but it still bothers me all the same……

e: – t: @DrippingTap


2 Responses to “Staring Into the Abyss……”

  1. Science Devil November 11, 2012 at 2:57 pm #

    I like the article. Good work. You might be interested in a couple I have written recently on similar topics, although satirical – that’s what I do.

    This one on recent research into creativity and mental illness:

    or this one on VS Ramachandran who gives a neuroscientist perspective on these questions.

    Keep up the good work.

  2. Science Devil November 11, 2012 at 2:59 pm #

    oops sorry forgot the link to the second one:

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