Thank you, Alastair, for posting this Sunday Times review of Graham Farmeleo’s book on Paul Dirac. It came at an opportune time. Several comments in the review were applicable to a significant discovery I made about Spinoza last week, which has been fermenting in my brain since then.
Although I have been reading and meditating on Spinoza’s writing for almost a decade and have especially read the Emendation, Short Treatise and Ethic, over and over, last week I realised Spinoza does not consider science to be a rational activity but rather an intuitive one. (Short Treatise on God, Man And His Well Being, Chapter IV, ‘What Comes From Belief,” pp 102-104 in Edwin Curley’s, The Collected Works of Spinoza, Vol 1, especially see fn a on p. 102).
As Spinoza says, ” …science which does not consist in convictions based on reasons but in immediate union with the thing itself…” Science makes us enjoy intellectually what is in us, (paraphrase of a sentence presented in negative about true belief/reason).
As the review about Dirac says: ‘…he insisted that the quantum world could not be expressed in words or imagination… Its beauty revealed itself only in mathematical formulae.” (p1) and :”[Dirac's] ideas came as intuitions. They were not derived from experimental observations but from contemplation of pure mathematics.” (p.2)
These two comments gave me an example of what Spinoza called his third kind of knowledge in the Ethic: intuitive knowledge,” as Curley translates (Part II, Prop 40, sch II) and “intuitive science,” as White translates. (Ibid).
Spinoza says humanities thinking would have been kept in darkness;” …if mathematics, which does not deal with ends but with the essences and properties of forms, had not placed before us, another rule of ruth.” (Underlining, mine – Ethic of Benedict De Spinoza, trans. W. Hale White & Amelia H. Stirling, Oxford, p. 41, Appendix to Part one). I like White’s translation of this passage better than Curley’s because, as any mathematician can tell you, the essence of mathematics is, ‘forms.’
Where am I going with this? In the Emendation, Spinoza says he is confronted with a dilemma. (p. 20, Curley). How can you articulate something which cannot be expressed in language, (a true idea) – and why should you try?
Reason is the child of language, but, as George Boole said, there are three laws of signs: 1) Literal symbols, such as x, y and etc., representing things as subjects of our conceptions. 2) Signs of operation as, +, -, x, standing for the operations of the mind by which the conception of things are combined or resolved so as to form new conceptions involving the same elements. (note – this is Euclid’s Common Notion: The whole is greater than the part). 3) The sign of identity- relations from which we form propositions (p. 27, An Investigation of the Laws of Thought On Which Are Formed The Mathematical Theories of Logic and Probabilities, Dover). Obviously Dirac believed the first two laws of signs preceeded and were more important in thinking about the quantum world, than the third law of signs: identity which produces language and the relations of one sign to another which we call reason.
This could be an example of what Spinoza called, ‘intuitive science’ i.e. science based on the logical/mathematical operations in our mind that makes us enjoy intellectually what is in us. Reflecting on this, I realized Spinoza limited the laws of mind by making them the exclusive property of science. I would redefine ‘intuitive science,’ as ‘created intuitions and include at least four subsets of this set: 1) Science (logic & mathematics) 2) Art 3) Music 4) Poetry – in which we examine’ the forms of language. All of these operate by the same law of signs as mathematics and have an emphasis on the first two laws, except poetry, which turns language around so we can examine its intuitive form.
I’m sure Dirac could have said all this with mathematics, in an elegance that language hinders. Thank you for this article.
The Sunday Times January 11, 2009
———————————————————————————————The Strangest Man: the Hidden Life of Paul Dirac, Quantum Genius by Graham Farmelo
Paul Dirac was the greatest British physicist since Newton. In the 1920s and 1930s, together with Bohr, Heisenberg, Schrödinger and Pauli, he opened up the field of quantum physics, changing the course of science. In 1933, aged 31, he became the youngest theoretician to win a Nobel prize. He died 25 years ago, yet no biography has appeared until now. It is not hard to see why. As a man he was pathologically silent and retiring, and as a thinker he was unintelligible except to mathematicians. Even his fellow physicists complained that he worked in a deliberately mystifying private language. For his part, he insisted that the quantum world could not be expressed in words or imagined. To draw its picture would be “like a blind man sensing a snowflake. One touch and it’s gone”. Its beauty revealed itself only in mathematical formulae.
These considerations might seem to doom Graham Farmelo’s project. But he rescues it by turning it into a panoramic survey of 20th-century physics, from Einstein’s relativity to string theory, scaled down in difficulty for unscientific readers, and showing how Dirac’s ideas interacted with those of colleagues and rivals. He also uses previously unreleased family papers to probe Dirac’s strange personality. Born in 1902, he was the son of a widely respected Bristol schoolteacher of Swiss descent, an expert in modern languages and a pioneer of Esperanto. Dirac blamed his father for his own oddities. At mealtimes, he told a colleague late in his life, he had been forced to eat with his father in the dining room and speak nothing but French, while his mother, brother and sister ate in the kitchen. However, there is no trace of this domestic tyranny in the family letters Farmelo has unearthed. It appears from them that Dirac had a happy childhood and a loving relationship with his father. Without his father’s encouragement he would never, it seems, have got to Cambridge, where his career took off.
Possibly his account was an unconscious attempt to shift blame for a family tragedy. In 1925, his elder brother Felix had committed suicide. Dirac clearly regarded him as an inferior, had not spoken to him for some years and would pass him in the street with an expressionless stare. It may be that guilt over this episode led him to reconstruct his childhood and make his father responsible.
Farmelo believes that the cause of Dirac’s condition was not paternal cruelty but autism. Like many autistics he was extremely taciturn. His fellow students invented a unit, “the Dirac”, for the smallest imaginable number of words someone could utter in an hour. He was literal-minded and lacking in empathy. The only time he was known to weep was when Einstein died. In the question time following one of his lectures, a student ventured that he did not understand an equation on the blackboard. Dirac remained impassive until prompted, and then replied, “That is not a question, it is a comment.” He did not see the point of literature or art. Looking at an impressionist painting, he remarked, “This boat looks as if it was not finished.” Urged to read Crime and Punishment, he worked through it sentence by sentence, and concluded it was “nice”, though “in one of the chapters the author makes a mistake: he describes the sun as rising twice on the same day”. He loved cartoons and comic strips, especially Mickey Mouse and Blondie, but found Peanuts too subtle.
His interest in politics was aroused by his friend the Russian physicist Peter Kapitza, and under his influence he swallowed the Soviet recipe for universal happiness with gullible enthusiasm. Visiting Russia in the 1930s, he remained unaware that millions were dying of famine as a result of collectivisation and he dismissed British press reports of Stalin’s purges as exaggeration.
He showed no interest in women until he was in his thirties. Acquaintances assumed he was gay. But as his powers as a mathematician waned he became more susceptible, and was snapped up by a garrulous Hungarian divorcée, Manci Balazs. They married in 1937, and she bore him two daughters. Physical love came as a revelation. “You have made me human,” he exulted. But she had not really. For her he remained an “emotional cripple”. His literalism was a continual headache. He drew up, in tabular form, an explanation of why he could not use the endearments customary with lovers, since they were not literally true. “What would you do if I left you?” yelled Manci. After a moment’s thought, he replied, “I’d say, Goodbye, dear.” Dining arrangements in the Dirac home do not seem to have been much more liberal than those he attributed to his father. Silence was observed at every meal, so that he could concentrate on eating, and no drop of alcohol was allowed anywhere, even in recipes.
But the tittle-tattle of Dirac’s daily life is ultimately irrelevant. What matters is his thought, and from that the majority of readers will inevitably feel excluded. It is not Farmelo’s fault. He explains patiently how momentous Dirac’s breakthroughs were. In 1927, he perfected an equation that “described the behaviour of every single electron that had ever existed in the universe”. It sounds staggering, but since most of us would not understand the equation even if Farmelo had cited it, we can only gape like ignorant bystanders. We might as well be urged to admire the colours in the infrared spectrum.
What does come across, surprisingly, is how far Dirac’s methods seem like those of an imaginative writer. His ideas came as intuitions. They were not derived from experimental observation, but from contemplation of pure mathematics. His discovery of antimatter followed this pattern. He deduced from his equations that if electrons exist, anti-electrons must exist also, though nobody had ever observed one. The universe, he suggested, was composed of equal parts of matter and antimatter, and though, for some unknown reason, human experience is confined almost entirely to matter, there may be parts of the universe made of antimatter. Most physicists greeted this with derision. Yet within months an experimenter at Caltech had photographed a positron or anti-electron; nowadays, Farmelo points out, particle accelerators generate billions of anti-electrons and anti-protons daily for use in industry and medicine, where positron emission tomography allows doctors to see inside patients’ brains and hearts.
Dirac’s decline makes sad reading. It was a joke in the Bohr group that physicists burn out in their thirties, and in this respect Dirac was true to type. During the second world war, J Robert Oppenheimer invited him to join the Manhattan Project, but he declined, possibly, Farmelo thinks, because he was too attached to his routines – another autistic symptom. In post-war Cambridge, although still the Lucasian Professor, he was an irrelevance. They even took away his departmental parking space. Sick of such slights, Manci persuaded him to accept an Eminent Professorship at Florida State University, where he became a revered curiosity. The fascination of Farmelo’s book lies in its earlier chapters, which challenge us with the paradox of a mind at once maimed and mighty.
The Strangest Man by Graham Farmelo
Faber £22.50 pp539
