“God is a mathematician of a very high order”

“God is a mathematician of a very high order” September 26, 2020


Dirac, by Ewald
A 1939 portrait of Paul A. M. Dirac, by Clara Ewald
(Wikimedia Commons public domain image)


Carlo Rovelli, in his Reality Is Not What It Seems: The Journey to Quantum Gravity, translated by Simon Carnell and Erica Segre (Penguin, 2017), offers a fascinating though brief portrait of the English theoretician Paul A. M. Dirac (1902-1984), who, he says, is “considered by many to be the greatest physicist of the twentieth century after Einstein” (101).  Dirac, who was famously inept, socially speaking, and possibly autistic, was no friend of “religion” and was a vocal critic of (at least conventional ideas of) God.


But he was deeply, almost mystically, committed to mathematics, and he was quite willing to use the term God in that connection.   Writes Rovelli,


His physics has the pristine clarity of a song.  For him, the world is not made of things, it’s constituted of an abstract mathematical structure which shows us how things appear and how they behave when manifesting themselves.  It’s a magical encounter between logic and intuition.  (102)


Here are some quotations from Dirac that I’ve noted.  I have the original sources for some of them, but will need to track the others down:


The mathematician plays a game in which he himself invents the rules while the physicist plays a game in which the rules are provided by nature, but as time goes on it becomes increasingly evident that the rules which the mathematician finds interesting are the same as those which nature has chosen.


God is a mathematician of a very high order and He used advanced mathematics in constructing the universe.


It’s more important to have beauty in one’s equations than to have them fit experiment. . . .  It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress.  If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further developments of the theory.  (“The Evolution of the Physicist’s Picture of Nature,” Scientific American [May 1963], 47)


Theoretical physicists accept the need for mathematical beauty as an act of faith. . . .  For example, the main reason why the theory of relativity is so universally accepted is its mathematical beauty.  (“Methods in Theoretical Physics,’ in A Life of Physics: Evening Lectures at the International Centre for Theoretical Physics, Trieste, Italy.  A Special Supplement of the IAEA Bulletin [1968], 22)


He seems to have believed in the importance of intuition for scientific progress or, to put it in Latter-day Saint terms, in personal inspiration or even revelation:


I found the best ideas usually came, not when one was actively striving for them, but when one was in a more relaxed state. . . .  I used to take long solitary walks on Sundays, during which I tended to review the current situation in a leisurely way.  Such occasions often proved fruitful, even though (or perhaps, because) the primary purpose of the walk was relaxation and not research.  (“Methods in Theoretical Physics,’ in A Life of Physics: Evening Lectures at the International Centre for Theoretical Physics, Trieste, Italy.  A Special Supplement of the IAEA Bulletin [1968], 24)



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