Wednesday, 3 June 2009


Incommensurables series (2008)

Based on dysfunctional conversations between leading figures in the 20th century, this part of the series explores the probability of success in communication.

Here, the graphical form of a dysfunctional exchange is derived from the idea of an immeasurable mid-point on the diagonal between corners of the unit-length square, i.e. pixel.

These four figures of modernism are, in attempting to communicate and understand each other, trying to unscramble Dedekind's "secret of continuity", the irrational diagonal of the unit square. In using rationality, they spend their time chasing their tails. However, all dialogue between them, no matter how extensive, could be encoded into the infinite decimals of the unit square's diagonal length.



Formal axiomatic system



The set of all unmentioned words




B radiation

 T makes a point to W

Lines of argument

Radiating communication (ideal)


Unknowable Centre

The diagonal of a unit length square is the incommensurable √2.

The diagonal of a square drawn is pixels is equal to the length of its side:





Each pixel is a unit length square.


Each pixel contains incommensurability.

I was inspired to work on this part of the Incommensurables series by reading of the meeting between Bohr and Heisenberg during October 1941 in Copenhagen. This is an example of how dysfunction in conversation can help to steer the coarse of history. Bohr was sent to meet his former pupil in order to assess Germany's ability to produce an atomic bomb. Heisenberg who, although leading the German atomic research, was engaged in 'active resistance' with the aim of slowly not producing a weapon. It was Heisenberg's intention to communicate this to Bohr but it was not straight forward as any explicit message would inevitably be interpreted by the Gestapo as treacherous.

The following quotations are from 'Brighter Than A Thousand Suns' by Robert Jungk (1956):

But unluckily the important interview in Copenhagen between Heisenberg and Bohr was ill-starred from the beginning. It had been reported to Bohr that Heisenberg had defended, at a reception given in his honour shortly before, the German invasion of Poland.  The fact that Heisenberg in order to disguise his true sentiments, was in the habit of expressing himself quite differently in society, especially abroad, from the way he talked in private. Bur Bohr, that fanatical devotee of truth, neither could nor wished to recognize such a double game, learned in the hard school of totalitarian compulsion. Accordingly, when Heisenberg came to see him, he at once assumed an extremely reserved and even chilly attitude towards the pupil who had once been his favourite.

...unfortunately [Heisenberg] never reached the stage of declaring frankly that he and his group would do everything in their power to impede the construction of such a weapon... The excessive prudence with which both men approached the subject caused them in the end to miss it altogether.

When Heisenberg took leave of his master he had the impression... that the conversation had made matters worse rather than better. Bohr's mistrust of the physicists who had remained in Hitler's Germany had not been lessened by his pupil's visit. On the contrary, he was now convinced that the men in question were concentrating intensively and successfully on the manufacture of a uranium bomb.




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