"I am seeking a distant point at the origin of creation; where I sense a single formula for … all the forces surrounding us." Paul Klee

13 Chapter 9

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Pythagoras – Tetratys – ‘nature perpetually rolling along.

Most people are familiar with the ‘Zeno’ Binary Tree. An apex with indeterminate attributes bifurcates, descending half way down the tree to produce a visualization of the values ‘0’ and ‘1’. Repeating the process the two becomes four with the values ‘00’, ‘01’, ‘10’ and ‘11’. Repeating the process once more and the four now becomes eight, generating ‘000’, ‘001’, ‘010’, ‘011’, ‘100’, ‘101’, ‘110’ and ‘111’. With each new bifurcation the tree descends half the remaining distance until ultimately we reach the base, where the number of values represented have become infinite. The paradox being that the number of steps from apex to base would be infinite in number too.

It would seem that after just a few dozen steps we’d be straying into the realm of quantum mechanics. According to the Uncertainty Principle these distances would be so small as to make the act of measurement pointless, even from a theoretical point of view: uncertainty would be too prominent. According to quantum theory, it can never be possible to measure distances with any greater accuracy than one Planck Length (about 1.616252 × 10−35 metres) nor times less than one Planck Time (about 5.391 24 × 10−44 seconds) apart. These findings suggest that for physical systems the infinite series described by the above may not occur at the subquantum level.

In the meantime the layman’s conceptualization of this tree’s base would be an Euclidean line. Moreover, taking the logic of the above to its ultimate conclusion, a line any portion of which could conceivably contain an infinite number of points. A descent into madness only held in abeyance by the statute of limitation of quantum theory, which defines a rubicon beyond which we stray into a reality of virtual particles where the improbable reigns supreme.


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