Between A Platonic Solid And A Democritus Hard Place.

The would-be rationale idealists fifty years on continue to seek validation from the empirical scientists. It is not enough that the String theorists play in Plato s shadow world for its own sake, they need to see their particular representations actually played out by Nature. As such, of late, Materialism has ceded to Idealism as the guiding principle to rooting out fundamental truths within physics. Nineteenth century scientists read the runes of Thermodynamic phenomena and reduced its to the material atomised interplay in the spirit of Democritus. Twenty first century Naturalists play with Plato s ideal forms expressing those tendencies of fundamental objects to decay and interact with each other in the form of supersymmetric strings. While once content with real observable Brownian motion they conjure Fourier to conduct an immaterial string orchestra.

[While Plato s symmetries were a far cry from conformal causality or isospin group invariance his insight was, that nature at its most fundamental (at least) is characterised] by mathematical symmetries.

Heisenberg, The Debate between Plato and Democritus.

A simple syllogism reveals the impasse we are in at the moment. To be fundamental is to be indivisible. Indivisible elements have no substantial spatial extension to render them observable. An observable proton is not fundamental rather quarks form its aggregate tendencies: we are at the rub between Democritus rock and Platonic solid forms.

The electron s very realisability, renders absurd the notion of its substantial elementariness. Modern elementary Platonic forms are rather characticatured mathematical idealisations. The tenuous threads on which reality purports hangs: be it the string, knot, loop, second quantised gauge fields or twistor are conceived in the spirit of Plato not of Democritus. Why hope to conjure them from the shadows? When the physicists of the LHC, CERN seek to pierce the only apparent (presumably) particulate indivisibility we observe to date by fixating on smaller scales they will be just parsing twine versions of Plato s five solids.

The tried and trusted way to test the truth-value of a mathematical theorem, historically has not been to seek confirmation from such sensory evidence. Rather, validation has traditionally come from that inward experience: the determination or otherwise of the mental coherence of a train of logical propositions. A coherence then checked by the minds of other equally trained mathematicians never then actively sought some physical correspondence for full affirmation. The mathematical method has ceded to the scientific method as the physicists got ahead of themselves and the mathematicians: mathematicians have strayed from their playground of irrefutable truth grounded by logical induction into science s inscrutable refutable universe. As such, it seems we need to expand our definition of the scientific method as, according to Wilder, Quantum Questions :

[ that involving] those knowledge-claims open to experiential validation or refutation.

Indeed Heisenberg in The Debate between Plato and Democritus foretold the demise of the scientific method in its once pure Popperian form:

That ideas can be described mathematically. The beauty of that is that amongst all the possible forms of understanding, the one form practiced in mathematics is singled out as [] true understanding. [ ] only the employment of a precise, logically consistent language, [the only] language so far capable of formalisation of proofs [, can it] become possible [to] lead to true understanding.

Reductio ad absurdum is a form of argument that attempts to disprove a statement by showing it inevitably leads to a ridiculous, absurd, or impractical conclusion. That Reduction program of the fundamental physicist, to explain the complexity of the universe by cornering and compartmentalising its myriad of features: patent materiality induced from ultimately (at some scale?) nonsubstantive mathematical objects would seem an instructive archetype.

Einstein held Maxwell-Boltzmann s Thermodynamics in highest esteem: that all we can do is fairly ascribe a coarse temperature scalar to a system, a hidden variable explanation by way of the average kinetic energy of constituent molecules just the beginning of a reduction venture down the Platonic rabbit hole.

Science s Reduction program has become so obscure that tangible Democritus atoms have diffused into metaphorical Platonic forms. The rationalists as has been the traditional should content themselves with determining what is merely plausible, leaving the Empiricists to reveal nature s apparent instantiation.