The "irrational gap" between perception and explanation can be appraised historically and identified in three stages: Plato's Timaeus furnishes the first example of a scientific theory dealing with a realm of ideality that cannot be derived from immediate sensible perception; the Big Bang model is constituted on the basis of the purely geometrical notion of symmetry; and in the more recent Algorithmic Theory of Information, the analysis of the purely symbolic language expressing physical reality reveals the level of complexity of any given theory formulated in this language. The result is that the probability of the universe actually conforming with simple mathematics is zero.
In a formal system, a theorem contains more information than can be found in the set of axioms of this system, and it remains undecidable. In Aristotle' s language, the theorems that can be proved within a theoretical model are already potentially contained in the system of axioms under lying these theorems.
