Turing and Chaitin's results on algorithmic information theory show that the descriptive complexity of encoding structured data in single integers grows unboundedly, making the claim practically and theoretically vacuous for sufficiently complex types.
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Unboundedly(how the complexity grows according to Turing and Chaitin)
Growing without any limit or cap; there's no maximum point it reaches.
descriptive complexity(Descriptive complexity theory, contrasted with computational complexity)
A measure of a problem's complexity in proportion to the logical resources required to describe its instances, defined using formulas that characterize the problem's instances relative to an appropriate background class of finitary structures.
encoding(Contrasted with exemplification; characterized as 'internal' predication. E.g., the winged horse encodes the property winged without exemplifying it.)
The mode of predication attributed to non-existent objects, by which such objects bear a property without instantiating it in the ordinary sense.
vacuous(describing what happens to 'artistic identity' if we blur important differences)
Empty of meaning or usefulness; a concept becomes vacuous when it loses all real significance or explanatory power.