Similar to how the interesting number paradox relies on a "shortcut statement" to force-up the number of non-interest, If Kolmogorov complexity were computable you could create a "shortcut program" to force-down the shortest length of the program:

Given: TM length of a JS runtime is 1,000,000 cells.

Assume: KC is computable, and TM length of a `function KolmoglorovComplexity(string s)` is 4,000,000 cells.

Known: KC's of values grow infinitely large - only 2^n-1 possible values can ever be encoded by n bits.

Take: function Shortcut() { for (const s in generateEveryStringFromShortestUp()) { if ( KolomoglorovComplexity(s > 10,000,000) ) return s } }

You see that the Shortcut function is encoded in 5,000,135 cells (plus that string generator, but that's small/constant), but it computes a value of arbitrarily large complexity (rather, one cell increase in the program length causes 10x increase in the complexity). A contradiction.