Untangling untanglables.

By Andrew|A|-∞<A<+∞

I conjecture (i.) a stochastic “mechanical algorithm” that untangles untanglable strings in finite iterations, (ii.) a class of heuristics that reliably reduce stochasticity and increase efficiency of this algorithm, and furthermore (iii.) a subclass of such heuristics that renders the algorithm superior in average- and worst-case time-complexity to any algorithm that must analyze a topological relationship between two points on the string.

Let there exist a function, pull(a, b, F), where a and b represent points on a string (say, as scalar displacements from a common origin on the string) and F represents a force, that simultaneously pulls an untanglable string by force F at a and -F at b, until there is no movement.  I conjecture that for any untanglable string there exists a scalar f such that invoking pull on a random a, random b, and F > f untangles the string in a finite number of iterations.

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I metawrite for the utility of metawriting.

By Andrew|A|-∞<A<+∞

I write for the utility of writing.  These are, broadly, (i.) the utility of the present, and (ii.) the utility of the future.  These are, refined, (i.a.) the utility of transcribing thoughts and feelings which in large numbers become too cumbersome to persist in my mind, like the utility of paging memory (in computing), (i.b.) the utility of satisfying my ego with words that satisfy my sense of aesthetics, and (ii.a.) the utility of recollecting forgotten reas and ideas, i.e. memories of things that happened, and memories of things that unhappened.  I write for the utility of writing.