OK, this blog has made some pretty wild predictions over the years; from loss of privacy & security, through societal decay from social media & 24/7 connectivity, mass unemployment by AI & automation, to industrial environmental catastrophe and a technocapitalist Armageddon. Now there’s clear evidence of the first of these forecasts coming true, any chance of taking any of the others seriously? Maybe before it’s too late might be a good idea?
Category Archives: Algorithms
The concept of a ‘reasonable amount of time’ figures a fair bit in abstract computational complexity theory; but what is a ‘reasonable amount of time’ in practice? This post outlines the problem of balancing between the two competing ideals of determinism and adaptability and offers a flexible working definition. (Not to be taken too seriously: it’s summer vacation time.)
A standard text on combinatorial problems and optimisation algorithms – perhaps discussing the TSP, for example – might read something like:
“… so we tend not to be as interested in particular complexity values for individual problem instances as how these complexities change as the input problem size (n) increases. Suppose then, that for a given problem, we can solve a problem instance of size n = L in a reasonable amount of time. What then happens if we increase the size of the problem from n = L to n = L+1? How much harder does the …?”
or, filling in a few gaps:
“… so we tend not to be as interested in particular complexity values for individual problem instances as how these complexities change as the input problem size (n) increases. Suppose then that we can solve a TSP of 20 cities on a standard desktop PC in a reasonable amount of time. What then happens if we increase the number of cities from 20 to 21? How much longer does …?”
All good stuff, and sensible enough, but what’s this ‘reasonable amount of time’?
A walk in a Manchester Park on a Sunday morning …
Tucked away between Manchester Piccadilly and Oxford Road train stations is a quiet – but very touching – memorial to Alan Turing. In Sackville Park (or Sackville Gardens, depending on which map you consult), a figure sits, holding an apple, on a bench. Both are cast in bronze. The relief reads, ‘Alan Mathison Turing 1912-1954′ along with an ENIGMA-style coding of, ‘Founder of Computer Science’. At the figure’s feet, a further inscription reads, ‘Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice … Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture’, the second part being a quotation from Bertrand Russell.