Author Archives: Paul Crowley

No architectural leap required

I recently listened to the Yudkowsky-Hanson debate that took place at Jane Capital in June 2011.  It’ll surprise no-one that I’m more convinced by Eliezer Yudkowsky’s arguments than Robin Hanson’s, but the points below aren’t meant to recap or cover the entire debate. At roughly 34 minutes in, Hanson leans hard on the idea thatContinue reading “No architectural leap required”

Lambda calculus and Graham’s number

Very big numbers like Graham’s Number are often expressed with lengthy, clumsy, semi formal explanations. But it’s concise and convenient to express such numbers precisely in the pure lambda calculus, using Church numerals. Starting with Knuth’s up-arrow, if we define fn,a(b) = a↑nb, then f0,a(b) = ab and fn+1,a(b) = fn,ab(1). From this we get thatContinue reading “Lambda calculus and Graham’s number”