An algebraic view of computation

I am not particularly interested in doing philosophy, as my research is about using computers to extend mathematical knowledge. But it turns out that this involves questions that are not mathematical or technical, but of fundamental nature. I write code and run computer experiments all the time, so the question `What is computation?’ is on my mind continuously. Here is an attempt, a draft version of a somewhat philosophical paper to address the question for the $(n+1)$th time. Spoiler alert! After doing semigroup theory for about 15 years, not surprisingly, I view computation algebraically. Taking the abstraction to the extreme, even beyond Turing machines and finite state automata, computers are semigroups. And computation is tracing a sequence in the composition (multiplication) table of a semigroup.

DRAFT paper on the algebraic view of computation (PDF, updated 2018.01.01)

final, thoroughly revised version 2018.05.11