In type theory and some fields of logic, 2 is usually defined as (λf.λx.f (f x)); essentially, the concept of doing something twice.

That's the number of all directed graphs, some of which certainly have cycles.

"http://en.wikipedia.org/wiki/Epicycle#Epicycles"

Ha!

Surveyed. Looking forward to the data and analysis, as per every year.

That's not how Big O notation works: O(100,000) = O(1).

You presumably mean "in the order of 100,000", which is sometimes written "~100,000".

This is at least as old as Leibnitz.