I'm only finding out about this today, but back in August, Eliezer Yudkowsky of LessWrong fame wrote a blog post posing the question, "why is googology not a mainstream field of mathematics?" He offers the following conjectures:
- 1) "The process of determining which two large numbers is larger, is usually just boring tedious legwork and doesn’t by itself produce new interesting insights."
- 2) "By Friedman’s Grand Conjecture, most proofs about numbers can be formalized in a system with an ordinal no greater than ω^3 (omega cubed). Naturally arising huge numbers like Skewes’ Number or Graham’s Number are tiny and easily analyzed by googological standards. Few natural math problems are intricate enough or recursive enough to produce large numbers that would be difficult to analyze."
- 3) "Nobody’s even thought of studying large numbers, or it seems like a ‘silly’ subject to mathematicians and hence is not taken seriously. (This supposes Civilizational Incompetence.)"
I'm sure that Sbiis, our resident philosopher, would find this interesting. What do y'all have to say about this?