You have some interesting ideas, but in the end I actually voted −1 here because you are misusing the word arbitrage. You start off with the correct definition of buying low, then selling high, but the rest of the article isn’t using it correctly. Arbitrage isn’t just getting a lot of value cheaply, as in the introduction section or Yudkowsky sharing his knowledge.
An example of arbitrage would be learning Esperanto before you learn Spanish. I have heard that this can result in you learning Spanish even faster than if you had purely focused on learning Spanish. So here you have a currency (time), a primary good (Spanish ability) and a secondary good (Esperanto ability). Suppose you have a fixed amount of currency and more than a certain minimum. Then you can gain more of the primary good (Spanish) for the same amount of time by spending some time on Esperanto first, and even get some amount of the secondary good (Esperanto) tossed in for free!
(EDIT: Actually, this isn’t really an arbitrage, but rather a Pareto improvement, which is a closely related concept).
Eliezer writes: “But in any case, Godel’s Theorem surely does not show that natural numbers don’t exist. It says you’ll have trouble proving certain theorems. The observed universe is like the natural numbers, not like a theorem about them.”
I think whether Godels Theorem applies or not depends on how we define “understanding reality”. A lot of people would interprete it as not only being able to theoretically predict the state of the universe at any given time (ignoring the pratical issues of course!), but being able to determine stuff like what can exist. Answering these types of questions requires much more complicated logic and could quite possibly be non-computatable.