>>43Whoa, whoa, whoa! How did you get this far off base? Firstly, while it is true that the projections of all first class, ordered endotensors onto
Rn spans the set of of the contravariants of all such endotensors, but that in no way implies homoiconicity. Homoicinicity is unrelated to the study of endotensors, and quite honestly, I believe that it is harmful to the study of endofunctors as well, as it assumes the axiom of free choice when such an assumption is unnecessary for purely theoretical research.
Secondly, the set eigentensors of the endotensor identity matrix have infinite cardnality. This implies that it must be surjective. Granted, this is a proof by contraindication, but producing a formal proof has been shown to be NP-hard.
Lastly, you make a good point the hylomorphic properties of the catamorphic transformations. Indeed, it was one asked by my mentor early on. The solution lies in considering finite automata. The intersect of one regular language with another is itself a regular language. Since endotensors are not regular languages, nor are they even in the subset of context free grammars that do not forbid birecursion, they are not bound by this restriction. Thus, they are Turing complete yet also Godel incomplete. Hence the computability of the individual elements of the commutative field.
Interestingly enough, this property is the dividing difference between lambdas and closures.
>>44No he didn't, I was taking a shower. Why is everyone always ready to assume the worst? Anyway, I have I go to bed. Tommorrow I will begin lecturing a summer course as a guest lecturer at MIT, and after that I'm going to give a talk about Touhou and it's place in Asian-American literature and why Reimu should take a more proactive approach to governance at Harvard the next day. I'll still try to answer questions here when not being bombarded with them by students in real life though.
>>45Always feels great to eliminate a little ignorance in the world.