Not even Freud explains this!

Learning Objectives This chapter explains:

Freud

“Culture, Not Race, Explains Human Diversity”

Even Accelerating Machines are Not Universal

We draw an analogy between Godel's Incompleteness Theorem in mathematics, and the impossibility of achieving a Universal Computer in computer science. Speci cally, Godel proved that there exist formal systems of mathematics that are consistent but not complete. In the same way, we show that there does not exist a general-purpose computer that is universal in the sense of being able to simulat...

SOS Is Not Obviously Automatizable, Even Approximately

Suppose we want to minimize a polynomial p(x) = p(x1, . . . , xn), subject to some polynomial constraints q1(x), . . . , qm(x) ≥ 0, using the Sum-of-Squares (SOS) SDP hierarachy. Assume we are in the “explicitly bounded” (“Archimedean”) case where the constraints include xi ≤ 1 for all 1 ≤ i ≤ n. It is often stated that the degree-d version of the SOS hierarchy can be solved, to high accuracy, ...