Quantum Random Self-Modifiable Computation

Among the fundamental questions in computer science, at least two have a deep impact on mathematics. What can computation compute? How many steps does a computation require to solve an instance of the 3-SAT problem? Our work addresses the first question, by introducing a new model called the ex-machine. The ex-machine executes Turing machine instructions and two special types of instructions. Quantum random instructions are physically realizable with a quantum random number generator. Meta instructions can add new states and add new instructions to the ex-machine. A countable set of ex-machines is constructed, each with a finite number of states and instructions; each ex-machine can compute a Turing incomputable language, whenever the quantum randomness measurements behave like unbiased Bernoulli trials. In 1936, Alan Turing posed the halting problem for Turing machines and proved that this problem is unsolvable for Turing machines. Consider an enumeration E_a(i) = (M_i, T_i) of all Turing machines M_i and initial tapes T_i. Does there exist an ex-machine X that has at least one evolutionary path X --> X_1 --> X_2 --> . . . --> X_m, so at the mth stage ex-machine X_m can correctly determine for 0 <= i <= m whether M_i's execution on tape T_i eventually halts? We demonstrate an ex-machine Q(x) that has one such evolutionary path. The existence of this evolutionary path suggests that David Hilbert was not misguided to propose in 1900 that mathematicians search for finite processes to help construct mathematical proofs. Our refinement is that we cannot use a fixed computer program that behaves according to a fixed set of mechanical rules. We must pursue methods that exploit randomness and self-modification so that the complexity of the program can increase as it computes.Comment: 50 pages, 3 figure

Assumption without representation: the unacknowledged abstraction from communities and social goods

We have not clearly acknowledged the abstraction from unpriceable “social goods” (derived from communities) which, different from private and public goods, simply disappear if it is attempted to market them. Separability from markets and economics has not been argued, much less established. Acknowledging communities would reinforce rather than undermine them, and thus facilitate the production of social goods. But it would also help economics by facilitating our understanding of – and response to – financial crises as well as environmental destruction and many social problems, and by reducing the alienation from economics often felt by students and the public

Gertrude Wolf papers undated, 1899-1944

Primarly correspondence and material relating to Stephen S. Wise, including photographs, miscellaneous items and sermons preached at Congregation Beth Israel in Portland, Oregon. Also contains letters from Lawrence Gilman, John Haynes Holmes, Leo Katz, Charles A. Sherrill, Michael Banner, Fiske Kimball, and Philip James, a manuscript play "Everyday" by Rachel Crothers, and a autobiography in shorthandfar031