Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Philosophy to Program Size   Most work on computational complexity is concerned with time. However this
course will try to show that program-size complexity, which measures
algorithmic information, is of much greater philosophical significance. I'll
discuss how one can use this complexity measure to study what can and cannot be
achieved by formal axiomatic mathematical theories. In particular, I'll show
(a) that there are natural information-theoretic constraints on formal
axiomatic theories, and that program-size complexity provides an alternative
path to incompleteness from the one originally used by Kurt Godel. Furthermore,
I'll show (b) that in pure mathematics there are mathematical facts that are
true for no reason, that are true by accident. These have to do with
determining the successive binary digits of the precise numerical value of the
halting probability Omega for a "self-delimiting" universal Turing machine. I
believe that these meta-theorems (a,b) showing (a) that the complexity of
axiomatic theories can be characterized information-theoretically and (b) that
God plays dice in pure mathematics, both strongly suggest a quasi-empirical
view of mathematics. I.e., math is different from physics, but perhaps not as
different as people usually think. I'll also discuss the convergence of
theoretical computer science with theoretical physics, Leibniz's ideas on
complexity, Stephen Wolfram's book A New Kind of Science, and how to attempt to
use information theory to define what a living being is.

29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys