History and Philosophy Of Science | From Logic to Physics-What Computers Cannot Do
X227 | 28422 | Amit Hagar


In 1984, the TIME magazine ran a cover story on computer software.
In the otherwise excellent article, an editor of a certain software
magazine was quoted as saying:

Put the right kind of software into a computer, and it will do
whatever you want it to. There may be limits on what you can do with
machines themselves, but there are no limits on what you can do with
software.

A simple way of summarizing this course is that it is devoted to
describing and explaining the facts that refute – no, shutter! –
this claim.

In the 4 modules that comprise this course we will acquaint
ourselves with the logical limits of computation, as they were
conceived within the framework of the foundations of mathematics. We
will get to know the standard model for computation, the Turing
machine, and learn about problems that it can and cannot solve.
Turning to physics, we will find parallel definitions for
computability in dynamical systems and in spacetime theories, and
use notions from complexity theory to reframe long-standing problems
in the philosophy of mind about free will, creativity, and the mind-
body problem. Each module will be comprised of frontal lectures, two
writing assignments, and a group project that will be presented in
class. Typically, these projects will consist of a digital
presentation and an exposition of one of the concepts that will be
discussed in the respective module, with an emphasis on its use and
mention (or, as usually is the case, abuse and misinterpretation)
inside academia and outside it in the popular culture. These
projects will enhance the critical evaluation of the notions and the
ideas discussed in class as they appear from time to time,
surrounded by hype, in the “secular” press. The course is self-
contained and presupposes a mathematical background at the high-
school level.