CMSC 31100-1: Big Ideas in Computer Science

Autumn 2006

Potential topics

As long as the schedule is open, I'll type in potential topics that occur to me, in case someone wants to take them, promote them, attack them, ... You can think about them, even if we don't take any of them up in class.

• The program/data [in]distinction. (Stored-program computer, universal machine, S-m-n theorem, LISP representations, partial evaluation, point evaluation functionals in analysis, program metrics based on operator/operand counts, Language of Thought Hypothesis, ...)
  
  
• Quantum computation as a physics experiment. (Does computational complexity limit quantum coherence?)
  
  
• The genetic code as a programming language.
  
  
• Immune reaction as pattern matching.
  
  
• Many ways of connecting computation and reasoning. (Automated deduction, logic programming, deductive database, formulae as types, Π-2 definitions, proof normalization, constructive proof, proof as recursive enumeration.)
  
  
• Philosophical meaning of uncomputability and incompleteness.
  
  
• Computations that kill. (E.g., the Terac disaster.)
  
  
• Optimistic computation and virtuous cycles. (Memory hierarchy, networking, parallel computation.)
  
  
• The engineering dynamics of the computing business. (Why have programmed general-purpose devices almost always beaten specialized circuits (my ceiling fan runs Unix)?)
  
  
• Computation rules. ("Architecture is politics," John Perry Barlow. "Architecture is policy," me. "Code is law," Larry Lessig. How programmers may create company policy while executives make illusory decisions. To say nothing of politicians.)
  
  
• Correctness vs. safety. (All programs are wrong. How can we design programs so that the errors are least harmful?)
  
  
• Human interactions mediated by computing. (Not the obvious stuff, such as email. How does a continually changing piece of code and/or database provide for particular types of co-operation, conflict, and exercise of power between the different parties who create and use it? The three most important issues in interactive software design are binding time, binding time, and binding time.)
  
  
• The physics of computation. (Reversible minimal energy computation. The thermodynamic cost of erasing information.)
  
  
• Top-down vs. bottom-up vs. sideways design. (The serious differences in good design for applications vs. infrastructure, model vs. interaction.)
  
  
• How trivial can a model of computation be? (2 and 3 counter machines. Combinator calculus.)
  
  
• Computational characterizations of life. (Not simulations of life as we know it. Computational definitions of what it means to be alive.)
  
  
• Computational aesthetics.
  
  
• Automatic programming. (This problem has been solved repeatedly, but each solution changed the nature of programming so that it was no longer a solution.)
  
  
• Why unrealistic models of computation are realistic. (Asymptotics are empirically predictive of practical behavior. They also capture invariants under rapid technological change.)
  
  
• The big picture is always bigger than you think. (At some points in history, the fastest way to solve a particular problem is to drink coffee and listen to lots of music for 10 years waiting for faster algorithms and computers.)
  
  
• What do we really need supercomputers for? (Patterns of human interaction may be more important than problem structure.)
  
  
• Halting problem undecidablity as a very short Python program.
  
  
• Hilbert & Descartes were both talking about computation, and saying approximately the same thing.
  
  
• Who said that the universal set is enumerable?(Conventional asymptotics in computability theory become impractical in certain places. E.g., in practice a set may be recognizable (decidable) but not listable(recursively enumerable). Maybe sometimes we shouldn't assume that we're working inside of an effectively listable universe. E.g., logical constructions are essentially computations, but arguably not in a listable universe. Dana Scott's meagre sets.)
  
  
• Overdefined elements in Scottery. (This is a Turing Award waiting to be won. Semantics based on Scottery with underdefined values, and only a trivial use of a small number of overdefined values, can be expressed as a coarsening of Tarskian semantics. But rich structures of overdefineds are new, and can represent localized inconsistency. So, why doesn't anybody study them?)
  
  
• Information can be measured in bits.