Impossible Programs

Impossible Programs

Every aspect of our lives has been transformed by the invention of general-purpose programmable computers. As a result, it’s tempting to believe that computers can solve any logical or mathematical problem; that if we throw enough time, money and nerds at a question, we can produce a program which answers it.

Unfortunately the universe is never that convenient. There are hard theoretical limits on what programs are capable of doing, and there will always be easily-stated problems which are impossible for any computer to solve.

This talk uses Ruby to tell a nail-biting, maths-free story about the source of a computer’s power, the inevitable drawbacks of that power, and the impossible programs which lie at the heart of uncomputability.

Given at Scottish Ruby Conference 2013 ( and GoGaRuCo 2013 ( There’s a video of this talk at This talk is adapted from chapter 8 of Understanding Computation (


Tom Stuart

May 12, 2013