Episode 11: Programming and boolean algebra

This week the topic was boolean algebra. We interviewed Robie Basak, who's a computer programmer at Canonical, about his work on the Ubuntu operating system, and how he and his colleagues use mathematics and mathematical thinking in order to write computer software.

Interesting links:

• Canonical Website
• Ubuntu website
• Boolean Logic, at HowStuffWorks
• Domino computer video
• Blog post from Tanya Khovanova, on logic puzzles
• Knights and Knaves puzzles and examples, Wikipedia
• Knights and Knaves puzzles, on Maths is Fun

Puzzle: Anna and Bill are residents of the island of knights and knaves. Knights always tell the truth, and knaves always lie. Anna says "We are both knaves.” What kind of person are Anna and Bill? Chris and Diane are also residents of the island of knights and knaves. Chris says "We are the same kind", but Diane says "We are of different kinds”. What kind of person are Chris and Diane?

Solution:

Anna states they are both knaves; this can’t be true, as if it were she would be a knave and therefore would be lying. So, the statement must be false, and Anna is therefore a knave. Also, since she always lies, they can’t both be knaves, so Bill must be a knight.

In the second example, the two give different answers, one of which must be true, so one of them must be lying, and therefore Diane is telling the truth. This means Chris is a knave and Diane is a knight.