Leibniz dreamt of a characteristica universalis: a universal language that could express any scientific concept. He didn’t get too far – nobody was interested. But it involved a strange idea. Basic concepts would be encoded as prime numbers. More complicated ones would be encoded by multiplying these numbers. So, you could see which basic concepts a complicated one contained, just by factoring it!

When I heard this I immediately thought of Gödel numbering. This is a much better-worked out idea which Gödel used to encode statements of arithmetic as numbers. It also uses primes, but in a smarter way.

Did Gödel get his inspiration from Leibniz? I haven’t been able to find out. But I discovered that he was obsessed with Leibniz’s characteristica universalis!

— John Baez

2014.02.08 Saturday ACHK