In an essay by Marvin Minsky I read over the weekend, Communication with Alien Intelligence, Minsky explores the idea that arithmetic spontaneously arises in computing systems, analogously to the spontaneous assembly of amino acids in the Miller/Urey Experiment. In the process of exploring the first few thousand simplest Turing machine programs, he and his student discovered that the only really interesting behaviour exhibited was a simple form of counting.
After a bit of musing along the main theme of the paper, there’s this interesting aside:
I wonder if it’s dangerous to make our children think so much about arithmetic if, when it’s seen this way, it leads to such a singularly barren world. Some of us discover in it a universe of different ways to add, and different ways to think up more such ways. But most children find it dull just endless, pointless pain and rote the tedium of working abstract clay too cold and stiff to mold and shape. The only ones who benefit are those who, seeing that they cannot bend the rules, distort instead the ways they’re used.
In other words, arithmetic is such a cold, inflexible, crystalline structure, that you have to be really desperate for something interesting to do with it in order to escape from its boring homogeneity.