Speaking as one of those rare biologists who explored maths all the way up to A-level (though admittedly scraping a bare pass), and having read New Scientist's recent article on infinity (taking about 20 minutes - I had to read several bits twice and I confess my lips moved) I can grasp that there are infinities of infinities, but I can't help sympathising with Wittgenstein and Gwendolyn's teacher as it doesn't seem exactly in touch with reality.