Jamesian Philosophy Refreshed

Continuing yesterday's thoughts. Back in 1989, two chemists claimed to have created a simple table top apparatus that would work at room temperatures and that would create excess energy in amounts that, the chemists contended, had no explanation other than the incredible one: atoms were fusing. The scientists were: Stanley Pons and Martin Fleischmann. They were both sufficiently distinguished that the claim could not be dismissed lightly. Pons had a Ph.D. from the University of Southampton; Fleischmann from the Imperial College, London. That's Fleischmann in the photo that goes with this text, holding part of the apparatus, which was a little more complicated than Dogbert's. Their claims set off a frenzy of speculation about what this would mean. Some thought it would be bad news -- that the human race could not be trusted with the prospect of unlimited energy this implied. The more usual view was that this was great good news -- an apparently insatiable hunger ...

The story of another candidate for numberhood, the infinitesimal, is even stranger than the story of the irrationals or the imaginaries. The infinitesimal is the limit of a process, where the method stipulates that the end of that process can never be reached. Consider: can a single mathematical point have a slope? Our intuitive answer, trained by Euclid, is: no. A point is pure position. It isn’t a line, it isn’t even a tiny part of a line, so it can’t have a slope! Can there be a smallest possible line?   How short can a line get and still have a slope! That’s a question that Euclid taught us not to ask. It is akin to suggesting that we can have two adjacent points. If we could have two adjacent points, then they would presumably constitute the smallest possible line and they would have a slope. But we can’t. Between any two points, properly speaking, infinity of other points can fit. In the seventeenth century it was common for the mathematicians at its cuttin...