Important discovery: it is possible to split tasks so that separate cores can work on them independently. I happen to have four on my machine, which is already a substantial speed increase.
In the case of my Wordsquares project, it is possible to split the word list into number-of-cores parts, and apply the process to each (whilst keeping the entire list for the actual building of the squares). This is in effect a linear increase: had I access to ten, twenty cores, I could divide the computation by that number.
Python works under what is known as the GIL (Global Interpreter Lock), which prevents any Python operations to occur simultaneously (all operations, at the bottom level, occur one after another in a specific, traceable order). In order to work with mutliple cores, one has to use the multiprocessing module, where it is possible to assign a number of cores, and tell Python which tasks should be taken care of by which core. (It creates entities called ‘workers’, which has a sweet Marxian overtone to it.)