Mathematician John Baez has a paper on the arXiv called Struggles with the Continuum, which he concludes with this:
We have seen that in every major theory of physics, challenging mathematical questions arise from the assumption that spacetime is a continuum. The continuum threatens us with inﬁnities. Do these inﬁnities threaten our ability to extract predictions from these theories—or even our ability to formulate these theories in a precise way? We can answer these questions, but only with hard work. Is this a sign that we are somehow on the wrong track? Is the continuum as we understand it only an approximation to some deeper model of spacetime? Only time will tell. Nature is providing us with plenty of clues, but it will take patience to read them correctly.
As readers of this blog well know, the assumption that spacetime is a continuum is absolutely wrong. The spacetime model that is the main subject of this blog is a discrete model that avoids all of the struggles that John discusses. I’ve pointed this out to him in an e-mail, but I don’t expect it to do any good.