The following is a paraphrase of an argument for the discreteness of spacetime, made by Smolin in his popular-level book Three Roads to Quantum Gravity. The Bekenstein bound says there's a limit on how much information can be stored within a given region of space. If spacetime could be described by continuous classical fields with infinitely many degrees of freedom, then there would be no such limit. Therefore spacetime is discrete. I gather that this argument is far from being universally accepted. Where are the holes in the argument? I would appreciate nontechnical answers. My background is that I did my PhD in low-energy nuclear physics, and I have a pretty good understanding of general relativity, but I don't have any technical expertise in quantum gravity. My only knowledge of quantum gravity comes from popular-level books like Smolin's and Susskind's.