No; I'm saying the amount of information at any given time is finite, which is what the original article was talking about. But even if there is growth in memor

No; I'm saying the amount of information at any given time is finite, which is what the original article was talking about. But even if there is growth in memory size (say that memory size increases linearly), the information you get at any specific instant is finite (even if unbounded)... just as you have infinite natural numbers but none of them has an infinite value. But anyway, with finite space even in infinite time you couldn't build an infinite memory. And also... the original article was talking about the size of the system at a specific instant, so growth doesn't matter here.