I've recently been criticized for not using quantum computing arithmetic in my meaningless arithmetic post. I assumed that the amount of "stuff" in the universe amounted to rougly 10^80, using fundamental particles. Berkenstein and Schiffer* put a limit on quantum information in the universe at 10^122. Fine. In fact, let's say that even the various quantum computing cheerleaders are all hopelessly narrow-minded and we aren't even near the real upper limit. There is still an upper limit. The point is this: the amount of possible information about a finite universe (and therefore encodable by the universe) is also finite. It must be, if reality exists at all.
*Jacob Bekenstein and Marcelo Schiffer, "Quantum Limitations on the Storage and Transmission of Information", International Journal of Modern Physics v1, pp. 355-422, 1990.