answer:I went to a lecture presented by Prof. Lawrence Krauss, in which he said that if Moore’s Law holds true for another 42 years (I think) then all the energy in the observable universe will have been used in the resultant computer. That refers to processing power more than memory, but it is a similar idea. The Israeli physicist Jacob Bekenstein has discovered the Bekenstein Bound which limits the amount of information it is possible to have within a given volume, which also limits the amount of computing power or memory it is possible to have. So yes, it is certainly the case that computer memory capabilities are finite.