Memory of a blockchain is simple the number of blocks, pieces of information, transactions or state variables that are hashed together and are represented in the final hash pointers. Regarding the final hash pointer of a standard blockchain solution, it has infinite memory, regarding that the information is hashed back to the genesis block. However this should not always be the case, certainly an infinite memory provides a better security, however after a certain point, it seems to be irrelevant if we keep the history only for a couple of years or to forever. In this sense, it makes sense imagine blockchain platforms that have less than infinite memory.
