You know what is memory. It is in your memory. But what is it? It is defined vaguely as 1) something remembered; 2) preserved data for retrieval. How do I know that someone has memory? It is simple - if his behaviour adequate to his past experience. But what if that someone does not reveal any behaviour? In such case to assert that the memory exists is problematic. In the simplest case the memory is a table device with input and output entries. For any particular input the device manifests output. In a computer, memory input is the address of a memory cell and output is the value stored in the memory cell. Note that in computer computation it is important that the addresses in memory are associated with each other by arithmetic operations; otherwise no useful computations would be possible.
Behaviour or output is necessary in memory definition. If no behaviour present (for example one cannot extract values from the memory) then it does not matter whether a device has anything in its memory or not. For an external observer memory is not present.
Time is necessary for memory definition. Memory links two events distant in time. And the opposite is true, if two events distant in time are linked, then there memory exists.
Space is required for memory associations. Different memories can be liked in space by association. In other words memory about memory maps time link into space link. The most interesting thing here is that mapping back space link into time link can be done arbitrary by a device. For example time can shrink or be reversed. In the first case, the device reveals ability to predict and in the second to infer.