An Address Is Also a Number
The memory lesson said it in passing: cells are numbered, and the number of a cell is its address. Today that innocent remark detonates. Addresses are numbers — and everything the course has established about numbers instantly applies to them: they can be stored in cells, and they can be computed. Half of the machinery of programming falls out of those two clauses.
Start with the question
Cell 7 holds the number 100. Question: what is in cell 7?
After the agreement lesson you know to answer carefully: the number 100, and nothing else — meanings depend on the reader. But consider one particular reading agreement, modest-looking and world-carrying: "the number in cell 7 is the address of the cell I actually care about." Under this agreement, cell 7 does not hold a quantity — it holds a direction: "go to cell 100". A number read this way is universally called a pointer (or reference) — one word to learn, a lifetime of use.
Say the crucial sentence aloud: the machine stores no arrows. Cell 7 holds the number 100 — a perfectly ordinary number that another reader could take for a temperature. The pointing is a reading agreement, exactly like "letter" or "brightness" — and like them it can be applied, withheld, or (with consequences a later tier will relish) misapplied.