Nilufar has run a small cafe near the bus station for six years, and every Sunday evening she writes the same sheet of paper: the week's order.
The order arrives in three deliveries. On Monday the van brings 4 crates of milk and 3 sacks of coffee beans. On Wednesday it brings 6 crates of milk. On Friday it brings 5 crates of milk and 2 more sacks of coffee.
Nilufar does not write nine numbers on her sheet. She writes two. Milk, she writes: 15 crates in total. Coffee: 5 sacks. Everything of the same kind goes together on one line, and the two kinds never meet.
Last spring a new assistant wrote the sheet for her while she was away. He added every number on the page and wrote one line: total, 20 items. It was arithmetically correct and completely useless. Twenty of what? The supplier could not fill the order, the van came on Tuesday with nothing on it, and the cafe served tea for two days.
The prices make the same point. A crate of milk costs $8 for each crate; a sack of coffee costs $22. So the milk cost her $120 that week and the coffee cost $110, and only at the very end, when both lines are finished, do the two numbers join into one: $230.
«You can add crates to crates,» she told the assistant, «and sacks to sacks. You cannot add a crate to a sack and call the answer a number.»