Concrete devices

Computing is intimately tied to the representation of numbers. But long before abstractions like the number arose, there were mathematical concepts to serve the purposes of civilization. These concepts are implicit in concrete practices such as :

• one-to-one correspondence, a rule to count how many items, say on a tally stick, eventually abstracted into numbers;
• comparison to a standard, a method for assuming reproducibility in a measurement, for example, the number of coins;
• the 3-4-5 right triangle was a device for assuring a right angle, using ropes with 12 evenly spaced knots, for example.