For some reason today, I was thinking about a World Civilization class that I took in 1962 at what is now the University of Central Missouri.
There was a section in the accompanying textbook on the Egyptian pyramids and how the pyramid builders multiplied numbers. A bonus question on a pop quiz was to show how the Egyptians multiplied two numbers, say 26 and 67.
Suppose you were an Egyptian in charge of building a pyramid and had to multiply those two numbers 26 and 67. We could, today, pretty well come up with the answer as 1,742 in just a few seconds without using a calculator.
But the pyramid builder had to take several compound steps to arrive at that same number. He knew no other way.
Step 1. He took the first number 26 and halved it to 13. Since he needed to work with even numbers he subtracted 1 to get an even number of 12. He then took the second number 67 and doubled it to 134. Because he had to subtract 1 from his first answer, 13, to get an even 12, he made a note of the 134 for later use.
Step 2. He now halved the number 12, above, to 6. He then doubled 134, above, to 268.
Step 3. He now halved the number 6, above, to 3 but subtracted 1 to get an even number of 2. He then doubled 268 to 536. Because he had to subtract 1 from his third answer, 3, to get an even 2, he made a note of the 536 for later use.
Step 4. He took the number 2, above, and halved it to 1 but subtracted 1 to get zero. He then doubled 536 to 1072. Because he had to subtract 1 from his fourth answer, 1, to get zero, he made a note of 1,072 for later use.
His original problem was to multiply numbers 26 and 27. Because his first number, 26, was now computed in steps down to zero, he was finished with the multiplication problem except for adding up the numbers he had previously noted for later use.
Step 5. The pyramid builder then consulted his notes and added 134, 536, and 1,072 and came up with a multiplication answer of 1,742.
I can do that.