Before Computers: Calculation and Automation
From Manual Counting to Mechanical Calculation
Understand how gears represent numbers and automate carrying between decimal positions.
In this lesson
Lesson goals
Understand how gears represent numbers and automate carrying between decimal positions.
The idea explained
Adding one to nine requires a carry into the tens position. A gear mechanism can perform that step physically instead of leaving it to the operator. Blaise Pascal developed his first calculator in 1642; its models handled addition and subtraction. The historical advance was the mechanization of repetitive arithmetic. A machine that adds, however, does not thereby choose new algorithms or run arbitrary software: its mechanism constrains its operations.
Dates and milestones
- 1642: Pascal’s first calculator, a milestone in mechanical arithmetic.
Why was this a turning point?
Some calculation steps became embodied in machinery, separating execution of an operation from control of a sequence.
Activity: try before reading the answer
Represent 99 with two paper wheels and add one. How many carries are required, and what if there is no hundreds position?
Answer and explanation
The carry passes through units and tens into hundreds. Without another position, 100 cannot be fully represented: a simple model of limited representation capacity.