Great IdeasNature and science
Measuring the world
Turning size, weight and time into numbers.
The question
How did people learn to turn size, weight and time into numbers, and why does measuring matter?
How the books answer
Oldest first. Each stop is our own short summary of what the author argued; follow the link to the rung for the whole lesson.
c. 300 BC
Euclid, The Elements, Books XI–XIII
Euclid proves exact relations between solids, such as that a cone holds one third as much as a cylinder with the same base and height. He does it without any units at all, by comparing one shape with another. Measurement begins as ratio.
“Any cone is a third part of the cylinder which has the same base with it and equal height.”
3rd century BC
Archimedes, On the Equilibrium of Planes, On Floating Bodies, Measurement of a Circle, The Sand-Reckoner, On the Sphere and Cylinder, and others
Archimedes traps the circle between polygons of 96 sides to pin down the ratio of circumference to diameter. He proves it lies between 3 10/71 and 3 1/7. It was the best value for centuries, and his method of closing in on a number is still used.
“The ratio of the circumference of any circle to its diameter is less than 3 1/7 but greater than 3 10/71.”
c. AD 150
Claudius Ptolemy, The Almagest
Ptolemy measures the heavens. He builds tables of chords, an early form of trigonometry, and uses old and new observations to set the planets' cycles. His careful numbers let astronomers predict eclipses.
1628; the letters On the Circulation of the Blood, 1649
William Harvey, On the Motion of the Heart and Blood in Animals, and On the Circulation of the Blood
Harvey does a simple calculation: how much blood does the heart push out with each beat, and how many beats in half an hour? The total is far more than the body could make from food. So, he argues, the same blood must go around and around.
“Now in the course of half an hour, the heart will have made more than one thousand beats, in some as many as two, three, and even four thousand.”
Go to the rung: Harvey: On the Motion of the Heart and Blood
1638
Galileo Galilei, Dialogues Concerning the Two New Sciences
Galileo times balls rolling down ramps by weighing water that flows from a vessel during each run. The distances, he finds, grow as the squares of the times. Measurement turns a guess about falling into a law.
1647–1654
Blaise Pascal, Treatises on the vacuum, the equilibrium of liquids and the weight of the air, and the arithmetical triangle
Pascal has his brother-in-law carry a tube of mercury up a mountain, the Puy de Dôme. The mercury stands lower at the top, showing that the weight of the air above us pushes it up. A measurement settled an old argument about whether nature abhors a vacuum.
1690
Christiaan Huygens, Treatise on Light
Huygens uses Ole Rømer's timings of Jupiter's moons to show light takes time to travel. He estimates its speed as hundreds of thousands of times faster than sound. Huygens also invented the pendulum clock, which made time far easier to measure.
“But Sound, as I have said above, only travels 180 toises in the same time of one second: hence the velocity of Light is more than six hundred thousand times greater than that of Sound.”
1726
Jonathan Swift, Gulliver's Travels
Swift has fun with measurement. The Lilliputians, one-twelfth Gulliver's size, calculate that he needs food enough for 1,728 of them, which is 12 times 12 times 12. Swift mocks scientists elsewhere, but here he gets the math right.
“…the emperor stipulates to allow me a quantity of meat and drink sufficient for the support of 1728 Lilliputians.”
1789
Antoine Lavoisier, Elements of Chemistry
Lavoisier weighs everything that goes into and comes out of a reaction, using balances of great precision. The totals always match. This careful weighing founded modern chemistry.
For young readers
Measuring means finding out how big, heavy or long something is, using numbers. You might measure your height on a door frame each birthday.
Great discoveries often came from careful measuring. Harvey counted heartbeats and figured out that blood goes around the body in a circle. Try it: count your heartbeats for one minute, then do 20 jumping jacks and count again!
Talk about it
- Why did Gulliver need food for 1,728 Lilliputians, not just 12?
- How could you measure the height of a tree without climbing it?
- Count your heartbeats in one minute. How many in a day?
- Before clocks, how might people have measured time?
Where else on the site
Every rung tagged with this idea:
These pages are our own short synthesis, written for families. They were inspired by Mortimer J. Adler's Syntopicon, the index of great ideas in volumes 1 and 2 of Great Books of the Western World, but the questions, summaries and groupings are ours, not the Syntopicon's. Short excerpts come from public-domain translations, credited where they appear.