When Isaac Newton died in 1727 he was given a funeral fit for a statesman and buried in Westminster Abbey. A young French exile in the crowd was astonished. In France, he wrote, a mathematician would never be honored like a king. The exile was Voltaire, and he went home determined to make Newton famous. The poet Alexander Pope summed up the mood in an epitaph: Nature and Nature's laws lay hid in night; God said, Let Newton be! and all was light. This level is about how the new science stopped being a specialist pursuit and became the model for an entire age.

Why Newton mattered beyond physics

Newton's Principia (1687) showed that a few mathematical laws could explain both a falling apple and the orbit of the Moon. For readers who would never follow the mathematics, the lesson was larger than gravity. The universe appeared orderly, knowable and open to patient human inquiry. If nature had laws that reason could discover, perhaps society, morality and government did too. Enlightenment writers spoke constantly of a science of man that would do for human affairs what Newton had done for the heavens.

John Locke supplied the other half of the picture. His Essay Concerning Human Understanding (1689) argued that the mind begins as something like blank paper and that our ideas come from experience. If people are shaped by experience, then better education and better institutions could produce better people. That optimism ran through the whole century.

The popularizers

New ideas spread through people who could explain them clearly. In 1686 Bernard de Fontenelle published Conversations on the Plurality of Worlds, a charming set of evening dialogues in which a philosopher explains astronomy to a curious marquise in her garden. It became a bestseller and showed that science could be written for a general audience, including women, who were shut out of universities.

Voltaire's Letters Concerning the English Nation (1733 in English, 1734 in French) praised Newton, Locke and English religious toleration so openly that the Paris authorities had the French edition burned. In 1737 the Italian writer Francesco Algarotti published a popular book whose title translates as Newtonianism for Ladies. Science had become fashionable conversation.

Émilie du Châtelet

The most accomplished of Newton's French champions was Émilie du Châtelet, a marquise who studied mathematics with leading scholars and lived for years with Voltaire at her husband's château at Cirey. Their house had a laboratory and a library that rivaled many universities. She wrote a major physics textbook, Foundations of Physics (1740), and then took on the work of her life: a French translation of the Principia with her own commentary. She finished it shortly before her death after childbirth in 1749. Published in full in 1759, it remains the standard French translation today.

Inoculation: a test of trusting evidence

The new respect for experience showed up in medicine. Smallpox killed and scarred millions. In Constantinople, Lady Mary Wortley Montagu, the wife of the British ambassador, saw local women deliberately infect healthy people with matter from a mild case, which usually produced light illness and lifelong protection. In 1721 she had her daughter inoculated in London. The same year, during an epidemic in Boston, the minister Cotton Mather and the physician Zabdiel Boylston promoted inoculation against fierce public anger. Their records were striking: roughly 2 percent of those inoculated died, compared with about 14 percent of those who caught smallpox naturally. Voltaire praised inoculation as an example of reason defeating prejudice. Counting outcomes, rather than trusting custom, was exactly the habit the Enlightenment wanted to spread.

Science also became a public spectacle. Traveling lecturers charged admission to demonstrate air pumps, prisms and electrical machines, and audiences gasped as sparks flew from a charged volunteer. In London and Paris, instrument makers sold telescopes and microscopes to curious amateurs. Scientific societies such as the Royal Society of London, founded in 1660, and the Paris Academy of Sciences, founded in 1666, published their findings and corresponded across borders, showing in practice the international, evidence-based community the philosophes admired.

Worked example: settling the vis viva dispute

In the 1740s, du Châtelet waded into a quarrel over how to measure the "force" of a moving body. Followers of Descartes and Newton said it was mass times velocity. The German philosopher Leibniz said it was mass times velocity squared, which he called vis viva, living force. How could the question be settled?

• Find a test: the Dutch scientist Willem 's Gravesande had dropped metal balls into soft clay from different heights and measured the dents.
• Read the results: a ball arriving twice as fast did not dig twice as deep. It dug about four times as deep.
• Draw the conclusion: the effect grew with the square of the speed, which supported Leibniz. Du Châtelet defended this view in print, even though it put her at odds with Voltaire and with the Newtonians she admired.
• See the legacy: her quantity is closely related to what physicists now call kinetic energy.

The lesson is the one the Enlightenment took from Newton: loyalty to a famous name matters less than what careful measurement shows.