Aristotelian thought had dominated mathematics and astronomy for centuries, until revolutionaries like Nicolaus Copernicus and Galileo Galilei challenged those views. However, their theories still had holes, which Isaac Newton then filled. Newton’s contribution to scientific thought included his four basic laws: three laws of motion and the law of universal gravitation.
Crucial Developments in Mathematics
The mathematization of physics was a crucial step in the advancement of science. It was realized that the mathematical tools we had at the time weren’t strong enough.
However, in the following generations, Rene Descartes developed analytic geometry and Isaac Newton created calculus, giving scientists increasingly powerful methods to develop mathematical theories to describe the workings of the world.
This is a transcript from the video series Redefining Reality: The Intellectual Implications of Modern Science. Watch it now, on The Great Courses Plus.
Johannes Kepler, a contemporary of Galileo, took the data of the Danish master astronomer Tycho Brahe and worked to find an account of planetary motion that would rid humanity once and for all of the epicycles—the circles in circles.
By trial and error, Kepler worked and worked until finally, he hit upon the shape that worked—elliptical orbits with the Sun at one focus. It turned out to perfectly fit the known observations.
Kepler derived three numerical laws setting out not only the shape of the orbits, but also the relations between the distance from the Sun and the period of revolution. They were stunning results, but no one knew why they would be true. Aristotle’s circular orbits had a philosophical basis—the perfection of the aether from which everything out there was made.
The Church’s adherence to the circles of their modified Aristotelianism had a theological foundation. But why ellipses, an egg shape? Why? It was an open problem of the highest order. It was an anomaly in the classical paradigm. None of this was revolutionary. The basic concepts which ordered the universe and the picture of reality they gave rise to had become wobbly, but had not fallen.
Isaac Newton’s Four Basic Laws
Isaac Newton developed a simple theory—four basic laws: three laws of motion and the law of universal gravitation.
Newton’s first law of motion concerns any object that has no force applied to it. An object not subject to an external force will continue in its state of motion at a constant speed in a straight line. Now, suppose someone is on ice skates, just standing in the middle of an ice rink. What’s going to happen? The person just stays in the middle of the rink. But if they are on ice skates and moving forward at two miles an hour, they will continue to move straight ahead at two miles an hour until something pushes them or stops them.
So, the first law describes the behavior of an object subjected to no external force. The second law then describes the behavior of an object that is subjected to an external force.
So again, if a person is on ice skates moving forward at two miles an hour and they are pushed from behind, they now go faster in the same direction. If they are pulled from behind, they slow down.
If pushed from the side, they change direction. The bigger the push, the more the change; the heavier the object, the less the change. An object is either subject to a force or it isn’t, so the first two laws are sufficient to describe the behavior of the object.
But what about the object or thing that applied the force? What happens to it? The force felt from a push is felt in the opposite direction, but in the same amount. Again, if a person is on ice skates and someone pushes them, they accelerate forward because of the force and the other person goes backwards because of it. To every action there is always an equal, but opposite reaction.
These three simple laws explained a lot, but they become incredibly powerful when combined with the fourth law—the law of universal gravitation, which says that gravitation is an attractive force, a very attractive force.
Take any two objects with mass and there will be an attraction between them, along the lines connecting their centers of mass. This pull will be proportional to the product of their masses—make one twice as heavy, twice the attraction. And it will be inversely proportional to the square of the distance between them—move them twice as far away, feel only one-fourth the pull.
When these three laws of mechanics and the law of universal gravitation are used together, we suddenly have an explanation for Kepler’s elliptical orbits. Not only that, we can explain the tides, the motion of cannonballs, virtually everything we see in the world around us.
This theory was gigantic in terms of scientific thought. When Edmond Halley, a friend of Newton’s, used it to predict the coming of a comet, it was hailed—rightly so—as one of the greatest achievements of the human mind in all of history.
Learn more about Newton, who inspired the Age of Enlightenment
Comparing Newton’s Theories with Aristotle’s
When these three laws of mechanics and the law of universal gravitation are used together, it was not only successful in terms of explaining and predicting, but, theoretically, it also undermined the old foundation—Aristotle.
Aristotle said that an object’s natural state of motion is at rest in is natural place. Newton has no natural places and says that its natural state of motion is in a straight line at a constant speed. Aristotle says that objects move themselves, seeking their own natural place.
Newton says that an object can’t move itself. Aristotle gives completely different accounts for the motions of objects close to the Earth and heavenly bodies.
Newton’s law of universal gravitation is universal. It applies to everything equally. Aristotle’s worldview was enforced by the centralized power of the Catholic Church. Newton’s worldview came not from authority, but from observing, something anyone could do.
How the Enlightenment Endorsed Equality
And so Newton’s success supercharged an intellectual movement developing around him, the Enlightenment. The picture of reality that emerged from the Enlightenment is one in which the universe is well-ordered according to principles that are accessible to the human mind.
We live in a world that we can understand. Humans are perfectly rational beings, made to understand the world we inhabit. Since rationality is the hallmark of humanity and all people have it, then none of us is better than any other. Human equality is a basic axiom.
This view stands deeply opposed to the hierarchical structures found in religion and monarchical governments that were the holders of power at the time. The Enlightenment gave to all people the ability to understand the world.
No longer were we subservient to superior authorities, if justice be done. We didn’t need to be told the truth from above. There is no one above, and we could discover the truth ourselves. Let all of us hear the arguments, and we’ll select the best one ourselves.
When it comes to distribution of political power, let us vote. Since humans are rational, we will select the best person to oversee the implementation of laws. If humans are rational, then our choices will reflect that.
We all feel pleasure and pain, preferring the pleasurable to the painful, and so we will act as perfectly rational maximizers of pleasure over pain. Put us all in a marketplace, and we will all act to bring about the best consequences for ourselves.
Since our best interests are often at cross-purposes—I want to spend as little as possible on this sandwich I am buying from you, while you want to charge as much as possible when selling it to me—there will be rational, predictable prices governed by forces in the marketplace that look exactly like Newton’s forces on billiard balls. Like Newton, we just need a combination of observation and reason to derive what must happen.
This is the picture of reality we get from the Enlightenment in the 17th and 18th century. We live in a well-ordered, predictable universe full of things we can observe. We exist in it as perfectly rational agents capable of observing everything there is, capable of using our reason to find the laws that govern their behavior. As such rational agents, we, too, become predictable, allowing new human sciences to explain how we behave.
Learn more about chaos theory
The Backlash to the Enlightenment
Needless to say, the views derived from the Enlightenment did not please everyone. There were those who thought that it took the mystery away from the world, mystery that gives meaning. Humans were reduced to robots with no passion or love. The Romantic backlash of the 19th century strove to put the irrational back front and center as the basis for true humanity.
What makes us human is not that which makes us glorified billiard balls, but that which sets us apart from the rest of the world. We make and appreciate beauty. We have free will, which we exercise in ways that are often capricious and bizarre. We are not just numbers; we’re romantic beings full of life in a universe that hides the unknowable deep at its core.
This was the battle over the shape of reality that was raging at the start of the 20th century. The Enlightenment ideals, with the scientific advances that they generated, had given rise to human progress as was seen in the incredible advances in every field of scientific endeavor and the emergence of democratic states with market economies.
The romantics objected, but the scientists and their supporters marched on. And then as the 20th century dawned, the cracks started to appear. Strangely, they arose in the last place anyone would have suspected—mathematics.
From the lecture series Redefining Reality: The Intellectual Implications of Modern Science, taught by Professor Steven Gimbel
Who Invented Calculus: Newton or Leibniz?
A Search for the Theory of Everything
William Blake’s painting “Newton” [Public domain], via Wikimedia Commons