Chapter Five - Newton and the Need for Speed

CHAPTER FIVE

Newton and the Need for Speed

ISAAC NEWTON DIDN’T want to invent calculus.

He just wanted to explain everything.

Why planets orbit.
Why apples fall.
Why tides shift.
Why motion is motion.

But as he started working through it, he hit a wall. The math he had wasn’t enough. Algebra was strong. Geometry was decent. Trig got you some cool diagrams. But none of it could track how things change. Not precisely, not continuously.

He didn’t have the tools.
So he built them.

Most people remember Newton for the apple. You know the story, he’s chilling under a tree, one bonks him on the head, and suddenly gravity is born. That’s not what happened.

What really happened was plague.

Cambridge shut down during the Great Plague of 1665. So Newton, age 22, went home and started thinking. And when Newton starts thinking, the laws of the universe start trembling.

He wanted to understand planetary motion. The elliptical paths, the speeds, and the accelerations. But motion wasn’t clean. It was messy. Curved. Always changing.

You couldn’t use geometry. It wasn’t precise enough. You couldn’t use algebra alone. It didn’t track speed at an instant.

So Newton asked himself: What is speed, exactly?

Not just “distance over time,” that’s fine for average speed. But what if you want to know the speed of something right now? Not across a trip. Not from A to B. Just the speed in this exact instant?

There was no formula for that.
So Newton made one.

He didn’t call it calculus. That name came later.
Newton called it “the method of fluxions.”

He imagined quantities flowing, like time itself was a river. And as one quantity flowed, another changed with it. He called the changing thing the fluent, and the rate of change the fluxion.

Today we call those functions and derivatives.

It was a radical shift. Instead of solving static problems, he was solving dynamic ones. Not what something is, but how it moves. Not where something is, but how it’s shifting.

It let him explain acceleration, gravity, inertia, orbits, and all the stuff that made the universe tick.

He didn’t publish it right away. Newton was notoriously paranoid and secretive. But in his notes, he’d already laid out the blueprint. This wasn’t just math anymore.

It was physics in raw form.

And he was doing this in his twenties.

Like, all of it.
Calculus. Gravity. Optics. Motion.
Just vibing through the plague years, reinventing reality.

Most people spend their twenties trying to pay rent.
Newton spent his inventing modern science.

He didn’t have modern notation. He didn’t have Leibniz’s smooth symbols.
But he had the idea. The power. The method.

Calculus had officially entered the world.
Newton just hadn’t unleashed it yet.