For the last few hundred years, all our theories of physics have been mathematical.
If Stephen Wolfram is right, from now on, our most fundamental theories of physics may be computational.
This shift from mathematics to computation feels to me like a scientific revolution.
Recently, I asked Jonathan Gorard, who was instrumental in the founding of The Wolfram Physics Project, whether it feels to him, too, like a scientific revolution.
“I think so,” he said. “I mean, it’s a strong statement, but I don’t think it’ll end up being too inaccurate.”
Here’s why, in my mind, Wolfram Physics is the next scientific revolution.
The first scientific revolution
A few hundred years ago, Galileo peered through his telescope, timed pendulum swings, rolled balls down ramps, and expressed his findings using mathematics.
Why do we remember these observations, measurements, experiments and mathematics?
Sure, they established the laws of motion, as well as evidence that the Earth moves around the Sun. These contributions alone would have made Galileo a monumental figure in the history of science.
But they’re not the most compelling reasons to remember Galileo’s work.
We remember his observations, measurements, experiments and mathematics precisely because they were observations, measurements, experiments and mathematics.
This was a scientific revolution.
Obvious observations
It seems obvious, now, that scientists should make observations, take measurements, perform experiments and apply mathematics.
But it wasn’t obvious then.
That wasn’t the way science was done before Galileo’s time.
Back then, science was called natural philosophy. The name is telling. Science wasn’t so much observing nature. Science was more philosophizing about nature.
Why observe the way nature is when you can philosophize about the way nature should be?
Take falling objects, for example. If you drop a stone and a feather, the stone’s going to hit the ground first. That’s because heavier objects fall faster than lighter objects, right? That’s the way nature should be, when you think about it. Why bother measuring whether heavier objects fall faster than lighter objects? Why go to all the trouble of experimenting by rolling balls down ramps? If all your thinking tells you that heavier objects should fall faster than lighter objects, why not just leave it at that?
For nearly 2,000 years after Aristotle philosophized that heavier objects fall faster than lighter objects, natural philosophers did leave it at that.
Sure, there were lone voices of dissent. Nearly 1,000 years after Aristotle, John Philoponus repudiated the notion that heavier objects fall faster than lighter objects. He might even have performed experiments similar to Galileo’s rolling balls down ramps. But his ideas didn’t catch on. A lone voice of dissent does not make a revolution.
Or take the the Earth and the Sun as another example. The Sun follows a circular path across the sky. That’s because the Sun circles the Earth, right? That’s the was nature should be, when you think about it. Why bother measuring the paths of the Sun, the Moon, the planets and the stars? Why go to all the trouble of observing by peering through a telescope? If all your thinking tells you that the Earth should be at the centre of the universe, why not just leave it at that?
For nearly 2,000 years after Aristotle philosophized that the Earth is at the centre of the universe, natural philosophers did leave it at that.
Again, there were lone voices of dissent. Even before Aristotle was born, Aristarchus of Samos repudiated the notion that that the Earth is at the centre of the universe. He even measured the radius of the Earth’s orbit around the Sun. But his ideas didn’t catch on. Again, a lone voice of dissent does not make a revolution.
But when Galileo observed mountains on the Moon and moons in orbit around Jupiter, when he measured the period of a pendulum swing, when he experimented by rolling balls down ramps, he was not alone.
He might have felt alone when the Catholic Church threatened him with torture unless he disavowed his conclusion that the Earth moves around the Sun.
But all over Europe, Copernicus, Bruno, Kepler, Bacon, Descartes, Leibniz and Newton were abandoning the ancient, philosophical dogma and adopting a new, scientific reasoning founded on observation, measurement and experiment.
This was a true revolution.
Show me the math
And there was one more thing.
Once you start observing, you run into numbers.
How many moons of Jupiter did Galileo see through his telescope? Four.
Once you start measuring, you run into quantities.
How far does a pendulum swing? Maybe sixty degrees, maybe fifty, maybe thirty, or ten or eight or four or two.
And once you start experimenting, you run into relationships.
Not just any old relationships.
Mathematical relationships.
What’s the relationship between the length of a pendulum and how long it takes to swing? Turns out the period is proportional to the square root of the length.
That’s a mathematical relationship: T ∝ √L
Perhaps it was inevitable that once Galileo and his fellow revolutionaries started measuring quantities, they’d end up using mathematics to describe the relationships between those quantities.
After all, that’s what an equation is: a relationship between quantities.
Or perhaps it wasn’t inevitable. If it’s difficult to imagine a universe that defies mathematical description, that might just be a failure of imagination.
In the event, our universe proved highly susceptible to mathematical description.
Leibniz and Newton developed calculus, and ever since, physics has been firmly founded in mathematics.
This too was a true revolution.
Call that a revolution?
In the extraordinary century that opened with Galileo’s discoveries and closed with Newton’s, science was transformed from natural philosophy to a different discipline, based on observation, measurement, experiment and mathematics.
Nothing that’s happened in physics since can be truly called a revolution.
Even Einstein’s discovery of relativity didn’t come close. His reformulation of the laws of motion and gravitation was revolutionary, in a narrower sense, challenging the earlier dogmas of absolute space and time. But it emerged from the same kind of scientific reasoning as Newton’s earlier laws. And just like Newton’s laws, it was founded in mathematics.
Even the discovery of quantum mechanics didn’t come close. Again, the new probabilistic theories were revolutionary, in a narrower sense, challenging the earlier dogmas of determinism and certainty. But again, they emerged from the same kind of scientific reasoning as Newton’s earlier laws. And again, just like Newton’s laws, they were founded in mathematics.
How revolutionary?
What makes a scientific revolution?
A fundamental shift in our scientific theories is not enough. That’s not a scientific revolution, that’s just science, doing what it does, replacing one way of looking at the universe with another way of looking that explains all the old observations, along with some new ones that couldn’t be explained by the earlier way of looking.
What makes a scientific revolution is a fundamental shift in the way science is done.
The shift from philosophy to observation, measurement and experiment? That was a fundamental shift in the way science is done.
And the shift from describing the universe in a natural language, such as Latin, to describing the universe using mathematics? That, too, was a fundamental shift in the way science is done.
Galileo himself reflected on this shift beautifully: “Mathematics is the language with which God has written the universe.”
Up the revolution
Except that, now, suddenly, something has happened in physics, something new, something revolutionary.
The Wolfram model and other computational models of physics are not founded in mathematics. They’re founded in computation.
This turns physics upside-down.
Instead of starting with complex observations and postulating mathematical equations to fit those observations, these computational models start with simple rules and apply those rules to simulate universes that might mirror our own.
The shift from describing the universe using mathematics to describing the universe using computation seems to me like a fundamental shift in the way science is done.
We have yet to see whether this shift will prove successful, but if it does, the reframing of physics in terms of computation might be as profoundly important as the reframing of physics in terms of mathematics in Galileo’s time.
To me, the Wolfram model, too, feels like a true revolution.