Fumfer Physics 26: Can We Understand the Universe Without Math?
Author(s): Scott Douglas Jacobsen
Publication (Outlet/Website): Vocal.Media
Publication Date (yyyy/mm/dd): 2025/10/25
Rick Rosner riffs on whether a civilization could grasp physics without mathematics, imagining whale societies that count heads but lack equations. He argues math is essential for precise theories, yet many core ideas—projectiles, orbits, relativity—begin as pictures and principles before formalization. Examples include Einstein’s thought experiments refined with tensor calculus, Big Bang nucleosynthesis by Alpher, Bethe, and Gamow, and Newton’s insight that orbits are continuous free-fall obeying an inverse-square law. Scott Douglas Jacobsen notes everyday intuition—throwing a ball, braking for a light—mirrors calculus. Rosner concludes: you can teach physics conceptually without equations, but doing physics ultimately requires mathematics. Precision demands symbolic tools.
Scott Douglas Jacobsen: Could we understand the universe if we did not have any math whatsoever?
Rick Rosner: That reminds me of a scenario. What if there were no people—how would whales understand the universe? Imagine a planet with no land, only aquatic creatures. Would they ever be able to understand the universe, given that their view of the heavens is obscured? They do not have hands. Would aquatic creatures ever develop hands, or is that a purely terrestrial thing? Your question is like asking whether a civilization could arise with minimal math. That is conceivable. A primarily aquatic civilization might only need counting numbers—for instance, to keep track of group members: there are twenty-five of us, but I count twenty-four. Who is missing? Oh, Jerry. Where did Jerry go?
Math is convenient for describing physical concepts. You can tell things in words, but it is much harder to be precise. In the absence of wind resistance, a projectile follows a parabolic path up and back down to Earth. You could describe a parabola in words, but it is much easier to use an equation like y = –x². Once you have math, you can understand the concepts of the universe. You can translate those concepts into words. There is an entire industry of physics for laypeople, where highly trained physicists make the universe and modern physics comprehensible without math. Stephen Hawking was told by his publisher, while writing A Brief History of Time, that every equation in the book would cut sales in half.
So he included only one—E = mc². It was already so well known that it did not scare readers, even if they did not understand what it meant. You need math. I do not think you can develop physical understanding without it. But can you convey an understanding of the universe without equations? Yes, I think you can. You can teach smart people how physics works without math. The most famous example in quantum mechanics, besides Schrödinger’s cat—which most people reference without understanding its full implications—is the double-slit experiment.
You said, “Can you do physics without math?” That depends on what kind. You can have equations without numbers, like F = ma. I’ll give you three examples. Einstein was a visual thinker. Special relativity began when he imagined “chasing a light beam,” asking what electromagnetic fields would look like if you moved at the speed of light. For general relativity, his key insight was the equivalence principle—freely falling frames feel weightless—which he explored through thought experiments. He was good at math, but didn’t initially have the right tools. Marcel Grossmann, a mathematician friend, helped him adopt tensor calculus and differential geometry (not “matrices”) to rigorously express the theory. To a large extent, Einstein’s physics began with pictures and principles and only later took an entirely mathematical form. So visual reasoning can lead to profound insight before the equations are formalized.
Take Gamow. He’s often linked to early Big Bang cosmology, but the core ideas predate him. Alexander Friedmann, in 1922, found non-static solutions to Einstein’s equations. Georges Lemaître, in 1927, proposed an expanding universe and the “primeval atom.” Edwin Hubble, in 1929, provided observational evidence of the expansion of the universe. Gamow’s significant contribution, with his student Ralph Alpher and his work with Robert Herman, was Big Bang nucleosynthesis in the late 1940s: they calculated that a hot, dense early universe would produce mostly hydrogen and about a quarter of it helium by mass, and they predicted a residual cosmic microwave background. The famous 1948 “αβγ” paper listed Alpher, Bethe, and Gamow; Hans Bethe’s inclusion was partly a pun on the Greek letters. Bethe himself is best known for explaining how stars generate energy and elements through stellar nucleosynthesis.
So Gamow wasn’t first, but he refined and extended earlier insights. Then there’s Newton. With universal gravitation, he was one of the greatest mathematicians of all time—he co-invented calculus—but he also had extraordinary visual intuition. He realized that an orbit is continuous free-fall: an object falls toward Earth while having enough sideways, or tangential, speed that it perpetually “misses” the surface. Mathematically, his inverse-square law F=GMmr2F=Gr2Mm and the orbital relation for a circular orbit v=GMrv=rGM capture this: gravity provides the inward acceleration v2/rv2/r, while the orbital speed remains constant in a stable path.
Velocity increasing at a constant rate—like ten meters per second added every second—and that comes from Newton’s laws of motion: an object in motion stays in motion unless acted upon by an outside force. So he’s thinking, what would that look like? You’ve got an object in motion being pulled toward Earth. It already has some velocity, and gravity keeps adding more at a constant rate. That kind of reasoning is best expressed through math, but you can still conceive of it without doing the math explicitly. So intuition first, formalism later.
Also, gravitational force decreases inversely with the square of the distance from the gravitating body. That’s identical to the inverse-square law of illumination: the intensity of light decreases as the square of your distance from the source. You can think about that conceptually. If light radiates outward in all directions, then at any given radius, that light is spread over the surface of a sphere. The surface area of the sphere increases by the square of the radius. Since the total light remains the same, its intensity per unit area decreases with the square of the distance from the source. You can picture that without math—it’s a spatial intuition.
Jacobsen: So, visualization plays a significant role even in something as mathematical as physics. Math facilitates physics; it lets you expand your theories and rigorously test them. You do need math to formalize physics, but you can still grasp a lot conceptually. When I asked whether you could do physics without math, you were already doing it. When you throw a ball or play catch, you have an intuitive grasp of trajectories, velocity, and timing. So we all carry a kind of informal physics toolkit in our heads.
Rosner: Definitely. Anyone who drives understands aspects of calculus without realizing it. When you approach a stoplight, you brake gradually to come to a smooth stop—that’s an intuitive understanding of rates of change, or derivatives. You’re adjusting your acceleration continuously so you don’t collide or stop too soon. And when you think the light’s about to change, probability enters the picture. You might be approaching two cars at a light you’ve seen a thousand times, and you estimate whether the light will turn green before you reach them. You’re unconsciously running a probabilistic model—predicting timing, adjusting speed, minimizing wasted motion. People have an intuitive understanding of dynamics, and that’s a profoundly mathematical thing.
Many people who don’t know quantum mechanics still understand the double-slit experiment—where you can get a single photon to pass through two separate slits in a barrier and interfere with itself.
Many have heard of it, but only a much smaller fraction understands what it actually means. You could teach that without any math whatsoever, without any equations. You can teach people to understand physics conceptually without resorting to many equations. But you can’t do physics without, at some point, involving people who are good at turning those concepts into math.
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