Do We Ever See the World as It Really Is?
The Picture-Maker’s Surprise
In 1894, the physicist Heinrich Hertz (1857–1894) said something that sounded almost like science fiction: we never get to see the world the way it truly is. Instead, he said, we make up images or symbols of things out there. A force, an electron, a beam of light — these are mental pictures we build. The only thing that matters is that the consequences of our picture match the consequences we observe in nature. What the world “really looks like” underneath? That question, Hertz thought, is beyond us.
He wasn’t being gloomy. He was describing a deep puzzle about how physics works. His idea became an early whisper of what later thinkers called structuralism in physics — the view that physical theories are about the structure of the world, not about the hidden stuff carrying that structure. If you’ve ever drawn a treasure map that leads exactly to the buried chocolate but doesn’t show what the dirt looks like molecule by molecule, you already understand half of this story.
The Problem of the Circle: Mass, Force, and a Seesaw
The puzzle gets sharper when you look at a real law. Think of Newton’s second law: Force = mass × acceleration ( F = m a). That looks like a solid fact about the world. But watch what happens if you try to define the words inside it.
Suppose you say, “A force is just whatever causes acceleration.” Then F = m a isn’t a testable claim; it’s merely a definition — you can’t be wrong about it, because you’ve defined force to make the equation true. Now add mass. If you also define mass the usual way — “mass is the ratio of force to acceleration” — you’re caught in a loop. The same equation is being used to pin down two different things. An acceleration gives you the ratio F/m, but it won’t tell you F and m separately. That’s the problem of theoretical terms: the very concepts a theory uses (force, mass) and the law that connects them can seem to define each other in a circle, leaving no room for the theory to be tested against the world.
Physicists escape by adding more structure. For instance, require that all forces are gravitational and that gravitational mass equals inertial mass. Then you get an independent way to figure out the force from all the masses in the universe, using Newton’s inverse-square gravity law. Suddenly F = m a becomes a genuine claim — it could have been false — and the circle is broken. But this only works because you used other theoretical terms (gravitational mass, the universal constant G) that also need anchoring. The web of concepts grows, and the same puzzle lurks underneath almost every fundamental theory.
Escaping the Circle: the Structuralist Trick
Philosophers who called themselves structuralists in the late twentieth century believed this wasn’t a loose end to ignore. They invented a meta-toolkit — a way of talking about theories — to show exactly how the pieces fit together. Two of the leading programs came from Joseph D. Sneed (born 1938) and Günther Ludwig (1918–2007).
Sneed’s idea was to stop pretending that theoretical terms like “force” are given in advance. Instead, rewrite the whole theory as: “There exist quantities — call them forces, masses, whatever — such that the laws hold.” That move is an existential claim: you don’t define force directly; you say the universe is arranged so that something plays the role. Then you add extra laws, called constraints, to tie everything down. A constraint might say, “Every particle keeps the same mass across all situations,” or “The gravitational constant has the same value in every model.” With those constraints, the theory gains teeth; it says something about the world that can actually be tested.
Ludwig took a bolder route. He aimed to build an axiomatic basis for a theory, where every theoretical term is eventually spelled out in terms of things we can already observe or measure — often by studying all possible motions of a system, not just a single orbit. The math gets enormous (some of his books run hundreds of pages just to reconstruct quantum mechanics), but the goal is the same: show that the structure is what does the work, and that the mysterious-sounding words like “mass” aren’t magic — they’re defined by the role they play in the whole network.
Both Sneed and Ludwig relied on the mathematical idea of a species of structure from the Bourbaki group: a theory describes a type of structure, and physics is the art of matching that structure to bits of reality. And both acknowledged that real measurements are always fuzzy. You can never pin down a force perfectly; you can only get it within a blur of error bars. That blurriness, far from being a flaw, turns out to be essential when theories change.
When Theories Collide: Is Newton Just a Blurry Einstein?
One of the most dramatic moments in science is when a brand-new theory swallows an older one. Einstein’s relativity didn’t just throw Newton in the trash. Instead, it showed that Newton’s laws are a good approximation when things move slowly compared to light. This process is called reduction: theory T (Newton) is recovered as a limiting case of theory T′ (Einstein), the way a blurry photo can be seen as a special case of a sharp one.
The structuralists gave this vague idea a rigorous backbone. They defined reduction relations between theories by translating the non-theoretical vocabulary of one into the other, often using an approximate blur — a controlled definition of “close enough.” For example, Kepler’s ellipses turn into Newton’s slightly wobbly orbits, which in turn emerge from general relativity when gravity is weak and speeds are low. The older theory is never strictly true, but its successes are explained: it worked where the new theory’s corrections were too tiny to notice.
Erhard Scheibe (1927–2010) stressed that no single reduction recipe fits all cases. He examined example after example — Newtonian gravity vs. general relativity, thermodynamics vs. kinetic theory, classical vs. quantum mechanics — and argued that real reductions are messy patchworks. This led him straight into a philosophical fight known as the incommensurability debate.
Worlds That Won’t Translate
Historians like Thomas Kuhn and philosophers like Paul Feyerabend had argued that when a big theory change happens, the old and new worlds are literally “incommensurable” — you can’t fully translate the old concepts into the new language. To a Newtonian, “mass” is a fixed property of a chunk of stuff. To a relativist, mass depends on speed. The words survive, but the meanings shift.
The structuralists could take this challenge on because they already had fine-grained tools for comparing theories. Ludwig’s reduction relations, for instance, require a translation manual at least for the non-theoretical parts, so his approach effectively denies radical incommensurability at that level. Sneed’s program, using approximate reductions, could admit a spectrum of untranslatable leftovers — some structural mismatch might remain even after the best blurring. Scheibe tackled the issue head-on: he noted that in the shift from classical to quantum mechanics, the mathematical map between observables isn’t a perfect homomorphism (the algebra doesn’t carry over cleanly), which he considered a genuine case of incommensurability. The debate isn’t settled, but the structuralist toolkits let both sides argue with precision instead of hand-waving.
Why It Still Matters: Are You a Picture-Realist or a Picture-User?
The Hertzian puzzle follows you home. When your science teacher says “atoms are mostly empty space” or “gravitational waves ripple through spacetime,” are those sentences about real stuff out there, or are they about the sturdiest picture we happen to have right now? The structuralist doesn’t dodge the question; she says: what matters is that the structure of the picture locks onto the structure of reality. The labels you pin on the nodes of that structure — “mass,” “charge,” “spacetime curvature” — might be like the names on a subway map. They’re indispensable, but they don’t tell you what the tracks are made of.
Ludwig went so far as to call some overconfident interpretations “fairy tales” — stories that cannot be anchored to anything we can actually measure. For him, the single‑particle‑state picture of quantum mechanics was one such fairy tale; the statistical picture, where the wave function describes an ensemble of possibilities, was the one with a genuine claim to reality. You don’t have to agree. But the next time you feel certain that electrons are tiny blue marbles or that forces are invisible rubber bands, you are doing exactly what Hertz described: building an image of the world and checking whether its consequences match. Structuralism just asks you to be honest about which parts of the picture you actually see, and which parts you invented to make the math hold together.
Think about it
- If you define “happiness” as “how much you smile,” have you discovered a fact about happiness, or have you just created a rule that makes happiness impossible to be wrong about? Can you think of a feeling that a definition like that would miss completely?
- When people once believed the Sun orbited the Earth, were they talking about something real, or was the whole picture a mistake? If you say it was a mistake, what makes you so sure your current picture won’t look like a mistake in two hundred years?
- Imagine a video-game character whose entire world is made of pixels. If the character invented a theory of “gravity” inside the game that perfectly predicted every jump, would they be describing something real? What if the game engine kept changing, but the character never noticed?
