In the popular imagination, studying physics is often confused, in whole or in part, with memorizing ad hoc formulas for every phenomenon: a set of rules, more or less simple, to be combined or, in easier cases, applied directly to predict the outcome of some event.

Even years after school, many still believe there’s a special formula for the time it takes an object to fall, another for the speed of a car that goes ten meters in ten seconds, and so on.

This sterile, mechanical approach makes us lose sight of the big picture—not only of the meaning and limits of the models behind those formulas, but also of the way everything fits together without contradiction. The sense of wonder disappears too: the realization that one and the same abstract relation between physical quantities works just as well for a car as for an electron—within limits, of course.

So, we need to put the pieces back together and give what we’ve studied a broader, deeper sense.

When ideas get too abstract—as in this talk about method—it helps to lean on a good analogy. But we must remember: an analogy can help us grasp the spirit of an argument, not its exact mechanics. Push it too far, and it becomes misleading.

For what follows, I’ll use the game of chess as a model.

Here’s what a beginner’s manual says:

Chess is a strategic game for two players, played on a board with sixty-four squares of alternating light and dark colours. Each player controls sixteen pieces: a king, a queen, two rooks, two bishops, two knights, and eight pawns. The goal is to checkmate the opponent’s king—threaten it in such a way that it cannot escape capture.

Each piece moves in a particular way. The king moves one square in any direction. The queen moves any number of squares in a straight line—horizontally, vertically, or diagonally. The rook moves only in straight horizontal or vertical lines. The bishop moves only diagonally. The knight moves in an L-shape: two squares in one direction, then one perpendicular to it, and it’s the only piece that can jump over others. Pawns move forward one square (two from their starting position) and capture diagonally.

There are special rules: castling lets the king and a rook move together under certain conditions; promotion turns a pawn that reaches the far end of the board into another piece, usually a queen; and en passant allows a pawn to capture an opposing pawn that has just moved two squares.

The game ends with a checkmate, a draw, or one player resigning.

Read that description with physics in mind, and some immediate, striking analogies appear. The pieces are the phenomena; their specific ways of moving are the formulas that govern them. Combine the two, and you get the game.

The temptation to push the analogy further is irresistible. That’s exactly what we’ll try to do.

First, in the game of physics, it’s hard to isolate the individual pieces. Even when we do, they’re mostly abstract—quantities of energy showing up one way or another, their properties defined by nature and by how they interact.

Who among us has ever seen an electron or a neutrino? And yet, each of us inhabits a region of space filled with an absurd number of electrons, constantly pierced by billions of neutrinos every second, mostly from the Sun.

In chess, by contrast, a rook or bishop can be lifted off the board and stored in a box for years without any danger of decaying into a pawn or, by mutual interaction, spontaneously generating a king or queen. The pieces exist independently of the board, with no need for metaphysics.

Let’s proceed step by step. Suppose we want to study a number of phenomena (the pieces) through their interactions and evolution (the moves) within a portion of the universe—namely, the laboratory. We’ve already made a choice among all possible ways to interpret the game.

One player stands for the experimenter; the chessboard is the local patch of spacetime where observation happens. The fact that it’s flat makes for a nice image of a geometry not distorted by strong gravitational fields—in simpler terms, a beam of light is a straight line.

So far, so good.

Now, against whom (or what) are we playing? And why?

Those questions quickly become tricky, even metaphysical. They tempt us to imagine a mysterious opponent and to speculate about the ultimate purpose of the game—but that’s outside the experiment itself.

So let’s imagine instead that the second player is represented by the laws of an entire universe made of board and pieces. We sit down to play, knowing only some of the rules—roughly, perhaps—and test them directly by playing. That way, we remove the shadow of an all-knowing designer who moves everything behind the scenes.

In Aristotelian terms, this means giving up the idea of a prime mover. In modern terms, it means abandoning the notion of an absolute reference frame—the old ether—to which all laws must refer. That’s a very Einsteinian insight: you can imagine such a figure if you like, but it’s unnecessary and, more importantly, unprovable.

The next question—why the game and its rules exist—admits two lines of thought.

If we can’t accept, even theoretically, a beginning without cause or purpose—or if we question the idea of a beginning at all—we might imagine a bored, quarrelsome pantheon of gods who, to pass the time, invented a game. We and all physical phenomena would then be their pieces. The rules appear to us as physical laws, and checkmate would be the system’s entropic death.

Or, since chess is a finite, closed model with open and chaotic dynamics, we might consider both beginning and end as external to the system—neither provable nor even directly conceivable from within. Despite the staggering number of possible games (estimated by Shannon at 10¹²⁰), that number still exceeds the total count of atoms in the universe (around 10⁸⁰) by forty orders of magnitude.

Both approaches rest on unverifiable assumptions, but neither affects the game’s internal logic. Even the old debate over free will and determinism could be folded into the rules of the system itself, much like the quantum collapse of the wave function—neither moral nor directional.

At this point, the analogy starts to illuminate the deep connection, in the quantum world, between observer and phenomenon.

To develop it fully, we must stop thinking of a move as a simple, deterministic, perfectly local act. The classical physicist tends to believe that he controls his moves completely, at least in principle. He knows their effects, and he attributes any unpredictability to complexity—not to the nature of the game itself.

But in the quantum realm, cause and effect unfold through a network of possible choices and probable outcomes—calculable, yes, but not decidable in advance.

It’s like a tangled ball of thread: pull on one end, and you don’t know exactly which knot will tighten—or whether any will.

Think of entanglement: two particles whose measurements are instantly correlated across distance. Not because one acts on the other, but because they share a single quantum state, independent of where they are.

In chess terms, imagine a knight and a rook so mysteriously connected that moving one instantly moves the other—no matter where they are on the board—according to some hidden rule.

Even in ordinary play, a capture isn’t strictly predictable from the start. It results from a chain of possibilities, none of them necessary. In quantum terms, every move is a measurement: it forces the system to collapse into one of its possible states, temporarily reducing uncertainty.

Since the system can’t remain isolated forever—and no player can think infinitely long—between one move and the next all strategies coexist in a kind of tactical superposition, resolved at each reply.

That reply isn’t a mechanical reaction; it’s the emergence of one outcome among many, shaped by the conditions of play that have just been reset. The opponent becomes part of the environment itself, actively reshaping the field of possibilities.

Every move redraws the potential relationships among all the pieces—even those not directly connected. There’s a sort of invisible non-locality at work.

As we can see, the analogy we introduced to escape a narrow, formulaic view of physics becomes increasingly delicate the closer we press it for detail.

Heisenberg’s uncertainty principle gives another perfect example. In its original form, it says that if you determine the x-component of an object’s momentum p with an uncertainty Δpₓ, then the corresponding position cannot be known more precisely than ℏ/(2Δpₓ), where ℏ is the reduced Planck constant. More generally, for any conjugate pair of quantities, their uncertainties multiply to at least ℏ/2. You can’t know both with arbitrary precision—the more you nail down one, the fuzzier the other gets.

Translate that into chess: suppose the precision of momentum corresponds to a piece’s movement. The more precisely you know how it moves, the less certain you are about where it is. And if you insist on knowing exactly which square it’s on, you must give up predicting its move. If, in a fit of rigour, you tried to divide the chessboard into infinitely many squares to improve your accuracy, you’d end up making the game itself impossible to play.

In other words, there’s a built-in limit to how precisely you can control both the where and the how of the game. Just as in the quantum world, it isn’t the object itself that defines the field—it’s the unstable relationship between its coordinates and the actions that make them visible.

And perhaps that’s the most unexpected insight of all: the game doesn’t happen on the board—the board itself emerges from the game.

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