When “Genius” Ideas Create Simple Tricks

2.1. A Dropout Who Became a Genius

Einstein, the man who sparked a revolution in physics, is famously said to have been a hopeless underachiever in his elementary school days. His story is often cited as proof that even students who struggle academically can go on to achieve great things.

The roots of relativity lie in Einstein’s childhood, and understanding how the theory was built requires revisiting that period. Yet the tale inevitably leaves the impression that skipping a bit of elementary school work is harmless.

But if we recognize the simple fact that a single boy’s lack of attention in class eventually produced an imaginary theory—one that went on to reshape history—our evaluation of the whole story might look very different.

Relativity is not built on just one or two tricks.

It contains an astonishing number of them—far more than one would expect in a serious scientific theory. And at the core of every one of these tricks lies the very same kind of simple oversight.

Ordinarily, such mistakes would never make their way into a theory. After all, everyone learns how to avoid these errors in elementary school. Einstein, it seems, must have listened to that lesson with his mind somewhere else.

Judging from the direction physics took afterward, he never again had the chance to be taught that basic method.

2.2. “Match Your Units”

In elementary arithmetic, children learn numbers and how to count. Before long, they move on to addition, subtraction, multiplication, and division—the basic operations that no mathematics can do without. The entire foundation of math rests on these simple skills.

But mastering arithmetic in any practical sense requires more than just knowing the operations. It takes endless drills—those dull, repetitive exercises that train students to use arithmetic as a real tool. It’s no wonder young Albert lost interest; few children could stay enthusiastic through such monotonous practice.

During those tedious lessons, his teacher must have repeated the same warning countless times:

“Make sure your units match before you calculate.”

Unfortunately, that advice never reached the boy whose mind was already drifting toward the mysteries of a magnetic compass.

Practicing how to match units begins with simple questions such as: “How many centimeters are in one meter?” Once students get used to that, they are given more practical problems like:“Add one meter and one centimeter.”

Of course, simply adding the numbers is not the correct approach.Although these exercises look trivial, their importance lies in the process required to solve them.

Matching units means converting one number into another.If you ignore the units and perform the calculation as written, you get:

What deserves attention here is that merely ignoring the units eliminates the necessary conversion and produces the completely wrong result—2, far from the correct 101.From the perspective of the required answer, you could even say that this is the real “conversion,” albeit an unintended and meaningless one.

The specification of units provides essential clues for how numbers must be transformed.Forget the units, and you trigger irrelevant transformations instead.And the difference in units serves as a reminder that even identical-looking numbers must not always be treated as equivalent.

Thus, the practice of matching units naturally teaches a wide range of concepts—units, numbers, quantities, conversion, and reference standards.At the same time, it conveys an essential realization:

A number is nothing more than a temporary stand‑in for a quantity.

In pure mathematical calculations, numbers and symbols contain all the information.But in the formulas we use in everyday life, they represent only a small fraction of what matters.In most cases, a number gains meaning only when a unit is attached to it.

The same holds true when mathematics is applied to physics.If a theory is constructed without constant awareness of both numbers and their units, oversights are guaranteed.

Had Einstein understood that those dull “match your units” drills were actually training to prevent such oversights, he might have taken those lessons a bit more seriously.

2.3. “Mathematics, the Universal Cure‑All”

Could a boy who missed the most important lessons in school really go on to construct a revolutionary theory? Surprisingly, yes. At some point—no one knows exactly when—Einstein acquired a kind of mathematical cure‑all.

That cure‑all was the function. For a student who had once been considered a hopeless underachiever, the encounter with functions must have been transformative. When he first discovered this convenient tool, he likely saw it as a miracle drug—something that could solve mathematical problems in an instant.

The concept of a function seems to have been so fresh and striking to Einstein that his theories are filled with them. Most people, however, would not be nearly as impressed. After all, the essence of a function is fundamentally the same as the concepts already learned during the basic training of matching units. A function is simply that same idea reshaped into a form that fits smoothly into equations and expands their range of application.

Because this transition from arithmetic to mathematics happens naturally, most students are not shocked by the appearance of functions. But what happens if someone is shocked? If a tool suddenly makes previously difficult calculations easy, who wouldn’t want to use it everywhere? It would be no surprise if one began to believe that anything and everything could be solved with functions.

Still, without a solid foundation, one cannot truly wield functions. So sooner or later, some inconsistency or dead end should have appeared. The fact that Einstein managed—by sheer luck—to construct his theory without running into disaster suggests something important:

What he overlooked and what the function does are, in essence, the same.

The oversight generates the function, the function hides the oversight; the function triggers new oversights, and the oversights conceal the function. This cycle continues endlessly—until the very first oversight is finally uncovered.

2.4. Patterns of Problem‑Solving

Einstein followed a very particular pattern whenever he hit a conceptual wall: he would abandon the common sense that had been limiting his thinking and make a sudden, dramatic leap. Not one step or two, but sometimes a hundred—far beyond the boundaries set by conventional reasoning. Such leaps can produce results far greater than anyone would expect.

When he encountered an obstacle, he did not try to push straight through it. Instead, he stepped back, examined whether his assumptions or everyday logic were blocking the jump, and then looked for a way to vault over the barrier using an unconventional idea. Once he found the slightest hint of a solution, he discarded common sense entirely and leapt over the wall in one bound.

Most of us would fail miserably if we tried to imitate this method. What matters here is sharp observational insight—an ability to detect what is restricting the jump in the first place. It certainly requires thinking far removed from ordinary reasoning or standard problem‑solving levels. A genius is someone who can instantly recognize what is holding the leap back. Perhaps this method is a privilege reserved only for geniuses.

At first, I paid little attention to this pattern. But after examining many of the tricks embedded in his work, I suddenly noticed a remarkable similarity.

Einstein’s method of problem‑solving and

the very process that generates mathematical tricks

are almost identical.

In other words, by following this thought process to solve problems, Einstein ended up inventing numerous tricks—without ever realizing it himself.

2.5. Einstein’s Magic

Even Einstein could not have overcome conceptual walls without abandoning common sense. If everyone else remained trapped by ordinary assumptions while he alone leapt effortlessly over the barrier, it is reasonable to suspect he was using some kind of special technique.

That technique was a kind of hidden trick. When he found himself stuck in front of a problem’s wall, he did not force his way forward. Instead, he simply changed the setup.

The danger of this method is that, during the jump made under Setup 2, the original conditions are no longer intact. In a thought experiment, there is no real wall, so when the setup is switched back to Setup 1 immediately after the jump, it can easily look as though the wall has been cleared.

By cleverly avoiding the small constraints imposed by the initial conditions, one can appear to land on the far side of the wall—as if the obstacle had been cleanly overcome. But any jump that succeeds only by breaking the original setup is meaningless. The focus shifts entirely to “getting to the other side,” and the purpose of solving the problem is forgotten. At that moment, what seemed like a brilliant leap transforms into a subtle trick.

This technique was the secret that made Einstein appear like a genius problem‑solver. But once the trick is revealed, it becomes clear that it was nothing more than an oversight—and that the essential problem remained completely unsolved.

2.6. With the Light

It is said that even as a child, Einstein pondered the following question:

If I held a mirror in front of me and accelerated until I reached the speed of light, would I still see my own reflection?

A simple, almost charmingly “Einstein‑like” question.

Ordinarily, we cannot see light in motion directly. What we perceive as “light” is merely the reaction of objects or dust struck by it. Einstein’s thought experiment attempted to understand the nature of light by observing his own reflection in a mirror.

If I were flying at the same speed as light, the light would never reach the mirror. Without light, there would be no reflection—so I wouldn’t see my face at all.

As one approaches the speed of light, classical reasoning using the Galilean transformation suggests that light would lose speed relative to the observer. At the moment the observer reaches light speed, the light would fail to reach the mirror. This was a perfectly ordinary assumption at the time: the speed of light should depend on the observer’s motion.

Further investigation was impossible. There was no experimental data, and the technology required to test whether light truly slows under Galilean transformation was far beyond reach.

Most people would have stopped there.But Einstein resolved the puzzle in a completely unexpected way.

If my reflection disappeared, I would immediately know I was moving at the speed of light. But Galileo’s principle of relativity says that motion cannot be detected without looking outside. If the principle is to be respected, then my reflection must always look the same—no matter how fast I’m moving. Therefore, light must always appear to travel at the same speed, regardless of the observer’s motion.

And thus was born the principle of the constancy of the speed of light—the idea that light always appears to move at the same speed to any observer. For Einstein, this was simply the natural conclusion of his thought experiment, and elevating it to a principle seemed perfectly reasonable.

Light has been treated as something sacred since ancient times, yet its true nature remained elusive. Many scientists struggled with it for centuries. Without Einstein’s imaginative thought experiment, the solution might have been delayed much longer.

To use the well‑known principle of relativity to uncover a decisive property of light—using nothing but a thought experiment—was an astonishing leap. Perhaps Einstein really was a genius after all.

2.7. Galileo Must Be Weeping

Up to this point, we have accepted the principle of the constancy of the speed of light without question and expanded the algebra accordingly, leading inevitably to relativity. If the theory is to be challenged, then the thought experiment that produced it must also contain an error—otherwise the logic would not hold together.

So where is the oversight in this thought experiment?

The principle of relativity, as its name suggests, concerns the relative motion of objects. It states the very ordinary idea that:

Uniform motion cannot be detected without reference to another object or coordinate system.

For example, imagine a rocket flying through space. If the astronaut recognizes the motion by looking out the window, then blocking the window—or simply not looking outside—makes it impossible to detect the rocket’s motion.

One might object:

Why not just look at a speedometer?

But how does such a device work? Ultimately, it must rely on some mechanism that senses an external coordinate system and displays that information inside the rocket. Galileo’s “outside” does not mean the physical exterior of a structure—it means:

“another coordinate system moving relative to the observer.”

Thus, the principle requires not merely closing the window, but avoiding any reference to a coordinate system other than the rocket’s own.

Under these conditions, motion cannot be detected with a single coordinate system. In such a world, nothing moves relative to anything else. Galileo understood this perfectly; his phrase “looking outside” was simply a convenient expression.

Now, in classical physics, light was assumed to possess its own coordinate system. The belief that an observer’s motion could change the speed of light arose because:

light was thought to carry an independent frame of reference.

According to this classical view, emitting light inside a sealed rocket creates a new coordinate system within it. This new frame becomes a valuable source of information for detecting motion or calculating relative velocity—essentially functioning as a measuring stick.

Thus, inside the rocket, the situation becomes no different from “looking outside.”

The same applies to the mirror experiment: light emitted earlier forms its own coordinate system and provides crucial information. The thought experiment implicitly assumes that light can be used as a measuring tool.

Detecting changes in the reflection or in the speed of light would allow the observer to recognize their own motion—without violating the principle of relativity in the slightest. Therefore, the principle of the constancy of the speed of light is unnecessary.

People were impressed that Einstein used the relativity principle to uncover a property of light. But in their excitement, they failed to notice that they were interpreting Galileo’s words as if they belonged to an era when light could not be used to detect motion.

In the end, this thought experiment applied the relativity principle—meant for a single coordinate system—to a situation involving multiple coordinate systems, and thus adopted the completely unnecessary principle of constant light speed.

By overlooking the additional coordinate system, Einstein arrived at the constancy of light. And in constructing relativity, he once again:

forgot to include the coordinate‑transformation function.

A theory built on a principle born from a coordinate‑system oversight must inevitably rely on missing transformation functions. This is the simplest—and most difficult to detect—way to create a reset‑style equation.