This text is describing several instances in which the recognition of given limitations of nature has led to great new discoveries. In my opinion, this constitutes an important principle: we have to recognize our own limitations in order to progress.

From Alchemists to Chemistry

Throughout the middle ages, the most popular form of what would become a high-tech startup today, was alchemy. One of the most important goals of alchemy was the production of gold. Countless generations of nerds focused their resources and fantasy on this futile endeavor.

Some of the failed alchemical experiments led to noteworthy inventions. For example, the re-invention of porcelain in Europe. The know-how about the production of this precious commodity used to be a well-kept secret of the Chinese before. However, the production of gold never actually succeeded.

The major breakthrough in natural science occurred when Lavoisier stated that it was impossible to make gold: This principle is called the law of conservation of matter. It is the foundation of modern chemistry.

Modern chemistry has led to fabulous new inventions: fertilizer, without which earth could not feed as many people as there live today. All the pharmaceuticals, plastics, and colors were unthinkable without modern chemistry.

From Perpetuum Mobile to the Steam Engine

Another example in which the observation of natural limitations leads to new discoveries is the perpetuum mobile. Over long periods of time, it was tried to develop a machine that performs physical work by generating continuous motion.

The lack of success in building such kind of machine led to the statement of the laws of thermodynamics. Most importantly, the law of conservation of energy. By the recognition of the impossibility of the creation of energy, engineers rather searched for different forms of energy that might be converted into mechanical energy.

This new way of thinking resulted in the invention of the steam engine. Today, from the car engines, the Diesel engines in big trucks and ships, to the jet engines in air planes: they all work on the principle of conservation of energy.

From Speed Limit to Relativity

Another puzzling observation in physics of the 20th century was the fact that nothing was going to go faster than light. Only the smallest elementary particles, like electrons and protons could be accelerated to speeds anywhere near the speed of light, though.

It was a bold step of Einstein to assume that the speed of light is fixed. By this assumption, the previously well-established space and time needed to be abandoned. That theory of relativity was discussed very controversially in the scientific community for a long time. Ultimately, with color-TV and GPS, we have every-day devices that work with relativistic physics.

From Uncertainty to Quantum Mechanics

While relativity is well-understood these days, another discovery of the 20th century is as mysterious as ever: quantum mechanics.

Quantum mechanics is based on a mathematical theory that describes physical systems in a way that is totally inconsistent with day-to-day experience. For example, it states that these particles don't have a position and a speed at the same time. That there state is inter-woven with each other. And that a cat can be dead and alive at the same time until it is looked at.

This is all very counter-intuitive. However, it is the best description that we have. In the intuitive physics, for example, atoms would not be stable. Electrons are circling around the atomic core, and electrically charged particles that are moving are supposed to emit electromagnetic radiation. Thus, in intuitive physics, atoms would not even exist. So, quantum mechanics is more real than intuitive.