That is the difference between mathematics and physics. Mathematicians, or people who have very mathematical minds, are often led astray when “studying” physics because they lose sight of the physics. They say: “Look, these differential equations—the Maxwell equations—are all there is to electrodynamics; it is admitted by the physicists that there is nothing which is not contained in the equations. The equations are complicated, but after all they are only mathematical equations and if I understand them mathematically inside out, I will understand the physics inside out.” Only it doesn’t work that way. Mathematicians who study physics with that point of view—and there have been many of them—usually make little contribution to physics and, in fact, little to mathematics. They fail because the actual physical situations in the real world are so complicated that it is necessary to have a much broader understanding of the equations. — Richard Feynman, The Feynman Lectures on Physics

What are First Principles

First principles are basic truths about a complex system from which all other truths can be logically derived. In mathematics, these principles manifest as axioms—self-evident truths. In the realm of physics, they take the form of fundamental laws, such as Newton’s Laws of Motion and Maxwell’s equations for electrodynamics.

We generalise the concept of first principles to other fields of knowledge beyond science. When analyzing and predicting the behavior of individuals or organizations, we can identify their ultimate objectives as the first principle, with intermediate goals representing logical implications. For instance, one might posit that the foundational assumption in economics is that individuals act rationally to maximize their utility or happiness.

There are also more cynical first principles that we might observe. For example, we might see that the first principle of a government is to extract resources from citizens and territory for the benefit of those in power, as opposed to prioritizing the welfare and utility of the public. Similarly, one might argue that the core principle guiding private companies is to maximize profit for shareholders rather than focusing on providing customers with desired products.

The consequences of First Principles are complex

The first principles are really important to understand. Newton’s discovery of the fundamental laws of motion, for example, paved the way for precise calculations of celestial body motion and the strategic placement of satellites in orbits tailored to our needs, such as synchronizing with the Earth’s rotation every 24 hours.

Similarly, comprehending the first principle of rational agents is key to unraveling the workings of economic activities and making reasonably accurate predictions. Remarkably, the ability to derive precise consequences from first principles using logic alone, without direct observation, is a testament to the power of foundational understanding.

Catiously, we need not to overesimate the power of first principles. Even though the first principles are quite simple on the surface, one might be tempted to underesimate the need to fully learn their implications. After all, why waste time learning about consequences when you can work them out yourself in your head. In reality, the resulting consequences are complex and not at all obvious. In the realm of mathematics, the derivation of complex and profound theorems from basic axioms and definitions exemplifies the depth and richness that emerges from seemingly straightforward principles. Often entire fields in maths like set theory is built upon really simple, straightfoward and intuitive axioms.

The complexity of consequences is also apparent in systems like Conway’s Game of Life, where intricate behavior arises from simple rules.

Moreover, recognizing these consequences is not an innate skill for most individuals, highlighting the limitations of relying solely on first principles, even though theoreciallinfinitely intelligent beings are able to successfully derive them.

Not only are the consequences complex, but people are not usually able to realise the consequences themselves in a vacuum, even though it is possible for a theoretically infinitely intelligent being. This underscores the importance of not only understanding first principles but also acknowledging their limitations and the need for practical exploration and observation in complex real-world scenarios.