What is the difference between first principles and axioms?

Let's put it this way: these two terms sound very similar, both seeming to refer to a 'most fundamental starting point,' but their origins and applications are actually quite different.

Axiom

You can think of it as the 'rules of the game.'

For example, in chess, a knight moves in an L-shape. You wouldn't ask, 'Why does the knight move in an L-shape?' This is an axiom: a premise that is universally agreed upon, requires no proof, and must be accepted when we discuss problems or build systems. In geometry, 'the shortest distance between two points is a straight line' is an axiom. You don't need to prove it; you use it as a basis to prove other, more complex theorems.

Therefore, the key to an axiom is to 'accept it, don't ask why, and let's start from here.' It is a static, given starting point.

First Principle

You can think of it as 'breaking things down to their smallest components to see what they truly are.'

It's not a ready-made rule, but rather a way of thinking. This approach requires you to relentlessly question and dig deeper until you uncover the most fundamental, basic 'facts' or 'truths' of a problem. These 'facts' are like the laws of physics; they cannot be broken down further.

For example, if someone wanted to build a faster horse-drawn carriage, they might think of finding faster horses (this is analogical thinking based on the existing carriage). But if you apply first-principles thinking, the question becomes: 'My goal is to get from point A to point B quickly; what is the most fundamental way to achieve this?' Thinking this way allows you to break free from the 'carriage' framework and consider fundamental elements like wheels, energy, and friction, potentially leading to the invention of the automobile.

Therefore, the essence of first principles is to 'don't trust existing assumptions; instead, take matters into your own hands, break down the problem into its core, undeniable elements, and then reassemble them from those elements.' It is a dynamic, exploratory process.

To summarize the difference between the two:

• An axiom is a conclusion, a starting point for your thinking. It tells you: 'The rules are like this.'
• A first principle is a method, a process that helps you find that most reliable starting point. It encourages you: 'Question, dig deeper, until you find the true rules.'

Simply put, an axiom is a map's starting point given to you by someone else, while first principles teach you how to create your own map.