New ideas

New ideas are how we progress. They allow us to come up with more efficient ways to achieve our goals, or even to change the goals themselves. Novel ideas can range from something as big as a new fundamental physical theory which enables a significant technological revolution, to a change of your morning routine. It should be clear that these are pretty important. But how do we go about producing new ideas?

By definition, copying existing ideas doesn't produce new ideas. In the world of financial markets, professional investors spend all day trying to find inefficiencies in the pricing of assets and profit from these mistakes. All the well known strategies to try to find mis-pricing don't work - once the strategy has been made public the returns are no longer available. You won't be able to make excess financial returns by copying others' ideas. ¹

Another place this shows up is in corporate strategy. Trying to perfectly copy what another company does is a losing strategy. By nature of that company existing they have a significant head-start on you. For a company to be successful it has to differentiate itself from the competition. Certain companies make hard work their differentiator, and outwork everyone else. There are many ways to do this, but you need a unique combination of traits to stand out and be successful.

To understand where new ideas come from, there are two concepts we need to define - axioms, and the arena they operate in.

Axioms are the assumptions that you have to take as true to use your theory. You always have a set of assumptions that you can't prove ², even if you don't make them explicit. The English language and the assumption that the generation of new ideas isn't random are two axioms in this essay.

The arena defines where axioms are valid. For example, I can imagine a universe where plants don't exist. But this axiom isn't valid when applied to the universe we live in. The environment constrains the set of valid axioms.

With these building blocks, there's two potential ways to generate new ideas:

1. Change the axioms within a set arena
2. Change the arena for a set of axioms

Both of these approaches require us to play and experiment with combinations that no one else has tried before. However, many of the combinations won't be valid. Random trial and error isn't an effective strategy when there are an infinity of possibilities. Intuition and using the subconscious plays a key part to subvert this infinity. Although we may not understand it, intuition can help guide us in the right direction.

We can see an example of this in science through the work of Richard Feynman. Feynman would use his intuition to identify idea spaces that he considered to have more potential and be less crowded. He was unafraid to change the arena and move into different areas of Physics if he deemed it necessary. Moreover he was adamant in always taking the axioms of an idea and working through to the conclusion himself. This meant he built up a great intuition for how different sets of assumptions led to different results, and he became more comfortable playing with and changing these assumptions. ³

To put this into practice, you can try to find mistakes in existing assumptions. This will require you to find and understand the axioms of as many ideas as possible. Then for each idea try changing something and see what follows. You'll need to validate that what you've changed remains valid in the arena. Alternately you can disregard existing ideas in the environment and try to come up with a novel set of axioms. An example of this is going from Newton's classical mechanics (where space, time and mass are all constant) to Einstein's relativity (where the speed of light is constant and space-time can vary).

The second approach is to look to ideas that exist in other arenas and see if they can be applied to the environment you are focused on. Often this means taking existing ideas and increasing the generality to see if it remains valid in a broader domain. Taking the Moneyball statistical approach to baseball and applying it to other sports like football is an example here.

One strategy isn't better than the other. Trying to incorporate both will give you the highest chance of making progress. We are all predisposed to prefer one of the strategies. Identify which strategy you are naturally drawn to, and see if you can start to use the other approach more. This will be particularly useful when you are stuck on a problem.