The Concept of Depth in Representations

The concept of depth and layers of understanding is quite apparent in the formal sciences but is generally vague enough that it is worth clarifying.

Let's start with an example:

• A driver tends to kick the mess to fix his car because once he saw his father do that and say it works.
• A mechanic has a much better representation of the engine and can fix many breakdowns.
• A physicist in applied physics has a much better representation of the physical functioning of the engine and can invent improvements, like an engine with better energy efficiency.
• A theoretical physicist has a much better representation of physics and can invent new tools for applied physics.
• A mathematician has a much better representation of the theoretical physicist's mathematical framework and can discover new mathematical objects or truths that are useful to them.
• A logician in mathematical foundations has a much better understanding of the nature of mathematics and may eventually discover a better mathematical framework.

We see that there are layers of understanding, and the deeper one goes, the more significant the domain's consequences become. For example, a physicist making a discovery will likely have far more significant consequences than a mechanic improving their understanding of mechanics.

Many fields that seemed hazy in ancient times (psychology, weather, astronomy, etc.) have turned out to be structured. This progression leads us to think that this structure, which is very visible in formal science, exists everywhere. This is equivalent to saying that science has no boundaries. We then come to the conclusion that the informal is merely a complication of the formal, which, lacking a good formal representation, requires heuristic rules to be understood. This subject is debated and corresponds to a representation of reality that can have broad consequences when conviction resides deep within.

In practice, a project like this needs to allocate a substantial part of its energy to improving representations across all layers of understanding. This is equivalent to well-thought-out decisions on an individual level: we need to implement "thinking well," and this involves, among other things, the layers.