Thinking About Thinking (Metacognition)

In this post, I explore the notion that we can observe experts in different fields and distill their underlying patterns of thought via the right syntax in order to adapt the “optimal style of thought” for that field (e.g natural sciences, computation, humanities).

A field is just an area of study. My idea is that understanding complexity is about linking things together, but each field has different things, and each thing has its own type of link. As we link things together, we can build a clearer visualisation in our head.

The Right Words

I posit how to think about these things and links can be captured by invoking the right word or syntax.

We have just seen, through an example, how important words are in Mathematics. One can hardly believe how a well-chosen word can provide economy of thought.

— Henri Poincaré

Thus, by observing experts in respective fields, like a scientist, mathematician, programmer, investor being interviewed, and examining their choice of words, we can capture how they think. Sounds simple enough!

Fields

I categorize fields (subjects of study) into three types: deterministic, semi-deterministic, and humanistic.

Deterministic fields are the sciences and their derived fields. Physics, mathematics, etc. These have fixed laws (of nature).

Semi-deterministic fields just refers to computing: it has fixed laws that are modifiable by humans (e.g we make the laws via telling the computer what to do via programming).

Humanistic fields refers to fields studying human behavior: economics, finance, history, politics, etc. The laws arise due to human behavior.

I argue each field can be thought of in two ways: a primal form, involving linking things together as a graph, and a dual form, which is basically visualising something in your head.

So, let’s try to find the right words to express the things and their links.

A textual representation is how the concept appears on text, or on paper. Aka how we learn. An innate representation is what we need to connect the textual representation to.

The Three Frameworks

Framework	The things	Key prompts
Deterministic	Concepts (abstraction) and physical quantities	“Connections”, “Visualisation”
Semi-Deterministic	Nodes (information) and edges/pipes (operations)	“Abstraction”, “Decomposition”
Humanistic	Actors, actions and motivations	“Perspective”, “Big Picture”

Deterministic

Example fields — Mathematics, natural sciences, engineering.

The things — There are two fundamental things: concepts (abstraction) and physical quantities. On the underlying side, they are just numbers, quantities that can vary, basically. But what they represent are two different things. Their textual representation is a symbol and innate representation is a visual.

A concept (more towards the field of mathematics) and a quantity (more towards the field of physics) are the two main players. The difference is in their treatment: both can be visualised, but the former exists in abstract space whereas the latter exists in physical space (e.g our physical reality).

The links — They are linked via connections. These can be direct or latent. Direct connections are obvious. Latent ones are sudden inspirations between seemingly unrelated things. The idea is to build up a dense, well-connected network of things in your head.

Another idea is that of dependency, whereby to understand or make connections of certain concepts, there must be a backlog graph of existing concepts that you have to build in sequential fashion, aka prerequisites.

The key skill

• Visualising the concept or quantity.
• Connecting them together in a system.

What the experts say:

There are moments where you put something together and realize this is how the story has to go.

— Jacob Lurie, Breakthrough Prize Acceptance (2:15)

There is a beauty in the way things fit together in an unexpected way.

— Richard Taylor, Breakthrough Prize Acceptance (2:00)

Notice their choice of words: they imply connecting things together. What about the other type of thing aka measurements?

Atoms in the coffee jiggle, which makes the cup jiggle. Heat is just jiggling spreading, which is easy to understand.

— Richard Feynman, Fun to Imagine (1:20)

It’s a mixture of partial solving of equations … and having some sort of picture of what’s happening that the equations saying.

— Richard Feynman, Fun to Imagine (56:18)

Feynman is imagining a measurement (the jiggling) and showing how that interacts with another measurement (another bunch of atoms jiggling).

Key prompts — “Connections”, “Visualisation”.

Semi-Deterministic

Example fields — Computing.

The things — A system consists of edges/pipes (operations/tools/parts) and nodes (information).

The links — Together, they form a graph operating at an abstraction level.

The key skill — Start top down. A problem here is defined as a set of source nodes and a set of destination nodes. You want to build a system using edges/pipes to get from the source nodes to the destination nodes. And you do this via:

• Decomposing/breaking down an edge in a system into another system of nodes and edges, going to a deeper level of abstraction.
• Building up a node and edge system to be a node or edge in a higher abstraction level system.

This would be top-down thinking.

What the experts say:

Input → system (computation) → output. This is my core paradigm for understanding anything.

— George Hotz, What is Programming? (Noob Lessons!) (54:00)

There’s a relatively good understanding of abstraction layers. Atoms, silicon, transistors, logic gates, functional units, processing elements, instruction sets, languages - abstraction layers from the atom to the datacenter.

— Jim Keller, Jim Keller | Lex Fridman Podcast #70 (4:10)

Being able to see something at lots of levels and go between them smoothly seems to be more pronounced in people that resonate with computing.

— Donald Knuth, Donald Knuth | Lex Fridman Podcast #62 (9:13)

Key prompts — “Abstraction”, “Decomposition”.

Humanistic

Example fields — Economics/markets, finance, history, politics.

The things — The humanistic framework is concerned with modelling human behavior at a macro scale. The idea is to understand the big picture, the situation, by somehow looking at things evolving from the perspective of multiple actors, all at once!

• Humans/Players/Actors — Frame of reference. Bunch of humans. Who. Perspective, shoes, empathy, imagination.
• Actions — What/when/where/how. Non-precise visualisation (top-down map view). Effects (assigning numbers - comparison and aggregation).
• Motivation — Why? Intended outcome, context.

The key skills here:

Non-Precise Visualisation — Visualise the entire situation happening. “Where” is most important. Map view. Flows. Visualise matter, substance, force and actors. This is what Yet Another Commodity Guy does to an extremely precise level.

Data Origination — The system/situation consists of very complex actors doing actions. High dimensional. As such, want to get as much variance in datasets to try and span as much as possible to capture as much human behavior in the system.

Data Organisation/Routines — How you ingest, organize and visualise data (tabular or verbal!) into your workflows. Good organisation, visualisation, and habits/processes/routines (scrape, organize, curate, process) in doing so. Systematic in process.

Forecasting/Understanding the Big Picture — What you try to do here is to forecast or understand how the big picture or situation will play out over a long time horizon at a very macro level. From commodities X, two people who consistently exhibit this style of thinking to learn from: John Arnold and Gavin McKracken.

What the experts say:

The most interesting thing in the world is trying to see if you can understand what drives other people, putting yourself in their place and mind

— Emanuel Derman @emanuelderman.bsky (@EmanuelDerman) January 19, 2026

Key prompts — “Perspective”, “Big Picture”.

Intelligence and Blending the Frameworks

Thus, intelligence is the mastery you have in these frameworks, both in the cross section (the ability to master multiple of these in breadth and blend them together) and depth (mastery into an individual framework), applied to different disciplines.

Each person has a different calibration in depth and width, applied to different disciplines, which makes them unique.

Whenever approaching any cognitive task, it is important to remember this idea of blending the frameworks in the cross section and in the time series (or depth-wise).

Conclusion

Clearly, complexity or understanding it is about linking things together and having a good mental picture of them. But different disciplines have different ways to approach this. By observing interviews of experts and their thought process, we can put the right words to them and try to adapt them so we can learn faster.