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 - Anything to do with forecasting or understanding human behavior at a macro level.
The things - An actor performing an action: who (perspective), when (time), where (spatial), what/how (action/quantified effect), why (motivation/intended outcome). Most important is the perspective, to put yourself in another persons mind. To understand a node: we use non-precise visualisation - a technique to visualise actors nodes from a top-down map view.
The links - A node (actor performing action) triggers a reaction function causing other actors to perform their own actions. The trick is to form a causal chain of how to process nodes and connect them together to understand how situations evolve and forecast them. Node triggers nodes.
Data Origination — Curating a wide, spanning, diverse dataset that spans as much as the complex high dimensional situation of the world.
Data Organisation/Routines — How you organize/categorize the data via the above schema. Then you feed it into your mental model/mind to make connections.
Connecting - We can form a causal link of nodes and forecast what connections will happen.
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
The above is Derman explaining the “who” or perspective part of a node. Now, below is an example of markets. We react to the nodes above, try and connect the nodes that ultimately lead to the price of an asset. A price of the commodity is ultimately supply and demand. A price of a stock is future cash flows.
Apprentice: “Master, they keep trying to make me learn a fixed set of rules, math and reaction functions to events and price variability but every single day the path is different in some way to the day before.
— Anyon (@AnyonCurve) September 14, 2026
Then, the next day, when pressed for an explanation, they then say “… ahhh but you are not considering XYZ..”
It’s almost like I need to ignore the best and brightest, their fixed dogma and inflexibility, I need to find my own way”
Master: “Look in your hand young Apprentice- you have taken the stone from my hand.”
Humanistic > renormalisation > deterministic - Humanistic is simply a renormalisation (fancy word for zooming out) of the deterministic framework. Why? Laplace’s demon-ing every neuron firing to form a thought isn’t going to work. So we renormalise.
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.