On Atoms and Knowledge

June 8, 2026 • 16 min read

For themLifeMental Models

This started as a note to my daughter. Which means it is partly about physics. But mostly about how to learn.

Hey Darling,

Your young old man here again. Or, depending on when you read this, maybe just your old old man.

Today I want to talk to you about my favorite formula:

E_{start} = E_{end}

The conservation of energy.

Not because I prefer being sloth-like, or because I love shortcuts, though to be fair both are true. I love it because it was my first favorite atom of knowledge. And atoms are one of the most important things you can learn to look for.

I’ll come back to this one. But let me start somewhere you have already been, with an atom you mastered before you could even read this letter.

What I mean by atoms

You can’t memorize how to say every word. There are too many of them, and people make up new ones all the time. So nobody tried. Instead, someone taught you the sounds of just twenty-six letters. And the first time you saw a word you had never seen before, something like galumphing or persimmon, you could already say it out loud.

Nobody taught you that word. You built it yourself, out of letters.

That is an atom of knowledge. The letters are the atoms. The words are the molecules. You learned twenty-six small things instead of a million big ones, and in return you can say any word there is, including the ones nobody has invented yet.

More generally, an atom is a small truth that helps you derive bigger truths. Atoms matter because they reduce the number of things you have to simply “remember.”

Knowledge works a bit like chemistry:

Level	Meaning
Atoms	Simple truths
Molecules	Combinations of those truths
Structures	Bigger systems built from those combinations

On their own, each atom is useful. But when you combine them, they become molecules of understanding.

Why bother? It is harder than memorizing

It is. But it is worth it.

Memorizing is easy today and exhausting forever: you collect molecule after molecule and have to carry every single one. Learning the atoms costs more up front, then pays you back for the rest of your life. Three reasons:

You carry less. A handful of atoms can rebuild dozens of molecules. You never memorized every word in the language, and you never had to: twenty-six letters carry all of them. Learn four ideas about energy and you can derive the speed of a roller coaster, a ramp, a pendulum, and a spring, formulas you would otherwise memorize one at a time.
You can rebuild what you forget. You will forget almost everything you memorize. You can never forget how to rebuild it. A molecule you lose is gone; an atom you keep makes the molecule again.
The atoms travel. Memorize physics and you know physics. Understand its atoms and you walk into chemistry, biology, even people already half-fluent. Molecules stay home; atoms come with you.

So memorizing is renting answers: cheap this week, and you pay again every week after. Learning the atoms is owning them.

Memorize the molecules and you have to carry all of them. Learn the atoms and you can build any of them.

The same trick, everywhere

The reason I love atoms so much is that this move, small truths combining into bigger ones, is not a physics thing. It shows up almost everywhere. So as you grow up, I hope you do not worry too much about whether you are a “math person,” a “science person,” a “creative person,” or a “people person.” Those categories are mostly fake. What matters is learning how to find the atoms in whatever world you are drawn to.

Below are a few of those worlds. Start with the one you love most, but peek at the others too, because the pattern is the point: different costumes, same atoms.

If you love physics

This is the world that taught me all of this. Here are four of its atoms:

Atom	Idea	Formula
A	Energy is conserved	$E_{start} = E_{end}$
B	Height stores energy	$PE = mgh$
C	Motion stores energy	$KE = \tfrac{1}{2}mv^2$
D	Springs store energy	$SE = \tfrac{1}{2}kx^2$

Each one is useful on its own. The interesting part is what happens when you combine them.

Molecule 1: height becomes speed

Take a roller coaster rolling down a hill, a skier going down a slope, a ball falling from a window, or a pendulum swinging downward. At first those look like different problems. Say you just want the speed at the bottom, and you have forgotten there is an atom underneath.

So you do the honest, exhausting thing. You track the forces down the slope with Newton’s laws:

\begin{aligned} F &= mg\sin\theta \\ F &= ma \\ a &= g\sin\theta \\ s &= h / \sin\theta \\ v^2 &= u^2 + 2as \\ v^2 &= 2(g\sin\theta)(h / \sin\theta) \\ v &= \sqrt{2gh} \end{aligned}

Look at everything that road made you carry: forces, angles, acceleration, distance, the equations of motion, trigonometry, substitution, and cancellation. And after all of it, you discover the angle never mattered. The path never mattered. The time never mattered. Only the change in height mattered.

Now remember the atoms. Underneath, all four of those scenes are the same molecule:

Conservation of energy + height energy + motion energy

Or:

A + B + C

Which is just height energy becoming movement energy:

mgh = \tfrac{1}{2}mv^2

Mass is on both sides, so it cancels:

gh = \tfrac{1}{2}v^2

So:

v = \sqrt{2gh}

Same answer. A much shorter road. And this time you never needed the shape of the hill, how long the fall took, how heavy the object is, or the exact path it traveled. If you know the height, you know the speed. And if you ever forget $v = \sqrt{2gh}$ , it does not matter. You just rebuilt it from the atoms in three lines.

That is what an atom of knowledge does. It helps you see the thing that matters sooner. This is not a trick I invented, by the way. It is the whole reason physicists invented energy methods: a way to skip the moment-by-moment forces and ask only what the system had at the start and where it went by the end.

Molecule 2: spring becomes speed

Another one: a spring launching a toy car.

Forget the atom again and you are back to going moment by moment. The spring’s force follows Hooke’s law:

\begin{aligned} F &= kx \\ F &= ma \\ a &= kx / m \end{aligned}

But x keeps changing as the spring expands. So the force changes, which means the acceleration changes, which means the velocity changes, which means the position changes, which means the force changes again. Now you are describing a system where force, position, acceleration, and velocity are all moving together. Not impossible. Just messy.

The atoms cut straight through it:

A + C + D

Spring energy becomes movement energy:

\begin{aligned} \tfrac{1}{2}kx^2 &= \tfrac{1}{2}mv^2 \\ v &= x\sqrt{k/m} \end{aligned}

Simple. Beautiful.

I do not need to know every tiny moment. I just need to know what energy was stored at the start, and where it went by the end.

Spring energy became motion. Done.

Same truth, different costume

A roller coaster. A falling ball. A skier. A pendulum. A ramp. They look like different problems, but often they are the same molecule wearing different costumes. The useful questions are always:

What energy exists at the beginning?
What energy exists at the end?
What changed form?
What stayed the same?

Before I understood this, physics felt like memorizing separate formulas for roller coasters, ramps, falling objects, pendulums, and spring launchers. But conservation of energy showed me that many of those formulas were not separate things. They were combinations. Molecules made from the same atoms. And if I understood the atoms, I could rebuild the molecules.

That was the breakthrough. Not that I had learned a trick, but that I had learned what understanding feels like.

It feels like carrying less.

If you love design

At first, design can look like taste. One room feels beautiful, one outfit looks right, one website feels clean, one painting feels balanced. But design has atoms too, and most of them have real names that people have studied for a long time:

Atom	What it does	Some laws / patterns it relates to
Color	Sets the emotional temperature	Complementary colors, analogous colors, color temperature, saturation, contrast ratios
Contrast	Tells the eye where to look	Figure-ground, visual weight, emphasis, accessibility contrast
Proportion	Makes things feel balanced or tense	Golden ratio, rule of thirds, scale, symmetry, negative space
Hierarchy	Decides what matters first, second, and third	Gestalt grouping, typography scale, spacing systems, information architecture
Repetition	Makes things feel intentional	Rhythm, pattern, consistency, design systems
Alignment	Makes things feel orderly	Grid systems, baseline grids, visual axes
Proximity	Shows what belongs together	Gestalt proximity, grouping, chunking
Whitespace	Gives ideas room to breathe	Negative space, simplicity, focus, signal-to-noise

Notice how many of those trace back to a handful of real principles. The way your eye groups things that sit close together, or reads light shapes against a dark background, is the set of Gestalt laws: proximity, similarity, figure-ground, closure. The reason some rectangles just feel right is the golden ratio and the rule of thirds. Designers did not invent these out of nowhere. They named patterns that were already true about how human eyes and brains work.

Once you understand the atoms, design stops being “make it pretty” and becomes a set of questions: What should someone notice first? What should they feel? What belongs together? What needs breathing room? What pattern should repeat, and what should stand apart?

Posters, rooms, paintings, apps, books, buildings. Different molecules, same atoms.

If you love programming

The atoms might be:

Atom	Meaning
State	What something is right now
Transformation	How it changes

A light switch has state: on or off. A bank account has state: how much money is in it. A game has state: where the player is, how much health they have, what level they are on. A program is often just state being transformed:

name = "Paige"             // state
name = name.toUpperCase()  // transformation: "Paige" → "PAIGE"

Tiny example. Huge idea. Computer scientists have real names for both halves. A thing that holds a state and moves between states by rules is a finite state machine, and a light switch is the simplest one there is. A transformation that takes a value and hands back a new one without secretly changing anything else is a pure function, and that habit of not mutating the old thing is called immutability. You do not need the jargon to use the idea, but it is nice to know the idea has a name.

Program	State	Transformation
Photo app	Pixels	Filters, crops, edits
Calendar app	Dates and events	Schedules, reminders, conflicts
Banking app	Transactions	Balances, categories, reports
Map app	Location and destination	Routes, timing, directions
Game	Player, world, rules	Movement, damage, progress

Once you see that, programming stops being a giant pile of languages, frameworks, libraries, and strange punctuation. It becomes a few questions: What is the state? How should it change? What rules control the change? What happens next?

If you love people

People can seem mysterious. They say one thing and mean another, they resist good advice, they get defensive when you are technically right, and they change their minds slowly, then all at once. But people have atoms too, especially in friendship, sales, leadership, marriage, parenting, and conflict.

Atom	What it means	Useful question
Attention	People want to feel seen, not processed	What are they trying to have noticed?
Status	People protect their sense of importance	Am I raising or lowering their status?
Dignity	People resist less when they can keep self-respect	Can they change their mind without feeling stupid?
Incentive	Behavior follows wants, fears, hopes, and pressures	What do they gain, lose, fear, or need?
Trust	Trust is repeated evidence	Have my words and actions kept matching?
Autonomy	People want to feel they are choosing, not being forced	Do they still feel in control?
Reciprocity	People feel pulled to return genuine value	What can I give before I ask?
Emotion	People need to feel safe before they can think clearly	What emotional state are they in?
Narrative	People understand through stories, not facts alone	What story are they living inside?

Some of these are studied laws of persuasion with real evidence behind them. Reciprocity, social proof, and authority are not folk wisdom; they are reliable patterns in how people decide. Once you understand the atoms, a lot of little people-rules stop being things to memorize and become things you can derive.

Molecule	Atoms inside it	What it really does
Bring a thoughtful gift to a prospect	Reciprocity + attention	Gives value before asking for value
Ask permission before giving advice	Autonomy + dignity	Lowers defensiveness
Disagree by first proving you understand	Attention + dignity	Makes disagreement feel respectful
Give them a graceful out	Dignity + autonomy	Lets them change course without feeling trapped
Make the next step tiny and obvious	Autonomy + trust	Lowers friction

The trick is not “bring a gift.” The atom is reciprocity, and a gift is just one molecule that falls out of it. The gift does not even have to be wine or swag. It can be a useful introduction, a thoughtful question, a benchmark, a teardown, or an idea they can use even if they never buy.

The trick is not “repeat their point back before disagreeing.” The atoms are attention and dignity. People do not always need to win, but they usually need to feel heard. If they feel ignored, embarrassed, or cornered, they defend. If they feel understood, they can think.

That is why good sales and good leadership are not really about tricks. They are about understanding people clearly enough to act with care. A prospect is a person trying not to waste money, lose status, or back the wrong idea. And almost all of that is one atom, loss aversion: we feel a loss far more sharply than the same-sized gain, so most of the time people are protecting against losing more than they are reaching for winning.

Once you see the atoms, the molecules become easier to read:

Listening is attention + dignity.
Leadership is trust + direction + status.
Friendship is attention + trust + reciprocity.
Love is attention + trust + repeated care.

Again and again, the work is the same:

See people clearly. Protect their dignity. Understand what they want. Earn their trust. Give before you ask.

That is not manipulation. That is care with eyes open.

If you love biology

A living thing is not just a pile of parts. It is a system trying to stay alive. The atoms might be:

Atom	Meaning	Useful question
Energy	Every living thing needs fuel	How does it get, store, and use energy?
Information	Bodies carry instructions	What information is copied, read, passed along, or changed?
Structure	Shape and function are connected	Why is this shaped this way?
Adaptation	Traits solve survival problems	What problem did this help solve?

Each of those is a real, named idea. Energy obeys the laws of thermodynamics, the same conservation we started with: life does not create energy, it just captures and spends it. Information rides on heredity, and the path it takes has a name, the central dogma: instructions flow from DNA to RNA to protein. Structure follows the old design rule that form follows function. And adaptation is the visible result of natural selection, the slow filter that keeps whatever helped something survive.

Example	Atom underneath
Plants capture sunlight	Energy
DNA gives cells instructions	Information
Wings are shaped for flight	Structure
Cacti store water	Adaptation
Polar bears have thick insulation	Adaptation
Babies cry before they have words	Adaptation + communication

Once you understand those atoms, biology becomes less like memorizing endless names and more like asking better questions. Different organisms, same atoms.

The lesson underneath the lesson

Whatever you love, look for the atoms.

Field	Some atoms to look for
Reading	Letters and the sounds they make
Design	Color, contrast, proportion, hierarchy, repetition, alignment, proximity, whitespace
Programming	State, transformation
People	Attention, status, dignity, incentive, trust, autonomy, reciprocity, emotion, narrative
Biology	Energy, information, structure, adaptation
Physics	Conservation, force, motion, energy

The subject almost does not matter. The pattern is the same. Do not just collect the leaves; find the roots. Do not just memorize the molecules; find the atoms.

Because once you understand the atoms, the world gets lighter. You can rebuild what you forget, recognize an old truth in a new costume, and walk into a strange field already knowing how to begin. That is why conservation of energy became my favorite formula: not because it made me good at physics, but because it taught me what understanding feels like.

So do not try to carry everything, my darling. Find the few small truths that let you build the rest. That is one of the great joys of learning. Memorize the molecules and you have to carry all of them. Learn the atoms, and you can build any of them.