The Symbol for All of Us is Null

The Symbol for All of Us is Null

You might be thinking, "What is this guy even talking about?"

But if you've found your way to this post, I have a feeling this will click for you somewhere along the way.

Give me five minutes.

• There's something humanity does unconsciously to make sense of the world.
• AI does the exact same thing.
• Mathematics describes it beautifully.

And at the end:

• Why is Null the ultimate symbol for everything?

It all connects in a single thread.

And once you see that thread, the world starts to look a little clearer.

Let's walk through it.

To Understand Is to Divide

The world is full of things we don't understand.

But we have a trick for dealing with that: we give different things names and sort them into categories.

Round fruits? We split them into:

• Apples
• Oranges
• Pears

…and that's how we make sense of them.

This is the logic of cognition that every one of us runs unconsciously.

AI Does the Same Thing

AI understands words as vectors in absurdly high-dimensional space.

What does that even mean? Let's--true to form--divide and understand:

• Words: assign IDs to things and concepts
• Absurdly high-dimensional: thousands or even tens of thousands of indices
• Vectors: array-format data you can think of as arrows with direction and magnitude
• Understands: tidies them up nicely

In pseudocode:

apple  = [2, 3, 5, ...]
orange = [3, 5, 7, ...]

dirOfApple = GetDirection(apple)
lenOfApple = GetLength(apple)

• In real LLMs, these vectors live in thousands or even tens of thousands of dimensions. From a human perspective, the combinations are just… endless.

Visually, it looks something like this:

This is roughly how LLMs like ChatGPT and Gemini work under the hood--it's called embedding.

For a deeper dive, check out 3Blue1Brown's videos. Absolute masterpieces:

• Transformers, the tech behind LLMs – Deep Learning Chapter 5

Analogy ↔︎ Contrast / Induction ↔︎ Deduction / Concrete ↔︎ Abstract

Most sports and martial arts have fundamental forms. So does the way we see and think about things.

These three pairs are the basic stances of reasoning. Most people use them without realizing it. But once you name and practice them consciously, you'll understand anything faster and deeper.

Analogy ↔︎ Contrast :  
      Apples and oranges are both sweet.
                        ↑↓
      Apples are red; oranges are yellow.

Induction ↔︎ Deduction:  
      An apple fell from the tree. There seems to be gravity.
                        ↑↓
      An orange detached from a branch will fall due to gravity.

Concrete ↔︎ Abstract :  
      There's a round, red, sweet apple  
      and a round, yellow, sweet orange.
                        ↑↓
      There are two round fruits.

"Obvious?" Okay, let me explain a bit more carefully.
It's going to get gradually more serious from here.
We'll use some light math, but nothing super rigorous,
so take it easy. Skipping the formulas is totally fine.

Analogy and Contrast Are Mappings

Analogy is finding what's the same.
Contrast is finding what's different.

An example:

An apple is round, red, and sweet.

An orange is round, yellow, and sweet.

Apply analogy and contrast:

Analogy: a linear transformation toward the same direction  
             → Apples and oranges are both sweet and round  
          
Contrast: a linear transformation toward opposite directions 
             → Apples are red, but oranges are yellow

As a vector diagram:

In notation, using linear maps $T_{analogy}$ and $T_{contrast}$ :

• $\text{Analogy} : T_{analogy}(\vec{apple}) \uparrow T_{analogy}(\vec{orange})$

• $\text{Contrast} : T_{contrast}(\vec{apple}) \downarrow T_{contrast}(\vec{orange})$

Induction and Deduction Are Vector Subtraction and Addition

Induction is searching for laws from specific past observations.
Deduction is inferring specific future events from laws.

Newton's universal gravitation is the classic example.

Induction:  Extracting a law vector  
  → An apple fell from the tree. There seems to be gravity.

Deduction:  Superposing a law vector  
  → An orange detached from a branch will fall  
     to the ground due to gravity.

As a vector diagram:

In notation:

• Induction is estimation. You stack multiple observations, cancel out the noise, and let the hidden law float to the surface.
• Deduction is certainty. A law applies to the future, no ifs or buts.

Concrete and Abstract Are Information Gain/Loss for Shifting Levels

• To concretize: is to add parameters (attributes),
  gain information, and move down a level of cognition*.
  No special rules.

• To abstract: is to remove parameters (attributes),
  lose information, and move up a level of cognition,
  toward the nice essence.

An apple is round, red, and sweet — that's specific.
A fruit is just something round and edible — that's general.

Concretize: Add parameters, gain information, move down a level.
  → "fruit" + round + red + sweet = "apple"

Abstract: Remove parameters, lose information, move up a level.
  → "apple" - color - taste = "round thing"

As a diagram:

In notation:

• $\text{Concretize}(\vec{object}) \Rightarrow \vec{object} \oplus \vec{parameters}$

• $\text{Abstract}(\vec{object}) \Rightarrow \vec{object} \ominus \vec{parameters}$

Take the abstraction "human." Add the parameters "47 years old" and "male,"
and you get "middle-aged dude." 🍺

The Nice Essence

When you abstract by stripping away information, doing it haphazardly leads to nonsense.

Remove the stubble and wrinkles from a middle-aged man and you just get a boy.

That's not what we want -- we want to extract the information that actually matters.

That's where PCA (Principal Component Analysis) comes in.

PCA? Sounds fancy? You've probably already experienced it though.

You know those personality quizzes with ~50 questions

that plot you on a matrix like "Instinctive ↔ Logical" vs. "Extroverted ↔ Introverted"?

Those 50 questions are basically a 50-dimensional vector.

PCA squishes it down to 2 dimensions to make a "personality map."

In notation:

• $Z$ : Zero-centering
• $W$ : Weight matrix
• $\lambda$ : Eigenvalues = the size of each MECE-organized component of information
• MECE: Mutually Exclusive, Collectively Exhaustive

Set $k = 2$ and you get a 2D matrix.

This is pretty much the same thing we do unconsciously when we "get the gist" of something.

For more, this video is excellent:

• Abstract vector spaces – Chapter 16, Essence of Linear Algebra

A Symbol Is a First Principal Component

When we organize information about something, some of it matters more than the rest.

Naturally, we want to pin a simple mark on the most important piece so it sticks.

That's what symbols are.

Flags, logos, kings, pop idols…

When people rally around a symbol, here's what they're actually doing:

from everyone’s messy, sprawling vectors, they converge on the single most important direction.

That most important vector = PCA's first principal component.

PCA extracts the dominant direction of variance.

The first principal component can be interpreted as a symbol capturing shared structure.

The arrow that best represents everyone.

What's at the End of Abstraction?

Abstraction strips away information toward the nice essence.

• Strip a solid down and we get a plane.
• Strip a plane down and we get a line.
• Strip a line down and we get a point. → $\mathbb{R}^0$ still contains the information "a single point exists."
• Strip even that away, and…?

What remains is primordial space, prior to any structure.

That Is Null.

Here, Null means the ultimate absence after abstraction.

If we keep abstracting everything in the universe, we arrive at Null -- nothingness.

And so Null:

• Belongs to no one.
• Carries no attributes.
• Is the ultimate symbol, with every vector stripped away.

Apples, oranges, you, me — all of us.

Strip away the infinite-dimensional noise, and everyone arrives at the same space. That space is Null.

Primordial space before creation. Form is emptiness. The Big Bang. They all point to the same thing.

Friends who share the same symbol — let’s get along. ♪

(c) 2026 GoodRelax. MIT License.