Tools: The Symbol for All of Us is Null

The Symbol for All of Us is Null ## To Understand Is to Divide ## AI Does the Same Thing ## Analogy ↔︎ Contrast / Induction ↔︎ Deduction / Concrete ↔︎ Abstract ## Analogy and Contrast Are Mappings ## Induction and Deduction Are Vector Subtraction and Addition ## Concrete and Abstract Are Information Gain/Loss for Shifting Levels ## The Nice Essence ## A Symbol Is a First Principal Component ## What's at the End of Abstraction? ## That Is Null. ## Strip away the infinite-dimensional noise, and everyone arrives at the same space. That space is Null. ## Friends who share the same symbol — let’s get along. ♪ 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. 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. 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: …and that's how we make sense of them. This is the logic of cognition that every one of us runs unconsciously. AI understands words as vectors in absurdly high-dimensional space. What does that even mean? Let's--true to form--divide and understand: 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: 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. "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 is finding what's the same. Contrast is finding what's different. An apple is round, red, and sweet. An orange is round, yellow, and sweet. Apply analogy and contrast: In notation, using linear maps TanalogyT_{analogy}Tanalogy​ and TcontrastT_{contrast}Tcontrast​ : Analogy:Tanalogy(apple⃗)↑Tanalogy(orange⃗)\text{Analogy} : T_{analogy}(\vec{apple}) \uparrow T_{analogy}(\vec{orange})Analogy:Tanalogy​(apple​)↑Tanalogy​(orange​) Contrast:Tcontrast(apple⃗)↓Tcontrast(orange⃗)\text{Contrast} : T_{contrast}(\vec{apple}) \downarrow T_{contrast}(\vec{orange})Contrast:Tcontrast​(apple​)↓Tcontrast​(orange​) 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. 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. Concretize(object⃗)⇒object⃗⊕parameters⃗\text{Concretize}(\vec{object}) \Rightarrow \vec{object} \oplus \vec{parameters} Concretize(object​)⇒object​⊕parameters​ Abstract(object⃗)⇒object⃗⊖parameters⃗\text{Abstract}(\vec{object}) \Rightarrow \vec{object} \ominus \vec{parameters} Abstract(object​)⇒object​⊖parameters​ Take the abstraction "human." Add the parameters "47 years old" and "male," and you get "middle-aged dude." 🍺 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." Set k=2k = 2 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: 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. Abstraction strips away information toward the nice essence. What remains is primordial space, prior to any structure. Here, Null means the ultimate absence after abstraction. If we keep abstracting everything in the universe, we arrive at Null -- nothingness. Apples, oranges, you, me — all of us. Primordial space before creation. Form is emptiness. The Big Bang. They all point to the same thing. (c) 2026 GoodRelax. MIT License. Templates let you quickly answer FAQs or store snippets for re-use. Are you sure you want to hide this comment? It will become hidden in your post, but will still be visible via the comment's permalink. Hide child comments as well For further actions, you may consider blocking this person and/or reporting abuse CODE_BLOCK: apple = [2, 3, 5, ...] orange = [3, 5, 7, ...] dirOfApple = GetDirection(apple) lenOfApple = GetLength(apple) Enter fullscreen mode Exit fullscreen mode CODE_BLOCK: apple = [2, 3, 5, ...] orange = [3, 5, 7, ...] dirOfApple = GetDirection(apple) lenOfApple = GetLength(apple) CODE_BLOCK: apple = [2, 3, 5, ...] orange = [3, 5, 7, ...] dirOfApple = GetDirection(apple) lenOfApple = GetLength(apple) CODE_BLOCK: 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. CODE_BLOCK: 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 CODE_BLOCK: 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. CODE_BLOCK: 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" - There's something humanity does unconsciously to make sense of the world. - AI does the exact same thing. - Mathematics describes it beautifully. - Why is Null the ultimate symbol for everything? - 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 real LLMs, these vectors live in thousands or even tens of thousands of dimensions. From a human perspective, the combinations are just… endless. - Transformers, the tech behind LLMs – Deep Learning Chapter 5 - Analogy:Tanalogy(apple⃗)↑Tanalogy(orange⃗)\text{Analogy} : T_{analogy}(\vec{apple}) \uparrow T_{analogy}(\vec{orange})Analogy:Tanalogy​(apple​)↑Tanalogy​(orange​) - Contrast:Tcontrast(apple⃗)↓Tcontrast(orange⃗)\text{Contrast} : T_{contrast}(\vec{apple}) \downarrow T_{contrast}(\vec{orange})Contrast:Tcontrast​(apple​)↓Tcontrast​(orange​) - 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. - 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. - Concretize(object⃗)⇒object⃗⊕parameters⃗\text{Concretize}(\vec{object}) \Rightarrow \vec{object} \oplus \vec{parameters} Concretize(object​)⇒object​⊕parameters​ - Abstract(object⃗)⇒object⃗⊖parameters⃗\text{Abstract}(\vec{object}) \Rightarrow \vec{object} \ominus \vec{parameters} Abstract(object​)⇒object​⊖parameters​ - ZZ Z : Zero-centering - WW W : Weight matrix - λ\lambda λ : Eigenvalues = the size of each MECE-organized component of information - MECE: Mutually Exclusive, Collectively Exhaustive - Abstract vector spaces – Chapter 16, Essence of Linear Algebra - 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. → R0\mathbb{R}^0 R0 still contains the information "a single point exists." - Strip even that away, and…? - Belongs to no one. - Carries no attributes. - Is the ultimate symbol, with every vector stripped away.