Representing text as TypeScript arrays

A computer has no concept of what 'joy' feels like, yet it can mathematically prove that 'joy' is closer to 'happy' than it is to 'angry'. When we work with Large Language Models (LLMs), we don't treat words as strings of text. Instead, we treat them as locations in a map where the coordinates are not north or south, but characteristics like 'happiness' or 'urgency'. By converting ideas into numbers, we allow computers to perform math on human meaning.

The Vector as a Coordinate

In programming, we think of an array as a list. In geometry, we think of a vector as a point in space. When we combine these views, we get a Vector as an array of numbers. Imagine we are analyzing customer reviews. We decide that the first number in our array represents how 'Happy' the review is, and the second number represents how 'Urgent' it is.

A review saying "I love this!" might be represented as [0.9, 0.1], while "FIX THIS NOW!" might be [0.1, 0.9]. These numbers are Coordinate axes as features. Each slot in the array represents a specific dimension of meaning.

Semantic Direction and Higher-Dimensional Space

As we add more features—like 'Sarcasm', 'Length', or 'Language'—we move into Higher-dimensional space. While we can't visualize 100 dimensions, the math remains the same as 2D. Every point in this space is also an arrow starting from the center (0,0).

The angle that arrow points is its Semantic direction. If two reviews both point in the same direction, they share the same meaning, even if one is "louder" (longer) than the other. This direction is how AI distinguishes between a positive review and a negative one.

Minimal Working Example: Review Vector Class

// A ReviewVector represents a document in 2D semantic spaceclass ReviewVector {  // data stores [happiness, urgency]  // This is a 2D higher-dimensional space simplified for learning  constructor(public data: number[]) {}
  // A method to describe where this vector 'points'  getDirectionSummary(): string {    const [happy, urgent] = this.data;    if (happy > urgent) return "Primarily positive";    if (urgent > happy) return "Requires immediate action";    return "Neutral or Equally balanced";  }}
// Create a vector for a 'Happy' reviewconst cheerfulReview = new ReviewVector([0.95, 0.05]);console.log(cheerfulReview.getDirectionSummary()); // "Primarily positive"

Example Breakdown

In the code above, the data property is our vector. Note that we use a number[] instead of individual variables like let happiness = 0.9. Using an array is crucial because linear algebra operations (which we will learn later) require the data to be in a structured list format.

The constructor takes the array and assigns it. This structure allows us to scale. If we wanted to add a 'Sarcasm' score, we simply change the array size to 3. The logic of the "Vector" doesn't change just because the space becomes more complex.

Extended Example: Mocking an AI Embedding

In real AI applications using tools like the ai-sdk, we don't manually pick these numbers. An "Embedding Model" looks at text and returns an array of 1,536 numbers. Each number represents a subtle nuance of the word.

import { embed } from 'ai'; // Example import from ai-sdk context
interface ReviewData {  text: string;  vector: number[]; // The higher-dimensional representation}
const processReview = (text: string): ReviewData => {  // In a real app, 'embed' produces these coordinates automatically  // Here, we simulate a 3D coordinate: [Joy, Stress, Sarcasm]  const mockVector = [Math.random(), Math.random(), Math.random()];    return {    text,    vector: mockVector  };};
const results = processReview("The battery died in two days, great design guys.");console.log(`Vector space coordinates: [${results.vector.join(', ')}]`);

Common Mistakes

1. Thinking magnitudes are everything: Beginners often focus on the "length" of the vector (e.g., how high the numbers are). In LLMs, we care much more about the direction. A long vector and a short vector pointing the same way usually mean the same thing.
2. Mixing Feature Order: If your first index is Happiness and your second is Urgency, you must never swap them. [0.1, 0.9] is a completely different semantic location than [0.9, 0.1].
3. Visualizing only 3D: Don't get stuck trying to "see" the space. Trust the array index. Index 402 in a 1,536-dimensional vector is just as valid a "direction" as X or Y on a graph.

Real-World Application

This coordinate-based approach is how Netflix knows that two movies are similar. They don't just look at the genre tag. They represent every movie as a high-dimensional vector based on thousands of features (pacing, color palette, actor chemistry). When you finish a movie, the system looks for the closest vectors in that massive 1,000-dimensional space. By treating movies as coordinates rather than titles, the computer can find patterns that no human tagger would ever notice.

In the next lesson, we will learn how to actually calculate how "close" these vectors are using a mathematical tool that measures the overlap between these digital directions.