Vector data simplified

Vector embeddings convert real-world content, like documents and images, into 1-D numerical
representations (arrays).
These arrays have N values, representing N dimensions. They are called vectors and can be
compared with each other efficiently.
These vectors aren’t random blobs of numbers. They live in a semantic multi-dimensional
space, and their position encodes real meaning.
Placing Documents in Space
Let’s say you’re plotting every document in your system onto a 2D graph:
● X-axis: Length of the document (short → long)
● Y-axis: Realism (fictional → real)
Let’s place some documents in this space.

Emergent topological meaning
Looking at a document, you can immediately classify it as one of four types.
● Bottom-right: Long, fictional books.
● Top-right: Long, real books (textbooks, reports).
● Top-left: Short, real texts (scientific papers, news).
● Bottom-left: Short, fictional content (flash fiction, jokes).
Without ever assigning a label, meaning starts to emerge from position.
But two dimensions aren’t enough. If we want to account for popularity, creation time, and
author country, we need more dimensions.
So we move to a D-dimensional space, where every axis represents a property of the input.
In short, a vector embedding encapsulates the input into a position in high-dimensional space.

Key Takeaways
● Vector embeddings = position in a multi-dimensional space.
● Each axis can be thought of as representing a property: realism, length, time, and
popularity.
● Similar vectors = semantically similar content.
● Clusters = emergent structure from data, not hard-coded