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Understanding Vectors in Adobe Illustrator and in Machine Learning

At their core, vectors are a set of numbers used to represent information. They can describe positions, relationships, or attributes—such as the coordinates of a point or the features of an object. Vectors appear in both graphic design and machine learning, but they serve different purposes. Here's a deeper look into how they compare:

What Are Vectors in Adobe Illustrator?

In Adobe Illustrator, vectors represent graphical elements like shapes, lines, and colors using mathematical descriptions. For example:

A red circle might be defined by:

  • Position: [x, y] (coordinates on the canvas)
  • Radius: 50 pixels
  • Color: [255, 0, 0] (RGB values for red)

These numbers form a vector that encodes all the necessary information about the circle. Unlike pixel-based images, vector graphics can be scaled infinitely without losing quality because they are defined mathematically.

How Are Illustrator Vectors and ML Vector Embeddings Related?

While they serve different purposes, Illustrator vectors and machine learning embeddings share key similarities:

Numerical Representation:

  • Illustrator: Vectors describe visual and geometric properties (e.g., shape, position, color).
  • ML Embeddings: Vectors describe abstract relationships (e.g., a word's similarity to other words).

Encoding Relationships:

  • Illustrator: A vector describes the relationship between graphical elements (e.g., overlapping shapes, gradients).
  • ML Embeddings: A vector describes relationships between data points (e.g., "dog" is closer to "cat" than "car").

Mathematical Foundations:

Both rely on the concept of a vector: a set of numbers that define a position or set of properties in a space.

Colors Are Like Words to a Computer

One compelling analogy is how computers interpret colors and words:

  • Colors: A color like red is stored as an RGB vector [255, 0, 0]. To a computer, this is just a series of numbers, even though humans perceive it as "red."
  • Words: A word like "dog" might be represented as a vector [0.3, 0.7, -0.2, ...]. To a computer, this is also just numbers, but it encodes relationships humans interpret as meaning.

Why This Matters

Understanding Illustrator vectors helps demystify ML embeddings:

  • Both encode complex information into numbers.
  • Both rely on the concept of vectors to describe relationships or attributes.
  • The principles are transferable, showing how mathematics powers diverse applications from graphic design to artificial intelligence.