Coordinates: positions on a grid

On a map, positions are indicated by squares, for example «C4». In mathematics and data processing, we instead use coordinate pairs like (3, 4). This means: move 3 units along the x-axis (to the right) and then 4 units along the y-axis (upwards).

The first number is always x (horizontal position), the second y (vertical position). The order is critical: (3, 4) and (4, 3) point to entirely different locations.

Computers and AI systems use coordinates to handle positions. This can refer to where a button is located on a screen, where a cursor points, or how words are represented in an internal model. In such systems, concepts with similar meanings are placed close to each other in a coordinate system.

Positioning on a grid: Imagine a grid with axes ranging from 0–9. You have three objects placed at specific coordinates. Another person tries to find them by guessing coordinates (x, y). Each guess gives a response: hit or miss.

Distance: How far is it between the point (1, 1) and (4, 1)? Since the y-value is the same, the distance is 3 units (4 − 1). Between (1, 1) and (4, 5), the distance is greater than 3 but less than 7 (3 + 4). Calculating the distance between points is a fundamental method for measuring similarity or difference between data objects, for example to determine if two concepts in an AI model are related.