did you know Spotify can measure how similar two songs are?

imagine every song as a dot on a map — not a map of places, but of qualities. songs that feel alike sit close together.

your listening history places you on that same map. recommendations are, roughly, the dots nearest to you that you haven’t heard yet.

one classic approach needs no understanding of music at all: if people who love the songs you love also love something you haven’t heard, that something is a good bet.

millions of listening patterns compress each song and each listener into a list of numbers — a vector — capturing the shape of their taste.

similarity(a, b) = cos θ = (a · b) ÷ (|a| × |b|)

a simplified sketch. production systems blend many models and signals.

cosine similarity measures the angle between two vectors. an angle of zero means identical taste; ninety degrees means unrelated.

it ignores loudness and size and focuses purely on direction — which is exactly what you want when comparing patterns.

the eerie part: the dimensions have no names. the model invents whatever axes best separate listening behaviour, and we just call them coordinates.

cos θ = (a₁b₁ + a₂b₂ + … + aₙbₙ) ÷ (|a| × |b|)

• the cold-start problem: brand-new songs have no listeners yet, so systems also analyse audio features to place them.
• the same vector maths powers search, image recognition and large language models.
• spotify has published engineering posts on how discover weekly and similar features evolved — worth a read.