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But what is a convolution?

A 23-minute video by 3Blue1Brown about probability and statistics, on the Mathematics shelf. It was posted to r/3Blue1Brown as “New video: But what is a convolution?”. It is pitched at introductory level.

3Blue1Brown, Video, 23 min, 2022, on the Mathematics shelf

Constructs discrete convolution from simple examples connecting probability, image processing and transforms.

Study notes

Introductory, Visual intuition. Step 10 of 13 in The mathematics of change and signals

Helpful first

• Basic arithmetic
• Basic probability

What it builds

• Introduce convolution as a new way to combine lists.
• Find probabilities for sums by pairing outcomes.
• Relate convolution to image processing.

Useful moments

• 0:20A new way to combine lists
• 3:04Flipping and sliding dice outcomes

Check yourself: Why does adding two random variables involve combining many pairs of possible values?

Next in the path: The intuition behind Fourier and Laplace transforms I was never taught in school

Notes are based on metadata, Reddit context and selected English caption passages. They are not a review of every claim in the video.

Constructs discrete convolution from simple examples connecting probability, image processing and transforms.