sampling

Numberphile interviews Grant Sanderson of 3blue1brown about Bertrand's paradox, where different reasonable ways of picking a random chord of a circle give different probabilities.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.

Mike Pound explains the discrete cosine transform and how it underpins JPEG compression. It is part two of Computerphile's JPEG series.

Huygens Optics explains the Fourier transform and shows how a lens performs one optically. A DLP projector is used as a Fourier filter to do simple pattern recognition on lithographic character patterns.

Tom Scott explains for Computerphile how Unicode and UTF-8 grew out of messy older character encodings to become the web's standard. It covers why the design works and how it handles worldwide text.

Technology Connections explains why the superheterodyne radio has its name and how mixing frequencies lets it tune stations well. It walks through the underlying wave phenomena and algebra and why the design solved a hard tuning problem.

Tom Scott explains why confetti and snow wreck video quality, using interframe compression and bitrate. He demonstrates it live by changing the quality on screen.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

Geoff Cumming uses a simulation to show how wildly the p value varies from one replication to the next because of sampling variability. He argues for estimation and confidence intervals over null hypothesis significance testing.