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The Bottleneck

principialabs.org · 1,383 words · saved by 4 readers

The problems that matter most in science — the ones everyone has given up on — tend to fall the same way. Not to a new instrument or a bigger budget, but to mathematics. For decades, every MRI machine on earth was built around the same constraint. The Nyquist-Shannon theorem said that to reconstruct an image, you need to sample the signal at twice its highest frequency. The theorem is from information theory: if a signal contains no frequency higher than 𝑓 f, you can perfectly reconstruct it from samples taken at 2 𝑓 2f per second. They built faster machines and wound stronger magnets. They spent billions. They tried everything except questioning the rule, because the rule was mathematics, and you do not argue with mathematics. This made MRI machines slow. A cardiac scan meant six minutes of holding your breath, over and over. Breathe at the wrong moment and the image blurred; the whole scan started over. If you had heart failure — if you were one of the people who needed cardiac

The Bottleneck Harry Sanders , 03/24/26 The problems that matter most in science — the ones everyone has given up on — tend to fall the same way. Not to a new instrument or a bigger budget, but to mathematics. For decades , every MRI machine on earth was built around the same constraint. The Nyquist-Shannon theorem said that to reconstruct an image, you need to sample the signal at twice its highest frequency. The theorem is from information theory: if a signal contains no frequency higher than f f f , you can perfectly reconstruct it from samples taken at 2 f 2f 2 f per second. They built fas

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