Most important, I’ve used it to show that PLMs are meant for a certain kind of target: discriminating or classifying things that look the same to the untrained eye but are not. To me it’s absolutely worth the extra time if there’s one specific perceptual knot that’s giving you a migraine. The difference between sine, cosine, tangent, cotangent. Intervals and cadences in music. Between types of chemical bonds. Between financing strategies, or annual report numbers. Even between simple things, like whether the sum of two fractions (3/5 and 1/3) is greater or less than 1. Run through a bunch of
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