To clarify, these aren’t the normal Feynman lectures. He lectured at a different institution and the author of this webpage transcribed those lectures to produce this set of notes. The content covered is different from the famous set of lectures.
iOS repeated “learns” new words that I use that are misspellings of real words (because I mistype things in a predictable way). It becomes so convinced that it will autocorrect the real word into the typo. And knowing how the keyboard works, I wouldn’t be surprised if it enlarges the touch targets for the typo once it thinks I meant to use the typo.
The cause is obvious: Apple is training on what I type, not what I send. Apple does not consider that I actually care about the accuracy of what I send and will fix errors; perhaps they optimize for people who are careless enough to send typoed messages, yet niche enough to commonly use words not in the default dictionary.
It is infuriating that I have ~50 manual corrections telling Apple to leave words alone and correct certain typos to the real words.
Strang does include that. I just checked the fourth edition, like you say you did. Scrolling down two pages to get to the first page of the table of contents, I see the heading “cosines and projections onto lines”. I navigate to that section and it explains all the logic, proof, and intuition behind the connection between angles and dot products. Please don’t spread misinformation…
That's page 171, 13 dense pages into the section on orthogonality, long after he's introduced the dot product, in a section where he says, in italics, "the orthogonal case is the most important"; he gives cosines about half a page before going back to a perp b.
Nobody said Strang never mentioned cos θ --- that would be weird --- only that his sequencing doesn't treat the angle formula as fundamental, even in the section introducing it. And nobody has ever read Strang and thought projections didn't matter.
It would be like a speaker who can’t distinguish the uh sound in “but” with the ih sound in “bit”. Is it really the native English speaker’s fault if he can’t understand that personal dialect?
France’s vowel inventory is bigger than (or just as big as) English’s, and it has a lot more homophones. I imagine all the context goes toward disambiguating the actual homophones and not the arbitrary sets of words foreigners can’t pronounce because they don’t want to learn the accents (the system is not that hard and completely predictable).
> the solution of any one of which would change not only the career of the person who solved the problem, but possibly life on Earth. Many have stood like mountains in the distance, rising above the clouds, for generations.
Whether or not this is AI, this comment is not true. An axiomatic derivation of a formula doesn’t change how it’s used. We knew the formulas were experimentally correct, it’s just that now mathematicians can rest easy about whether they were theoretically correct. Although it’s interesting, it doesn’t change or create any new applications.
The article specifically points out WaniKani as an example of a very bad implementation of spaced repetition (see the "FSRS in practice" heading, under the paragraph "for Japanese language learning specifically...").
As a senior in high school, I devoured this game in elementary school and got way better at math than my peers. Now taking differential equations and multivariable calculus through our college in the high school (CHS) program. When I looked for it out of curiosity I was sad to see it transformed into a subscription service.
The normal Feynman lectures are here: https://www.feynmanlectures.caltech.edu/