Was just teaching this stuff to my 12 yo son - this is way more thorough! What a gem of an interactive blog post.
Sound
121–130 of 222 posts
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#122This man needs a genius grant, and this is about the 6th time I've thought this. Any one of these pages would be a feat, an achievement to be proud of, but as a collection, it forms one of the greatest educational resources of its type that I have known. These things can give you more intuition about a subject in 45 minutes than a textbook might be able to in 3 months, because it's interesting and not dry. I wish I h…
I saw your comment and was like: "wait a minute... surely its not the same guy as the mechanical watch thing, is it?!?!?!"
Absolutely blown away. As someone with a "design for learning" degree which I've found to be rather useless, I'd gladly have traded by dozens of thousands of dollars for a chance to learn with this guy. The technical sophistication combined with the incredibly didactic and clear flow of his work is truly insane.
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#123I haven't taken beyond high school physics, so this question is probably obvious, but I haven't been able to find the answer (probably don't know the right terms to search). When I increased the slider that allows you to change the flow of time for the gas in the cube, it really looked like visualizations I've seen of increasing the temperature of a gas. Is there a deeper relationship here? Could an observer tell the…
IIRC temperature is proportional to velocity squared so increase in simulation speed will result in squared increase in temperature. But even if we account for that we are not dealing with ideal gas in real world, there bound to be collisions that break molecules apart or even start nuclear fusion at certain speeds
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#124Earlier quoted context omitted.
Your intuition is right, in that most of the heavy math is simply unnecessary or irrelevant at the practical level. Complex number notation doesn't fall into that category, though. The notion of frequency is intimately tied to the notion of vector rotation, and just as you can't represent Cartesian translation without negative numbers, you can't represent Cartesian rotation without complex ones. The Smith book is def…
Saying that you can't represent cartesian rotation without complex numbers seems a bit much? You do need two numbers. But you can teach a trigonometry class without complex numbers, using either cartesian coordinates or polar notation. And matrices do work.
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#125…and the fact that site works perfectly under load from being top of hn shows his skill with selecting and maintaining right kind of server setup.
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#126In addition to all the recommendations about supporting his Patreon, I also recommend following him on Twitter and clicking the bell icon: he only tweets when new articles are published, a very worthwhile notification.
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#127Earlier quoted context omitted.
> Lagrange had insisted that such an approach could not be used to represent signals with corners, i.e., discontinuous slopes, such as in square waves. Isn't that true though? You can only approximate it, right?
In the same sense that a circle does not exist, because you can only approximate it with an arbitrary number of points/lines. But an infinite number of points the same distance from the origin is a good definition of a circle. In a similar way, an infinite set of sine waves approximating a square wave is a square wave, mathematically speaking.
Sort of. The error at a square wave's "cliff" does shrink in width as you add higher and higher frequencies to the approximation, but the height of the error does not diminish, so you have to be explicit about what you mean by "converge". If you considered MAX(ABS(approximation(x) - square(x))) as your error metric it would not go to zero even in the limit; for most intents and purposes we don't care about that, though, and in any case the limiting behavior is much nicer for "normal" functions that don't have discontinuities like a square wave.
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#128Mind blown, what a guy he is !!! and all his JavaScript is open source and not uglified.
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#129+1 for the recommendation for "The Scientist and Engineer's Guide to Digital Signal Processing" by Steven W. Smith. I spoke to Steven many years ago about his putting all of the book PDFs online for free and since then have recommended at least 5 university libraries to buy it because the students could get free copies of a great book that can be referenced in the library. FWIW the The Scientist and Engineer's Guide…
The book is amazing: http://www.dspguide.com/ (link for the lazy)
pdfs are the chapters are available freely on that website, but if anyone wants to spare themselves the effort of combining them all into one for easier perusal, feel free to email me (in bio) and I can send the combined pdf. I'm currently around page 200, and it's been great as an introductory resource as someone with no other background in DSP.
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#130>If it wasn’t for the collisions with other molecules, those fragrant particles could travel the distance to your nose in a fraction of a second.
That's kinda crazy to think about. Someone across a gymnasium room farts, and you smell it milliseconds later. Ugh.