Hearted Youtube comments on Welch Labs (@WelchLabsVideo) channel.

  1. I have a beautiful solution to Kepler's equation, but it could not be contained within the margins of this comment section
    2400
  2. Nice animations 😉
    2400
  3. Euler was like, nahh bro you’re both wrong
    2000
  4. I hardly understand whats going on but luckily some guy already figured it out a few thousand years ago and wrote in on a stone tablet. Humans are amazing.
    1300
  5. Part 1 - 9 : Okay thats some cool maths Part 10 : Whoa now we're talking Part 11 : There's some demonic powers at work here.
    1000
  6. Your complex numbers series was my introduction to higher math education! It’s a pleasure to see you continue it.
    864
  7. holy sh** it really is the first engineer's tool! I LOVE the idea that slide rules existed around the birth of modern scientific method (Galileo)
    815
  8. I have a physics PhD, and while of course nothing here was new to me per se, I really appreciate the way you tie the story together. The undergraduate physics curriculum is more focused on establishing the model and using it to make predictions that illustrate its key features (like the double slit results), but the "origin story" doesn't often get explained. Thanks for that!
    738
  9. Oh man this brings back memories. KSP used three different methods to compute E. The Newton-Raphson method actually turned out to be very unreliable for several cases, and would often blow up. What worked pretty well was a binary partitioning method, where you start with a large correction and half the search space at each iteration. It was slower to converge, but almost always found a decent solution. There was also a dedicated solver for extreme eccentricities, and of course another one for hyperbolic cases.
    668
  10. The quality of your videos is worth the wait
    619
  11. More like "The Neuroscience of AI"
    591
  12. The animation and explanation of interference being caused by the phase of the wave function was so well done!
    585
  13. many years ago your "neural networks demystified" pretty much changed my life. I ended up spending months writing a whole deep learning library in C# on CPU after watching it, before realizing things like tensorflow and pytorch exist. Learning everything the hard way paved the way to a deep fundamental understanding and a life long passion. Glad to see you still making these videos.
    555
  14. And now im the 14 year old watching his videos 🫠
    522
  15. You should make a video deeply explaining how modern transformers and attention mechanism works. Love your content!
    467
  16. I solved it actually. Will post proof in a sec
    465
  17. This is by far THE best AI deepdive Ive ever seen. I actually understand now not just how the attention arcitechure works but how and why DeepSeek's changes to the architechure result in such an incredible performance AND efficency improvement.
    406
  18. As a space nerd who loves this sort of math, I'm astounded that I never realized how central Kepler's equation was to the historical development of calculus!
    393
  19. Euler's motivating example and insight that the i's should cancel; so log(-1) should have an I somewhere is such important knowledge. I hated how they taught math with no context or motivation. This is great!
    382
  20. 9:33 You define a conjugate as "flipping the sign of the imaginary component" but what you're doing here is not flipping the sign of the imaginary component, but flipping the sign of the exponent, which happens to be imaginary. Of course in reality it amounts to the same thing, but that's what we're trying to prove! We don't know yet if 2^(-bi) is the conjugate, so we can't use this fact to prove the magnitude of our number is 1.
    189
  21. When I studied engineering in the 80s, I had a circular slide rule. Awesome video.
    158
  22. This is so cool! The idea of doing all this by hand without any digital instrumentation or computation is incredible.
    153
  23. This has got to be by far the clearest explanation on solar eclipses I've ever seen or heard. Easy to understand as well. Very well done. Thank you.
    146
  24. This video is absolutely top drawer. The animations, the lesson, the historical pages, the actual visualization of how the imaginary unit shapes the wave function. Just brilliant. I have to get the book.
    138
  25. Amazing work diving into the details to clearly. Bravo Stephen!
    136
  26. I remember trying to solve this before knowing it was a famously difficuly/impossible problem, got to the exact form of M=E-esin(E), though with different variable names, and tried to use the taylor series to make an estimate. Worked well for low eccentricities, but lets not even talk about the high ones haha. Great video about this topic, so here is a comment for the algorithm :)
    134
  27. The videos on this channel are all masterpieces. Along with all other great channels on this platform and other independent blogs (including Colah's own blog), it feels like the golden age for accessible high quality education.
    96
  28. When I learned (decades ago) that multiplying by i causes a rotation in the complex plane, I wondered why no one ever seems to talk about that in quantum mechanics. Thanks you so much for the beautiful animated images and the detailed explanation. Wonderfully done, and it explains so much I never learned in my advanced physics courses in college.
    87
  29. It's one of those ideas that look so so obvious when you see it, yet it is not at all! Very nice work from DeepSeek.
    82
  30. Honorary 14th part of Imaginary Numbers Are Real
    69
  31. Good derivation walkthrough
    68
  32. Welch Labs + 3Blue1Brown = Happiness
    63
  33. In the first 60 seconds of the video you managed to show me WHY the log equivalencies are true, that my teachers failed for years. I mean I now and use them, but I never SAW why they work, why multiplication becomes addition and so on GOOD JOB!!!
    60
  34. 15:00 wow, that was an enlightement moment for me
    51
  35. Oh god, a Welch Labs video on mech interp, Christmas came early! Will be stellar as usual, bravo! Edit: Fantastic as usual, heard about SAEs in passing a lot but never really took time to understand, now I'm crystal clear on the concepts! Thanks!
    50
  36. As a machine learning graduate student, I LOVED this video. More like this please!
    38
  37. Excellently detailed and well explained.
    33
  38. Thanks for including references in the description, I really appreciate that.
    33
  39. One of the most underrated channels on YouTube. Keep up the great work and we hope Fatherhood has been fantastic so far!
    32
  40. bro your videos are awesome, just discovered your channel, binge-watch all your content now! Please continue your excellent work
    29
  41. Outstanding work! I love the vibe of these old-timey book illustrations. Kepler's crazy 3d frame looking thing MC Escher drawing belongs on a psychedelic rock album cover
    28
  42. I really hope expanding to international shipping works out well! Looking forward to one day hold your book in my hands. Love your style, keep up the great work.
    26
  43. Thanks Euler for discovering the mathematical base for eletrical engineering. And thank you for making me able to visualize it 😄
    23
  44. This is quickly becoming one of my all-time favorite physics channels. Excellent balance between depth and clarity, really nice visuals, and a very pleasant voice and speaking style.
    23
  45. Yess another Welch Labs. You're quickly becoming my favorite youtuber next to Veritaseum
    22
  46. I really want your book.
    19
  47. Remarkable, excellent job.
    18
  48. I never understood these logic tables. Your explanation was so intuitive! Thank you!
    17
  49. This is an amazing video. I really appreciate that you went into depth on how they were actually calculated. The realization that you can essentially do a binary search with an iterative algorithm to find any value of a function is so, and even cooler when you learn that this is how computers calculate logarithms, trig functions, etc. to this day. Basically any time you can find a relationship where x/2 = f(y) or vice versa, you can do this. It is just so cool that you can do something a crazy as logarithms or trig by hand with enough will power, and it's not even that crazy difficult lol. I would love more content like this, so keep it up!
    16
  50. Your videos are always a delight!. So glad you are back on Youtube.
    15