kalid

16 ms·

1. 151.▲
   by kalid 12y ago

   I sell math books and courses at http://betterexplained.com and on Amazon. It's about 3k/m currently, hoping to improve that with better landing pages, a/b testing, retargeting, drip campaigns, etc. [the patio11 p
2. 152.▲
   by kalid 12y ago

   (Replying to myself since we hit the nesting depth.) 1. Here's a deeper intuition: any circle is just the unit circle, scaled up or down. Any number is just 1.0, scaled (and rotated, if complex) by the exponential function that was run
3. 153.▲
   by kalid 12y ago

   Oh yeah, after getting the direction, figuring out the numbers is the next step :). Having i as a base means "we plan on rotating 90 degrees" which actually means pi/2 radians. e^rt models growth rate of r, for time of t. so
4. 154.▲
   by kalid 12y ago

   Yep, I think so. My philosophy, at least, is that any idea can eventually be intuitive, no matter how difficult at first, if we find the right analogies. I see any exponent like a^b as starting at 1.0, intending to apply a rate of change of
5. 155.▲
   by kalid 12y ago

   That is really humbling and gratifying to hear, thank you.
6. 156.▲
   by kalid 12y ago

   Thanks! The business side of things is coming along, I've just finished up a hectic few months (wedding, honeymoon) and am looking to crank on the site again. Long term I want the site to be an ever-growing part of my life. I'm ve
7. 157.▲
   by kalid 12y ago

   Wow, thanks for the plug and the kind words! Glad to hear the site is helping -- most of the time I miss the intricacies too, and end up adding things years later [after a re-read] or in response to a comment from the article. As a more gen
8. 158.▲
   by kalid 12y ago

   Glad you enjoyed them so far :). "Cheatsheet" might not be the best term for the summary page, perhaps "quick reference". I picked cheatsheet because it's a little more approachable than "reference", which
9. 159.▲
   by kalid 12y ago

   Definitely not an expert, but I found a few good articles on this (just updated the article): http://seedmagazine.com/content/article/prime_numbers_get_hi... Nice summary: http://carbonatoms.wordpress.c
10. 160.▲
    by kalid 12y ago

    That's awesome! I hope you can make use of the site. One goal for the site is to provide "ammo" to teachers who are looking for other ways to present difficult concepts.
11. 161.▲
    by kalid 12y ago

    Great point. I use the word "intuition" but feel it might be overloaded, things with intuitive knowledge, psychics, going with your gut despite the facts, etc. The sense I mean is closer to "grokking" or "clicking&q
12. 162.▲
    by kalid 12y ago

    Thanks so much, and for originally submitting the cheatsheet to HN. (I hope it helps people untangle concepts that confused me for literally a decade.) I really appreciate the encouragement and hope to keep cranking as long as I can.
13. 163.▲
    by kalid 12y ago

    I agree. A few years after doing articles, I started seeing the power of historical context. For example, the Fourier Transform was originally _rejected_ as implausible when presented to the mathematicians of the time. They needed a decade
14. 164.▲
    by kalid 12y ago

    Great example, I like that. I started realizing that many instructors don't necessarily have an intuition for the topic they're teaching, and it's often up to the individual student to seek it out. I'm hoping to do more
15. 165.▲
    by kalid 12y ago

    Thanks so much. My meta goal is to help people gain confidence in what it means to learn (in general, not just math) and ideally encourage people to share their insights with others. No reason for us to all bump our shins on the same coffee
16. 166.▲
    by kalid 12y ago

    Great tidbit, thanks. I forget if I have a mention that logs were developed before e, but I love it because it's a little mosquito in the ear for the over-rigorous mathematicians who define e up front (as a limit) and then say "th
17. 167.▲
    by kalid 12y ago

    It drives me batty because we learn the properties of logarithms before (if ever) internalizing what they mean. Here's my intuition if it helps someone: http://betterexplained.com/articles/think-with-exponents&#x2F
18. 168.▲
    by kalid 12y ago

    Whoops, I probably wasn't clear enough in my reply -- the classes on transistors, logic gates, etc. are available to CS majors but are definitely not a requirement for programming. I completely agree that trying to teach about digital
19. 169.▲
    by kalid 12y ago

    I definitely agree -- context matters. For a potential math major [i.e. people for whom metric space refers to a measure and not a flat in Europe :)], you definitely want the ground-up understanding. In CS it's similar, where you learn
20. 170.▲
    by kalid 12y ago

    Thank you Jacob, I really appreciate it. I try to imagine that I'm writing to a younger version of myself, who hasn't seen the material yet. It helps me remove potential anxiety about not knowing everything, or trying to impress -
21. 171.▲
    by kalid 12y ago

    Thanks! I'd love to do more elementary school topics. I still encounter revelations about things like basic counting (fencepost problem) and arithmetic. My meta goal is to raise people's standards for what it means to understand s
22. 172.▲
    by kalid 12y ago

    Glad it was helpful! There's a strange tendency in technical explanations to expand, expand, expand. A heuristic I have: Imagine you're writing a letter to yourself, before you started the course. There's no reason to waste y
23. 173.▲
    by kalid 12y ago

    Thanks, glad to hear you're enjoying it. I realized that until I could explain a concept intuitively, I didn't really understand it -- and it became a mission to find some analogy that really clicked for me. Hope it gives you some
24. 174.▲
    by kalid 12y ago

    (Kalid from BetterExplained here) Thanks for the comment. There's this weird notion in Calculus education that we need to start from first principles. Limits were invented a century after Newton died, yet they're taught first. &qu
25. 175.▲
    by kalid 13y ago

    Exactly, many lessons are written to be defended from assault, not to be inviting. A castle, while romantic, is not as comfortable as a hotel. (My personal mission is to find/share the aha! moments that actually make the details click.
26. 176.▲
    by kalid 13y ago

    Analog electronics is a great domain, and something I want to explore more myself (I did CS, only had 1-2 analog classes, and didn't build an intuitive understanding for electricity, a gap I want to cover). For books, I don't have
27. 177.▲
    by kalid 13y ago

    Beautiful point. It's along the lines of "How can you learn programming without the details of how to turn a series of tokens into an AST?"
28. 178.▲
    by kalid 13y ago

    Thanks for the suggestion!
29. 179.▲
    by kalid 13y ago

    Great point, thanks for the comment. I think the key missing insight for me was that a continuous process and a discrete process can both point to the same result. A pixellated word on a screen ("cat") conveys the same meaning as
30. 180.▲
    by kalid 13y ago

    I was the same way :). I have an intuition-first guide to calculus, here: http://betterexplained.com/calculus/lesson-1 I think the essentials on how to think with calculus can be conveyed in 1 minute. Let me know if th