Much appreciated, thank you.
2,455 karma · joined April 1, 2007
I vividly remember cramming for a test my freshman year of college, not having things click, and the final Aha! when a semester of pain disappeared with a few visualizations. The contrast between how most classes presented the material and what actually worked for me was jarring, and I had to share what helped. I hope other people share what works for them, in any format they can.
Luminaries in a field (Einstein, Feynman, Tao) have "post-rigorous" understanding (https://terrytao.wordpress.com/career-advice/there%E2%80%99s...). Pure research without sufficient explanation doesn't help others build this level of depth and leaves the findings as a black box.
Some posts have needed the 100-200 hours of thinking/visualization, labeled with things like "Interactive Guide to the Fourier Transform" (https://betterexplained.com/articles/an-interactive-guide-to...)
Others are smaller insights, written in a day ("Quick Insight: Easier Arithmetic With Calculus" -https://betterexplained.com/articles/calculus-arithmetic/).
Others are more essays/thought pieces, learning strategies, etc.
Setting the expectation up front that not every post is a big thesis-style conclusion can take away the pressure to only create those. (You can have appetizers, entrees, and desserts on the menu!)
Often your big articles are built after working through ideas in smaller ones. (The Fourier Transform emerged after getting insights on e, imaginary numbers, Euler's Formula, degrees vs. radians, etc.).
Right? :)
* Can quickly ("analog-y") adjust brightness and volume. Similar to a volume dial in a car vs. up/down volume buttons. In 2 seconds you can dial it in.
* YouTube videos (in Safari) have the playback controls in the touchbar, not in the interface. You can watch a fullscreen video and scrub through / jump around while keeping your real estate
* TouchID is really nice with 1Password
* I can see things like Pomodoro timers, etc. being useful in the touchbar. I haven't looked at extensions yet.
* Things like the print dialog have a big, colorful button. It immediately stands out and highlights the most common action from where you are in the program. "I don't need to hunt around to adjust margins, paper handing, I just want to print."
* The escape key has a larger hit target than is shown so you can still use vim effectively.
Overall, for developer tools, I'm willing to invest in even marginal gains if it makes my life better. We use these machines hours every day, for years.
Over time, you notice patterns about what really energizes you. For me, this is the high-order bit, more important than any specific time or life hack.
(Examples and analysis here: https://betterexplained.com/articles/life-lessons-10-years/ )
That discussion was an eye opener for me (in a good way), it showed me of how easily things get muddled in online discussions as context goes missing. It always reminds me to really see what the other person is thinking.
Agree on updating articles over time. Text is infinitely tweakable and there's so many ways to improve it over time (often in response to comments I'll reword things, create/update diagrams, fix typos, etc. -- if there's an issue with a YouTube video, there's not much you can do.)
I wasn't sure about email either, but Patrick's post demanding I do something convinced me:
http://www.kalzumeus.com/2012/05/31/can-i-get-your-email/
(He actually sent an email saying that was the most important thing to do, yelling it, and said 1% of people would actually follow it. I decided to start it just not to fall into the trap.)
Here's what I've found personally:
1) It has a better chance of being seen than other social channels. I don't want to be buried under political news and entertainment on Facebook, twitter, etc. Also, many older folks aren't as familiar with tech, but check their email.
2) It's a self-selected group. Here's a set of people who want to hear from me, which means I can be myself a bit more when writing a newsletter update. I imagine I'm writing to some friends who want to know what's going on. I used my email list to get 50 paid beta customers for my Calculus class, which was itself delivered by email in its first iteration.
3) Marketing is way better. I sold more books by announcing it to my 20k email list (at the time) vs. getting on Reddit and HN homepages, with ~1M pageviews.
4) Engagement is higher. Many people reply to the email and we have a quick (or long) conversation, but they don't want to leave a public blog comment. Also, it helps keep in touch with a larger set of people.
5) For numbers, I have about 38k people, 35% open rate, maybe 5-10% click rate depending on the content. If your audience isn't engaged you should prune/remove people who haven't opened it in a while. But, for an engaged audience, you can get thousands of people to take a look at something.
6) Help people get started. I have a short auto-sequence that goes out with 3 lessons (I'd like to make more). Getting a gentle nudge every week with some new content helps people (vs. having to remember each week to find some articles to read).
When people think of "newsletter" they think of spammy groupon emails designed to sell sell sell. I aim for simple, plain-looking updates (not technically plaintext, sometimes I have images), with a casual vibe. "Hey, have something new you might like. Enjoy."
7) On what I write: announcements of new articles, new product launches, requests for beta customers. I probably email 1-2 times per month on average.
8) Lastly, it's fun for me. I don't like the FB/twitter environment that much -- it feels too much like a stage -- with email, I feel like I'm chatting with friends around a table.
https://aha.betterexplained.com - forum to discuss ideas. It's in the background currently but I'd like to make it into more of a public place.
If you like, shoot me an email, I'm putting together a list of people who might want to be contributors. Thanks!
The newsletter is fully optional, basically to get alerted to new articles & other site news. The homepage should be fully scrollable with a big list of articles, you can also check out:
https://betterexplained.com/cheatsheet/
for a visual guide. That said, I'll definitely think about rewording things, and I've long wanted to make a "Getting started" section for students, teachers, parents, etc. Really appreciate the feedback!
Hope it helps someone do the same.
On paper it reached "success" (sold for millions, is now a Top 500 site) but unfortunately it's far away from its original mission.
There's been countless studies about happiness and income, but I realize once my reasonable needs are met, my life satisfaction comes from things that can't be bought (getting in the zone, helping people, feeding my curiosity).
The impact of evergreen content was my biggest eye-opener. The more time, the better, but don't beat yourself up about "lost time". Just start today. Before we know it, 2, 5, 10 years will have passed.
This worked for blog posts, starting an email newsletter, selling books on Amazon, making YouTube videos (for standard math concepts), design improvements to the site, etc. You plant the seed once and it bears fruit for years.
Yeah, my only linear algebra content is:
General Overview:
https://betterexplained.com/articles/linear-algebra-guide/
Matrix Multiplication for Programmers:
https://betterexplained.com/articles/matrix-multiplication/
Hoping to flesh it out over time.
The notion of a "visual Turing test" was interesting (can humans distinguish real from simulated images). The sample sizes (and p-values, for all their issues) were fairly small (10 participants, 100 images each).
I wonder if there are volunteer participant efforts (similar to HealthKit) to help automate these types of evaluations. You could even have a Recaptcha-style service to show your simulations are realistic enough.
I often go to the history of a concept for both historical appreciation and, practically, to understand it better. We often study Calculus without looking at what Archimedes was able to do -- break shapes into smaller parts -- and without really seeing how the notion of infinitesimals come into play. (Epsilon/delta definitions don't give the same insight.)
The natural log was discovered before e -- why would that be? Sine, cosine, trig functions -- they started as measurements of triangles, evolved into analytic definitions of their own -- why does this progression make sense?
In my mind, truly understanding a concept means you understood the path it took to the current state.
(I hadn't studied complex analysis when I wrote that post, learning it now. The various possibilities for the multi-valued solution follow a pattern however.)
One of the biggest lessons of my Ivy-league education was, paradoxically, that it wasn't sufficient (or even necessary). At least not for the goals I wanted.
If you want access to the elite Wall St. or consulting jobs, then yes, you need it. Once you're in, it's almost impossible to be kicked out. Finish, interview, and you're on the path.
But I had longstanding doubts about the state of my actual education. Despite numerous engineering classes, I couldn't, for example, work out i^i in my head instantly.
Imagine someone asked you "Roughly, what do you think 2^512 to be?"
"I don't know exactly, but it's an enormous positive number, probably more than the atoms in the universe."
Ok. You should spit that out instantly. Now imagine someone asks "Roughly, what do you think i^i is?"
Is it positive? Negative? Real? Imaginary? Close to 1.0? Microscopic? Even if you eventually work it out after a minute, does your long delay mean you understood exponents or imaginary numbers? Is this something that should be solidified before, say, studying the Fourier Transform?
Despite scoring well in classes taught by famous professors, I couldn't answer such basic questions. This was literally middle school operations (exponents) used with high-school parameters (imaginary numbers). I was stuck -- and it didn't seem like anyone thought this a reasonable thing to understand.
It led me on a journey of self-education, but I needed to see firsthand that even in an Ivy-league environment, the basics could still be missed. It ended the fantasy that things were transformatively different in some other place -- it was up to me to fill the gaps.
ps. If you want to work out i^i in your head: https://betterexplained.com/articles/intuitive-understanding...
With our "modern" understanding of algebra and geometry, we know to do
Area = 1/2 * base * height
Area = s^2
therefore
s = sqrt(1/2 * base * height)
"Squaring the circle" (https://en.wikipedia.org/wiki/Squaring_the_circle) was an ancient challenge, proven to be impossible with a straightedge and compass in the 1800s. He may have been trying to square the triangle with just those tools.