There’s always a better way to understand an idea. I’m writing down the explanations that helped me, hoping they’ll help you too. No pretenses, no “teacher”, just an excited friend sharing an idea that finally clicked.
A few observations on learning:
Ideas start hard and finish simple. Complicated ideas get easier. The idea is the same, it’s our thinking process which has been improved. Multiplication, reading and even tying your shoes seemed tough at first and are trivial now. I know that math, science, business, or any topic can become intuitive, after overcoming the initial complexity.
The best teacher is you – after you’ve learned the subject. You, 10 minutes after learning a new idea, are the perfect tutor for your current self. You overcame the difficulties and can explain the solution in language that makes sense. We can’t go back in time, but we can capture Aha! moments as soon as they happen. Some lucky soul can avoid the pothole we just climbed out of.
Get a map, not directions. Memorization isn’t understanding: follow the recipe, crank through the formula, get from A to B without asking why. Directions are easy, but what about wrong turns? New destinations? Helping a friend who’s starting at point C, not A? This site is about sharing maps, the deep intuitions taking you from any point to any other point. Let’s leave the raw details for the encyclopedias.
I still don’t know (and that’s OK with me). Learning is a constant process of updating what you thought you knew. Don’t see gaps as “holes”, see them as leaks in your roof that you can patch up. Found a mistake in your thinking? Great! Now you have one less misconception. And we can keep going from there.
I’m still far from a real understanding of most ideas, and that’s where you come in. I’m always scrounging for more insights, so send ‘em along :).
About Kalid Azad
I’m an extremely curious person and love sharing insights with others. At Princeton University I started a site to explain concepts as I would have liked to learn them; BetterExplained is a continuation of that idea. I’m grateful to report the site reaches 250k monthly visitors, is assigned as reading in dozens of university courses, and has been referenced in Science Magazine, along with the blogs for the New York Times, The Atlantic, O’Reilly Radar, Scientific American, and the National Academy of Sciences. The book Math, Better Explained is a well-received Amazon bestseller.
I worked as a program manager at Microsoft after college, have several projects (such as InstaCalc, a real-time, shareable calculator and ContestMachine (Y Combinator) and currently do software development for MindTouch. Feel free to ping me at email@example.com. I’ve done a few interviews and am happy to answer questions.
Note For Students/Educators
BetterExplained is a grocery store of explanations that have worked for me. Please print, excerpt, quote, or modify any text, images, or videos that you like (example: supplemental reading or even part of your lessons). I’m growing tomatoes, eat them whole or work them into your own creations.
For commercial use, please contact me.