10 ms·

This site is a hidden gem on the internet. This guy deserves a lot more credit. I think he's doing something at the level of Khan Academy, but for seemingly sim

by typon 11y ago

This site is a hidden gem on the internet. This guy deserves a lot more credit. I think he's doing something at the level of Khan Academy, but for seemingly simple concepts we all take for-granted. An article I really enjoyed was his explanation of Quake's inverse square root method: https://web.archive.org/web/20150530232103/http://betterexplained.com/articles/understanding-quakes-fast-inverse-square-root/ https://web.archive.org/web/20150530232103/http://betterexpl... What I also appreciate is that he admits when he doesn't understand something and doesn't pretend to give an incomplete, vague explanation and just straight up says he does't fully get it (like why the specific 'magic' number in the Quake algorithm). Thankfully he linked the original paper and I read up on it myself. But his initial explanation provided a solid background for the paper.

morley 11y ago
This is fascinating! I wanted to know more about the history of that function at id, which lead me to this beyond3d post (which was the topic of the reddit post that BetterExplained listed as a source): https://web.archive.org/web/20070208003255/http://www.beyond3d.com/articles/fastinvsqrt/ https://web.archive.org/web/20070208003255/http://www.beyond...
kalid 11y ago
Hey, Kalid from BetterExplained here, thanks! My general philosophy is to be really, really honest with myself if I understood something. It's ok (really!) to admit when we haven't fully understood a concept. Want a fun example? How about percentages. Yeah, that thing we mastered in 4th grade or whatever. That thing we use every day. Well, did you know that a% of b = b% of a? Let's say you want 16% of 25. Ugh. Ok, let's multiply it out... divide by 100... no! How about 25% of 16? Well, that's 4. Easy. But are they the same thing? a% of b = a/100 * b b% of a = b/100 * a Either way, it's ab/100. Now every percentage problem has a 50% chance of being expressed more easily. How did we miss this? (Argh!!!) Math is full of insights like that. Trig functions (sine, cosine, tan, etc.) are actually themselves percentages. A sine of .95 means you are at 95% of your maximum height (where the max is the hypotenuse). Sine and cosine are unitless numbers, and that's why the can be each other's derivatives (the percentage change of a percentage change...). So many things click! What else have we overlooked? Anyway, really appreciate the note!
- themartorana 11y ago
  What?! I've wasted so much of my life.
  - kalid 11y ago
    I think I left a palm-print on my forehead when I saw that.
  - nickpsecurity 11y ago
    Me too. I was even a math geek but didn't understand most of it. I knew all the rules for equations plus heuristics for how to apply most of them. I can only imagine how much more effective I'd have been if there was a constant, parallel learning process focusing on intuitive understanding of all foundational concepts in various math branches.
  - twobits 11y ago
    Indeed. The site is amazing, and Kalid is to be praised to heavens and back. But a man is a man, and he can do so much. My main, very sad, take away from that site, was how ridiculously bad math teaching is everywhere else. It's easily in the criminal area. To put but the simplest of examples, I have an MSc in math, and I was never told in uni (or figured out by myself), that "i" is "turn 90 degrees". That site should be required reading in many unis, to teach people how to teach. At least save the new generations :-/
- spdionis 11y ago
  The trig part was intuitively obvious for me, but the % part was wow!
- ThrustVectoring 11y ago
  Euler's Identity is often explained in terms of mysterious language as well. Like, e^i*pi = -1 makes a lot more sense when you consider the exponential function as "proportional growth", i as "sideways", and pi as "halfway around a circle" - all Euler's Identity does is rephrase "going halfway around a circle" in terms of continuous and proportional sideways growth.
timdierks 11y ago
Here's the best explanation I've seen: http://h14s.p5r.org/2012/09/0x5f3759df.html http://h14s.p5r.org/2012/09/0x5f3759df.html
dkersten 11y ago
A slight correction: the technique existed long before the paper, so I wouldn't exactly say that its the "original" paper. The paper was written by Chris Lomont in 2003, when the gamedev.net community first started investigating the code (I thought Beyond3D did their investigation earlier, but it looks like they did it in 2004). There is a different paper that published a similar idea in 1997 (Floating Point Tricks), but its not the one linked. The code first appeared in the wild on comp.graphics.algorithms around 2002, apparently. I remember this because I followed the discussion on Gamedev.net when Chris Lomont wrote his paper. Some years after, I found the Beyond3D articles where they traced the origin back to Ardent Computer. https://www.gamedev.net/topic/139956-carmacks-sqrt/ https://www.gamedev.net/topic/139956-carmacks-sqrt/ http://www.beyond3d.com/content/articles/8/ http://www.beyond3d.com/content/articles/8/ http://www.beyond3d.com/content/articles/15/ http://www.beyond3d.com/content/articles/15/
mrestko 11y ago
Why did you use the archive.org link?

by typon 11y ago

morley 11y ago

This is fascinating! I wanted to know more about the history of that function at id, which lead me to this beyond3d post (which was the topic of the reddit post that BetterExplained listed as a source): https://web.archive.org/web/20070208003255/http://www.beyond3d.com/articles/fastinvsqrt/ https://web.archive.org/web/20070208003255/http://www.beyond...

kalid 11y ago

Hey, Kalid from BetterExplained here, thanks! My general philosophy is to be really, really honest with myself if I understood something. It's ok (really!) to admit when we haven't fully understood a concept. Want a fun example? How about percentages. Yeah, that thing we mastered in 4th grade or whatever. That thing we use every day. Well, did you know that a% of b = b% of a? Let's say you want 16% of 25. Ugh. Ok, let's multiply it out... divide by 100... no! How about 25% of 16? Well, that's 4. Easy. But are they the same thing? a% of b = a/100 * b b% of a = b/100 * a Either way, it's ab/100. Now every percentage problem has a 50% chance of being expressed more easily. How did we miss this? (Argh!!!) Math is full of insights like that. Trig functions (sine, cosine, tan, etc.) are actually themselves percentages. A sine of .95 means you are at 95% of your maximum height (where the max is the hypotenuse). Sine and cosine are unitless numbers, and that's why the can be each other's derivatives (the percentage change of a percentage change...). So many things click! What else have we overlooked? Anyway, really appreciate the note!

themartorana 11y ago
What?! I've wasted so much of my life.
- kalid 11y ago
  I think I left a palm-print on my forehead when I saw that.
- nickpsecurity 11y ago
  Me too. I was even a math geek but didn't understand most of it. I knew all the rules for equations plus heuristics for how to apply most of them. I can only imagine how much more effective I'd have been if there was a constant, parallel learning process focusing on intuitive understanding of all foundational concepts in various math branches.
- twobits 11y ago
  Indeed. The site is amazing, and Kalid is to be praised to heavens and back. But a man is a man, and he can do so much. My main, very sad, take away from that site, was how ridiculously bad math teaching is everywhere else. It's easily in the criminal area. To put but the simplest of examples, I have an MSc in math, and I was never told in uni (or figured out by myself), that "i" is "turn 90 degrees". That site should be required reading in many unis, to teach people how to teach. At least save the new generations :-/
spdionis 11y ago
The trig part was intuitively obvious for me, but the % part was wow!
ThrustVectoring 11y ago
Euler's Identity is often explained in terms of mysterious language as well. Like, e^i*pi = -1 makes a lot more sense when you consider the exponential function as "proportional growth", i as "sideways", and pi as "halfway around a circle" - all Euler's Identity does is rephrase "going halfway around a circle" in terms of continuous and proportional sideways growth.

timdierks 11y ago

Here's the best explanation I've seen: http://h14s.p5r.org/2012/09/0x5f3759df.html http://h14s.p5r.org/2012/09/0x5f3759df.html

dkersten 11y ago

A slight correction: the technique existed long before the paper, so I wouldn't exactly say that its the "original" paper. The paper was written by Chris Lomont in 2003, when the gamedev.net community first started investigating the code (I thought Beyond3D did their investigation earlier, but it looks like they did it in 2004). There is a different paper that published a similar idea in 1997 (Floating Point Tricks), but its not the one linked. The code first appeared in the wild on comp.graphics.algorithms around 2002, apparently. I remember this because I followed the discussion on Gamedev.net when Chris Lomont wrote his paper. Some years after, I found the Beyond3D articles where they traced the origin back to Ardent Computer. https://www.gamedev.net/topic/139956-carmacks-sqrt/ https://www.gamedev.net/topic/139956-carmacks-sqrt/ http://www.beyond3d.com/content/articles/8/ http://www.beyond3d.com/content/articles/8/ http://www.beyond3d.com/content/articles/15/ http://www.beyond3d.com/content/articles/15/

mrestko 11y ago

Why did you use the archive.org link?