Fluid Simulation (with WebGL demo)
Very good writeup of fluid dynamics, I've been down Wikipedia crawls regarding Navier-Stokes but have never seen those equations applied like this in such a step-by-step manor.<p>It occurs to me however that we really don't have long-form ways of expressing the equations (especially in more than one dimension).  The math can't be simplified, but I was still lost about a quarter of the way through the work even though I used to know partial derivatives quite well.  The article requires something like 4 or 5 semesters of calculus to grok.<p>I think what makes math so hard to translate from written form to a mental map is that we’re still expressing it in sort of a write-only language like APL:<p><a href="http://c2.com/cgi/wiki?AplLanguage" rel="nofollow">http://c2.com/cgi/wiki?AplLanguage</a><p>I’m curious if anyone knows of any other way to express equations.  For example:<p>* can variables be longer than a single letter without making equations too large to “see” at first glance?<p>* can all of the notation like the one for partial derivative be rewritten as ordinary functions?<p>* is there a way to “break up” long functions into shorter expressions (like sub-functions) without losing their relationships?<p>What I’m getting at is that people are able to visualize large, complex abstractions like SQL, OpenGL, matrices (barely), but not really statistics, probability, calculus, and so on.  Have these other disciplines just not had time to be expressed in layman’s terms?  I don’t buy that they are fundamentally more difficult than other disciplines.  Just more.. esoteric.  Thoughts?