Awesome example about the derivative! I think the best part of geometric thinking is running ideas on your "native hardware". Our brains are massively parallel

Awesome example about the derivative! I think the best part of geometric thinking is running ideas on your "native hardware". Our brains are massively parallel, visual-processing monsters... and we try to think about ideas linearly, like we're a turing machine. No -- use that GPU! :). When I think visually, I can immediately grok the idea (it's running in hardware) and my software layer (my conscious thought process) can work on stitching together deeper ideas. Shameless plug, but I've written about visualizing Euler's Identity (http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ http://betterexplained.com/articles/intuitive-understanding-...): * Radians are distance from the mover's point of view * e is continuous growth * i is a rotation (so e^i*anything is imaginary growth, i.e. growth in a perpendicular direction) Combining ideas like this is just so enjoyable! It brings out the natural beauty in learning.