This was the title of a 5-minute 'lightening talk' by Allen Downey, author of Think Python <http://www.greenteapress.com/thinkpython/html/index.html>, during the educational summit here at PyCon. Main points: * - Nat ural L ang uage : expressive and readable, but verbose and imprecise. - Math ematical notation : concise and precise, but not readable or executable. - M ost programming languages: precise and executable, but verbose and not readable. Hmmm ... can anyone think of an expressive, readable, concise, precise, and executable symbolic language? : ) He went on to show a traditional mathematical formula representing Bayesian inference and compared it to the corresponding Python code. The Python code was similar to natural language and represented a flow of ideas. It was comprehensible. His point was that we often think we need to first express our ideas in traditional mathematical notation and then translate the math into executable code. But his point was no, we can code our ideas directly. It is a new kind of mathematical expression. I was so delighted to hear this, as these are the conclusions I have come to as well. It's absolutely true that coding reflectively helps clarify one's ideas, and this is why it belongs in education. I've repeatedly had the experience that coding something I had long taken for granted in math got me to see it in a new light. I've come to view traditional math syntax as a kind of clever shorthand we developed before we had computers. I think the traditional syntax creates a kind of cognitive illusion in students and teachers that that's 'really' the math. And then throwing calculators into the mix just solidifies the illusion. Everyone in K-12, students and teachers, thinks that the math is 'really' on a piece of paper, in traditional notation, and that the technology is something on the side we turn to in order to help us get the math onto the paper when the calculations get too tough. I think that picture is flawed and antiquated. The technology itself is the new paper. Computational languages are the new algebra. * PyCon was amazing. It was my first one. Very inspiring. Time definitely well spent. -- Michel =================================== "What I cannot create, I do not understand." - Richard Feynman =================================== "Computer science is the new mathematics." - Dr. Christos Papadimitriou ===================================