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Applied Mathematics

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Game Theory. Angel Problem. The Unreasonable Effectiveness of Mathematics in the Natural Sciences. The Unreasonable Effectiveness of Mathematics in the Natural Sciences is the title of an article published in 1960 by the physicist Eugene Wigner.[1] In the paper, Wigner observed that the mathematical structure of a physical theory often points the way to further advances in that theory and even to empirical predictions. The miracle of mathematics in the natural sciences[edit] Wigner begins his paper with the belief, common to all those familiar with mathematics, that mathematical concepts have applicability far beyond the context in which they were originally developed.

Based on his experience, he says "it is important to point out that the mathematical formulation of the physicist’s often crude experience leads in an uncanny number of cases to an amazingly accurate description of a large class of phenomena. " He then invokes the fundamental law of gravitation as an example. The deep connection between science and mathematics[edit] Responses to Wigner's original paper[edit] 1. 3. 4.

2: Example sampler.

Fractal

Blog : Self-Description. September 7, 2010 — Jon McLoone, International Business & Strategic Development I am a big fan of Randall Munroe’s web comic strip xkcd. (Apparently I am not alone.) A while ago, Randall posted a strip with a self-referential chart of the amount of black ink in the image. If you have read my past blog items, you know I like recursive pictures.

So I thought I would create a Mathematica version of this strip. First, I generated each of the charts, which are all pretty straightforward chart types in Mathematica. The work was in making them roughly follow Randall’s style choices. The pie chart: The bar chart: The ink location chart: Next, I solved the equation f[x]=x, where f is the function that generates an analysis report on the ink in an image and x is the image of the report. If the equation is substituted into itself, it also solves f[f[x]]=x, and for that matter f[f[f[f[f[f[f[x]]]]]]]=x. So all I needed was a function that generates a cartoon strip based on the analysis of a cartoon strip. Ask a Mathematician / Ask a Physicist. TED Math Talks. Bruce Bueno de Mesquita predicts Iran's future. Sean Gourley on the mathematics of war. Benoit Mandelbrot: Fractals and the art of roughness. Dan Meyer: Math class needs a makeover.