About Singular Values

I am a mathematician, and this is my blog. When mathematicians look at the world, they model everything in terms of mathematically constructed spaces that are locally defined by multiple parameters. Transformations are approximated by tangential matrices, and a matrix is analyzed by decomposing it into its singular values.

Besides numerical values, there are also the values that represent the qualities or beliefs that people consider important, such as loyalty and respect. Some values are singularly important, and yet are commonly overlooked.

Nunquam praescriptos transibunt sidera fines is Latin for "Never pass the prescribed limits of the stars." It has also been translated as "Nothing exceeds the limits of the stars" and "Never do the heavenly bodies transgress their prescribed bounds." The French mathematician Henri Poincaré submitted an anonymous paper under the name of this code phrase to an 1887 contest to solve a celestial mechanics problem. He won a prize from the King of Sweden, and proved the existence of chaotic orbits, a possibility that was previously not imagined. As he later described chaos, "It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible."

I interpret the Latin quote as meaning to think big, but to remember that even the grandest plans have their limits. Poincare himself was both cautious and fearless in his analysis. He stuck to what he could prove, and he never shied away from the consequences of his ideas. Poincare did not know that chaos was a possibility when he wrote that phrase.