Flatland

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe:" but now my mind has been opened to higher views...

 The Pareto Distribution

The Pareto distribution shows up in a remarkably wide array of complex systems. Together, “the” and “of” account for 10 percent of all words used in English. The most volatile day in the history of a stock market will typically be twice as volatile as that of the second-most volatile and ten times the tenth-most. Tag frequency on Flickr photos obeys a Pareto distribution, as does the magnitude of earthquakes, the popularity of books, the size of asteroids, and the social connectedness...

 Mathematics Lies Outside Ourselves

I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply the notes of our observations. * * * Let us suppose that I am giving a lecture on some system of geometry, such as the ordinary Euclidean geometry, and that I draw figures on the blackboard to stimulate the imagination of my audience, rough drawings of straight lines or ...

 Focusing Light Increases Heat Where Focused

The sun's rays proceed from the sun along straight lines and are reflected from every polished object at equal angles, i.e. the reflected ray subtends, together with the line tangential to the polished object which is in the plane of the reflected ray, two equal angles. Hence it follows that the ray reflected from the spherical surface, together with the circumference of the circle which is in the plane of the ray, subtends two equal angles. From this it also follows that the reflected ray, t...