02 MAR 2019 by ideonexus

## Triangles on Earth Exceed 180 Degrees

The idea that space and time can be curved or warped is fairly recent. For more than 2,000 years the axioms of Euclidean geometry were considered to be selfevident. As those of you who were forced to learn geometry at school may remember, one of the consequences of these axioms is that the angles ot a triangle add up to 180 degrees. However, in the last century people began to realise that other forms of geometry were possible in which the angles of a triangle need not add up to i8o degrees...25 MAY 2015 by ideonexus

## Martin Rees: We'll Never Hit Barriers To Scientific Under...

We humans haven't changed much since our remote ancestors roamed the African savannah. Our brains evolved to cope with the human-scale environment. So it is surely remarkable that we can make sense of phenomena that confound everyday intuition: in particular, the minuscule atoms we're made of, and the vast cosmos that surrounds us. Nonetheless—and here I'm sticking my neck out—maybe some aspects of reality are intrinsically beyond us, in that their comprehension would require some post-h...24 JUN 2014 by ideonexus

## The Laffer Curve

The horizontal axis here is level of taxation, and the vertical axis represents the amount of revenue the government takes in from taxpayers. On the left edge of the graph, the tax rate is 0%; in that case, by definition, the government gets no tax revenue. On the right, the tax rate is 100%; whatever income you have, whether from a business you run or a salary you’re paid, goes straight into Uncle Sam’s bag. Which is empty. Because if the government vacuums up every cent of the wage you...29 MAY 2014 by ideonexus

## The Kiss Precise

Four circles to the kissing come, The smaller are the benter. The bend is just the inverse of The distance from the centre. Though their intrigue left Euclid dumb There's now no need for rule of thumb. Since zero bend's a dead straight line And concave bends have minus sign, The sum of squares of all four bends Is half the square of their sum.If four circles A, B, C, and D, of radii r1, r2, r3, and r4, are drawn so that they do not overlap but each touches the other three, and if we let b1 = 1/r1, etc., then

(b1 b2 b3 b4)^2 = 2(b1^2 b2^2 b3^2 b4^2).

16 JUL 2013 by ideonexus

## Directionality in Zero-G

Phrases like “things are looking up” and “look at the upside” once meant something like “consider the good in the situation,” but they went through an ironic shift in the solar system’s early spacecolonial culture, mutating in the microgravity of early tin-can stations to mean a variety of practically sarcastic sentiments, typically something like “be careful” or “let’s be realistic.” The joke (that is, that there is no “upside”) wore off in a hurry, but use it wit...Many of the phrases we use on Earth make no sense in space.

17 MAR 2013 by ideonexus

## Geometry Divides the World

This meant, then, that the Greeks, in attempting to communicate their mathematical conceptioning, defined the circle as "an area bound by a closed line of equal radius from one point," the triangle as "an area bo)ound by a closed line of three angles, three edges, and three vertices." The Greeks talked only of the area that was "bound" as having validity and identity, while outside (on the other side of the boundary) existed only treachenerous terrain leading outward to boundless infinity—a...By describing shapes as bounded, the Greeks reflected (or influence?) our thoughts about our own boundaries.