27 JUL 2018 by ideonexus

 Fluid Intelligence has Made the Most Gains

So which kinds of intellectual performance have been pushed upward by the better environments of recent decades? Surprisingly, the steepest gains have not been found in the concrete skills that are directly taught in school, such as general knowledge, arithmetic, and vocabulary. They have been found in the abstract, fluid kinds of intelligence, the ones tapped by similarity questions (“What do an hour and a year have in common?”), analogies (“BIRD is to EGG as TREE is to what?”), and ...
Folksonomies: intelligence iq
Folksonomies: intelligence iq
  1  notes
 
16 APR 2018 by ideonexus

 Euclid's Elements as a Game

"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook, he would have designed a video game." Peek at any of his proofs, Devlin said, and you'll quickly find that the great Greek mathematician, often called the father of geometry, ...
Folksonomies: mathematics classics gaming
Folksonomies: mathematics classics gaming
  1  notes
 
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...
  1  notes
24 JAN 2015 by ideonexus

 Superstring Theory

It is time now to try to describe what a superstring really is. Here I run into the same difficulty which the geometer Euclid encountered 2,200 years ago. Euclid was trying to convey to his readers his idea of a geometrical point. For this purpose he gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." This definition would not be very helpful to somebody who was ignorant of geometry and wanted to understand what a point was. Euclid's notion ...
  1  notes
 
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.
Folksonomies: poetry mathematics
Folksonomies: poetry mathematics
  1  notes

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).