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...

 The Anthropic Principle

As an example of the power of the Anthropic Principle, consider the number of directions in space. It is a matter of common experience that we live in three-dimensional space. That is to say, we can represent the position of a point in space by three numbers. For example, latitude. longitude and height above sea level. But why is space three-dimensional? Why isn't it two, or four, or some other number of dimensions, hke in science fiction? In fact, in M-theory space has ten dimensions (as wel...

 Beyond Three Dimensions

“In One Dimensions, did not a moving Point produce a Line with two terminal points? In two Dimensions, did not a moving Line produce a Square wit four terminal points? In Three Dimensions, did not a moving Square produce - did not the eyes of mine behold it - that blessed being, a Cube, with eight terminal points? And in Four Dimensions, shall not a moving Cube - alas, for Analogy, and alas for the Progress of Truth if it be not so - shall not, I say the motion of a divine Cube result in...

 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...