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...

 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...

 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...

 The Origin of Trigonometry

Trigonometry had to start with sea-people. It is the conclusion of British, German, and U.S.A. navies' experts that celestial—offshore—navigation be¬ gan with the South Pacific's island peoples. Much has been published on this subject. What is not as well pubHshed is the fact that the navigators on all those islands live entirely apart from the other humans in their native groups. When the supposedly God-ordained chieftain of those islands finds his prestige and popular credence declin...