Number Theory

You know where you are with numbers.

With all that goes on in the world at the moment, the un-coloured truth of numbers is quite comforting. They will always behave the same way even if we haven't yet discovered all the ways in which they do behave. There is not going to be a day in this Universe when the behaviour of numbers suddenly switches to some new state. Pi will always be the same regardless of anything we can do, even allowing for the Indiana Pi Bill which thankfully never got adopted. The fact that it was passed unanimously points to an attempt to show up how far legislators will go to pretend they actually understand something when they don't. Maybe we should try it with some of today's politicians. I propose to put a Bill before parliament to set the square root of minus 1 to be minus one. It'll wipe out that pesky Mandelbrot set in one go. Brilliant! And now for all you electricians out there I propose to define i = j.

I have just read this page by Patrick Moore. The bit about Einstein not being able to define Infinity in non-mathematical terms is heartening. I can quite happily accept the maths and implications of a fourth spacial dimension but I cannot imagine it. Sometimes a rotating hypercube gives me an inkling. (Click the stereo button until you get TWO completely separate cubes and then go cross-eyed to bring them together to get the 3d effect). There is so much that a person can understand intellectually but which cannot be imagined emotionally. A belief in a proclamation of the absolute existence of a 4th dimension needs a blind faith in the truth of that proclamation. You will NEVER directly experience it. Number wise though, you can think of it. All you need to calculate the one dimensional distance between any two points in n-dimensional space, is good old Pythagoras. We raised this idea when we did simple three dimensional distance calculations at school but our maths teacher bottled out and said it introduced 'complications'. Teach kids how to think not what to think.

Just as an exercise try and imagine infinity for a few seconds ... and then zero ... and then minus infinity .. and then the smallest positive number.

Still here? or have you turned into a benzene ring? The Person from Porlockjust failed to reach Kekule in time didn't he.?