Number Rotation??(?)

*To*: mathgroup at smc.vnet.net*Subject*: [mg30107] Number Rotation??(?)*From*: edward.griffin at ireland.com (Edward Griffin)*Date*: Sat, 28 Jul 2001 01:51:07 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Okay, you can laugh if you want, but not 'till you've read the whole thing. This is something that's been bothering me for a while, and I'd kind of like to get it cleared up. Some time ago (Whilst a mathematics student in college)I toyed with the idea of numbers (as whole and real values) being represented on a cartesian plain as a point in space, and then being 'rotated' around x=0 & y=0 to give a point representing the same value, but in another position. If it's supposed that the observer is at x=0 & y=0, is it fair to say that the value in it's 'rotated state' is still the same value, but just seems to be different because it is being judged from a different perspective. I guess what I'm trying to do is place a real life object in the same situation as the point on the cartesian plain which represents the real value of this object. Okay, here's what I really mean. Y | | 5| 4| * 3| 2| 1| ----------0---------- X -5-4-3-2-1| 1 2 3 4 5 -2| -3| -4| *1 -5| | | Above, * represents the value 16, and I get it's initial position on the cartisian plain from x = root of 16 and y = root of 16, hence x = 4, y = 4. I now have a point that represents 16 on the cartesian plain (to my mind anyway). If I rotate * through 90 degrees around the point 0, it will end up in the position shown by *1. At this point x is still 4, but y is now -4. To the observer at point 0, I have taken the value on the cartesian plain (16) and rotated it around so that it represents -16 (x=4, y=-4, and to arrive back at the true value of the rotated value, x*y = -16). This can be performed with any value at any angle by using the expression below.. {n} = nCos(2t) t I think that we spend too much time thinking of numbers and values as flat boring two dimensional objects, what if they could have sides, a back and a front, and maybe on a three dimensional plain, a top and a bottom. Okay, the men in white coats are comming soon... but is any of this valid?