spacetime parameters

[AntonioLao]

The parametric equations of a straight line for two dimensions of X and Y are X=a+bT and Y=c+dT. For three dimensions X, Y, and Z; the equations are X=a+bT, Y=c+dT, and Z=e+fT. In these equations a, b, c, d, e, and f are all parametric constants of the parameter T. If they are all equal to unity then the 3D line subtends 45° to all three planes: X-Y, X-Z, and Y-Z. On the other hand, the parametric equations of a circle on the X-Y plane are X=acosaand Y=asina. On the X-Z plane, they are X=bcosband Z=bsinb . On the Y-Z plane, they are Y=ccosgand Z=csing. For these circles to be congruent requires that the parametric constants a, b, c are equal while the three angular parameters: a, b, andgcan simultaneously take different values. To be continued.

[mkirkpatrick]

Consciousness seems to transcend the spacetime parameters?



regards michael.

[AntonioLao]

Absolute consciousness is bounded within 2 spacetime parameters of 1 dimensional space and 1 dimensional time.

[AntonioLao]

Consequently, wherever and whenever there are only two orthogonal unit circles, say, one in the X-Y plane with center at (0,0) and the other in the X-Z plane with center displaced 1 unit in the positive X-axis (1,0) then the parametric equations are: X=cosa, Y=sina, Z=sinb, and X=1+sinb such that cosa=1+sinb or cosa-sinb=1. Although the two unit circles simultaneously exist, the real values of aandb do not.

[AntonioLao]

On the other hand, the center displacements at (-1,0) would change the parametric equation to cosa=sinb-1 or sinb-cosa=1 while the real values of both aandb still remain disconnected in the real spacetime domain. Therefore, although the unit circles indicate space and time continuity their local infinitesimal motions can be described only by their discontinuous or quantized angular parameters: aandb. These imply that the identity matrices of any order describe precisely the orthogonality of multi-dimensional unit circles and their displacements and each unit displacement indicate a particular basis. For two dimensions the basis are (1,0) and (0,1). In three dimensions they are (1,0,0), (0,1,0), and (0,0,1).

[AntonioLao]

Achieving perfect spacetime symmetry must in turn satify the 8 properties of directional invariance such that the basis for two dimensions would include (1,-1) and (-1,1). These formed the 1st and 2nd fundamental forms of Hadamard matrices.

[AntonioLao]

Take a sieve of Diophantus and arrange the elements in increasing row indices from left to right and increasing column indices from top to bottom. Next, extract any 2 by 2 matrix. Then calculate its inverse. The result is a building block matrix plus multiples of one of the two fundamental forms of Hadamard matrices.