Seems like the very first post wins the readers choice award... at least thats the way it seems from all the reviews pouring in !!! a long way from being a monograph i understand but then the increasing attention and discussion obligates me to rename the post sanity-insanity 101 :). In the same breath, this post happens to be sanity-insanity 201 :).
Equilibrium could refer to mental or emotional poise (sanity) and thus disequilibrium encompasses everything otherwise. Looking at a broader picture however, equilibrium is a state of balanced influences (counter or otherwise). Assuming that the world is in a state of equilibrium (valid assumption i think) w/ respect to the forces defined previously, I will now make a metaphoric projection of my 3 defined influences, namely sanity, insantiy and cuspy (LOL) onto the better understood vector spaces.
Starting with 3D space, every pt obviously has 3 coordinates (s,i,c). A vector (0,0,0) -> (s,0,0) is a sane vector, a vector (0,0,0) -> (0,i,0) is an insane vecotor, and a vector (0,0,0) -> (0,0,c) is a cuspy vector. Typically, this space will consist of as many vectors as the population in the world, and vectors classified according to the definitions. Generalizing, assuming any arbit shift or rotation of the axes, a plain containing all the cuspy vectors will always be orthogonal to the plane containing all other vectors... Since orthogonal forces on non-rotational systems have no effect, we now take a look at the eigen space projection, rejecting the cuspy vectors.
Continuing with the eigen analysis, i expect to see the eigen values of the cuspy eigen vectors to be insignificant as compared to the eigen values corresponding to the sane eigen vectors and the insane eigen vectors. Ignoring the vectors with lower eigen values, projecting the rest on to eigen space, i expect to see diagonally opposite lobes cancel each other.
Equilibrium could refer to mental or emotional poise (sanity) and thus disequilibrium encompasses everything otherwise. Looking at a broader picture however, equilibrium is a state of balanced influences (counter or otherwise). Assuming that the world is in a state of equilibrium (valid assumption i think) w/ respect to the forces defined previously, I will now make a metaphoric projection of my 3 defined influences, namely sanity, insantiy and cuspy (LOL) onto the better understood vector spaces.
Starting with 3D space, every pt obviously has 3 coordinates (s,i,c). A vector (0,0,0) -> (s,0,0) is a sane vector, a vector (0,0,0) -> (0,i,0) is an insane vecotor, and a vector (0,0,0) -> (0,0,c) is a cuspy vector. Typically, this space will consist of as many vectors as the population in the world, and vectors classified according to the definitions. Generalizing, assuming any arbit shift or rotation of the axes, a plain containing all the cuspy vectors will always be orthogonal to the plane containing all other vectors... Since orthogonal forces on non-rotational systems have no effect, we now take a look at the eigen space projection, rejecting the cuspy vectors.
Continuing with the eigen analysis, i expect to see the eigen values of the cuspy eigen vectors to be insignificant as compared to the eigen values corresponding to the sane eigen vectors and the insane eigen vectors. Ignoring the vectors with lower eigen values, projecting the rest on to eigen space, i expect to see diagonally opposite lobes cancel each other.
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cool
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