Vectors in latex

The vector relationships can be analyzed using the angles of their intersection. Here the triangle and the relationship of the shadow ( or projection on plane ) of a vector describes the relationship between perception, effect, and identity. The relationships of the sides of a triangle do not change the ratio of A:B:C when transformed in distance, however rotation on axis changes the perception (effect). These things are critical to understanding angular momentum, orbits, and gyroscopic effects.

This also serves to enhance my La^Tex skills with a new method \stackrel.

I am not a fan of the - and + signs applied to things that have more than one dimension and each time I see them I must now do a mental transform of my own to convert to what I consider a more proper representation of dimension without paired or even tripled negatives that are untangled after the fact. A string that vibrates down or up is not negative or positive, except by convention and position of observation. I may develop some symbols to represent a vector which is paired in symmetry. The attempts to unscramble a lack of complexity of description of the 3 space and its sets leads to many a bizarre work-around in practice IMHO.

If you look at the optical rotation of polarized light of biochemical compounds and their handedness rules it becomes quickly apparent that the symbol set is weak and poorly descriptive of systems of molecules with more than one chiral center. Even in a simple area like the relative rotation of hydrocarbon molecules C_n, the notation is incomplete and thus fails to be measurable complete. It is like a "case" statement in C which covers two of three possible conditions and simply ignores the third. I think it is bizarre, others are not troubled by paradox, I guess.

I think that the math system as it exists is like some huge software project that gets tweaks here and there to correct problems and is so ingrained and so heavily used that making a change is actually impossible, except for my own sanity. If you think that changing from English to metric measure is bad, think about changing the rules of math and retraining everybody in the world, ain't gonna happen in even 5 lifetimes.

The biggest problem with that is, if a machine can be given the proper rule set and has an advantage that can never be overcome, as machines don't care if you change the rules every millisecond, they just do what you program them to do, then they cannot be out thought and defeated in a worst case scenario of the Skynet decomposition. I can almost see the scenario. Programmer one finds it too difficult to resolve enemy combatants and so sets kill all in a certain scope and makes it a feature. Simultaneously another programmer finds that boundary conditions are screwing up analysis and sets scope to infinity. End result: Berserker.

It is possible that many of these things will not happen in the near future, however it is more possible that many of these things which are possible could crop up over time in a complex society. Some strange fluke could make a nano-machine that is just the right shape to screw up everything. Probability is the thing that is the worst contraption and I am afraid that will never be something that is controlled. The infinite probability engine might make me a liar one day IDK.