(subfile 41:  calculating axis angles)

Imagine the 2-dimensional version. Knowing the coordinates of two points allows the calculation of the distance between them, and knowing the coordinates of one point and the distance between, one can specify a locus on which the other point must be found.


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|         a
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|                     b
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Now assume that the numerical coordinates of a and b are fixed and known, and that we know the distance between the points. If the same pair of coordinate values must be retained, but the distance between them is known to be decreasing  (because conversational input tells us that they are more closely related than we thought), then the angle between the two axes must decrease also. It’s not possible to solve this concisely without knowing one other fact, such as the angle between the line ab and one of the axes, but that is not important for MS calculations, which involve fuzzy quantities and imprecise magnitudes to start with. Moving the axes away from orthogonality simply means that there will be a component of motion along one axis when there is change along the other, unlike the situation with right-angle axes. This is sufficient to deal with the types of resonance & vibration I have so far found to be necessary. It is also sufficient to establish that two axes are identical – a situation likely to occur once the program begins creating new axes of its own. (See Appendix V. Axis  arithmetic,  for the actual functions that allow these calculations to be made.)

As an example, suppose we have characterized Republicans and Democrats along all the axes of policy that exist. The values along these axes are known. No change in attitude towards the philosophy of human organizations/government can change the values. We can be sure (or, for the sake of this example, we assert that we are sure) that a Democrat will always favor the right to unionize, regardless of what wisdom about political science has surfaced recently.

Then suppose some brilliant aliens have arrived on Earth and explained to us, once and for all, everything that can ever be known about political science, and suppose that this wisdom tells us that there is in fact much less functional, meaningful difference between the two groups we have defined, than we had previously thought. This constitutes a new bit of knowledge that would require a reduction in distance between points a and b, requiring a reconfiguration of the axes such that the newly understood distance could be accommodated while retaining the values on all the individual axes.