Problems and Perspective

Interestingly, linear equations with either real or imaginary parts can be perfectly mapped into matrices. Sometimes this makes the equations easier to solve, or to show that there is no solution. In fact, with the form of the matrix being determined, and with the basic elementary transformations of matrices, whether or not there is an answer becomes readily apparent. The mapping of one problem from one system to another reminds me of Decartes’ Geometry, and the solution to the four line locus. Using plane geometry the locus problem is pretty involved, but if we could switch over to basic algebra, the problems become much more trivial (especially if we fix two of the lines at right angles).

A lot of times problems are like this, not only in mathematics. A simple transform, or change of perspective can do wonders. Aristotelian philosophy does wonders to describe how are knowledge can be in us and in the thing in different respects at the same time. But I do think that there are serious difficulties understanding consciousness within such a framework of act and potency. I guess my caveat is this: don’t mistake transformation for relativism.