When we encounter i, it seems like such an odd and miraculous thing that the square root of -1 should exist, because we've always been taught that a negative times a negative is positive, from a very early age.
An age, perhaps, before we take it upon ourselves to question such things, because the sign rules for multiply/divide really aren't totally intuitive either. What does it mean to multiply by a negative? We could say that in a times -b, perhaps, that we are adding a negative bs together, but what if they are both negative? Removing negatives doesn't really have a natural meaning, although the concept itself becomes quite concrete if you work with Constructive Solid Geometry 3D modeling.
Really, there should be nothing shocking about i at all; roughly speaking, math is defined by sets of things, and operations upon those sets which have been proven to behave in certain ways.
Math is difficult for me, and proofs require far more discipline than I have. But every complicated bit I have eventually "gotten", I enjoy and value immensely, and I never forget it. I hope in the future I can slowly absorb more. The only power I have is the ability to solve computer problems, and math is what the real amazing problems get solved with.
An age, perhaps, before we take it upon ourselves to question such things, because the sign rules for multiply/divide really aren't totally intuitive either. What does it mean to multiply by a negative? We could say that in a times -b, perhaps, that we are adding a negative bs together, but what if they are both negative? Removing negatives doesn't really have a natural meaning, although the concept itself becomes quite concrete if you work with Constructive Solid Geometry 3D modeling.
Really, there should be nothing shocking about i at all; roughly speaking, math is defined by sets of things, and operations upon those sets which have been proven to behave in certain ways.
Math is difficult for me, and proofs require far more discipline than I have. But every complicated bit I have eventually "gotten", I enjoy and value immensely, and I never forget it. I hope in the future I can slowly absorb more. The only power I have is the ability to solve computer problems, and math is what the real amazing problems get solved with.
3 comments | Leave a comment
