aka The Illusion of Accomplishing the Really Difficult
When in life we feel we are capable of the impossible; that undreamed of power might be ours, but also might not be; that we of course are not superhuman, but are yet on the brink of being so, it is important not to get too excited. Those of us familiar with encoding information for machines to understand– and a rapidly increasing group aren’t we–know that when things seem too complicated, it is because they are: two variables not being enough to capture what three things are doing, independently; one messy function a mask over several; our own frustration a distorted reflection of some better way.
I’m sure someone has stated better than I will this principle of reducing the complexity of a personal problem by adding complexity to its solution–what I’ve always called “adding a dimension” — giving yourself more room to work out everything that needs working out, and giving the things worked out more room not to get in each others’ way.
As each dimension is added the problem seems simpler, compared to our earlier view of it from our flattened perspective, and correspondingly our options seem less: who cares how x and y relate to each other–let them both simply be determined by some z that we cannot label or control.
Let me set a point, above this explanation and connected to it by some number of puppet strings:: most things we don’t understand aren’t connected. They’re connected to something else.
When I lived in Berlin, I had a close circle of friends who were all math students. Because we were in Germany, and math students, we had a club, actually an online community call e-pi. (pronounced ‘eh pee’ in german). Everyone in the community had an e-pi name, none of which I can recall right now. eponymous I feel sure was one. epigenesis maybe. How neat it would be if one of them stumbled across this page; how wonderful it would be to hear again from them; they were all magnificently clever people, and much kinder than I would have expected. I could never decide on an e-pi name for myself. I think I suggested epistle, but this was looked askance at, not being, I guessed, but much later, derived from the right Greek root? Now many years later I’m glad I couldn’t, having found the right one, which I never would have claimed at the time. It may even have been the name of the online community itself*, or should have been, if it wasn’t. I am epicenter.
Let us consider a few examples of adding a dimension to reduce complexity.
That was fun. And here’s a good one:
Imagine several hundred people moving in sync. Banal as the example is, you have to admit that witnessing such a thing without knowing what it is, you’d be baffled: how, why, would so many people do the same things; what could be the explanation? There is no acceptable pairing of phenomenon and observable cause: the two just won’t line up.
But add a third dimension—a third-party; to be exact— an aerobics instructor at the front of the crowd, facing away from you—and it makes perfect sense.
This example is very boring, radiation, you might say. Perhaps. But tell me then, you almost very powerful you: what is more likely: that you can compose opera in your sleep ala Mozart, or that someone else does, and sends it to you?
Who would send it? I’m so glad you asked, because I have no idea. Congratulations, by the way. I mean, nice opera.
Has anyone seen a post about fractions around here?