Topology 10 with Howard Schwartz

Being kind is not particularly easy, especially when the object of my kindness turns out to be me.  Still, I will say the kind thing.  I have always been a dilettante, a dabbler pursuing all the interests that I ever felt without much method.  Sometimes, even the smallest amount of dabbling, however, can have a lifelong impact and a deeper understanding of the world.

As a sophomore at UCSD I was hanging out with my roommates looking at potential class schedules for the upcoming quarter when Howie Schwartz discovered the Topology 10 class.  I had read the usual topological conundrums about the difficulties of turning a doughnut (or a coffee cup) inside out.  I thought that I was clever.  It fit a gap in our schedules and it looked like it would be fun without being too challenging.  Howie and I signed up.

One of these people may have been my topology professor.  Every one of these people had a story and a life.

The instructor had a lot of doubts.  Howie and I were pretty far out of our depth.  Topology is the sort of math that requires a special combination of in-depth mathematical expertise and geometric intuition.  It is as advanced as any branch of mathematics out there and ordinary human beings need every advantage to begin to grasp what is going on.  The instructor was not sure that he would even be able to bring a few basic concepts down to our level.  The whole class was like an experiment for reasons of his own.  We had a lot of fun and we laughed a lot.  At one point I acquired an old inner tube and conducted a practical demonstration of what happens when a doughnut is turned inside out.

One fundamental principle is "continuous mapping", i.e. without discontinuities.  Is this even relevant to anything at all?  It is pretty obvious that any wormhole in space is a topological analogue of a doughnut.  A wormhole cannot be continuously mapped to a standard Euclidean flat space, or even a space with a simple curve mapped to it.  I cannot go into a lot of detail about this partly due to my ignorance and also due to a lack of space for the little bullshit that I do know.

My little piece of bullshit pops out at strange moments, like when I realized that it is perfectly possible to map an infinite volume into a finite volume [of space].  Is it cheating to use a hyperbolic function?  Probably, but I am not operating within a rigorous system here.  I live in a world of wonder where wiser and more boring minds prevail.  The real point may be that when volumes are remapped and distorted the passage of time is also remapped and distorted.  I sometimes see evidence among some science writers that the consequences of this are not well appreciated.

"So time, space, and energy remain these three; but the most poignant of these is time."

There is more than one way to silence someone.  There is the actual physical inability to communicate.  There is the understanding that what one has to say is totally lacking in interest to the audience.  There is the need for decorum/discretion.  There is the consciousness that what one has to say will do far more damage than could ever be justified by speaking out.  I have spent my whole life not saying much about my work at Boeing.  My theories about reality are pretty much equally unwelcome.  The majority of the people I have known now exist in little hidden pockets of random memory within me.

Out of kindness, I avoid all expressions of despair.  Little by little over the years I have developed a mild form of Tourette Syndrome.  My usual vocal tic is a small cry of angst.  I started out trying to hide it, but now it is evident.  It is always triggered by a memory - a different memory every time.  Each little squeak amounts to a digression from what is going on around me.  My mind spans the immensity of physical space and all of eternity, yet it is focused on my own tiny little inconsequential life.  Sometime the tic reaches intelligibility: a cry for release.  Then the "voice within" silences me and soothes with the words "Soon enough, Bob.  Soon enough."

I can be patient.  I can be kind.  I can wait with my hands folded and a small smile on my lips.  There is no balm for my wounds, none for which I would pay the price.  Why do I cling to the tokens of cause and effect so tightly?  Why do I care about "meaning"?