Modern Algebra Story for Omid Oh-My   2 comments

This is an old story I have recounted endlessly, but a friend from Tucson brought up something that reminded me of it and I promised to put it in print.  It is long and tedious unless you just happen to be familiar with — and interested in — the madness of mathematics.  So, basically, this one is for you, Omid.

I had finished my bachelor’s degree at the University of Georgia and had three months to kill before starting a PhD in Environmental Engineering at Georgia Tech and decided to take some recreational graduate level coursework in mathematics to make sure I wasn’t missing out on anything more fun than sewage treatment.  One of the courses I took was in Modern Algebra.

Modern Algebra was developed as a computational regime for the new physics (quantum mechanics, etc).  It really is frightfully similar to the Algebra EXCEPT that everything is developed from a big pile of fuck-all.  Well, not quite fuck all: we started with the axiom that given two elements there is a function called the additive that can combine these two elements. From that we prove that an additive inverse exists (in the real world you call these first two things addition and subtraction).  From all that we in the course of a couple of weeks developed most of the basic elements of linear algebra and group theory based on axioms that must be proved to work based on previously proven axioms.  The fact that no numbers were involved and that familiar concepts were soon strange and foreboding unless we had developed proofs of their functionality ourselves served to whittle the class down from 14 students to 6 in this short period.

The six of us worked closely together the following week, spending late, hot summer nights over many pitchers of beer solving some of the most disturbingly difficult puzzles I have ever seen.  I neglected my pot plants (American, not British terminology) and my fungi almost went dry. When we would arrive in the class, Mitch, our instructor, would breeze in, ask if there were any problems, call someone up to work through the proof, and lay down some new rules for us to sort out.  Mitch was like some sort of weird, tall elf staring through you but not a million miles off; you just had the impression he was focused on some vein at the back of your cornea.  The Friday of that fourth week was where he turned into an evil, trickster elf.

I have long since blotted out the memory of exactly which group theory axiom we were stuck on but I remember distinctly that we were still working on it from two days before right up until class started when Mitch asked if there were any questions I asked why this and declared that every path toward the proof showed it to be a blatantly false axiom.  I was called up to show my work and did so in a couple of ways, uneasy in front of my friends in a way I usually wouldn’t even have been in front of a class of strangers.  He told me to take a seat and called someone else up.  He modified one of my boards to match another effort someone else had proposed and halfway through Mitch frowned said something like, “fer god’s sake, no…sit down.”  He called on one of the women, the most talented real mathematician in our group; her hands were shaking badly at the board and she broke the chalk on her first and only scratching.  Sobbing violently she walked to the door and left.  Then, there were five.

The next two called just lowered their heads and one said no.  He looked at the last kid who, in the ballsiest move of any of us said, “just show us, goddammit.”  There was a silence and Mitch stared at him, through him, and started to smile almost imperceptibly.  He restated the axiom while methodically erasing our work and then rewrote the bulk of it with some minor tweaks.  I got just a glimmer of recognition about where it might go, how to actually solve this puzzle. At this point he started describing the next section and occasionally turned to put up a mark or two.  I think he was staring at me when he said, “okay, here’s where it gets a little difficult.  Are you ready?”

I nodded but have no idea if anyone else was paying any attention at all.  I remember that he started talking again and that it was making sense but that I was starting to see trails off sharp immobile objects and that a sound like the ocean was starting to interfere with what he was saying and yet I was following the argument.  It was about twenty minutes into an hour-and-a-half class when his head split open revealing an intense blue-white light like burning magnesium and I was sucked out into outer space, floating but with the sensation of travelling at an enormous speed.  This was exhilarating and I felt giddy and only occasionally did the argument at hand begin to make its presence felt–felt, indeed, because I could hear nothing.

This seemed to go on for a minute or two more before the puzzle made perfect sense and I could see the end coming.  And, with that, my stomach fell out from under me the walls recrystallised around us and I realised that I was standing near the blackboard sweating profusely, nauseous, and giggling like a schoolgirl.  The next class was milling about taking their seats, bumping into us.  Mitch caught me as my knees buckled and said, “Q.E.D.”

“Holy shit,” I said.  “I need some water. Holy shit.” I looked up at him and he wasn’t looking through me this time.  He was looking like a concerned citizen that found a war refugee wandering around his garden.

“Pretty ego destroying, eh?” he said.  “You better get your stuff.”

I headed over to my desk and shakily stuffed my notes into my bag.  “Are you okay?”

“Fuck you, Mitch.  I can’t do this.  I have to be able to function in this world.  Fuck you and fuck all of this,” I said quite loudly while flinging my notes around the room. “I’m outta here, you psychopath.”

I’ve made a lot of bad career choices, but I really wish I had stuck with mathematics.

I caught the elevator to the Graduate School offices to drop out of that course and when I got to the desk they handed me a clipboard with the form already partially filled in before I could even ask.  With the events of the last hour, this didn’t register as strange.  I needed to sit and turned to find a chair where I saw the remaining four colleagues filling in the same form.  One of them asked, “how far did you get?”

“Q.E.D.  Kyooie-fucking-dee and I never want to see that motherfucker again.”  It was 103 degrees Fahrenheit, 95% humidity and I wandered around the campus and town until I could stop shivering.  Then, I went on a proper bender.

2 responses to “Modern Algebra Story for Omid Oh-My

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  1. Wow Denis, seems like you had a mathematical trip! This is an example of a case where an axiom is isomprphic to truths about reality. It pushed the right buttons for sure and probably triggered the release of some neurotransmitters in your brain to give you that trance like state of mind and opened your third eye momentarily to see a glimpse of the truth in a mathematical form. I have no doubt it was a very intense experience and maybe it was a sign that you should’ve stayed in mathematical field!

  2. Pingback: Four years in England « The endless British pub crawl

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