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On Mathematics, Star Trek, and James Joyce

February 10, 2016

"The more complex the mind, the greater the need for the simplicity of play."
- Capt. James T. Kirk, "Shore Leave," Star Trek

 

When he was young, one of my sons (who will remain nameless to protect his innocence) had a propensity to collect things. By ‘collect things’, I don’t mean Beanie Babies, Magic Cards, or anything resembling a cow. Rather I mean anything small, usually shiny, that he could find on the sidewalk and put in his pocket. In parent terminology: trash.

At the end of the day, we’d empty his pockets only to find sticks, rubber erasers, coins, bottle caps - you get the picture. We’d shake our heads and wonder what he would grow up to be. But to him, these were treasures so valuable to warrant dragging them with him even if it meant making his pants uncomfortable. Having them in his pocket gave him comfort.

Nonetheless, this memory has tracked with me for the past couple of decades. A pocket full of treasures. Always there, always handy. You reach in and pull one out to marvel at it. Your fingers roll it around feeling the texture; light reflect off its surfaces ever so slightly. The treasure brings a smile, one that will last for the rest of day. Back it goes to be pulled out another day.

So it comes as no surprise to me that I too have my pocket full of treasures. And a couple of months ago, I took stock of three treasures I had put in my pocket of treasures a long time ago.

Here’s a short posting about those three treasures.

James Joyce. Ok, I’m no James Joyce expert and no I have not read Ulysses.  But I have read Portrait of an Artist as a Young Man and that book is in my pocket of treasures. But more relevant it really is a particular part of the book that I really always come back to and I won’t bother to set up the scene. This way may be you’ll be intrigued enough to pick up and read the darn thing.

The beach scene, the woman in the distance, and the quote “To live, to err, to fall, to triumph”. Enough said.

Mathematics.  Let’s face it. Mathematics is hip these days. It’s everywhere - movies, science, psychology, the Wall Street Journal, Wall Street for that matter, outer space, inner space, the past, the present, the future. Can you tell I’m partial? Ok, you’d expect that from me. But the reason why mathematics floats my boat and is in my pocket of treasures is its beauty and elegance. Read The Divine Proportion by H.E. Huntley or Goedel, Escher, Bach: A Eternal Golden Braid by Douglas R. Hofstadler or a zillion other books if you want to explore this further. Or if you don’t have time, here are two reasons to love the beauty and elegance of mathematics:

I. Let G be a multiplicative semi-group with operation *. If e is a 2-sided identity element for G, then it is the only one. Proof: If f is another identity element, then e = e*f = f.

II. Let R be a ring and let J(R) denote the Jacobson radical of R. If e is an idempotent, then e(J(R))e = J(eRe). Proof: Really? I don’t even have to tell you why this appeals to my inner sense of beauty.

Star Trek. Aside from the great family memories of sitting around the black and white TV watching the first showings of the classic series, the reason that Star Trek is in my pocket isn’t what you might think it is. It isn’t the green aliens with tails, the foretelling technology, or the special effects (“That’s not even a good imitation of a styrofoam rock”). Rather the whole show for me was and is about human-human and human-alien interaction and how the very core human traits play such an important role in who we are. Spock wrestling with his human side, the first interracial kiss on TV, the ultimate friendship of Kirk, Spock and Bones. What’s not to love in this message?


Ok, there you have three treasures in my pocket. What’s in yours?