I was deeply distracted earlier today, working on my laptop. Working on numbers. So absorbed, in fact, I didn't even notice that the TV was on. It had been muted; someone else in the office was likely looking for weather. Or maybe, sports news. Either way, I generally don't watch TV outside of the research I do for my books as the #PopCultureProfessor. When I did finally come out of hyper-focus mode, A Beautiful Mind was on the screen. And, I couldn't help but cringe a little.
John Forbes Nash, Jr. was one of the most brilliant mathematicians the world has ever known. From a small town that was no more than nine-square miles in West Virginia, Nash made it through the rigors of academia to sit amongst Princeton's best and brightest. Not an easy feat, let me assure you. Though, it's no wonder Nash was later diagnosed with paranoid schizophrenia; the pressures of academic life can be both rigorous and vigorous, all on their own.
I wrote an essay about the disease in January 2015 called, "Truth Serum: Schizophrenia," after experiencing one of the most bizarre turn of events in my entire life. Whenever something unthinkable occurs, make no mistake, mental illness is involved. Not mine, mind you. No, I was the one attacked. With arrows, no less. Paranoid schizophrenia encompasses the feeling that people who know and love you want to also harm you. Delusions, accompanied by voices in your head, help feed the sense that people you know are "out to get you."
When you lose a person to mental illness, it's as if they truly died. There's no discernible trace of your loved one left. It's both shocking and surreal. You see, mental illness is not a disease unto itself; it stems from social resistance like childhood trauma and abuse. This often leads to continued vulnerability as an adult, including a predisposition toward addiction, and, the codependency that goes with it.
For nearly two years, it felt like a piece of me was missing. Because, it was. But life has a way of rolling ever-forward. Today, I count myself lucky. Not just for surviving, but for finding the ability to open my heart again. To imagine living again. It was not at all easy. It took a soul even more stubborn than mine to convince me that all I lost could be found once more. And, it has.
Numbers kept me sane in between then and now. It was the same for John Nash. He made sense of the world through numerical patterns. Like the Nash equilibrium. When balance went missing from my world, it was all in the numbers. The accounting error was in rightly assuming it would not benefit the other player to change his strategy. Because, it wouldn't. You never subtract a positive integer. It's like taking every dollar you have and burning it to stay warm on an August day in Georgia.
The Nash equilibrium depends wholly on the players in any game making the best possible decisions. If there's even a hint of madness in the mix, economic disaster will always follow. Sadly, I've had the opportunity to experience the proof of Nash's equation first hand. And yet, it is not Alicia Nash I relate to; it is John. Perhaps I see in him shades of a person I loved. That potential for greatness. But potential isn't enough, is it? Potential is just a fraction. A tiny piece of a larger puzzle. As it turns out, it is accountability, not accounting, that adds up to a whole number.
Alicia and John divorced in 1963, after only five years of marriage. But, as I've come to learn, the real deal goes no where. The couple reunited, remarrying nearly 40 years after their initial divorce. This time, the two remained together until dying in a car crash about a year and a half ago.
John Nash pinpointed the beginnings of his illness as manifesting after his wife became pregnant. The pressure of responsibility was too great. Or rather, his lack of desire to be held accountable, accounting for the multiplication of the cracks in Nash's already fractured psyche.
I now recognize that what happened to Alicia Nash, also happened to me. Irony...the one accessory I'll never lose. Well, that, and sunglasses. I have more than 20 pair stashed in my car. Mainly because I break them and/or lose them with such frequency, I need a host of spares. If only it were that easy with people....
The numbers show me that what is referred to as a Reimannian manifold, named after German mathematician Bernhard Riemann, was isometrically embedded in my Euclidean space; I just didn't see it. Perhaps it might be better to say, I took it for granted. That's part of Nash's theorems, too. Isometric simply means maintaining the length of a particular path. Inside the manifold is a family of inner products called a metric. Reimannian metrics are what identify the angles, the curves, and, the divergence of any two vector fields. You see, each field or space can be equipped with a family, or inner product. That "family," by design, restricts the space. Places limits. The limits are meant to keep a certain geometric order. You can think of it as equivalent to genetics, or even, familial social patterns. Whether from Nature or Nurture, the limits work in the same way.
Of course, humans are not numbers. We have the ability to expand beyond our inner products, to bypass the path our genetics and familial social "metrics" have in store for us. At least, in theory. Nash thought of it like folding a piece of paper and pressing it down, creating a crease. The paper represents Euclidian space, and the crease is that isometrically embedded Reimannian manifold. It's an analogy for the human condition. At least, that's what I see in Nash's math.
Mathematics are like a ballet of sorts. A beautiful dance. Graceful. Poised. If I applied Nash's theorem's to my life, I would know that there are three possibilities to my equation. One allows for the counterintuitive to happen. Two is the foundation on which the most likely outcome stands. And three, or what is known as the real analytic theorem, guarantees the uniqueness of two fixed points in space and time. That uniqueness provides a constructive method for finding those fixed moments, no matter what.
I believe humans call that level of mathematical mapping, magic....