Thursday, February 03, 2011

Mystery Solutions To Famous Problems By Important Mathematicians

I just finished reading 'Uncle Petros & Goldbach's Conjecture: A Novel of Mathematical Obsession', written by Apostolos Doxiadis, part of the team that brought us the wonderful graphic novel 'Logicomix: An Epic Search For Truth'.

While Logicomix focuses on the great mathematician Bertrand Russell, his work, and his association with other great mathematicians of the early 20th Century, 'Uncle Petros' is about a more obscure mathematician, and explores his path from early promise to obscurity.

The narrator is fascinated by his somewhat reclusive but kind uncle, labelled rather cruelly by his businessman father and his other uncle as 'one of life's failures'. He learns that his uncle was a promising young mathematician who became so obsessed with proving Goldbach's Conjecture (still unproved as of this writing!) that his career went off the rails.

This 'most favored nephew' develops his own interest in mathematics, and tells his uncle of his plans to become a mathematician. His uncle tells him that very few people can become mathematicians, and that he doubts his nephew has what it takes. His nephew persists, so Petros challenges him to solve this problem over the summer:
Prove that every even number greater than 2 is the sum of 2 primes.
Our narrator struggles with the problem all summer long, but fails. He then finds out what some readers will already have recognized - Uncle Petros asked him to prove Goldbach's Conjecture.

At this point we wouldn't blame him for never wanting to have anything to do with his uncle again, but his interest in mathematics and in his uncle's story persists.

Gradually we learn about Petros' early career: a very useful technique he developed as a Ph.D. student which he dismisses as 'Calculation of the grocery bill variety', his work with the great G.H. Hardy and Ramanujan, and his long and ultimately futile struggle to solve the Conjecture. His isolation and his fear of revealing any of his early results lest his competitors use it to beat him to the proof causes him to miss some great opportunities to publish, and gradually his career disintegrates.

Petros is a fascinating character, flawed but with a wisdom and a sort of contentment with his lot in life, spending his days with gardening and chess. His nephew develops an obsession of his own, trying to get at the true reason Petros ultimately gave up, and to understand the course of Petros' life and career.

In my favorite quote from the book, Petros explains his preference for obscurity over minor but forgettable successes:
'I, Petros Papachristos, never having published anything of value, will go down in mathematical history - or rather will not go down in mathematical history - as having achieved nothing. This suits me fine, you know. I have no regrets. Mediocrity would never have satisfied me. To an ersatz, footnote kind of immortality, I prefer my flowers, my orchard, my chessboard, the conversation I'm having with you today. Total obscurity!'
While I don't agree with that sort of 'all or nothing' thinking, being more of an incremental and a 'set attainable goals' guy like the narrator's father, it is rather romantic in its way and I can respect his attitude. I do very much agree that obscurity is underrated (or at least that's what I tell myself here in this comment-free blog).

Being in the over 40 phase of my life, I find myself reviewing my own past successes and failures, identifying along the way regrets and things I could have done differently, trying to come to an acceptance of the things that didn't go as well as hoped. There's no sense in wallowing in failures or regrets, but I'd also say it's essential to be (sometimes painfully) honest in your assessment of your past and yourself, and that's a lot of what this book is about. There's also a kindness and empathy in the book, the book has, for lack of a better word, 'heart'.

I'd strongly recommend the book (and Logicomix) even to the non-mathematicians. Mathematicians are interesting characters, and while many struggled with mental illness, there was so much more to them as people.

As for my own mathematical pursuits (which fizzled out early) I can say with complete honesty that I have no regrets. In retrospect I can see the value of realizing it wasn't 'in me' to be a great mathematician and changing course, as painful as it was at the time. And for a while, I truly loved math, and it was all I wanted to do, and it was almost all I did. I can understand the appeal and I know there is a joy in being obsessed.

Tuesday, February 01, 2011

Facebook's Fakeness Makes Us Feel Worse, Comedians' Honesty Makes Us Feel Better

'I see the people happy, so can it happen for me? 'Cos when I have no energy, there's nothing that can move me'
-Kate Bush, 'Sat in Your Lap'
Recently a group of Stanford scientists led by Alex Jordan published an article in the 'Personality and Social Psychology Bulletin' about a tendency people have to overestimate other people's happiness, which usually ends up leading to increased dejection and unhappiness. A good write up can be found on Slate, and there has been considerable discussion since in the blogosphere, Twitt-o-sphere, really all the spheres.

The fact that the research was inspired by one of the less-fulfilling aspects of Facebook triggered much of the discussion:
Jordan got the idea for the inquiry after observing his friends' reactions to Facebook: He noticed that they seemed to feel particularly crummy about themselves after logging onto the site and scrolling through others' attractive photos, accomplished bios, and chipper status updates. "They were convinced that everyone else was leading a perfect life," he told me.
I have noticed that I tend to have a feeling of emptiness and disappointment after nearly every interaction I have with Facebook, but hadn't thought thought about the underlying reasons for that so much. It does make sense, although I also hate Facebook for other reasons, including the fact that it's 'walled off' from the otherwise more open web, and the occasional feeling of being pressured to 'friend' people I am not really friends with (mainly co-workers or distant relatives I'm not particularly cozy with), which then leads to a pressure to to be fake about how happy you are and how great everything is, which in turn brings everybody down, as science has now proved, because you forget everybody else is frantically trying to fake being happy, too.

This ties in to a broader tendency I've noticed for people to focus on the positive to an absurd and unrealistic degree, almost to the point of seeing any kind of negativity as pathological, and seeing 'negative people' as pariahs to be avoided at all costs. Not to be too negative, but I think this emphasis on 'positivity' is destroying the world. Some examples:
  • Being optimistic that invading a country and establishing a new U.S.-friendly regime and society there will be a 'cakewalk'
  • Thinking home prices will go up forever
  • Not being a gloomy Gus and worrying about energy dependency
  • Believing you are great at multitasking, including texting and driving at the same time
  • Thinking you don't have to pay taxes because you are Wesley Snipes
The list could go on and on.

It is possible the over-optimism is a reaction to the over-pessimism of the 90s. I'm looking at you, Billy Corgan. Billy was only one of the many songwriters in the 90s who'd say some variation on the following in interviews:
People ask why my lyrics are so depressing and negative. When I'm happy, I want to celebrate that I'm happy and have fun, I don't want to write about it.
Kurt Cobain was the patron saint of 90s mope-rock. He became a superstar singing about how crappy life is, and then shot himself in the head with a shotgun.

There are some promising signs that a more balanced view of reality is on the rise in popular culture. A good example is Louis CK's show 'Louie'. Louis is a very talented comedian, and the show is very funny, but at the same time Louis does not in any way shy away from talking about some of the unhappy realities of life after 40, including the gradual decline in health and realization that your best days may be behind you. He deals with really nasty people - a heckler, a kid threatening to beat him up, Nick DiPaolo - but on the other hand he really loves his daughters and finds great fulfillment in his role as their father, and he has the respect of his peers and confidence in his capabilities as a comedian.

Marc Maron's very popular WTF podcast includes Marc's honest observations about his life and life in general, including some things that are real downers like career disappointments and divorce. I've also learned from listening to his show that almost all of my favorite comedians are on medication.

It's strange that comedians (except Kyle 'Be positive at all costs' Cease) are the ones bringing us back to our senses, but somebody needed to do it, and best that it's people who can also make us laugh help us deal with it all.

As for Facebook, I can't quit it (yet), but I take some comfort in the fact that I'm not alone in finding it to be not only a time-suck but a soul-suck, too.