The Odds Are Always Changing

Once you know the truth about Monte Carlo simulation, it spoils everything.  Like finding out about Santa Claus.  Or watching your childhood home run hero testify in front of Congress about steroids.  Discovering that Mickey Mouse is actually a cigarette-wielding, middle-aged woman with a Cheap Trick tattoo, not because you wanted to but because what 8-year old can possibly resist peeking through the propped open back lot door while Mom and Dad are juggling his 4-year old brother and trying to pay for $12 ice cream cones?

Innocence lost.

I sat down in one of my first college courses a couple of decades ago, and knew I’d found the right course of study.  There it was, right there on the syllabus — Monte Carlo simulation.  I knew of two Monte Carlos:  the fancy European city that serves as a playground for the rich and famous, and the bitchin’ hot rod (the 1985 SS model — black with the red stripe down the side that traces the wheel wells — what a gorgeous vehicle).  I didn’t know which of those 2 things we’d be simulating, but either way it was gonna be cool.

So it turns out that Monte Carlo simulation is the most misleading name for anything in the history of everything.  To my 19-year old dismay, I discovered that it has absolutely nothing to do with chic European cities or bitchin’ American hot rods, and everything to do with probabilities and mathematical equations.

Bummer.  Talk about a buzz kill.

It turns out Monte Carlo simulation is a statistical method that allows the user, given a set of event probabilities as input, to mathematically describe the potential outcomes of that set of events.  It can be used to predict any number of outcomes — from whether or not you’ll get a flat tire on your way to work tomorrow to how many total points will be scored in the Super Bowl.  The more completely you can describe the inputs in terms of their real probabilities, the more accurate your prediction will be.  Nate Silver had a really, really well defined set of inputs to the 2012 US presidential election, and used Monte Carlo simulation to perfectly predict Barack Obama’s near-landslide victory in the electoral college, when most media outlets were calling his race with Mitt Romney a dead heat.

It’s pretty cool stuff.  Not mullett-cool like a black ’85 Monte Carlo SS, but cool nonetheless.  And unlike the chic European city, it’s anything but elegant.  It ain’t calculus.  There are no integrations, no derivations.  No tricky LaPlace transformations.  It’s nothing more than running the same set of equations over and over and over and over, adjusting the potential probabilities and examining the outcomes.  Once the inputs are defined, computers run the probability equations thousands, hundreds of thousands, maybe millions of times in order to converge on a solution set.

Before computers, when math was elegant, this type of analysis was near impossible.  Mathematicians and scientists derived equations, beautiful equations that perfectly captured the essence of the principle.  Equations describing universal truths, you can find God in those equations.  Real mathematicians didn’t just chuck a bunch of percentages into a computer to see what it spat out.  Mathematics is refined elegance.  Monte Carlo simulation is uncivilized brute force.  F1 versus top fuel dragsters.  Tchaikovsky versus Metallica.

Hardcore mathematicians cringe at the very idea of Monte Carlo simulation.  It’s a special kind of cheating.  Shoving a bunch of equations through a microprocessor thousands of times per second certainly can’t solve anything.  Can it?  The elegant derivations themselves are the perfect predictors, aren’t they?

We were at the doctor’s office, at the appointment that was to cap off the first trimester of our second pregnancy.  The appointment that was going to tell us we were through the woods, that we could tell family and friends, that we really were going to have a baby this time.  With one pregnancy ending in miscarriage prior to this point, we’d been looking forward to this appointment with nervous anticipation ever since the home test had first suggested the news.  That day, at that appointment, the calculations were clear.  The probabilities resulting from the simulation had never been higher — we were going to have a baby of our own.

Then the probabilities changed.  Drastically and quickly.  The nurse couldn’t find a heartbeat.  For several minutes that seemed like days she searched, passing the monitor over my wife’s stomach again and again, our own hearts sinking with every pass.  “I’m sorry,” she finally said without making eye contact.  “I’ll get Dr. Kindig.”  We were destroyed.  It was happening again, in what seemed like the cruelest way possible.  In the course of minutes, the inputs to the simulation had changed drastically.  The probabilities plummeted.  This didn’t fit the elegant equation, either.  Not at all.

I put my arm around my wife and kissed her forehead, through my own stunned tears.  Her body shook as she sobbed.  It was happening again.

Dr. Kindig came in and immediately recognized what was going on.  She’d been with us through the first one, which had turned out to be something called a molar pregnancy.  Without getting into details, her words at the time were, “Sometimes pregnancies go wrong, and sometimes they go really wrong.  This is one of those times.”  And here we were, almost two years later, convinced that we were going through it all again.  The calculations were certain.  In that moment, it was impossible to argue with the probabilities.

Dr. Kindig put down the medical files, grabbed the heartbeat monitor and locked eyes with my wife.  “Lay down.  I’m finding that heartbeat.”  Everything about her was sudden fiery determination, as if by brute force of will she was going to bring that baby to life.  Somewhere, the coefficients in one of the equations adjusted ever so slightly.  The probabilities marginally improved.

The moment the monitor touched belly, a heartbeat, too fast to be an adult’s, sounded loud and clear through the speaker.  “There it is,” she said.  Brute force.  The probabilities adjusted instantaneously.  The resulting odds suddenly improved.  Dramatically.  That perfect equation?  It had long since fallen apart in a flurry of chalk dust.  There was no single equation that could predict this.

I was slower to adjust than the probabilities.  I didn’t believe it.  “Are you sure?”

“Trust me.  I’ve done this a few times.”  Brute force.  The probabilities smiled down on us.

Desperate sorrow morphed into joy.  Sobs turned to laughter then back to sobs.  The simulation settled on a solution.  The probability had never been higher.  We were, indeed, having a baby.

We’ll never know if Joe (he’s now 11) was just hiding, playing the first of many jokes on us, or his heart really wasn’t beating.  Part of me is convinced that through brute force of will and touched by the divine, Dr. Kindig didn’t just find his heartbeat.  She got it beating again.

Do the probabilities take divine intervention into consideration?

As disappointed as I was to discover the truth about Monte Carlo simulation, the truth about that tattooed lady in the Mickey Mouse getup, I’ve come around on brute force.  Brute force, perhaps with a touch of the divine — kind of like an ’85 Monte Carlo SS.