A Drunkard’s Walk…with Drift

I just finished Leonard Mlodinow’s book, A Drunkard’s Walk:  How Randomness Rules Our Lives.  It’s a superb guide to properly interpreting seemingly improbable events and should be a mandatory read for anyone in Business, Sports, Politics, Economics…pretty much everybody.  A part of me enthusiastically devoured the myriad examples of long shots and how when taken in the proper context are easily explained by random chance.  A different part of me struggled to reconcile my belief in the laws of chance that can explain remarkably well chaotic events (from Roger Maris to Warren Buffet) and my certain knowledge of Divine Providence.

First, a thought experiment that captures how randomness can explain that 1 in a million shot.  What’s the probability of flipping a fair coin and getting 20 heads in a row?  It’s about 1 in a million for a specific run.  Now, imagine a million people flipping coins; those whose coin lands on heads get to flip again.  After the first round you’d expect about half to be eliminated and half again after the next round and so forth.  You would expect 1 person on average to end up making it 20 rounds.

Most of life’s experiences are of the sort where there are multiple players with a distribution of possible outcomes.  Take the stock market.  There are only a few Warren Buffets.  Those few believe they are able to leverage market inefficiencies and we all bow down in deference at their knowledge.  Or it could just be that there are millions of traders and hedge fund managers and a few of them would be expected to perform a great deal better than the market just by chance.

My favorite thing about this book is its wealth of examples.  It’s a very compelling case.  So how do I reconcile a belief in Randomness and a perfect knowledge of Divine Providence?  The answer came as I turned the final digital pages of the book.  Mlodinow’s  allusion to a Random Walk is incomplete.  We are not particles suspended in a liquid being bombarded by molecules which, in aggregate, move us along in a Brownian motion.  Our life is not a random walk…it’s a random walk with drift!  The drift is guided by an active God who is able to influence our lives and His work in ways that can only be perceived by those with adequate methods of estimation.

This explains how God can build a church, a nation, or a life when everything looks like chaos. He can move things along despite free will, natural disasters, and market turmoil.  The drift also explains how God can influence human events without being responsible for the random walk component, the devastating tsunamis, earthquakes, murder, war, hunger, etc.  He can use these events to guide nations and lives without being the cause of evil.

Here’s a graph of a random walk and a random walk with drift.  History clearly follows the latter as does evolution.  World Wars, depressions, global recessions, none have extinguished technological progress.  And as for biology, random permutations of DNA all tend toward improvement.

The noise and randomness may increase, and it may get harder to see the signal through the noise, but those with eyes to see will have the power (in the statistical sense) to estimate the drift parameter.

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1 Comment

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One response to “A Drunkard’s Walk…with Drift

  1. tgs

    Your post reminded me of a remark that I’ve never forgotten. I’m not even sure what question sparked the back-and-forth, but I vaguely recall one student challenging Dr. Tolley on some point about the nature of chance. To the student’s question, he responded: “That [randomness] exists! It’s not clear to me that randomness exists.”

    At that moment I was reminded of the start of my math major career. I had proved some fantastic properties of a set. Only I had forgotten to check that the set existed. It doesn’t.

    Since then, I’ve been careful when philosophizing about chance and life and the Divine. I’m not sure randomness exists. It is a reflection of our ignorance of the true underlying causes. Randomness is a model, not a truth.

    -tgs

    P.S. It’s good to see back in the blogger’s saddle.

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