The Rest of the Story

Subjective Estimates of Probability:

Earlier today, while waiting for something -- I can't even remember exactly what -- I pulled out my palm pilot (actually a Sony Clié) and started a game of yahtzee.  The very first roll gave me five ones.  (This really happened.) 

Everyone knows that such an event is rare, but we all accept that it could happen by chance.  There does not seem to be anything supernatural about it.  The probability of that happening, by the way, is 1/6^5, or 1 in 7,776.  Now, let's say I have a really big palm pilot, and a super-yahtzee game with one million simulated dice.  I don't happen to know what 6 to the one-millionth power is, since my calculator chokes on that one.  It doesn't really matter what the exact number is, though, since it is pretty obvious that it is a really big number, and the inverse is a really small number.  If I walked into Sweetwaters Cafe and ordered an expresso, then did the same thing with my palm pilot, and got 1,000,000 ones on the first roll, that would be an exceptional event.  In fact, if I did that and showed it to the other customers there, most would think it had been rigged.  They would say that the probability of that happening by chance is so low (one over six to the one millionth power)  that it could not possibly have happened by chance.  The only conclusion that would seem reasonable to them is that it had not happened by chance. 

The next day, I walk into Starbucks, pull out my palm pilot, and get an unremarkable mix of ones, twos, three, fours, fives, and sixes.  I shout in amazement, and show it to all the customers.  They all think I'm nuts, because there is absolutely nothing special about that roll.  Guess what.  The probability of that particular combination is exactly the same: one over six to the one millionth power.*  That particular combination would only be interesting if I had predicted it ahead of time.

Now try a different thought experiment.  Say that we are not going to specify ahead of time what kind of outcome we expect from the roll.  We will accept any combination.  What is the probability that some combination will occur?  It is six to the one millionth power divided by six to the one millionth power, which is one.  Once you tap the button, it is guaranteed that some outcome will occur.  And the probability of any one particular outcome is exactly the same as the probability of any other outcome. 

Now try the really interesting experiment.  Get all six billion people on the planet to participate.  Start out by rolling one dice, then two, then three, and so on.  Except this time, the dice are rigged.  They always will turn up with the one spot on top.  After each trial, ask everyone whether that outcome could have occurred by chance. At first, everyone will agree that it could have, since it would not be unusual in a single roll of a single dice to get a one.  As the number of dice thrown increases, eventually you will get some dissenters. Keep adding more dice, and the proportion of dissenters will increase.  Eventually, everyone who is not up on their statistics will think it absolutely has to be rigged.  They will say that there is no chance whatsoever of getting all ones that many times is a roll, with that many dice.  Yet, the probability of getting all ones is no lesser and no greater that any other combination.  As much as that seems contrary to intuition, as much as it seems to contradict our everyday experiences, the mathematics of it does not lie. 

The Universe, of course, does not consist entirely of ones.  If it did, consciousness would not be possible, and even if consciousness were possible, we'd all die of boredom.  The actual Universe is made up of all kinds or numbers, some of them quite interesting.  As a result, consciousness is possible, and life is interesting.  The probability of this exact Universe occurring by chance is small.  However, it is exactly that same as the probability of any other Universe.  Therefore, it is nonsense to say that there must have been a designer in order for this Universe to have come into being. 

As strange as it may seem to think that there is nothing mathematically special about the organization of the Universe we live in, the fact is, it is not special in any mathematically meaningful way.  That is not to say it is not special at all: it is.  However, the reason it is special is that we think it is special.  We make it special.

Now try another thought experiment.  Examine every brick, every molecule, every atom of the Sweetwaters Cafe at 123 W. Washington Street.  Notice how carefully the bricks are arranged.  Notice how the pipes go exactly to where people expect water to be available.  Notice how the seats are exactly the right size for the average human to sit on.  Remarkable.  Now estimate the probability that another Sweetwaters will come into being at 407 N. Fifth Ave.  Seems rather unlikely, doesn't it?