Tuesday, September 12, 2006

Intelligent Design "Math" and Winning the Lottery

One of the principle arguments that the Intelligent Design advocacy offers in their refutation of the theory of Evolution, is that life is so "irreducibly complex" that the likelihood of its having evolved to its present state is so vanishingly small that we must have been explicitly designed by some more complex outside entity. The group tends, on a regular basis, to trot out "Math" in order to support their claims.

The ID "Math" argument goes something like this: In order for life to have evolved, a very long series of mutations must have occurred over a very long period of time, and each individual mutation has a very low probability of occurring. When you look at the entire chain of necessary fortuitous events (multiply each of the tiny probabilities together) the resulting likelihood is, as John Paulos has said "so minuscule and wildly improbably as to be essentially impossible." Therefore, some other larger intelligent power must be at work explicitly guiding the process.

It sounds rational to the layman, and it even supposedly has math to back it up and lend credibility.

But consider the following. Last week, Valerie Wilson of Long Island, NY won the "$1M" jackpot*(see below for a discussion on payout deceptions) in the state's "Cool Million Scratch-off game. And she beat the long odds of 1 in 705,600 to do it. But what really made the event interesting was that 4 years ago, lucky Valerie had won "$1M" after beating even steeper odds of around 1 in 5.2 million.

The press made the obvious calculation that overall, Valerie's chances of winning both games was an incredibly slim one chance in over 3.5 quadrillion, or 1:3,669,120,000,000. These chances are so small that they defy rational comparison. Someone would be about a billion times MORE likely to be struck by a meteorite.

But according to ID "Math" reckoning, something so wildly improbable should never have happened, as it was effectively impossible. And yet it did happen. Obviously, there must be a mistake in the ID calculations, but where is it?

It turns out that there are (at least) three key shortcomings in the ID Math proposition. The first is a subtle, but very important distinction that the ID crowd fails to make when modeling the likelihood of life's evolution, and it is exactly the same mistake the press tends to make when they highlight stupendously lucky events such as those around Valerie Wilson's gambling odds. They confused the likelihood of one specific outcome amongst many possible histories with the likelihood that any single outcome will emerge from the entire process, and apply the former to discredit the latter. Obviously in Valerie's case, there was a lottery, and somebody had to win. And while her chances of winning twice were low, she was part of the process that really did exist, and someone did, in fact, win.

In order to consider the probabilities with respect to the entire process, you need to start asking questions like:

"How many lottery games are held each year?"

"How many tickets, on average, are sold over the course of each lottery?"

"How many tickets does the average lottery player buy over a four year period?"

"Instead of looking at Valerie's chances alone, what are the chances that anyone might have won two lottery tickets over a four year period?"

When you dig into the actual math describing the entire process instead of one incorrectly singled-out and poorly-defined example, the numbers become much more reasonable and believable. More than 125 million American adults spend $45 billion annually on some 35,000 lottery games across 40 states. With 35,000 winning events randomly spread across 125 million gamblers, it turns out that the likelihood of having a single person win more than once is actually rather high. There is actually more than a 90% chance that someone will win twice after only 10,000 lotteries. So over the course of four years as 140,00 lotteries are held, you would actually expect more than 10 people to win twice. And indeed if you google lottery+win+twice you get many more hits than the press would otherwise believe. (As an aside, don't let the higher-than expected odds of winning deceive you. While you can win, you are highly unlikely to make money doing it.)

The identical realization applies to evolution and Intelligent design. There is clearly a process. Life has clearly evolved, and given the myriad species that have evolved over the millennia, there are clearly MANY paths that end up with something alive and wriggling.

Secondly, there is the issue that the method of multiplying the likelihood of each step in millions of years (generations) of mutation to obtain an overall probability would only be correct if each mutation were an independent event. But each evolutionary step is a small incremental change that begins with, and depends on the steps that have gone before. So the actually likelihood of any single mutation emerging at each step is rather high.

Finally, the usage of simple probabilities for each of the steps and multiplying them together would only be correct if the changes and mutations are completely random at each and every step. But one of the fundamental precepts of evolution is that the environment, through the process called natural selection, culls the population that survives to breed, and biases future generations towards those traits that aid survival to breeding age. When one step depends on the other, the use of conditional probabilities become necessary which are much more complex.

So in summary, ID "math" fails in that it incorrectly ascribes a single outcome probability to an entire process, it incorrectly assumes that each evolutionary step is independent, and it incorrectly assumes that the process is completely random.

As Pauli once said, "It doesn't even rise up to being wrong." It just doesn't even apply.

And besides, where would we be today if the ID doctrine of "a designer did it" was where we stopped instead of continuing to work on all the science and technology that underpins our society? Where will we be tomorrow, given this mind-boggling national resurgence of anti-science claptrap?

* It should also be noted here that the million dollar jackpot claim in the games is very deceptive, and is a further exploitation of people's innumeracy The actual payout for the "million dollar win" is actually paid in $50,000 installments over 20 years. But that doesn't take into account the time-value of money and the appreciation due to interest. Nor does it account for inflation and the decreasing purchasing power of today's dollars as prices rise. Ultimately, the state only needs to invest a little over $450,000 in a vehicle accruing 4% annual interest to make the $1M total payment over 20 years (i.e. they only pay out less than half of the take!). But people have to pay the full ticket amount up-front. But in the rules disclosures on the tickets, they tend to highlight the odds and payouts as if it was a one-to-one comparison, but really it's a giant kiting scheme which is somehow illegal when applied to bank profits and check management, but okay when the state is making the money. Okay, enough anti-gambling rant for one article.