## Thursday, January 14, 2016

### Targets, arrows, and the lottery fallacy

Sandwalk readers have been discussing the way Intelligent Design Creationists have been calculating probabilities [see Intelligent Design Creationists are very confused about epigenetics and Waiting for multiple mutations: Michael Lynch v. Michael Behe].

We've known for a long time that the most common mistake is assuming that there's only one solution to a problem. They see an end result, like a bacterial flagellum, or resistance to malaria, or the binding of two proteins, and assume that a few very specific mutations had to occur in a specific sequence in order to produce that result.

judmarc calls this the "lottery fallacy" and I think it's a good term [see lottery fallacy],
This is of course what I like to call the "lottery fallacy." It's used by virtually every ID proponent to produce erroneously inflated probabilities against evolution.

Lottery fallacy: The odds against any *particular individual* winning the PowerBall lottery are ~175 million to 1. But there were three winners just last night. That's because *someone* winning the PowerBall is not an especially rare occurrence. It happens every few weeks throughout the year.

In exactly the same way, Axe, Gauger, Behe, and the rest of the ID folks always base their math on the chances that a *particular* neutral or beneficial mutation will occur, and just as with the lottery, the chances of a *particular* outcome are utterly minuscule. The occurrence of *some* neutral or beneficial mutation, however, is, as with the lottery, so relatively common as to be completely unremarkable.

To summarize: ID proponents misuse probability math to make the common appear impossible.
As it turns out, someone on Evolution News & Views (sic) just posted an excellent example of this fallacy [Intelligent Design on Target]. Here's what he/she/it says,
In his second major treatise on design theory, No Free Lunch: Why Specified Complexity Cannot Be Purchased without Intelligence, William Dembski discusses searches and targets. One of his main points is that the ability to reach a target in a vast space of possibilities is an indicator of design. A sufficiently complex target that satisfies an independent specification, he argues, creates a pattern that, when observed, satisfies the Design Filter. There are rigorous mathematical and logical proofs of this concept in the book, but at one point, he uses an illustration even a child can understand.
Consider the case of an archer. Suppose an archer stands fifty meters from a large wall with a bow and arrow in hand. The wall, let us say, is sufficiently large that the archer cannot help but hit it. Now suppose each time the archer shoots an arrow at the wall, the archer paints a target around the arrow so that the arrow sits squarely in the bull's-eye. What can be concluded from this scenario? Absolutely nothing about the archer's ability as an archer. Yes, a pattern is being matched; but it is a pattern fixed only after the arrow has been shot. The pattern is thus purely ad hoc. [No Free Lunch, pp. 9-10, emphasis added.]
Most people have experience with target shooting of some kind, whether with bows and arrows, guns (including squirt guns), snowballs, darts, or most sports like baseball, soccer, basketball, hockey, and football. Children laugh when they picture an archer who "couldn't even hit the broadside of a barn" and rushes up to the arrow and paints a bull's-eye around it. Grown-ups might compare that to a biologist looking at an irreducibly complex biological system and simply stating, "It evolved." In each of these cases, Dembski would say that since the pattern was not independently specified, therefore it is ad hoc.
The unknown author included the image shown above in order to illustrate the point (Image: © Kagenmi / Dollar Photo Club).

Do you see the fallacy? Just because we observe a complex adaptation or structure does NOT mean that it was specified or pre-ordained. There are certainly many different structures that could have evolved—most of them we never see because they didn't happen. And when a particular result is observed it doesn't mean that there was only one pathway (target) to producing that structure.

To continue the analogy—at the risk of abusing it—there may be hundreds of targets in the woods and most of them have very large bullseyes. Imagine you're out for a walk in the woods and you see that almost every tree has a big target with a large bullseye. You find an arrow stuck at the edge of one of the bullseyes and lots of arrows stuck in the trees, the ground, and parts of most of the targets outside of the central bullseyes. Would you write a book about how good the archer must have been?

#### 31 comments :

DGA said...

I am sure I am missing something; it seems Dembski is claiming that the Archer's Fallacy somehow vindicates his position rather than illustrates why he is wrong.

Harriet said...

I usually explain it this way: I take a deck of 52 cards and then shuffle them and pass them out to a class of 20. Then I point out that the probability of each student getting exactly the card that they got is 20!/52! and exclaim: IT IS A MIRACLE!

Unknown said...

The most famous example:

http://www.ncbi.nlm.nih.gov/pubmed/15321723

Of course, since this was published in an actual journal, this has become the creationists' shining star.

Fair Witness said...

They explain the fallacy, and then proceed to hide the exact fallacy inside some naive mathematics. Kind of like the illusionist showing you that he has nothing up his sleeves, just before he deftly produces your card from a hidden pocket.

judmarc said...

To abuse the analogy still further:

The ID proponent sees an arrow stuck in the side of a barn, visualizes a target around the arrow, and proclaims only the Deit - err, Designer could have been so miraculously accurate.

Faizal Ali said...

This fallacy is illustrated in creationist Doug Axe's latest attempt to write a scientific article, on his blog BIO-Complexity (which, for some reason, he insists on calling a "journal):

Model and Laboratory Demonstrations That Evolutionary Optimization Works Well Only If Preceded by Invention--Selection Itself Is Not Inventive

Briefly, what he does is select a functional enzyme as a target, reconstruct an earlier ancestral form of this enzyme, and then lets it evolve. His finding is that the later functional enxyme is never produced, which he takes as evidence that evolution occurs thru "design". However, what he as essentially done is demonstrate that, when the arrow is shot from the bow, it lands randomly at other "targets" rather than the one selected. This as the ENV article states, is evidence of the absence of design.

It's very odd how the IDiots keep arguing against each other points, without realizing they are doing this.

Faizal Ali said...

It's very odd. Dembski defines "specified complexity" as an arrow that has been deliberately shot into the bullseye of a target. But then when he finds a target with an arrow stuck in it, he automatically assumes it is an example of "specified complexity" without determining whether the arrow was shot into the target, or the target drawn around the arrow after it landed.

But, then, why do you think they're called "IDiots"?

Anonymous said...

While the lottery fallacy is an important argument to make there are many other levels on which the IDists misconceptions need to be addressed.
The lf argument assumes that eventually some target that isn't prespecified will be hit. I'd ask an IDer what they'd think of an archer that would miss any target 99.9% of the time. Not very good I would think. But paleontologists tell us that at least 99.9% of the species that have ever lived have become extinct. What this means is that the vast majority of lineages eventually fail to hit the target - they fail to come up with the innovation that would allow them to continue to survive

Anonymous said...

....and while there's an obvious rejoinder to this argument I think the big picture is still at odds with any reasonable notion of a designer

Unknown said...

Not as much a miracle as you think, it should be (52-20)!/52!=32!/52! and that's about 10^17 times more likely...
I'd use an absolutely continuous random variable instead. For instance the probability of a radionucleus decaying at precisely the time it does is 0. Not close to 0, just plain 0. Still at some point it does decay.

What do you think are the chances that they will address this massive oversight on uncommondescent?

I bet they will be sweeping it under the rug

Faizal Ali said...

As I recall, his error there was not quite the same. But I don't know if I can be arsed to re-read the thing to find out. On top of everything else, Doug Axe is a painfully bad writer.

William Spearshake said...

Any time an IDist brings up probability as evidence against evolution, I ask them what the probability of them being alive is. Not someone like them, but the exact person that they are.

Given that a person is the result of one sperm and one ova, out of millions and thousands respectively, the odds are low. Add the odds of the parents meeting and having sex at just the right time lowers the odds considerably. Now expand this process for a few generations and you get to a probability that is so close to zero that the difference isn't worth measuring. Yet, he still exists.

And then Barry bans me.

Faizal Ali said...

Wait a minute, WTF?!

Children laugh when they picture an archer who "couldn't even hit the broadside of a barn" and rushes up to the arrow and paints a bull's-eye around it. Grown-ups might compare that to a biologist looking at an irreducibly complex biological system and simply stating, "It evolved." In each of these cases, Dembski would say that since the pattern was not independently specified, therefore it is ad hoc.

Larry's post, and most of the comments here, have been addressing the flaw in Dembski's analogy. But the last sentence in the above quote does not even follow from Dembski's analogy. A correct application of the analogy would be to say that biologists claim something like the flagellum arose thru unguided processes, but Dembski would say it is designed because it hits the "target" of performing a specific function. But the author of the ENV article doesn't say that. He/she/it instead says... Well, I don't really know what point is being made there. Maybe something about the "target" being evidence for evolution or something like that, but who knows? It would appear the author did not actually understand what Dembski wrote. So maybe it's fortunate that the author remained anonymous.

IDiots.

Gary Gaulin said...

I would like to propose an online database for 2D and 3D visualizations of the "search space" for a given string length, made by looking up each possibility in the existing genome databases. The graphs would fill in over time. Each sequence found sets a pixel in a color that indicates what the sequence would be useful to and/or what it is for.

A note can be added to indicate how much more can in the future be expected. Where that is slowly incremented to reflect data gathering progress it becomes like a goal-drive that encourages researchers with data that sets more pixels to upload it into the NCBI system. At a lab research level it seems like a rather mundane job on top of all else that goes unnoticed by the general public and "science paper" driven academia where filling in the gene information seems like a rather thankless job. But where it for-good puts an end to what Larry is annoyed by enough to have written this article to complain about it becomes heroic to help light up the pixels in graphs that (one way or the other) puts an end to all the arguments over what "search space" has inside of it.

Putting that in the classroom is as easy as printing posters to put on the wall that explain themselves, not something added to curriculum that takes away from class time. A question from a student about it would likely lead to what is already planned into their curriculum relating to (known and still unknown) genetic sequences.

I cannot exactly know what it would look like, but it seems more likely that "search space" is not as sparse as other ways of explaining what is in it have described. But there is a chance it comes out very spotty looking. So it's not favoring one side or the other, it's a scientific way to either way know for sure.

Any volunteers? I have a way to quickly search NCBI using code written in VB6 but I would need help from a biology expert that knows how to properly script the NCBI inquiry. A PC would at least work for the shorter length sequences. There might already be an app that would compile and display the data, but maybe not. Either way though: it can be done! Or maybe already was? Who knows?

Ed said...

Lutesuite wrote:
"Maybe something about the "target" being evidence for evolution or something like that, but who knows?"

It would fit from a creationist view that evolution has stopped with us humans arriving on the scene. Thus humans and flagellums are the end point of evolution for humans and bacteria, the final product, thus he/ she/ it 's designer was always working towards this product? Metaphorically speaking we're walking around with bull eyes painted around us.
Or something like this?

Mort Darby said...

In fact the Powerball winning odds are even slimmer accounting for 1 to about 292 mln (according to the official data and the latest amendments). Still there were 3 winners in the last draw. They split 1.5 bn dollars!

Faizal Ali said...

That still doesn't make sense of the ENV comment. It says that Dembksi's position would say of an "irreducibly complex biological system" that "since the pattern was not independently specified, therefore it is ad hoc." IOW, that irreducibly complex systems are not designed. That is a direct contradiction of the ID position.

judmarc said...

Yeah, I think the odds of a particular individual winning were considerably reduced for this last lottery from the average odds because of greatly enhanced participation due to the size of the jackpot.

This of course points out yet another very simple way the ID view of probability is completely wrongheaded. When lots of people enter, the odds of a *particular individual* winning go down, but the chance of *someone* winning go up. Same with evolution. The more "players" - individuals, genes, locations on the gene - the lower the odds of any particular one being the subject of a favorable mutation, but the greater the odds of a favorable mutation at some individual/gene/location. And of course those probabilities multiply when we're talking about not one single favorable mutation but pathways involving several neutral or nearly neutral mutations.

N.Wells said...

Your odds of buying a ticket with the winning numbers remains the same no matter the size of the jackpot or the number of players. However, as the number of ticket sales increases, your chance of having to share the jackpot gets larger.

Faizal Ali said...

And the chances that someone will win becomes higher. That's why this drawing was typical. You have draw after draw where no one wins then, after the hype has grown and the number of tickets sold has skyrocketed, you have three winners at once.

judmarc said...

@N.Wells, you're right of course. Thanks for the correction.

Diogenes said...

Doug Axe 2004, or rather misinterpreations of it, rebutted at Panda's Thumb:

http://www.pandasthumb.org/archives/2007/01/92-second-st-fa.html

Harriet said...

Oh crap...that is right (1/52)(1/51)....(1/33) = (32!)/52!...yes, in class I get it right. :-)

Faizal Ali said...

Not directly related to this thread, but there has been another defection from the Intelligent Design movement: Sal Cordova has announced he no longer supports it `(though he remains a creationist):

http://theskepticalzone.com/wp/id-falsifiable-not-science-not-positive-not-directly-testable/

Gary Gaulin said...

Update: I did some experimenting and found that short letter strings were more than the NCBI Blast system could quickly handle. Long strings have too many possibilities and sending batches of them might overwhelm their server.

After trying out random sequences of 20 or more letters I found that most combinations had no direct match. I expected that random "junk" would result in almost all random strings being found. Therefore in this case it would be far faster and easier to (one file at a time) download and process the genetic data found here:

ftp://ftp.ncbi.nlm.nih.gov/genomes/

This method would include "junk" DNA in the results, but as long as other data for harmful gene mutations are not included it would not contain harmful (to that organism) combinations. The information would thus be representative of normal healthy individuals.

Matt G said...

I like the bridge hand example. The probability of getting dealt all of one suit is tiny, but the chances of being dealt a hand that guarantees a win is far, far higher. The probability of being dealt "the hand you were dealt" is exactly the same as being dealt all of one suit.

Steve said...

Larry, the lottery fallacy is itself a fallacy. But moreso, lotteries are a perfect example of intelligent design in action.

They are designed to utilize a simple random number generator (pingpong balls in a wind bubble) but control the outcome by limiting or expanding the amount of lottery numbers required to win. In this way, they can calculate the probablity of how many lottery winners there will be. Thats why there are so many variations on the lottery design, from 3 to 6 numbers, each with their own probabilities and payouts. It it works like a charm. When's the last time we heard of a lottery company being bankrupted?

As it relates to biology, the amount of excess reproduction is equal to the number of lottery numbers put into the pingpong ball wind bubble. The variation is the random numbers generated by the wind bubble. Selection is equal to the numbers selected by a Vanna White lookalike.

And it works like a charm. When's the last time we heard life going bankrupt and having to start over again? At last count, 3 billion years and still going strong.

Now THAT is a brilliantly designed evolutionary mechanism.

Unknown said...

Steve once again displays his total lack of undersatanding. He seems to think that the success or otherwise of lottery companies is in some way dependant on the number of winners.
Nothing could be further from the truth! The success of lottery companies is directly attributable to the amount they cream off the top of each ticket sold. It makes absolutely no difference to them if there is a winner on every draw or if there is a multi - rollover (except in the latter case they probably sell a few more tickets). They make sure their share of each ticket sold ensures their success. The other people who misunderstand the reality of 'chance' ensure an adequate sale of tickets.
Recent changes to the UK National Lottery saw the chance of winning the jackpot fall from 1:14 million to 1:45 million. Guess who the real winners are!

Faizal Ali said...

Not even wrong, Steve. Not even wrong.

judmarc said...

Thats why there are so many variations on the lottery design, from 3 to 6 numbers, each with their own probabilities and payouts. It it works like a charm. When's the last time we heard of a lottery company being bankrupted?

Right, just like we've never heard of a life form going extinct - oh, wait....

Honestly, Steve, don't you even try to make your arguments seem sensible any more? I feel that there used to be a better class of IDiot on this blog.