You have to bear with me for a second, but this will get around to birds, I promise.

Timmy, my resident "special needs" pigeon. |

Over at Sciencewriter.org (possibly the coolest domain name ever), Davide Castelvecchi, who is a physical sciences and mathematics editor at Scientific American, has been stirring up controversy recently by revisiting what's known as "The Monty Hall Problem". If you're not familiar with it -- where have you been? It's been discussed over the years everywhere from hard science magazines to Car Talk. It's derived from the problem that Monty Hall often presented to contestants on Let's Make A Deal. You have three curtains. Behind one of them is a car, and behind each of the other two is a worthless gag gift (like a donkey). (I know, I know -- who says a donkey is worthless? But that's not the point of the problem). You have to pick one of the curtains. Let's say you choose number One. After you make your choice, Monty reveals what's behind one of the other curtains, and the one he reveals is always a donkey. Let's say Monty opens number Two. Then, he offers you a choice. Do you want to keep the curtain you chose, or do you want to trade?

Monty's problem (not my photo, obviously). |

For most of us, our intuitive guess is that it doesn't matter. We had a one in three chance of picking right the first time and that hasn't changed. Or, conversely, since there are now two unopened curtains, we have a fifty-fifty chance. Either way, switching can't increase our odds.

It turns out though, that isn't true. Statistically you are always better off switching. In fact it almost doubles your chances. I'm not good with this sort of math so I'll just refer you over to those who are -- and if you want to argue about it (as a lot of people do, judging by the comments section) you can argue with them. Proving the solution isn't really my point here. (Check it out here.)

The reason this came up again at Scientific American, though, is because of an article they published back in January of this year. John Allen Paulos, a mathematician at Temple University, noted that pigeons didn't seem to have the same difficulty with the Monty Hall Problem that humans do. On the contrary, pigeons (being good empiricists, as Paulos says) learn the best strategy after only a few tries. (You can see the article here.)

A few years ago another scientist -- Tim Pennings, a Professor at Hope College in Michigan -- was playing fetch with his dog, throwing a tennis ball into the water for the dog to retrieve. The dog, Elvis, would run along the shore and at some point plunge into the water toward the ball. What Pennings found was that, in most cases, Elvis was choosing a path that closely approximated the optimal path (the path with the shortest travel time) to the ball. The path can be worked out using fairly complicated calculus equation -- but Elvis seemed to be doing it "in his head" and "on the fly". (Again, I'm not going to try to explain the math -- you can look into it more here if you're interested.)

Precision landings almost every time. |

These kind of remarkable abilities are everywhere in nature. The small songbirds in my yard routinely land on the thin perches of a bird feeder that is swaying in the wind -- and they do so coming from across the yard, setting their trajectory as they approach. Only a couple of times have I ever seen a bird have to pull up and come at it again. Squirrels leap from the rail of my deck to the cherry tree nearby, and catch the thin branches, which again are often swaying in the wind. Birds also fly through the cherry tree despite its dense branches and (at this time of year) leaves. They can fly straight through and out the other side. Imagine trying to write a computer program to pilot something the size of a chickadee through such a complex space, complicated more by ever changing light conditions, wind turbulence, and so on. The amount of calculation that it requires is staggering.

The catch looks easy, but try writing a program to do it. |

But let's not leave humans out. Ichiro Suzuki does the same thing nearly every day. When an outfielder hears the crack of the ball leaving the bat and starts to run, he has time for almost no conscious thought about where it's going or how to get there. Again, it's a complex mathematical problem solved on the fly -- timing his leap to catch the ball just before it goes over the wall. And I've seen dogs playing with Frisbees or tennis balls who were as good as any major leaguer.

The greatest ball player I've ever known. |

Paulos warns against the mistake of thinking that these abilities reflect some kind of conscious knowledge on the part of animals. Of course, they don't. They represent the problem solving ability wired into brains over billions of years of evolution. (And in the case of dogs -- and to some degree pigeons -- of tens of thousands of years of intense breeding). Corgis, for instance, are herding dogs, whose job was to keep livestock moving in one direction. The ability to foresee the movements of a sheep and set your own course to intercept it effectively is not all that different from what Elvis was demonstrating on the beach.

If you want to drive the unconscious nature of these faculties home, I invite you to walk into a room sometime and ask if anyone there is good at calculus. When almost everyone predictably says no, toss a tennis ball to one of them. Almost certainly, they will catch it, and when they do you can show them (with the help of a mathematician friend, if you're like me) the equation that describes what they just did. We're all better at math than we think.

The furor over the Monty Hall problem does show, however, that for us humans our conscious thinking sometimes gets in the way. I learned this a long time ago in art school. One of the reasons why it's so hard for many people to learn to draw is because what we "know" about objects (say the size and form of a table) gets in the way of what we actually see before us. Most people asked to draw a table will draw an abstract representation of a table instead of the object they see before them, which is skewed by perspective and point of view and really looks nothing like our idealized notion of "table".

Oh, and I wanted to get back to pigeons. More on that very soon.

**If you like Birdland West, you might also want to check out our sister blog Books and Beasts, which focuses on reviews of books about animals and related topics.**

(Many of the original photographs featured on Birdland West are available for sale as art quality prints. You can check out all of our offerings at http://AlexWashoe.imagekind.com. If you see an image here that does not show up on our Imagekind site please contact me directly and I'll let you know about availability.)

"In fact it almost doubles your chances."

ReplyDeleteIt exactly doubles your chances,from 1/3 to 2/3.

You're exactly right, and I did know that. My wording was wrong and I was hedging my bet because I'm not confident with the math.

ReplyDeleteHi Alex,

ReplyDeleteI have a different take on why (adult) humans find the repeated Monty Hall problem so difficult (which is really what the study looked at), here: http://roslyndakin.com/archives/909

Be curious to know what you think. I'm a biology PhD student & aspiring science writer in Canada.

Roz Dakin