Image: Markus Botzek Corbis
-
What a Plant Knows
How does a Venus flytrap know when to snap shut? Can it actually feel an insect’s tiny, spindly legs? And how do cherry blossoms know when to bloom? Can they...
Read More »
A number of recent news stories have had a similar kind of message: animals viscerally understand certain mathematical operations better than humans do. Such stories are always interesting in a Sunday-newspaper sort of way, but do the abilities of animals to calculate really exceed those of humans? It may help to examine some of these claims.
In the infamous Monty Hall Problem, named after the television game show, human subjects seem to pale next to pigeons in mathematical reasoning. A guest on the show has to choose among three doors, behind one of which is a prize. The guest states his choice, and the host opens one of the two remaining closed doors, always being careful that it is one behind which there is no prize. Should the guest switch to the remaining closed door? Most people choose to stay with their original choice, which is wrong—switching would increase their chance of winning from 1/3 to 2/3. (There is a 1/3 chance that the guest’s original pick was correct, and that does not change.) Even after playing the game many times, which would afford ample opportunity to observe that switching doubles the chances of winning, most people in a recent study switched only 2/3 of the time. Pigeons did better. After a few tries, the birds learn to switch every time.
They learn, but do they calculate or understand? Not at all. Good empiricists, the pigeons simply follow the evidence. People, on the other hand, overanalyze and get confused.
Bees who seem to find the shortest path connecting many flowers in a meadow provide another example of what appears to be animal perspicacity. Even if the path they follow is optimal (and the only way to find out is to measure all possible paths), they cannot be said to have come up with a general algorithm, a task so complex that it belongs in a class of virtually unsolvable problems called NP-hard. Their path may often be a good approximation of the shortest path, but there is no good reason to think that they will always produce such an approximation, much less the optimal solution for all placements of an indefinite number of flowers.
Similar hyperbole arises in articles about dogs’ alleged ability to do calculus and spiders’ knowledge of geodesics (not to mention octopuses’ knowledge of soccer). Alas, although all these results (except for the last) are of real scientific interest, they are almost always mischaracterized as instances of understanding. By insinuating that animals’ innate instincts are superior to humans’ feeble attempts to mathematize, some of the journalistic accounts betray an anti-intellectual bias. “What good are our dry algorithms, our probability, calculus and geometry,” they seem to ask, “when pigeons, bees, dogs and spiders can do the math without thinking?”
This article was originally published with the title Animal Instincts.
Already a Digital subscriber? Sign-in Now
If your institution has site license access, enter here.
Rights & Permissions
See what we're tweeting about
20 Comments
Add CommentVery interesting! Many good points made in this article. However, in general I think that humans are much better at computation than animals because they also take into account MEANING.
Reply | Report Abuse | Link to thisPlease help me with my confusion about probability. As a human over-analyzer, here's how I would see it: the prize is equally likely to be behind any of the three doors. If I pick door A and I'm shown that the prize is not behind door B, it is still equally likely to be behind A or C. How does that likelihood change from before I pick a door to after?
Reply | Report Abuse | Link to thisPerhaps there's a cultural bias too since people have some sort of a belief system. In this regard this study might be more about how long does it take one to give up belief in favor of let's say reality. The stake for a person might be less than the stake for a pigeon since we're not talking primary motivation or survival as in the case of a pigeon.
Reply | Report Abuse | Link to thisThen again, at a psychological level, people who are in for such testing are well aware they could be cheated by the very people behind such tests: and if there's cheating involved, then perhaps people are the winners of such a test after all. In any case one might also be suffering more if they lose by not trusting their first instinct too.
And to prove that my math abilities are not that good either, I would say the chances to get the right door by switching after one empty door is revealed are in fact 1/2 and not 2/3. Perhaps simply flipping a coin on whether to switch or not might bring in more success, relieve some of the stress related to losing by not trusting first instict and, damn sure, drive the d*amn testing freaks crazy (just in case they are cheaters).
Hehe, although cheating is always possible, putting someone trusted (e.g. spouse, kid, friend) along with the prize behind the right door from the beginning would make a human subject accept "facts" easier...
Reply | Report Abuse | Link to thisOr otherwise just put a loaded gun at the poor subject's head or starve him to death, although even in such cases a human being might have higher motivation that goes beyond his individual survival. LOL
I truly believe excessive meaningless testing, obvious mistakes and lack of ethics within the scientific community that proves to be way to eager to treat human beings as nothing more than animals for the sake of prestige and money has led to a general mistrust (aka adaptation to reality). With all the current and future consequences... Am I wrong? :D
Chances change if you look at the problem from a different perspective: when picking up one door out of the three you have more chances to be wrong than right. Therefore switching your choice would increase your chances, the mathematician line of reasoning goes.
Reply | Report Abuse | Link to thisAnother line of reasoning would be to just think the problem anew which, following math reasoning, would mean only 50-50 chances.
The thing is, for a limited number of trials probabilities hold little meaning. E.g. Try flipping a coin only 7 times.... Hence I dare say that if those probabilities checked so well as this study author claim, there's very good chances we may be talking a psycho-scientist cheating test. LOL
I agree with mdiavaro99ro's explanation for the door problem. An important thing to remember is that the host gives you additional information after you made your initial choice. Given that you are more likely to have chosen the empty door initially, the host has shown you the "other" empty door, so when you switch it is more likely that you will win.
Reply | Report Abuse | Link to thisThe easiest way I have found to explain it (because it is really not intuitive) is this:
Reply | Report Abuse | Link to thisIf you stick with your original guess, the only way to win is if you picked right which has a 1/3 chance.
If you switch, the only way to lose is if you picked right the first time. We just agreed that picking right the first time has a 1/3 chance. So switching must have a 2/3 chance. Conditional probability catches most of us.
The Monty Hall problem is a great one. It is a demonstration of how our brains do not intuitively understand probability.
Reply | Report Abuse | Link to thisBefore being shown what is behind any of the doors, a person would have a 1 in 3 chance of correctly guessing the door hiding the grand prize. If the contestat's initial guess was correct, they would win if they did not change their guess after being shown what is behind one of the losing doors. So, 1/3 of the time, you would win if you did not change your guess.
A person has a 2/3 chance of initially guessing incorrectly. When we choose incorrectly, it means the grand prize is behind of the the two doors we did not choose. Monty, when he opens one of the two doors we did not choose, does not choose randomly. He opens the door which does not have the grand prize behind it leaving the prize behind the one unopened door. When we change our guess, we will win.
Since we are twice as likely to have an incorrect initial guess as opposed to a correct guess, we are twice as likely to win if we change our guess.
Cool, right?
The Drunkard's Walk: How Randomness Rules Our Lives, a book by Leanord Mlodinow, contains a longer discussion of this problem. He's a physicist at CalTech and co-wrote a couple books with Stephen Hawking - all that to say - he's no slouch.
And yet guys probabilities check out for high-number of trials and large groups. Moreover, in a lot of cases, probabilities are nothing more than statistics extrapolated at a given point in time: e.g. the risk of car accidents.
Reply | Report Abuse | Link to thisAt an individual level there are let's call them "deviations": people that beat the probabilities odds either positively or negatively at a given time. E.g. People that somehow switch or not switch in such a way that their rate of success beat even the "go for switching always" control-group. Or people who apply the "go always for switch" that have lower rates of success than others with the same or different strategy.
It would surprise me greatly if there wouldn't be significant differences related to the environment of the test too. E.g. computer-generated random allocations, human generated allocations etc.
At a psychological level there might be a lot of surprises as to why someone goes or not for the "winning strategy" even when told the "big secret". ;)
Pigeons are smart on this one.
Reply | Report Abuse | Link to thisNow, test them on that 'Bayesian' foolery,
where revealing the sex of one child supposedly changes the probability of the other child.
It doesn't, It isn't like the doors, I bet a Pigeon would agree.
Really, the Monty Hall problem? Fascinating. That is an interview favorite that many people miss if they haven't heard it before. Great article... - Adrian Meli
Reply | Report Abuse | Link to thisA woman is having twins and we are curious about the gender of the babies. Let's define the sample space: there are four options for the gender combinations for the babies - GG, BB, GB, BG. What are the chances that one of the babies will be a girl? 3 out of 4. Now, given that one of the babies is a girl, what is the probability that the other is a girl? 1 out of 3. If the first baby is a girl, what are the chances that the second baby is a girl? 1 out of 2.
Reply | Report Abuse | Link to thisHaving information on one baby or the other changes the sample space and the probabilities. I haven't had any pigeons weigh in. I wonder how many eggs they lay...
Dear John,
Reply | Report Abuse | Link to thisMany popular science articles reinforce deeply held, mythological views that humans are not animals.
"...animals viscerally understand certain mathematical operations better than humans do."
In my opinion, this type of separatist verbiage should be expunged from the modern scientific lexicon.
As you write in the future please consider the following: humans are animals too.
Back to visceral bird brain (sic) computations using computers as an example. When one requires (almost) perfect high speed solutions, there are 2 "algorthmic solution" methods.
Reply | Report Abuse | Link to thisEither compute the equation every time a solution is required, and this requires (most times many, many, many steps,)
or
precompute the solutions to a wide range of inputs (factors) for that equation and match each particular (set of - if required) inputs/factors to a "look up table."
This is often the quickest route to the solution. Cheat sheets are easier than learning.
Biologically, these "look up tables" are called instincts or intuition because the precomputation has been done by previous (obviously successful) generations and solutions are embedded in the (successful) genes.
Learned precomputations are called "conditioned reflexes.
This article makes many fine points explaining the ability of computational methods. However, the main ability this article fails to take into account is that humans' minds are much more complex. This means that the human mind also incorporates experience, emotion, meaning, etc. in the equation. The pigeon's mind is not as complex; almost like a simple, very simple computer.
Reply | Report Abuse | Link to thisThe subtitle of this story, "Are Creatures Better Than Us at Computation?" is curious. Aren't humans also "creatures"? Perhaps Mr. Paulos is a "speciesist" -- he assignins different values to beings on the basis of their species membership. He is not alone. Many people seem to disclude Homo sapiens when referring to "animals." A pity.
Reply | Report Abuse | Link to thisNice summary....
Reply | Report Abuse | Link to thisWE HAVE EVOVLED WITH INSTINCT....AND THEY REMAIN IN US WITH MORE MATHEMATICAL ACUMEN THAN DO ANIMALS.....HOWEVER WE LOST THEM AS WE BEGAN TO DEVELOP DEPEND AND USE OUR MINDS AND OUR PRAGMATIC THINKING SKILLS TO GET ABOUT....WE STILL DO HAVE THE LIBERTY TO REGRESS TO OUR INSTINCTUAL POWERS...ITS A MATTER OF CHOICE.....WE FOLLOW INADVERTANTLY...ON AGAIN...OFF AGAIN...THAY ARE THE MOST DEPENDENT SENSORY DATA THAT WE RECIEVE.
Reply | Report Abuse | Link to thisPOOR US CAUGHT BETWEEN GOD AND BEAST....
I am not a statistician, just an engineer, but it appears to me that the Monty Hall problem mentioned in this article ignores a very important fact: the odds of winning when there are three doors available are effectively 1/3. However, once one door has been opened, the number of choices is only 2 and not 3! There is no way that a 1/3 probability can apply to a number of choices equal to 2. Affirming that the odds have not changed, once one door has been opened is to forget the definition of probabilities, which is expressed by the number of events that meet a certain condition, divided by the total number of all possible events. If the conundrum mentioned was true, it would be possible to influence the outcome of any choice without changing anything in the initial configuration of the problem. Except possibly for quantum phenomena, the simple knowledge (measurement) of one state cannot influence the state of the others.
Reply | Report Abuse | Link to thisI have a different take on why pigeons beat (adult) humans at the repeated Monty Hall problem. It's about our tendency to rely on heuristics rather than learning from new experiences: http://roslyndakin.com/archives/909
Reply | Report Abuse | Link to thisRoz Dakin
(biology PhD student & aspiring science writer)