# Gorillas as Statisticians!

Chris

Chris lives in Austin, TX, where he once shook Willie Nelson's hand.

### 22 Responses

1. J@m3z Aitch says:

You know a bit about my interests, so I doubt you’ll be surprised to hear I’m not real surprised.

The question, though, is whether they’re rational to choose a smaller absolute amount of their preferred item just because its relatively more. Sounds like they’re as bad as humans in falling for relative gains vs. absolute gains. ðŸ˜‰Report

• Chris says:

Well, since they’re only getting one item from each bucket, choosing the relative over the absolute should be rational, right?Report

• James Hanley says:

But if the absolute gets them more of their preferred item than does the relative, that’s the rational choice, isn’t it? Or am I misunderstanding what they’re getting?Report

• Chris says:

Sure, if you’re not getting a single sample. Consider two populations:

a1111111110

b: 0000011100001110000000000111100001111100001111001110111100000000000

Now the second one has more 1’s, but the ratio of 1’s to 0’s is much smaller. I’m going to pick one number from each population. If I want 1’s, from which population am I more likely to get a 1? The answer is of course a., because the ratio of 1’s to 0’s is greater. Now, if I were picking all of the numbers from a population, I’d pick b., because it has more 1’s. If they’ve done that experiment, it’s not in the paper.Report

• James Hanley says:

Oh, I get it now. I thought they chose between different handfuls with the various distributions. Bad reading on my part. I withdraw my objection.

I love clever experiments like this.Report

• Chris says:

• James Hanley says:

Nah,

“two buckets with different absolute and relative amounts of carrots and bananas. The experimenters drew one item from each bucket (emphasis added)”

Is pretty clear.Report

2. Mike Schilling says:

Ook!Report

3. Reformed Republican says:

It’s not even Monkey Tuesday yet.Report

• Chris says:

I actually thought for a minute, “Wait, we have monkey Tuesdays?”Report

• Mike Schilling says:

Except in Chicago, where there ain’t nothing for Monkey Tuesday to do.Report

4. Glyph says:

1 comment: I wouldn’t want to be the researcher who gives the chimp a carrot rather than a banana. Those things can rip your face off.

And 1 question, which will betray my ignorance (and may have been covered under “several additional experiments ruled out alternative explanations”):

Isn’t this just a fancy description of “pattern-matching”, which all living organisms utilize to find food (among other things)? We can gussy it up in statistical terms, but isn’t it, at root, the equivalent of a monkey thinking “when I break open the small red gourds, lots of my favorite grubs are often inside (along with a few yucky beetles); but when I break open the larger yellow gourds, lots and lots of yucky beetles are often inside (along with some of my favorite grubs). So the small red gourds are a better bet.”

I mean, that IS an “inference about samples drawn etc.”, but isn’t it just the usual “perceive a probable pattern, then play the apparent odds for gain”, which we already knew all living things must do, or die?

Am I missing some deeper insight, or do I misunderstand the experiment?Report

• Chris says:

A few things. First, keep in mind that the apes only saw the contents of the bucket for a few seconds, and the “patterns” (which, within each distribution, would be random) they would see would have to tell them, in order to get these results, that there is more of my preferred food item (let’s say bananas) than my non-preferred item (carrots) in Bucket A, and more carrots than bananas in bucket B, regardless of the absolute number of carrots and bananas in each (because the same patterns might also say, in the later experiments, there are more bananas than carrots in Bucket A, but there are more bananas in Bucket B than bucket A). Distinguishing between these patterns: the differences in absolute number between the two buckets, and the relative differences within each bucket, if it is “pattern matching,” is a pretty complex form of pattern matching. What’s more, merely recognizing the pattern may not be enough to result in an inference about samples. That is, it’s entirely possible that, without a particular reasoning capability, the pattern matching algorithm just says, “It’s more yellow over here (Bucket B) than over there (Bucket A), so I should pick that hand!” In other words, even if we could explain this as simple pattern matching, it would be an impressive example of reasoning from patterns, an example that, until recently, we thought limited to human adults (we now know that human infants are really, really good at it, under the right conditions).

That said, we know a few things about nonhuman numerical discrimination that suggest there’s more than simple pattern matching going on anyway. First, we know that primates (including monkeys, not just great apes), some birds (parrots, crows), and at least some toothless whales have the ability to recognize relative numerical quantities (e.g., 4 vs 5) in ways that are not explicable with simple pattern matching (you’ll have to take my word for that, unless you want a much longer post, or to read the papers, which I will happily link you to).

Second, we know that non-human primates, maybe some birds, and maybe some toothless whales, along with human infants, can subitize quite well. That is, they can recognize small numbers (for great apes, <=4, for human infants, <=3) pretty much instantly, in ways that are not explainable via simple pattern matching. I imagine, though I don't have the paper in front of me to confirm, this is why the researchers chose 4:1 ratios in their first experiment.

Third, we have learned over the last decade or so that great apes are almost as good as us at discriminating absolute and relative numbers, again in ways not explainable via pattern matching, in very predictable ways (specifically, obeying Weber’s law).

So, while the researchers didn’t specifically test a simple pattern-matching explanation, what we know about primate numerical abilities, along with the nature of the task (picking a single sample based on the distribution) suggest that something more was going on.

Like I said, I’m happy to provide references if you’d like. There’s some really interesting stuff in there, and some really elegant experiments. Plus, crows are probably smarter than us, the sneaky little bastards, though perhaps not as smart as dolphins or mice.Report

• Glyph says:

Thanks. I realize now that I misunderstood the experiment, and thought that the apes were choosing their buckets after having gotten a “hit” or three (that is, achieving ‘success’, then tending to do the same thing that got them something they liked last time. I missed the part where they were shown the buckets’ contents first).

Also, if I ever get that repetition post together (yeah right), I had a little section on pattern-matching which actually touches on apes and corvids and cetaceans etc. So I will definitely want you to take a look and make sure I have that part right.Report

5. Shazbot11 says:

Dr. Zaius proves the Well-ordering theorem without the Axiom of Choice by drinking his own pee!

Report

6. Michael Cain says:

And pigeons consistently figure out the Monty Hall problem. While humans, even after being given an explanation and shown simulations, refuse to believe the answer.Report

• Chris says:

Yeah, I took a computational modeling course several years ago, and one of the other students in the class was an applied math guy who absolutely refused to believe that it mattered whether you switched or not, and came to class one day with a really long mathematical explanation for why he was right. This despite the fact that the assignment had been to write Matlab code that would simulate the problem, and everyone’s simulation had shown (over millions of trials) that you should switch. It was amusing and sad at the same time.Report

• Michael Cain says:

Wonder how he passed a basic probability class? Hell, you don’t even have to use conditional probability, you can just enumerate the nine possibilities and count things up. Stick wins in three of the nine, switch six times. Or assume that you’ll always choose door one as your initial selection and there’s only three possibilities, of which stick wins once and switch twice.Report

• Kazzy says:

How do pigeons figure it out and, more importantly, how do they demonstrate it?Report

• Chris says:

Kazzy, here’s the paper:

http://people.whitman.edu/~herbrawt/HS_JCP_2010.pdf

How they did it was with simple operant conditioning. The pigeons were trained for 30 days (10 trials the first day, 100 by the 5th, and 100 every day from that point on) on an apparatus with 3 keys. At the beginning of each trial, white lights over each of the keys turned on. When the pigeons pecked one of the keys, the lights all went off, at which point two lights (including the one over the key they pecked) turned back on, this time green. The pigeon then had to pick which key to select. The reward schedule was consistent with the Monty Hall probabilities: switching was right 2/3 of the time, staying 1/3.

On the first day, pigeons selected the same key more than 60% of the time. By day 30, they switched keys almost 100% of the time.

I will say this: I imagine that if we gave humans 100 trials a day over 30 days to figure it out, we’d switch about 100% of the time on day 30 too.Report

• James Hanley says:

if we gave humans 100 trials a day over 30 days to figure it out, weâ€™d switch about 100% of the time on day 30 too.

And understand the logic of it just as well as the pigeons, too.Report

• Mike Schilling says:

It’s common for intelligent people, even famous mathematicians to have bad intuition about probability. When Marilyn vos Savant first wrote about the Monty Hall problem, a lot of mathematicians write in to say she was wrong. Which I find excusable because:

* the result is very unintuitive
* she didn’t state the problem carefully enough to make the situation unambiguous
* it was Marilyn vos SavantReport