Many Animals Can Count | Hacker News Reader

Many Animals Can Count

nytimes.com

130 pointsdnetesn72 comments

It's not scientific, and based purely on my own observation, but I'm reasonably sure that one of my cats can count to a limited degree.

He's a rescue on a special diet for his weight, as we have a small scoop to measure out his portion. Both he and the other cat get two scoops each. I normally put one in his bowl -- which he starts eating immediately -- then two in the other cat's bowl, then his second in his bowl. He stops eating and watches each scoop being poured into the bowl.

He seems to be able to keep track/count of how many scoops each bowl gets, even if I vary the order they're delivered in. He'll switch to the other bowl if it gets an additional scoop, even if it gets one full scoop and two half scoops. He seems good at 'counting' the number of scoops, but poor at judging the quantity of kibble in the bowl -- he'll unfailingly pick the bowl with more scoops even if it has the same or slightly lower quantity of food in it. He only notices a quantity difference if it's reasonably large.

How do you know the cat isn't merely opting for the bowl that most-recently had food put in? Can you please test this and get back to us?

I think this actually calls for a whole series of tests. Feel free to do a "show HN" with your test plan.

Because the cat doesn't switch bowls unless a bowl gets >2 scoops.

One way to test this would be to use a scoop that's 2x bigger than the other scoop, and putting in 3 scoops using the smaller scoop vs. 2 scoops of the bigger scoop.

Tried that by using three half-ish full scoops against two full scoops. He always goes to the bowl which has had the highest number of scoops in it, even though it might actually have a lower quantity of food in it. He seems to be counting rather than comparing quantity, because his trigger is the other bowl getting +1 scoop versus his.

Can we measure when he loses count by using many small scoops? I expect if his current bowl has passed a certain threshold of scoops he won't bother switching no matter how many scoops are going there.

Bowls aren't that large y'know

You need a tall but narrow scoop and a short but wide one (https://en.m.wikipedia.org/wiki/Conservation_(psychology)#Li...)

I've tried to catch him out like that with a couple of variation, and he always sticks with the bowl with most scoops. I'll put a single scoop in his bowl -- which he starts to eat straight away -- then three scoops in the other bowl, then a final scoop in his. He stays with the other bowl, which has had one extra scoop of food, even though his own bowl has had the most recent scoop added to it.

If I put two scoops into his bowl, and two into the other, he stays with his bowl. He only switches when a third scoop goes into the other bowl. He's been consistent with this since I noticed him doing it, and I'm not sure how long before I noticed he was doing it that he started doing it.

Thanks for the good science!

Given my cat has figured out how to open three different kinds of doors (handle, slidding, and even knob) I'm sure they can figure that out.

Hell, my cat seems close to figuring out how to turn on our fire place. She goes and sits by the switch (out of her reach) and meows until we turn it on, then runs across the room to lay by it.

I'm confident given sometime they can count as well. Likely this would help them catch mice and what not, if they know how many there are.

Sounds like she isn't close to figuring it out, she already has :)

Definitely - the easiest way to get something done is to have someone else to do it. Taming is a two-way process.

The cat I had growing up had similar skills with doors, among other annoyingly intelligent behaviors. The only thing saving us from world wide cat domination is that cats aren't particularly social and don't really teach their young these skills.

> world wide cat domination

I'm careful to never let my cat have access to my computer. Otherwise she'd get on the Intercat and plot the Cat-astrophe.

It might already be too late: http://infinitecat.com/infinite/cat1.html

I can see some evolutionary advantages for a predatory animal like the cat in being able to subitize[1] (I suppose cats are also small enough to be prey themselves historically, so just as useful to count threats as opportunities). My cat like to turn on my bathroom faucet to play with the water, and will often unscrew the drain stopper once he's bored with that. I have to keep the drains closed and wire ties on the taps...

1: https://en.wikipedia.org/wiki/Subitizing

Historically? Round us, there are various predators (wild and feral) that would happily feed on a cat - hawks, owls, goannas, snakes, foxes, wild dogs. Mainly nocturnal, we keep our cats in at night (so they don't prey on native nocturnals themselves too). Plus our dogs roam the home yard, which helps keep predators at bay. We've had sheep killed though, and chickens, plus a rabbit that only has one ear left. People sometimes talk about a "natural death" as if it is some kind of peaceful alternative - but most deaths in nature involve being eaten alive by another animal.

Clever Hans Effect

https://en.m.wikipedia.org/wiki/Clever_Hans

It's definitely possible that's what's happening. He's never looking at me when he does it -- he's always eating, facing away from me, and I'm placing scoops into the bowls from behind him. I don't rule out that I'm reading too much into it, or seeing something that isn't there; I've tried to be 'scientific' about it, but I'm under no illusion that what I'm doing is in any way hard-scientific.

Would the cat be able to keep tracking of 3 or more bowls?

what if he is just switching because there is more in the other bowl?

The article implies but carefully doesn't state that all humans count. In fact at least one unintegrated tribe doesn't really count although like these animals they can tell that eight of something is more than three of the same thing. Adults from the tribe show no interest in learning how‡, even though from our perspective it seems obvious that since they trade goods with outsiders they could benefit from acquiring this skill. There is a lesson there.

‡ A child from that tribe is just another human child, if it was somehow transplanted to New Jersey at age six months it would learn to speak "English" with a New Jersey accent, and yes, of course, it would learn to count.

You're probably referring to the Pirahã. https://en.wikipedia.org/wiki/Pirah%C3%A3_language#Numerals_...

I remember reading somewhere that Everett's claims about the Piraha (and the implications for Chomsky's theory of universal grammar - apparently Piraha language has no subordinate clause, which is supposedly a necessary component) were eventually debunked. He had apparently not learned the language well enough at the time. Can't seem to find any source for this now but it is alluded to later in that wiki article.

Back in college, walking across campus one day, I was listening to the birds chirping. I suddenly noticed that the one of the birds was counting, and I was stunned. The chirps were in groups from 1 to maybe 9, consecutive, with 2-3 seconds between each group, and then repeat. I have no doubt it understood the concept of a number & counting on some level. Maybe it was because the birds were near the engineering building...

Chickadees lengthen the number of "dees" in their calls depending on the perceived threat of nearby predators based on size/speed:

Templeton and his colleagues tested the alarm call responses of a flock of six chickadees against the presence of 13 birds of prey predators, which ranged in size from the 40-centimetre wingspan pygmy owl to the 140-centimetre wingspan rough-tail hawk. They also tested responses against two mammals, a cat and a weasel. Each predator was inserted into the chickadees aviary and tethered to a perch.

After analysing 5000 recorded alarm calls, the team found that the number of “dees” in the bird’s trademark “chickadee-dee-dee-dee” call corresponded to the size of the poised predator. Smaller hunters – which pose the greatest risk – received the most vociferous response. The alert causes the flock to mob their sitting foe in an attempt to drive it away.

https://www.newscientist.com/article/dn7570-chirpy-chickadee...

My dog has a anti-barking collar that will beep on one bark, then do a small zap on subsequent barks. After 30 seconds, it resets. She quickly learned (half border collie) that she can bark once with no ill effects. She then learned that after a while she can bark again. It is uncanny how she often gets close to 30 seconds, and almost never goes under. The times I have timed it she's been 35-45 seconds, which is a lot more precise than I would have expected. She seems to be more accurate when she paces during the interval, so I've always wondered if she's "counting" her steps.

This is a very well understood phenomenon and is probably not implemented by counting [0, 1].

0. http://www2.oberlin.edu/faculty/psimen/Site_2/Interval_timin... 1. https://scholar.google.com/scholar?hl=en&as_sdt=0%2C5&as_vis...

You give your dog electric shocks??

These things are usually quite mild, especially for a dog with thick fur, and they only have to get shocked a few times before they learn. A bark collar is a great alternative to noisy dogs staying in shelters their whole lives.

So maybe use them on people then? Sounds like a great alternative to a life of prison. But seriously, why wouldn't you, if you think it's good doing it to dogs?

edit: (can't reply yet) I was going to ask if you'd do it to your children. I guess you're joking. Maybe people do that, I've no idea, I hadn't heard of giving pets electric shocks. But I don't see a huge difference between doing that to dogs and to people, maybe you do.

I still haven't got approval on my shock collar for children, but I guess you're right, I should pivot and pitch it for law enforcement uses.

Tasers exist and deliver much more of a jolt than a dog collar, even controlling for size.

True, I didn't think of tasers. I think the idea of giving your own loved ones (human or animal) shocks is a different thing though...isn't it?

Downvoters to my previous comment, could you explain why? thanks.

I see where you're coming from but there's a communication barrier between you and a dog that doesn't exist with children. That's without getting in to the rights of humans vs animals on which rational people can disagree. Most people probably wouldn't lock their kids in a kennel either but apparently that doesn't bother dogs at all.

> I was going to ask if you'd do it to your children.

Disciplining children when they do something undesirable has been done since we were swinging around in trees and probably before then. The punishment method has varied from belts, to paddles, to canes, to time-outs. The pinch of an electric shock would work but isn't necessary since we can communicate with children.

BTW, did you know that electric shock has been used on bed-wetting kids since the 60's?

No I didn't! Does it work? Now I'm ashamed I immediately asked that. "Would you want it used on you?" sounds like a better question, applying to the taser and dog examples also. I'd answer no, maybe others would say yes.

If I'm absolutely refusing to be reasoned with, only respond to immediate feedback and testing the limits over and over?

Yeah, go ahead and put the non-harmful zapper on me.

(Taser is in a different class entirely, not very relevant.)

Bark collars also have the benefit of calming a dog down. By preventing a dog from getting into a barking frenzy.

As a herding breed, she feels the need to control situations, often circling other dogs or children or taking away toys she deems dangerous (e.g. sticks, squirt guns). When the collar is on she immediately relaxes because she has effectively been relieved of duty.

Generally speaking, no. She learned very quickly how it works and knows that when the collar is on, she shouldn't bark (more than once). She only wears the collars in situations where barking is not helpful. She is free to bark at intruders and when she's playing with other dogs.

There is a way you can "count" steps without actual counting - if you're humming a tune or thinking of a poem with rhyme and rhythm.

Maybe dogs could "bark" in their heads for similar purposes.

i would imagine its possible to get a feel of what 30 seconds is without having to count a certain series of numbers. being shocked would probably force you to figure it out a lot quicker

More surprisingly so can some plants: https://nytimes.com/2016/02/02/science/the-venus-flytrap-a-p...

The plants basically use electrical charges to stimulate their cell and after X simulations an action is taken (like closing a trap).

The linguistic components are a bit overblown, at least as far as extending into the past. Just English to reconstructed Proto-Germanic, dropping any PG endings, and glossing over things like long vowels:

one: /wʌn/ vs /ɑi̯n/

two: /tu/ vs /twɑi̯/

three: /θri/ vs /θri/

four: /fɔr/ vs /ɸeð.wɔr/

five: /faiv/ vs /ɸimɸ/

This is only to early AD times. Pushing back into Proto-Indo-European gets weirder; you lose Grimm's law. Considering I've had trouble asking for a "map" in a Spanish train station (/mæp/ vs /mapa/), I don't see these being anywhere close to understood.

We had a cat that could count. She would show at the dining table during desert because she knew she was allowed to "clean" the desert plates. As soon as somebody finished, she got the plate ( or bowl ).

This cat retreated to her lair after she got all plates, whether there 2, 3 or 4 persons at the table.

Other cats in the household developed the same pattern ( showing up, cleaning plates ). But these cats had to signaled explicitly there was none left, otherwise they would stay around and keep asking.

I've got a counting dog. For much of her life there were 4 people living in the house. Intermittently through the day she would walk around the house until she counted 4 people, then settle down. It didn't really matter which 4 people it was, just that there were 4, if there were more people in the house she'd stop at 4. As children moved away she'd have bad periods where she couldn't make quota and would keep searching. Eventually she'd update the target house population and only count to 3 or now 2.

That's so cute!

Is it a herding breed?

My sister's dog is the same way with counting people in the house. She's a rescue, so we aren't sure exactly what her lineage is, but she has a color pattern somewhat reminiscent of a border collie, and she tries to herd people.

More likely the cat could still smell the food left over.

> like the ability to judge whether a sentence like this is true: “There is no non-vanishing continuous tangent vector field on even dimensional spheres.”

That's the statement of the Hairy ball theorem, by the way. https://en.wikipedia.org/wiki/Hairy_ball_theorem

I'm reminded of that scene in Rain Man where Dustin Hoffman's character instantly counts exactly how many toothpicks a waitress drops. No idea how realistic that was, but perhaps some humans are able to use those circuits dedicated toward counting that have long gone dormant in our species.

I blanking on keywords/sources right now, but I remember learning about this in college.

The gist was that we have have on O(1) counting system for small numbers and an O(n) system for larger numbers. It takes the same amount of time to count 3 apples as 5 apples cause you can just instantly perceive that magnitude. But it takes about twice as long to count 40 widgits than 20, cause you have to look at each one individually.

It seams reasonably that the threshold for the two systems would vary in different individuals.

Keyword: Subitizing - https://en.wikipedia.org/wiki/Subitizing

In Rain Man, Raymond sees three groups of 82 toothpicks instantly. The waitress recognizes instantly that there are 4 toothpicks remaining - that's a much easier number to see instantly.

I believe that the ordinary maximum that people subitize is 4. I can believe that the threshold may vary between a normal 3-5 up to something as high as 10. And when playing fast-paced card games with friends, I think that my range is much lower and theirs may be much higher! But 82 is just unbelievable.

He's portrayed as an autistic savant, so I don't find it entirely implausible. There are documented cases of autists showing extremely impressive performances in arithemetic and memorisation, so why not subitizing too?

"Laurence Kim Peek (November 11, 1951 – December 19, 2009) was an American savant. Known as a "megasavant", he had an exceptional memory, but he also experienced social difficulties, possibly resulting from a developmental disability related to congenital brain abnormalities. He was the inspiration for the autistic savant character Raymond Babbitt in the movie Rain Man."

https://en.wikipedia.org/wiki/Kim_Peek

I wonder if you can train yourself for higher numbers.

It is pretty eerie to see a reference to Aleister Crowley in a Wikipedia article that is not related to the occult.

I remember having learned that the maximum is somewhere around 7 for the average person. So most people will easily recognise 1-5 apples, find it slightly harder to recognise 6 and beyond 7 they most likely have to count or split them into smaller groups.

When I was young I heard someone claiming that Baboons could count to 3. The proof was that corn farmers learned to scare off raiding Baboons by hiding in the field (with a rifle). However, if a farmer was seen to go into the field, the Baboons waited until he or she came out before raiding. The solution was to send four farmers in, and three out. This apparently fooled the Baboons. At least until a Baboon named Isaac Babewton came along....

Dumb joke notwithstanding, the fourth farmer remains in the field? How's that 'fooling the baboons'? Or is the whole comment supposed to be nonsense?

The implication is that since they can only count to 3 they think it's safe to enter after 3 of the 4 leave. This allows the remaining one to shoot at the baboons.

No, it is supposedly the technique that was used by farmers in the Transvaal to discourage baboon packs from raiding their corn fields. The baboons apparently could not distinguish between groups of 3 and 4 people, so they did not realize that someone was waiting to ambush them in the field. Sorry for the bad joke. I should have left that out.

Humans have this ability too. It's called subitizing.

I'm glad you introduced this term vis-a-vis counting. I would distinguish between the experiencing/perceiving a quantity/magnitude of something (e.g., proportional to some stimulus) and the abstract apprehension or quantification of a quantity.

I was at an elephant rescue in Thailand and the people there said you always have to give each of them the same number of bananas because they count exactly how many their neighbor gets.

Equal pay for equal work.

You certainly don't want to have a disgruntled elephant close to you.

So can any neural network, we should not be shocked by this

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