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Bees can link symbols to numbers, study finds (phys.org)
163 points by dnetesn on June 5, 2019 | hide | past | favorite | 63 comments



>> Researchers have trained honeybees to match a character to a specific quantity, revealing they are able to learn that a symbol represents a numerical amount.

I don't know if this is very convincing. From what I see in the images shown in the article, the "specific quantities" are represented by different arrangements of various symbols- squares, stars etc.

The article doesn't say whether these arrangements were randomised in each image.

For instance - the number "3" could be _always_ associated with the same arrangement of any symbol. Say, a triangle formed by three identical symbol. In that case it would be impossible to know whether the bees learned to count the shapes or just identify their arrangment. Learning to identify a triangle doesn't say anything about the ability to identify quantities.

The fact that neither of the two groups trained on the two different tasks (character-to-quantity and quantity-to-character) could generalise their learning to the opposite task also doesn't bode well. It is exactly what you would expect to see if the setup for each task had some other, uncontrolled for, variable that the bees "overfitted" to, rather than learning what is theorised they did learn.


> The fact that neither of the two groups trained on the two different tasks (character-to-quantity and quantity-to-character) could generalize their learning to the opposite task also doesn't bode well.

I thought about it, and have found a similar phenomenon in my own experience. English is not my native language, I learned English mostly by reading books in English. I knew a loads of words from a several of authors and could grasp any grammatical construct easily. But I had a big problem with speaking or writing: I couldn't find words to express myself. I know words that means what I want. When I meet words, I could connect them to their meaning easily, but the reverse doesn't work so good. With a practice it becomes easier, but I guess I have to use a word to express myself at least once to master this word to a point, when I could remember it when it is needed.

There is one more detail, maybe unrelated, I have a great troubles when I need translate English into Russian (my native language). I understand an English phrase, but I couldn't find Russian words to match English ones. Though it is an easier task than to find an English word which I know but haven't used before. This task also benefits from practice.

Mind is a complex machine, sometimes two-way associative link could be established only by training this link in both directions.


>> I knew a loads of words from a several of authors and could grasp any grammatical construct easily. But I had a big problem with speaking or writing: I couldn't find words to express myself.

That happens, for sure, but we know that humans can also perform this task well. So that is maybe not such a good example? We know that humans can generalise learning very well, in general.

I mean, just looking at a single person's ability at a task doesn't help us understand the limits of human ability on that task.


> The article doesn't say whether these arrangements were randomised in each image.

It is a popular science retelling a story. In the original scientific article we can read

We used sets of stimuli with controlled surface area (set 1) and equal element size area (set 2) with achromatic properties (black elements on white background; electronic supplementary material, figure S1). The choice of stimuli for each trial was pseudo-randomized with regards to set (1 or 2), shape and arrangement of elements. Thus, bees were trained on both set 1 and set 2.

In Group 1, this test consisted of showing a sign as the sample and then a randomized set of abstract objects not previously seen by bees (set 3: random set with chromatic properties).

Your proposed possible mistake is a way too stupid for a modern experimental psychology.

> For instance - the number "3" could be _always_ associated with the same arrangement of any symbol. Say, a triangle formed by three identical symbol.

It is more interesting, I believe. I had not read the original article thoroughly enough to find out could this be as you describe. There is a figures with some stimuli, but I'm not sure that it contains all the stimuli (to be sure it needs more reading, not just skimming).

Maybe this issue needs more testing, but in any case it is impossible to catch all the mistakes like that. For example, our ability to see a figure formed by a changing symbols, it is a property of our visual processing. Bees could have some properties which we do not have, and it could be that their properties could allow them to see some shapes formed by symbols, where we could see just randomly placed symbols.

> The fact that neither of the two groups trained on the two different tasks (character-to-quantity and quantity-to-character) could generalise their learning to the opposite task also doesn't bode well. It is exactly what you would expect to see if the setup for each task had some other, uncontrolled for, variable that the bees "overfitted" to, rather than learning what is theorised they did learn.

Yes, it is the most interesting part, because it goes perpendicular to a common sense, and thus gives a direction to a subsequent research. It always work like this: an experiment (a good one does) reveals something about nature, but poses new questions. Then researchers all over the world start to spend their grants on a sequels for the first research. At some point the number of articles becomes overwhelming, and several especially proficient scientists read all of them, studying methodology, combining data from different research into one big data set, making statistics, and finally they'd write a meta-research with a few hundreds of references to experimental articles, trying to make sense of data.

Media just cherry-picking articles with a clickbait titles, and makes them even more clickbaity. The most interesting articles for a newcomer would be a meta-research articles, which do no sparky experiments itself, but analyze all the data they could reach.


>> In Group 1, this test consisted of showing a sign as the sample and then a randomized set of abstract objects not previously seen by bees (set 3: random set with chromatic properties).

Thanks for the clarification.

It's clear you find this subject very interesting. I guess I do too, but I'm very skeptical of claims like in the above article. I think it's very easy to fall prey to various cognitive biases while carrying out this sort of research, particularly when it comes time to interpret results.

This recent Aeon article seems to sum up my concerns (I am not affiliated with Aeon or the author of the article in any way):

How natural is numeracy?

https://aeon.co/essays/why-do-humans-have-numbers-are-they-c...


> Your proposed possible mistake is a way too stupid for a modern experimental psychology.

Bees have psychology now?


Not exactly. Non-human psychology is called ethology[1]. There are some differences (you cannot ask animal to fill a questionnaire or ask how it feels), but when it comes to an experimental psychology it is almost the same.

[1] https://en.wikipedia.org/wiki/Ethology


Seems like one set of researchers has had two breakthrough studies of bee intelligence. Has anyone reproduced this? I feel like for something this incredible, we should perhaps wait until another team can reproduce the results before getting too excited.


Reminds me of Neil deGrasse Tyson's comments on the "intelligence gap".

If bees can do this, how smart are we really? Compared to generally intelligent AI or extraterrestrials, the difference between our intelligence and a bees might not be much.

https://youtu.be/Tt0uV5d8tss


Your question is excellent but I sort of arrive at an opposite conclusion. Before I explain, I want to point out that bees and jumping spiders are exceptional as far as insect* intelligence goes.

The gist of my view is that evolution is the mother of all demo scene hackers. Imagine a programmer that build amazing AIs on whatever hardware you give it, whether a top of the line GPU or an old PIC microcontroller.

The AIs runnable on both will not be fully equicapable† but the fact that you could get the PIC to do abstract learning or image recognition and learning at all will be incredible. It's like the fact that you can get a strong Chess AI running in just a few kb doesn't mean that Stockfish9 is unimpressive. It's rather, that such a strong chess AI can exist given such few resources is impressive.

Regarding intelligent AIs or space aliens with more computational resources, I'm biased but, I do think they'd be impressed with what we can do with only 20 watts or thereabouts.

* Yes I know spiders are not insects.

† Corvids and parrots are sort of exceptions to this. They can outperform certain primates even though they have smaller brains, fewer neurons (even if still high) while using less energy.


The thing is, it's not that hard for an animal (or a machine) to do one thing that we do, sometimes even to do it better than we do. But doing everything that we do, in the same package, is really, really hard.


The thing that blows my mind about humans is how adaptable our bodies are to virtually any task, terrain, climate, etc.

Goats are, in general, much better climbers than humans. But the best human climbers are WAY better than the best goat climbers. For example, I've never seen a goat climb El Cap.

Beavers, on average, are much better dam builders than humans. But the best human dam builders are WAY better than the best beaver dam builders.

Rinse and repeat for nearly anything.


One thing I feel doesn't get as much hype compared to intelligence is just how versatile our metabolism is. Animals often have very narrow selection of what they can use for food, and adapting to different kind of food source is very difficult. Humans though can feed on almost everything, plants, meat, raw, cooked, carb-, fat-, or protein-heavy - not all of it is equally good for us, but our digestion system will take whatever you throw at it and be fine mostly.


Indeed. Orcas are found all over the world, from the tropics to near the poles, in more climates than nearly every other animal in the wild -- but they are still only #2 in terms of climate adaptability. #1 is humans.

As for building dams, beavers evolved to build dams. They build dams because they're beavers. When humans build dams, it's because at some point in the past, some humans somewhere intuited that a dam would bring benefits (perhaps more water for fishing), figured out how to build one, and passed that knowledge onto other humans who were otherwise cognitively completely unprepared to build dams. As the knowledge was passed on, ways to improve the dam-building procedures were invented, and better tools were developed and used, to the point where the average human-built dam far exceeds even the best beaver dam. That makes the human story even more compelling.

Tying it back to the OP, we've seen that humans can train bees to associate symbols with counts, and that's remarkable. But if we find evidence of bees spontaneously inventing numeracy in the wild, and teaching it to other bees, that would be really something. And we'd better get ready to welcome our new insect overlords.


I always think what the perspectives of a being that could live for millions of years and had the computing power and memory and sensors of all of Earths machines would be. I don’t think we could even comprehend the thoughts of this being.


If you zoom out, the market - or even further, our civilization - is such a being. Only couple thousand years old, and essentially developed its nervous systems only in the last few decades, but already its thoughts are incomprehensible.


Very true. That’s why I also think that you could easily classify an anthill as a single living being.


Yup. And the truth is, we might need to get comfortable with both. An ant is a living being, but it is also a self-propelled organelle of the anthill. Humans are living and thinking beings, but with near-lightspeed communication deployed worldwide, the whole humanity together becomes a superorganism that could be seen as thinking its own thoughts.


"the whole humanity together becomes a superorganism that could be seen as thinking its own thoughts."

And at this scale it's already impossible to comprehend the motives of this organism.


It may well be that we are subject to evolution, but the being is not -- in which case the situation would be really interesting.


As humans, we've left the regime of biological evolution a couple thousand years ago, ever since we've learned to talk and write. Our entire development now happens a couple orders of magnitude faster.


We haven't left genetic evolution, but we've started memetic evolution in parallel.


I suspect that being would get insufferably bored.


It would probably think up a way to strap boosters onto itself and cruise the galaxy. Beats hanging around here.


In the past week I've taken a better look at the work of John C. Lilly, who actually writes on the subject: the earth becoming encased in machine intelligence, which eventually exits the solar system, in search of its own kind. He's not as far as I know a fiction author, but merely recorded his floating tank visions.


How do I attach rockets to my brain?


What are you asking, exactly?

If you mean "you never said I had hands, gotcha", then yes you need to get hands first.

If you're talking about the physical task, I don't understand how that could be a problem. If you can move your body into a rocket, do that. If you can't, put a big dome over top, down to bedrock, and attach the rockets to the bedrock.


I should have been more precise, because even I don't understand what I meant anymore, & now can't even delete it.


In the book 2001 they don’t need rockets anymore but travel directly through space. Rockets are primitive ....


Not more or less than you within the constraints you live in.


"I am not an animal brain, I am not even some attempt to produce an AI through software running on a computer. I am a Culture Mind. We are close to gods, and on the far side. We are quicker; we live faster and more completely than you do, with so many more senses, such a greater store of memories and at such a fine level of detail. We die more slowly, and we die more completely, too."

Although, based on the novels I suspect the jump from a bee to human level intelligence is probably rather small compared to that from a human to a Mind.


So... it would get insufferably bored, then.


You are thinking too small.


> If bees can do this, how smart are we really?

Well, bees don't invent controlled experiments to test our symbolic reasoning, think through the results, form philosophical questions using arbitrarily complex language structures, and post them on the own worldwide information-sharing networks they invented. So I'd say there's a pretty big gap.

> Compared to generally intelligent AI or extraterrestrials, the difference between our intelligence and a bees might not be much.

Assuming that intelligence can be quantified, and that extremely higher values are physically possible, yes, the orders-of-magnitude difference between bees and humans might theoretically be dwarfed by some other comparison. Just like the size difference between a grain of sand and a mountain is not significant compared with the difference between the mountain and the Milky Way. But it's still a massive (get it?) difference.


that's an interesting thought tbh


How do we know the bees don't simply use a learned lookup-table rather than doing arithmetic?

During evaluation, did they present the bees with problems that they didn't see before?


But where is the line between a “learned lookup-table” and “actually doing arithmetic”?

Especially considering how numbers were presented to bees = number of shapes in a square (look at the second paper in my other comment).


How do we know that humans do not? My mental process for simple arithmetic does seem to involve multiple something that feels like lookup tables.


Yes, the difference is that you can synthesize numbers which are not (yet) in the look up table. It would be super amazing if one could show that bees are capable of doing that.


> Yes, the difference is that you can synthesize numbers which are not (yet) in the look up table. It would be super amazing if one could show that bees are capable of doing that.

Or rather, we can synthesize lookup tables from preexisting lookup tables.


Sure, but that extrapolation is called arithmetic.


>How do we know the bees don't simply use a learned lookup-table?

Perhaps by reading the freely available original paper[0], where we find that the bees were tested on samples with randomized positions, and which included shapes previously unseen by bees.

So the bees aren't using lookup tables to count.

We all, though, use lookup tables to map numbers to single digits: that's by definition. The digit 7 represents this many objects: * * * * * *; you need to memorize this after you learn to count.

The experiment doesn't establish the bees' ability to parse decimal notation (mapping numbers to character strings).

[0]https://royalsocietypublishing.org/doi/pdf/10.1098/rspb.2019...


> which included shapes previously unseen by bees

This only shows that bees can abstract away from the actual shapes, not that they actually count.


I use a lookup table for arithmetic. Figuring out 5*3 would take me a long time if I didn’t know already.


Exactly, that's why it takes an awkward long time multiplying two numbers greater than 10 in my head, anything less is instant.


I am sure there is an algorithm to split the problem into smaller parts until you can use your lookup table :). Just use it multiple times.


>How do we know the bees don't simply use a learned lookup-table

That was basically how i was taught times tables in school as a child, and many others.


Yeah, do they not teach times tables in school these days? O.o


I’m not sure if they teach the times tables anymore but the way they teach math has certainly changed a lot since I was in middle school. I volunteer as an after-school tutor and I have a really hard time when kids bring me the “common core” multiplication and long division. The kids do actually seem to learn math better with their criss crossy drawings that they do to “solve” the problems but I can’t wrap my brain around it.


They do teach times tables in schools still, at least in Ireland


Non-paywalled papers:

• Symbolic representation of numerosity by honeybees (Apis mellifera): matching characters to small quantities https://royalsocietypublishing.org/doi/10.1098/rspb.2019.023...

• Numerical cognition in honeybees enables addition and subtraction https://advances.sciencemag.org/content/5/2/eaav0961


bees can link symbols to symbols?


No. Small quantities are represented with previously unseen symbols in randomized positions.

This is what numbers are (cardinals, or equivalence classes of sets under bijection, if you wish).

So bees can count.


Don't most animals have the ability to learn associations? E.g. when the leash jingles the dog knows it is time to go for a walk. Not sure this is the same as humans doing arithmetic. Scientists seem quite anxious to make the jump from associations to human level abstract thought, for some reason.

Not saying it is impossible, but these kinds of studies seem very handwavy and not very careful with terminology.


I think the "abstract" part here was the concept of "three-ness" or "two-ness" - that the bees could see something that represents 3 and correctly choose the path with three shapes, regardless of what the shapes were.


Based on the picture of the experiment setup in the article, it's hard to infer the bee understands 'three-ness'.

Based on this reasoning, does the bee already understand 'flowerness' since it knows to get nectar from many different kinds of flowers?

Do dogs understand 'dogness' because they know to sniff the butt of any dog that crosses their path?

Pretty sure I can create a simple AI that can distinguish three of something under many different kinds and orientations within suitable constraints, and have that capability associated with another easily distinguishable visual code. Yet, I would never say I've made my computer understand 'threeness', as the computer has no abstract reasoning capabilities whatsoever.

In general, how do we know when something understands '____ness' in the way we understand '____ness'? Per my previous examples, either the article's meaning is trivial, or unsubstantiated.


How about you just look at the paper?[0]

The positions of symbols were randomized, and they used symbols previously unseen by bees.

The concept of three-ness (as a cardinal number) is just that: being able to identify sets of objects which can be put into 1-to-1 correspondence with the following set of asterisks: * * * .

The bees, according to the experiment, can do that.

Is this our understanding of three-ness? Maybe not; there's also the notion of ordinals (as in 3 is what follows 2, 2 is what follows 1, and 1 is where you start). We have at least two different notions for numbers. But the notion tested in the paper is good enough to do most mathematics with (cardinals and ordinals are kind of the same until you reach infinity).

[0]https://royalsocietypublishing.org/doi/pdf/10.1098/rspb.2019...


I won't deny it is a very interesting study and seems to be well put together.

However, the paper is trying to present the bee study as evidence that human cognition is on a spectrum with animals, instead of a unique thing not found in the rest of the animal kingdom as part of a larger project to identify whether/how human cognition could have evolved from animal cognition:

"Nevertheless, there is no evidence that any species apart from Homo sapiens have ever spontaneously developed symbolic representations of numerosity, which opens the question of which animals are capable of learning symbolic number representations, which are capable of generating such representations, and whether this implies a fundamental difference in the mental processing of Homo sapiens compared with other animals."

So, for the bee study to evidence an answer to their question, we need to know whether this symbol-to-numerosity association the bees learn is the same sort of thing as symbolic number representation that humans use. The study is certainly a good step in that direction, but it seems to me there is a more fundamental question that is not being asked. Are the bees really perceiving 'twoness' and 'threeness' in the cardinality sense you mention, or is there some analog property, such as shape surface area, general shade of picture (i.e. two will seem lighter than three), triangular configuration (three) vs dots (two), etc. that the bees are responding to instead of exact cardinality?

To take a contrary perspective, why couldn't the bee symbol to number association be the same sort of thing as the AI I mentioned in my previous comment? The AI can recognize 2 and 3 symbols effectively, but it cannot extrapolate beyond that, nor could we take the AI and build an arithmetic module out of it through some kind of incremental training. The 2/3 recognizer is a hardcoded piece of functionality in the AI that will never expand beyond its core functionality. Perhaps 2/3 recognition is part of the hardcoded bee behavior that is necessary for it to set landmarks and navigate. This is much different than human arithmetic capability, where we can learn about 2s and 3s through physical examples, and then realize there is such a thing as 'number' and eventually realize there are an infinite number of 'numbers'.

So, for these two main reasons, despite its well constructed sophistication, I don't see the study as very compelling evidence that the human cognitive ability is not unique and merely part of a continuum wherein the dial can be turned up from animal cognition to human cognition.


I expect one of these days I'll see an article titled "Bees proven to be Turing-Complete"


This really reminds me of the intelligent AI bees in Permutation City by Greg Egan


"Bee.js — a fast and modern bee framework written in javascript"


you don't need many neurons to do MNIST.


These creatures never cease to amaze me.




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