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Math Science

Honeybees Seem To Understand the Notion of Zero, Study Finds (sci-news.com) 154

A new study published in the journal Science finds honeybees are able to understand the concept of zero numerosity, joining the ranks of dolphins, parrots, and primates. Sci-News.com reports: The study authors set out to test the honeybee on its understanding, marking individual honeybees for easy identification and luring them to a specially-designed testing apparatus. The bees were trained to choose an image with the lowest number of elements in order to receive a reward of sugar solution. For example, the bees learned to choose three elements when presented with three vs. four; or two elements when presented with two vs. three. When the scientists periodically tested the bees with an image that contained no elements versus an image that had one or more, the bees understood that the set of zero was the lower number -- despite never having been exposed to an "empty set."

Honeybees Seem To Understand the Notion of Zero, Study Finds

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  • by Viol8 ( 599362 ) on Tuesday June 12, 2018 @06:11AM (#56770694) Homepage

    If they didn't understand the concept of zero or empty then they'd keep going back to flowers that had run out of nectar.

    Understanding quantity is a useful survival trait, I don't understand why some scientists find it so amazing that animals understand the concept of "none".

    • by AvitarX ( 172628 )

      Also, the concept of "0" seems very different than "none" to me.

      When I think "concept of zero" I think 10>2, since that's pretty much how the concept is taught (that it was invented/discovered and revolutionized mathmatics).

      • Re: (Score:3, Interesting)

        by Anonymous Coward

        Zero and none are not different, they are the same. Zero is the numerical notation for nothing.

        why is 10 > 2?

        Because 10 equals one ten and none ones. The revolution was assigning a symbol to a concept we all instinctively "get". Look at old Babylonian for math without a symbol for zero. They used empty spaces (nothing) to denote zero.

        • by gtall ( 79522 )

          You are arguing that extensionally, the two concepts are the same. However, intensionally (in the philosophical meaning of intension) the two concepts are different. The stock example is that Venus is both the morning star and the evening star.

          In Frege's terms, although the analysis is a bit different, the senses of morning star and evening star are different even though their references are identical. Here, we think of Frege's sense (Sinn) as the route to reference (Bedeutung) (see here https://en.wikipedi [wikipedia.org]

        • Zero and Nothing or Zero and Null really are different.

          For example if your credit card has a balance of 0 is different then if you do not have a credit card, or never had a balance.

          The balance of 0 means you have a paid an equal amount of money that you have purchased. Vs having no purchases or payment. This is factored in when calculating your credit score. If you have a 0 balance, your credit score will be factored in how much you have purchased and how much you had paid off. vs. not having a balance, me

          • by Junta ( 36770 )

            Now map this subtlety to the test of bees reacting to zero or none elements.

            The point is the distinction between those scenarios is not testable in non-sapient beings. The interesting nuance of zero being distinct from none is a human invention, and being amazed that an animal can tell nothing is there is a crazy eventuality of overthinking it.

            • by Bongo ( 13261 )

              Yeah, like everything, it’s with a context. Zero what? None what? And their experiment had to use a real world context. So it is arguable whether the bees “understood the concept” as if it is some piece of pure logic. Rather, their nervous system could fuzzily proceess the patterns. Just like animals won’t jump down from a height that’s too great, isn’t evidence that the animal understands the concept of gravity and acceleration and weight. It has some fuzzy processing of

            • I agree it is amazing overthinking here. All this study shows it that bees can be trained to understand negative correlations, e.g. fewer of these symbols is good. Until the bees demonstrate that they know zero is more than negative one, I think it is a big joke.

              • All this study shows it that bees can be trained to understand negative correlations, e.g. fewer of these symbols is good.

                Do you think it is remarkable that an animal can understand that 'fewer of these symbols is good'? I think such understanding is as valuable as understanding that "more of these symbols is good" in some cases. For bees "more flowers is good" -- learned lesson. Also for bees, "fewer yellowjackets is good", as yellowjackets are a natural predator for honey bees.

                As for the nonsense about the difference between "zero" (a current value) and "none" (no preexisting value) -- also not remarkable. Bees will be jus

        • Holy shit you're dumb.

          Zero is significant and conceptually different from none because it allows you to extend a numbering system beyond unary counting or some fucked up multiplicative system like the Romans had.

          • by ooshna ( 1654125 )

            0 is just a place holder for none. It happens to make the base 10 counting system very easy for us. Unless you're French.

            • Nope. 10 is not 1 and none. Further, every base (except base 1) is base 10.

              • by ooshna ( 1654125 )

                10 is one in the tens place and none in the ones. 202 is 2 in the hundreds place with none in the 10's and 2 in the 1s place.

                • How do you determine what those places are and what they mean, exactly? With the "none" concept and digit? Or the 0 concept and digit?

      • Actually, that was a step towards zero, but very much NOT what makes zero special or important.

        Using zero as a placeholder in a positional numeric system is natural... once you have a zero. But many (like the Babylonians) used various positional placeholder strategies without having a formal concept of zero.

        Zero in contrast stands on it's own. It's a formal, numerical symbol for nothing as a concrete concept, NOT just a placeholder. It's a necessary "pivot point" for much of higher mathematics. For exam

      • A new study published in the journal Science finds honeybees are able to understand the concept of zero numerosity, joining the ranks of dolphins, parrots, primates

        , and slashdotters counting girlfriends.

    • by asylumx ( 881307 ) on Tuesday June 12, 2018 @07:22AM (#56770852)
      Because they went to the zero case to RECEIVE a reward, which is the opposite of the instinct you described.
      • by Junta ( 36770 )

        Say instead of abstract number of elements, it was instead competing insects for the sugar. Then they would learn to prefer the less competitive environment as indicated by fewer elements. They learn a correlation, whether positive or inverse and they go with it to the natural conclusion of none. It would be odd if these natural mechanisms *did* short out when it goes from 1 to none, and yet we are repeatedly surprised to find that nature doesn't blow up at the complete lack of something.

      • How I understand it they did the numbered tests to train them, and once they were trained they were then tested for the first time with the empty card, not repeatedly with the empty card.

    • It's amazing because even humans living in Rome thousands of years ago created a way to write numbers but no way to write "none".

      • by epine ( 68316 ) on Tuesday June 12, 2018 @10:56AM (#56771822)

        It's amazing because even humans living in Rome thousands of years ago created a way to write numbers but no way to write "none".

        They had a way to write nothing: by writing nothing.

        The Romans were pragmatists. This saves paper. Imagine the cost of inscribing "zero Bugblatter Beasts" on every urn, vase, and ceramic dufflebag?

        Turns out, some nebbish recruit did invent zero, but the squadron leader spotted the unfamiliar symbol one day and then he said "what the fuck is this?" and somebody said "it means we didn't get any X in our rations this month" and then the squadron leader's veins bulged out of his neck while he barked "who's the jackass wasting a perfectly good resource to record what he didn't get?" and then the jackass had to run 100 laps around the Colosseum draped with a heavy marble placard reading "lion food / reward offered"—this while the people inside were cheering the lions (more than once he panted out excitedly "look, an elephant!" pointing at some unlikely bush when people got too close for comfort, while summoning yet another painful micro-sprint, and through this device he did avoid detection in the end).

        Never made that mistake again. Not ever. Neither did anyone else, which, of course, also means that no-one was foolish enough to write a line itemizing the empty set of damn fools (many of whom invented zero, but knew better than to write it down).

      • The way to write none was a dash, or "none" (with a long o, derived from nonus).
        How do you come to the stupid idea they had no way to write "none"?

    • Well, no. Bees can see that they've already visited a flower; the visitation itself marks the flower so they don't visit it again too soon—just because we can't see those traces doesn't mean they can't. Besides, flowers don't get 'empty' quite like that.

      Understanding none is an interesting thing; it wasn't part of our system of mathematics for a long time (though it's incredibly likely people understood 'none' before it was codified into our written math) and so that makes it interesting to us.

      I think

      • I think a lot of animals understand nothing. I don't think they necessarily understand that nothing is similar to zero and that nothing, being similar to zero, is a valid comparison against a quantity. The reason for this is that it's difficult for humans to adequately understand the difference between zero and nothing although they are able to infer nothing equates to zero when doing comparisons.

        I train you to select lower numbers and train you on 3 & 4 and 1 & 2. I am teaching you that the lower q

    • > I don't understand why some scientists find it so amazing that animals understand the concept of "none".

      /sarcasm Because dumb humans didn't (re)invent it until thousands of years later. What, an animal knew a concept before a human -- preposterous!

      --
      Homo Sapiens aren't the sharpest species in the galaxy They will advance to the next phase in development, Homo Spiritus, when they figure out how to live on the planet they were born on without money. Animals already figured this shit out millions of yea

    • by arth1 ( 260657 )

      Understanding quantity is a useful survival trait, I don't understand why some scientists find it so amazing that animals understand the concept of "none".

      Because humans have had a very difficult time with the concept.
      There are still many remnants of this aversion to empty sets. Many if not most people start counting at 1, not 0.
      The Jesus figure was said to have risen on the third day, less than two days after he died, because they counted the zero day as 1.
      A musical third is two whole notes apart from the base note, not three.
      Roman numerals don't have a zero.
      There is no year 0. 1BC was followed by 1AD.
      People in many countries still say "twelve oh five" ins

      • Many if not most people start counting at 1, not 0.
        It would be pretty pointless to start counting with 0, if that is indication the "first item in the basket", how would you count then items in an empty basket? Invent yet another meta zero? Like epsilon? And then in 50 years we have the same discussion again: most people start counting with 0, not with epsilon

        There is no year 0. 1BC was followed by 1AD.
        There is no temperature 0 either, there is the range from -1 to X and from X to +1, just like with BC and

        • by arth1 ( 260657 )

          People in many countries still say "twelve oh five" instead of "zero oh five" for five minutes after midnight, to avoid the zero.

          That is wrong again. They don't avoid the zero. They count like they are taught, they have two periods 12 hours long, one is the AM period, the other is the PM period, wow that was easy again.

          Easy because it's wrong.
          The lowest value of a clock is one o'clock, and the highest is twelve fifty-nine fifty-nine. But the clock starts at noon/midnight, not 1. People borrow the twelve from the preceding 12-hour period. Back when the 12 hour clock came to be, the numerical system in use did not have a zero.

          • The numerical zero exists thousand(s?) of years longer than a 12 hour numerical clock, which we have how long? 200 years?

            People borrow the twelve from the preceding 12-hour period.
            No, if at all they borrow it from the "preceding 12-hour mark!"

            • by arth1 ( 260657 )

              The numerical zero exists thousand(s?) of years longer than a 12 hour numerical clock, which we have how long? 200 years?

              You got this exactly wrong, I'm afraid. Sundials have been used since antiquity. Mechanical clocks came around in the 1300s, and were widespread by the 1500s. But Arabic numerals with a zero were resisted throughout the middle ages (partially for religious reasons; where there's nothing, there's no god, and god is everywhere went the argument), and only became commonplace in the 1600s. Before then, Roman numerals were used by almost everyone in the Western world. Which is why old clock faces have Roman

              • And modern clocks have a 12 there, because it is practical for looking at it, not because people are scared about a zero.

                But Arabic numerals with a zero were resisted throughout the middle ages Do you have any references for that? Never heard about such "nonsense" (not that you talk nonsense, but that people behaved that nonsense like)

                where there's nothing, there's no god, A zero does not mean there is "nothing", your idea about this is certainly nonsense. We always had creditors and debtors, and after the

                • by arth1 ( 260657 )

                  Here's a good article: https://www.livescience.com/27... [livescience.com]

                  Exerpt:
                  Medieval religious leaders in Europe did not support the use of zero, van der Hoek said. They saw it as satanic. "God was in everything that was. Everything that was not was of the devil," she said.

                  Wallin points out that the Italian government was suspicious of Arabic numbers and outlawed the use of zero. Merchants continued to use it illegally and secretively, and the Arabic word for zero, "sifr," brought about the word "cipher," which not onl

                  • Must be an american thing again ...
                    Medieval religious leaders in Europe did not support the use of zero, van der Hoek said. They saw it as satanic. "God was in everything that was. Everything that was not was of the devil," she said.
                    Van Hoek said this.
                    And you take it for granted? Arabic numbers/digits got introduced by a german monk, who later became pope. He picked them up in Spain. Hence there were no religious leaders against the zero.
                    There never was a 'conspiracy' against the zero. https://en.m.wikiped [wikipedia.org]

    • I guess some scientists are simply to dumb to grasp what the concept of zero actually means.

      Most known number systems have no zero, and beyond that don't even have a number system that is comparable with our decimal, octal, hexadecimal or binary systems.

      E.g. the roman, greek and hebrew numbers where simply other usages of letters, M for 1000, L for 50 etc. The "invention" of the "zero" made it possible to have number systems based on digits. Where every position of a digit has a different value, you all kno

    • It's notable because humans mathematicians struggled with the notion of zero. Roman numerals have the notable deficiency of having no way to represent zero, which caused huge problems and slowed down mathematical progress significantly.

      A lot of concepts that seem obvious to us are really just ways of thinking that were introduced at a young age. The idea that the sky is blue isn't even universal: https://www.dunnedwards.com/co... [dunnedwards.com]

      It's easy to mistake familiar concepts for obvious ones. But they aren't the sa

    • In fact, the test they gave the bees had nothing to do with recognizing quantities.
      What the testers were demonstrating was that
      more whitespace on the display -> more goodies.

      A display with 2 objects shows more whitespace than 3 objects,
      a display with 1 object shows more whitespace than 2 objects,
      and a display with 0 objects shows more whitespace than one with 1 object.
  • Or... (Score:5, Insightful)

    by RobinH ( 124750 ) on Tuesday June 12, 2018 @06:12AM (#56770698) Homepage
    Or they were trained to avoid the element itself. What's more likely, that an insect can "understand the concept of zero" or that it can combine two stimuli (I want to go towards this thing for the sugar, but I want to stay away from the element)?
    • Image processing (Score:5, Insightful)

      by Excelcia ( 906188 ) <kfitzner@excelcia.ca> on Tuesday June 12, 2018 @06:31AM (#56770744) Homepage Journal

      Or they were trained to avoid the element itself. What's more likely, that an insect can "understand the concept of zero" or that it can combine two stimuli (I want to go towards this thing for the sugar, but I want to stay away from the element)?

      Considering that insects don't have the same kind of image processing or, indeed, even the same kind of eyes, I find this far more likely than they are counting elements. It is far more likely that a bee is being trained to go where there is less overall of whatever color it is the "element" is and gravitating that way. Or, and this now strikes me as being even more likely, they are going where there is more of the background. A human can look at an image and with our image processing, break it down into elements and count them. Our brains do this in the background and it might not even strike us that the image with fewer elements has more background because that's not how our brains work. It is how our brains work so strongly that it is also appearing as a bias in the way these results are being interpreted. But from a color, shade, or pixel perspective, it can be equally said that the image with fewer "elements" on it also has more background.

      I must say I find it frustrating the article has no reference to what the images were of or what the "elements" were that the bees were supposedly counting.

      • by orlanz ( 882574 ) on Tuesday June 12, 2018 @07:16AM (#56770834)

        That would still count as zero recognition. If it's going after more of the background. Background is a concept in itself. It needs something in the foreground to define it. Else the bees would hover toward any similar color at various distances in the general environment.

        But zero means no foreground color. Nothing to define the background. So normally the bee should be confused or gravitate toward the single "option". If they trained the bee with zero, then that's leaves it kind of open. But they didn't. They trained it with two colors where one had less. There was always two options with both colors. Then the bee recognized zero which it was never trained for... thus it was already knowledge it had.

      • by dos1 ( 2950945 )

        The symbols on the cards were filled with ink and differentiated in size, so it wasn't the effect of gravitating towards less inky card, it was really counting.

    • by Anonymous Coward

      Did they repeat the experiment but instead of rewarding the bee when it selected the image with fewer elements, instead they rewarded the bee when it selected the image with more elements (including the occasional introduction of zero)? Perhaps that sort of control would have determined whether your assertion is true or not.

    • I want to go towards this thing for the sugar, but I want to stay away from the element

      So? That pretty much looks likes subtraction, which is how you arrive to zero to begin with. It feels natural that the bees information processing follows that logic.

    • I think you will find out that most species "understand zero" if it is about the number of predators in sight.
      • by arth1 ( 260657 )

        I think you will find out that most species "understand zero" if it is about the number of predators in sight.

        This seems like a far more likely explanation, and yes, I did read through the original post. My take is that the scientists here jumped to conclusions based on confirmation bias, and could just as easily have "proven" that they bees had a concept of 3/7.

        Less is less, and if less is good, go for less.

    • by Bite The Pillow ( 3087109 ) on Tuesday June 12, 2018 @11:28AM (#56771974)

      they did 3 years of control studies to eliminate any other possibilities.. Its right there in the article you incurious pseudointellectual.

    • Or they were trained to avoid the element itself.

      So you're saying they understood the concept of zero of an element?

  • Smart bees! (Score:3, Insightful)

    by hcs_$reboot ( 1536101 ) on Tuesday June 12, 2018 @06:25AM (#56770726)
    Understanding zero is comprehending the number of bees that will remain if we continue to use pesticides.
  • by Rei ( 128717 ) on Tuesday June 12, 2018 @06:26AM (#56770730) Homepage

    Their communication system alone is amazing. Their mental mapping when flying between locations is based on the direction of the sun, but they automatically adjust for how the sun will move (even at night or when it's otherwise not visible), in a manner that adjusts for latitude and the passing of the seasons. In the hive, they waggle dance to indicate the direction and distance to a resource (the static charges they build up can be perceived by nearby bees when they waggle). Moving straight up means "in the direction of the sun" - not "the direction of the sun when I last set out", but the current direction of the sun. Every second spent on the waggle before looping back to the start represents a kilometer of distance. A waggle dance is usually enough to bring another bee to within a couple hundred meters of a target, wherein they start searching visually. Bees don't blindly listen to waggle dances; if they're having good luck on their own, they're unlikely to listen to it, only bees that have been having trouble finding resources tend to follow them. If a bee had a *bad* experience with the location being danced to - found no resources, found a dead bee, etc - there's a "NO" buzz frequency (380Hz) which they can do. The more impressed a bee is with their location, the more vigorously they waggle dance, while the more opposed a bee is to a location, the more it does its "NO" buzz; they can even end up getting into physical fights over the issue. Advocates of different locations can also get into fights with each other.

    It's easy to think of individual bees as mindless drones as part of a "greater whole", but they really aren't; they're impressive even individually. In addition to solar navigation, they also have landmark navigation, visual navigation to small targets, and they learn what sort of things pay good rewards (which as this study shows, can involve significant reasoning). Contrary to the popular image, the queen doesn't "give direction"; she's not a "leader". She just "smells nice", and other bees want to be near her. But beyond that, each bee is an individual.

    They're fastidiously clean. They not only will remove debris and any dead bees from a hive, but they're adamant about not defecating in the hive. Honeybees will literally hold it until they die if they can't leave (e.g. in the winter due to weather) rather than foul their own hive. And maintaining the hive is a constant struggle because there's an endless list of pests and predators that want to eat either the bees, their larva, or the honey; a hive is such a tempting resource.

    Preserving the honey is of course quite the task, and bees have specific climate requirements in general. They do amazing job at managing the internal climate. Some bees will act like air conditioners, fanning with their wings to create airflow through certain areas. They'll add or remove propolis to the hive to adjust how "weathertight" it is, to get the right amount of airflow without letting in pests. In the winter, they cluster together for warmth in the "winter cluster", which slowly migrates across the comb, eating their honey stores as they go; their collective body heat keeps them from freezing, and they minimize their surface area by clustering together. Some (non-European) honeybees have taken this even further - made famous by The Oatmeal, Japanese honeybees fight off attacks from otherwise impervious Japanese giant hornets (aka real-life Tracker Jackers) by clustering around them and raising their body temperature to the point that they survive but the hornets effectively die of heat stroke.

    • by vikingpower ( 768921 ) on Tuesday June 12, 2018 @07:12AM (#56770816) Homepage Journal

      Son of a beekeeper here. All correct! Also, they have fairly intelligent swarming behaviour. When times are "economically" good, the sexless worker bees charged with feeding the queen will begin feeding certain larvae the special queen food, so these larvae - instead of becoming sexless workers - become queens. One of the new queens will then take part of the swarm with her (sometimes it will be the old queen btw). Individual bees decide on joining or not joining the outgoing swarm. We know they have a decision mechanism involving criteria - we simply don't understand the mechanism yet. Bees are fascinating.

      • by Rei ( 128717 ) on Tuesday June 12, 2018 @08:07AM (#56770980) Homepage

        Son of a beekeeper

        You know, I'm going to have to start using that as a minced oath [wikipedia.org]. ;)

      • This is not entirely accurate. Swarms always contain the old queen; the new queen stays put. This is because the swarming event actually takes place shortly before the new queen(s) emerge -- the old queen leaves so there is no fight with the new queen.

        One of my hive swarmed this spring...it was an awesome event, although bittersweet. I felt some sadness about losing half the bees in that hive, but I also felt happy that I was sending a new colony out into the world.

        • by Anonymous Coward

          One of my hive swarmed this spring...

          I'd like to show you my collection of stamp.

          Oh look, there's a flock of goose.

          Thank you. I'll be here all night.

        • That actually is also not correct ... you simlpy repeat the schoolbook version.

          A hive can have many queens, albeit it is rare, each with her own state. Often more than one new queen is born, hence many queens swarm out. Depending on many factors, bees also fly out alone after they got seeded by drones.

          I felt some sadness about losing half the bees in that hive,
          Well, you could have offered a nice box for her to fly in, or simply migrated her by hand into a different box (that is how most bee breeders do it h

        • That is new to me. AFAIK it could be any of the queens. But I may be referring to outdated knowledge on Apis mellifera.

          Seeing a swarming event actually happen is, indeed, awesome. Although I have no bees now because of my way of life, last summer a swarm temporarily settled in a tree close the veranda windows of my house - the buzzing ! - and stayed there over night (a sweet, warm summer night, they'd chosen their moment well). Next morning they were gone, and I still hope they're doing OK for themselves.

    • by GuB-42 ( 2483988 )

      That's especially impressive considering that an honey bee only has a million neurons. For the sake of comparison, a mouse has 71 times that, and we are at 86 billion.
      And while it is true that bees don't have a large body to support, that's still a lot of intelligence packed into a small space.

    • In the winter, they cluster together for warmth in the "winter cluster", which slowly migrates across the comb,
      Actually when the winter time starts, the queen is breeding special warm up bees (and most of the remaining stock dies), usually about 50 or so bees that have very short wings but much bugger muscles than the ordinary workers. So they produce a considerable amount of warmth.

    • Waymo should develop a bee-driven car.

  • by dohzer ( 867770 ) on Tuesday June 12, 2018 @07:21AM (#56770848) Homepage

    Sure, they understand '0', but do they understand what happens when you put a '1' or a '2' in front of it?
    I bet they don't.

    • What makes you think that bees understand decimal? Humans have 10 digits on their hands and feet, so decimal was pretty obvious. Bees would probably use base 6.
    • Why is that relevant? You are describing two very different mathematical concepts. You can do mathematics just fine without ever counting in a decimal notation. Maybe bees use roman numerals.

      • Maybe bees use roman numerals.
        It is actually not very easy to calculate in roman numbers. Precisely because they don't use positions to indicate value and have no zero.
        Play with a roman abacus and you understand.

        • Oh I know, but it was possible. Heck to be honest it's hard enough to count in roman numerals :)

          • Yeah, it is possible, but calculations like multiplication or division were usually done by math geniuses in their mind.

            I guess if you simply 'grasp' two numbers like vii and viii you simply add them in your mind, too, and then rewrite them as xv.

  • by Anonymous Coward

    Maybe they're not counting dots, but white space area? More white space area is better, no concept of 0 required.
    That would be fact similar to how human babies learn count. At an early stage in development they only notice/care about differences in surface area. Show them 2 objects with a 50% surface area each and 1 object with a 100% surface area and they will regard them as equal. Only later on human babies distinguish between the 2 situations.

    • by Anonymous Coward

      Maybe they're not counting dots, but white space area? More white space area is better, no concept of 0 required.
      That would be fact similar to how human babies learn count. At an early stage in development they only notice/care about differences in surface area. Show them 2 objects with a 50% surface area each and 1 object with a 100% surface area and they will regard them as equal. Only later on human babies distinguish between the 2 situations.

      I know this is against Slashdot policy, but I did take a look at the original article in Science, and the training images had clearly different sized items in them, with the total area being about the same, so your area theory does not quite hold.

  • by DrXym ( 126579 ) on Tuesday June 12, 2018 @08:29AM (#56771062)
    Even in the case of zero the bee is still being shown a picture. In the bee's brain that might count as a "something" where this pure "something" is more attractive than that dirty "something" when it is collecting nectar. It might not be anything more than that.
  • by Anonymous Coward

    Now let's design an experiment to see if they can comprehend the countably infinite.

  • by DontBeAMoran ( 4843879 ) on Tuesday June 12, 2018 @09:57AM (#56771508)

    We took the concept of "nothing" and made a TV show about it [wikipedia.org].

  • Of course animals understand that no stuff is less than any amount of stuff. No lions is less lions than 1 or 2 lions.

    Zero is a symbolic representation. The innovation is assigning a symbol.

  • Are any known examples of creatures who *can* count, but who *don't* understand zero? In other words, creatures who can be trained to pick the image with the smaller number of elements, but who fail to recognize that an empty image contains fewer elements than an image that is not empty?

    That would actually be a more interesting result (I guess). I'm having a hard time getting my ahead around why this is an important question. I know that *written* systems for counting did not always use a symbol for zero

  • Do honey bees understand?
    slime mold can solve a maze , but I would not impart to it the ability to 'understand' that it is solving a problem.
    Honey bees recognize quantity , but that seems a vast a difference between that and understanding that nothing is a quantity or even recognizing quantity as a property.

    Do computers 'understand' the programs we write? certainly I could program some drones to perform the same task , would a person then claim the computer 'understands' quantity?

    Responding to a stimuli and

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