That honeybee study raised eyebrows, not just because it showed that an animal with fewer than one million neurons in its brain (compared with the human brain’s 86 billion) could treat zero as a quantity, but because bees and mammals diverged in evolution 600 million years ago. Their last common ancestor “was [barely] able to perceive anything,” Avarguès-Weber said, much less count. According to Nieder, who was not involved with the insect work, this implied that the ability to grasp the empty set and other numerosities evolved independently in the two lineages.

“A whole different neural substrate … produced such high-level cognitive capacity,” said HaDi MaBouDi, a cognitive scientist at the University of Sheffield in England. Unfortunately, researchers have so far been unable to study the neural activity of honeybees as they perform numerical tasks, making it difficult to compare their representations of zero with those of monkeys. To get answers about how and why the ability to quantify “nothing” evolved more than once, scientists realized they would have to explore the brain of another animal.

A Parallel History

And so Nieder and his team turned to crows, which haven’t had ancestors in common with primates for more than 300 million years, and which evolved to have very different brains. Birds do not have a prefrontal cortex; instead, they have their own “intelligence brain centers,” Nieder said, with a distinct structure, wiring and developmental trajectory.

Yet despite these differences, the researchers uncovered a familiar numerical understanding of zero: The crows mixed up a blank screen more often with images of a single dot than they did with images of two, three or four dots. Recordings of the crows’ brain activity during these tasks revealed that neurons in a region of their brain called the pallium represent zero as a quantity alongside other numerosities, just as is found in the primate prefrontal cortex. “From a physiological point of view, this fits in beautifully,” Nieder said. “We see exactly the same responses, the same type of code, represented in the crow brain as in the monkey brain.”

One explanation for the same neural framework evolving in such different brains is simply that it’s an efficient solution to a common computational problem. “It’s actually exciting, because it suggests that it’s just the best way,” Avarguès-Weber said. Maybe there are physical or other internal constraints on how the brain can process zero and other numerosities. “There could be … a very limited number of ways in which you can build up a mechanism to encode numbers,” Vallortigara said.

Still, just because crows and monkeys seem to be encoding an abstract concept like zero in the same way does not mean that it’s the only way. “It could be that different solutions have been invented during natural history, during biological evolution, to perform similar computations,” Vallortigara said. Researchers will have to study other animals to find out. In a paper just published in Cerebral Cortex, for instance, Vallortigara and his colleagues identified a brain region in zebra fish that seems to correlate with numerosity, although they haven’t yet tested the animals’ ability to assess zero.

Bees might also hold some surprises as the foundation for their numerosity becomes better understood. In a study published last year, MaBouDi and his colleagues “showed that the bumblebee counts by a fundamentally different strategy” when presented with up to four objects, he said. He thinks their findings hint that the mechanisms underlying honeybees’ grasp of numerosities, including zero, might indeed be quite different from what’s been observed so far.

But perhaps the more fundamental question about numerical abstraction in the brains of diverse animals isn’t how the ability works but why it exists. Why should animals have to recognize specific quantities at all? Why has evolution repeatedly made sure that animals can understand not just that four is less than five but that “four squares” is in some way conceptually the same as “four circles”?

According to Vallortigara, one reason might be because arithmetic ends up being so important. “Animals continuously have to do arithmetic. Even simple animals,” he said. “If you have an abstract representation of numerosity, this is very easy to do.” Abstracting numerical information allows the brain to perform additional computations much more efficiently.

That’s perhaps where zero fits in as well. If two predators enter an environment and only one leaves, the area remains dangerous. Rugani speculates that an animal needs not only to be able to subtract in this situation, but also to interpret zero as “the result of previously performed numerical or proto-numerical subtraction” — which the animal can then associate with particular environmental conditions. In this case, “whenever you reach the lowest value, which is zero, the environment is safe,” Rugani said. When foraging for food, zero can map onto a need to search in a different location.

Nieder, however, isn’t convinced. He doesn’t see a pressing need for animals to understand zero as a numerosity, since viewing it as an absence should usually suffice. “I don’t think that animals use numerosity zero as a quantity in their day-to-day living,” he said.

An alternative possibility is that an understanding of zero — and numerosity more broadly — might simply have emerged from the brain’s need to recognize visual objects in the environment. In 2019, when Nieder and his colleagues trained an artificial network to recognize objects in images, the ability to discriminate numbers of items arose spontaneously, seemingly as a byproduct of that more general task.

A Glimpse of Math’s Building Blocks

To Nieder, the presence of talents for numerical abstraction in animals indicates “that there is something already laid out in the brains of these animals … that may constitute an evolutionary basis for what in us humans can develop into a full-blown understanding of the number zero.”

But impressive as the animals’ accomplishments are, he emphasized that there are critical differences between how animals have been shown to conceptualize numerosity and how humans do it. We don’t just understand quantities; we link them to arbitrary numeric symbols. A set of five objects is not the same as the number 5, Nieder said, and the empty set is not the same as 0.

Even when animals can be trained to associate two items with the symbol 2 and three items with 3, “that does not mean they could put those symbols together to [get that] 2 + 3 = 5,” Dyer said. “Now, that’s a trivial mathematical problem for an elementary school student.” But experiments designed to test for that kind of symbolic reasoning in animals, he noted, have yet to be performed.

By taking this step beyond numerosity and building a symbolic system of enumeration, humans have been able to develop a more precise and discrete concept of number, manipulate quantities according to specific rules, and establish an entire science around their abstract use — what we would call mathematics.

Nieder hopes that his work on zero can help demonstrate how an abstract sense of number might emerge from a more approximate and practical one. He is currently conducting studies in humans to explore the relationship between non-symbolic numerical representations and symbolic ones more precisely.

Vallortigara, Butterworth and some of their colleagues are now collaborating with Caroline Brennan, a molecular geneticist at Queen Mary University of London, to pin down the genetic mechanisms underlying numerical ability. They have already identified genes that seem to be associated with a math learning disability in humans called dyscalculia, and are manipulating the equivalent genes in zebra fish. “I think that the genetic part of this story is, in a sense, the future of this field,” Vallortigara said. “Identifying genes for number would really be a breakthrough.”

rnnn","settings":{"socialLinks":[{"type":"facebook","label":"Facebook","url":"https://www.facebook.com/QuantaNews","__typename":"SocialMediaLink"},{"type":"twitter","label":"Twitter","url":"https://twitter.com/QuantaMagazine","__typename":"SocialMediaLink"},{"type":"youtube","label":"YouTube","url":"http://youtube.com/c/QuantamagazineOrgNews","__typename":"SocialMediaLink"},{"type":"instagram","label":"Instagram","url":"https://instagram.com/quantamag","__typename":"SocialMediaLink"},{"type":"rss","label":"RSS","url":"https://api.quantamagazine.org/feed/","__typename":"SocialMediaLink"}],"newsletterAction":"https://quantamagazine.us1.list-manage.com/subscribe/post?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c","newsletterUrl":"http://us1.campaign-archive2.com/home/?u=0d6ddf7dc1a0b7297c8e06618&id=f0cb61321c","commentsHeader":"

n","itunesSubscribe":"https://itunes.apple.com/us/podcast/quanta-science-podcast/id1021340531?mt=2&ls=1","androidSubscribe":"https://podcasts.google.com/feed/aHR0cHM6Ly93d3cucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvcG9kY2FzdC8","spotifySubscribe":"https://open.spotify.com/show/7oKXOpbHzbICFUcJNbZ5wF","itunesJoyOfX":"https://podcasts.apple.com/us/podcast/the-joy-of-x/id1495067186","androidJoyOfX":"https://podcasts.google.com/feed/aHR0cHM6Ly9hcGkucXVhbnRhbWFnYXppbmUub3JnL2ZlZWQvdGhlLWpveS1vZi14Lw","spotifyJoyOfX":"https://open.spotify.com/show/5HcCtKPH5gnOjRiMtTdC07","popularSearches":[{"term":"math","label":"Mathematics","__typename":"PopularSearch"},{"term":"physics","label":"Physics","__typename":"PopularSearch"},{"term":"black holes","label":"Black Holes","__typename":"PopularSearch"},{"term":"evolution","label":"Evolution","__typename":"PopularSearch"}],"searchTopics":[{"type":"Tag","label":"Podcasts","tag":{"name":"podcast","slug":"podcast","term_id":"552","__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Tag","label":"Columns","tag":{"name":"Quantized Columns","slug":"quantized","term_id":"551","__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Series","label":"Series","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Interviews","tag":{"name":"Q&A","slug":"qa","term_id":"567","__typename":"Term"},"category":{"name":"Q&A","slug":"qa","term_id":"176","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Multimedia","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":"Multimedia","slug":"multimedia","term_id":"43","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Puzzles","tag":{"name":"puzzles","slug":"puzzles","term_id":"542","__typename":"Term"},"category":{"name":"Puzzles","slug":"puzzles","term_id":"546","__typename":"Term"},"__typename":"SearchTopic"},{"type":"Category","label":"Blog Posts","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":"Abstractions blog","slug":"abstractions","term_id":"619","__typename":"Term"},"__typename":"SearchTopic"},{"type":"news","label":"News Articles","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"},{"type":"videos","label":"Videos","tag":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"category":{"name":null,"slug":null,"term_id":null,"__typename":"Term"},"__typename":"SearchTopic"}],"searchSections":[{"name":"Mathematics","slug":"mathematics","term_id":"188","__typename":"Term"},{"name":"Physics","slug":"physics","term_id":"189","__typename":"Term"},{"name":"Biology","slug":"biology","term_id":"191","__typename":"Term"},{"name":"Computer Science","slug":"computer-science","term_id":"190","__typename":"Term"}],"searchAuthors":[{"id":"28087","name":"Adam Mann","__typename":"AuthorList"},{"id":"29794","name":"Alex Kontorovich","__typename":"AuthorList"},{"id":"56","name":"Alla Katsnelson","__typename":"AuthorList"},{"id":"29458","name":"Allison Whitten","__typename":"AuthorList"},{"id":"73","name":"Amanda Gefter","__typename":"AuthorList"},{"id":"59","name":"Andreas von Bubnoff","__typename":"AuthorList"},{"id":"8728","name":"Anil Ananthaswamy","__typename":"AuthorList"},{"id":"11648","name":"Ann Finkbeiner","__typename":"AuthorList"},{"id":"95","name":"Ariel Bleicher","__typename":"AuthorList"},{"id":"15493","name":"Ashley Smart","__typename":"AuthorList"},{"id":"450","name":"Ashley Yeager","__typename":"AuthorList"},{"id":"36490","name":"Ben Brubaker","__typename":"AuthorList"},{"id":"16315","name":"Bill Andrews","__typename":"AuthorList"},{"id":"2752","name":"Bob Henderson","__typename":"AuthorList"},{"id":"15492","name":"Brendan Z. Foster","__typename":"AuthorList"},{"id":"68","name":"Brooke Borel","__typename":"AuthorList"},{"id":"62","name":"Carl Zimmer","__typename":"AuthorList"},{"id":"13691","name":"Caroline Lee","__typename":"AuthorList"},{"id":"50","name":"Carrie Arnold","__typename":"AuthorList"},{"id":"15142","name":"Chanda Prescod-Weinstein","__typename":"AuthorList"},{"id":"8084","name":"Charlie Wood","__typename":"AuthorList"},{"id":"742","name":"Christie Wilcox","__typename":"AuthorList"},{"id":"11543","name":"Claudia Dreifus","__typename":"AuthorList"},{"id":"57","name":"Courtney Humphries","__typename":"AuthorList"},{"id":"7262","name":"Dalmeet Singh Chawla","__typename":"AuthorList"},{"id":"70","name":"Dan Falk","__typename":"AuthorList"},{"id":"19918","name":"Dana Najjar","__typename":"AuthorList"},{"id":"32676","name":"Daniel S. Freed","__typename":"AuthorList"},{"id":"13724","name":"David H. Freedman","__typename":"AuthorList"},{"id":"26310","name":"David S. Richeson","__typename":"AuthorList"},{"id":"30207","name":"David Tse","__typename":"AuthorList"},{"id":"19266","name":"Devin Powell","__typename":"AuthorList"},{"id":"13251","name":"Diana Kwon","__typename":"AuthorList"},{"id":"17000","name":"Elena Renken","__typename":"AuthorList"},{"id":"17149","name":"Elizabeth Landau","__typename":"AuthorList"},{"id":"5279","name":"Elizabeth Preston","__typename":"AuthorList"},{"id":"58","name":"Elizabeth Svoboda","__typename":"AuthorList"},{"id":"32612","name":"Ellen Horne","__typename":"AuthorList"},{"id":"25173","name":"Emily Levesque","__typename":"AuthorList"},{"id":"64","name":"Emily Singer","__typename":"AuthorList"},{"id":"47","name":"Erica Klarreich","__typename":"AuthorList"},{"id":"14784","name":"Erika K. Carlson","__typename":"AuthorList"},{"id":"98","name":"Esther Landhuis","__typename":"AuthorList"},{"id":"5830","name":"Eva Silverstein","__typename":"AuthorList"},{"id":"6793","name":"Evelyn Lamb","__typename":"AuthorList"},{"id":"75","name":"Ferris Jabr","__typename":"AuthorList"},{"id":"52","name":"Frank Wilczek","__typename":"AuthorList"},{"id":"69","name":"Gabriel Popkin","__typename":"AuthorList"},{"id":"77","name":"George Musser","__typename":"AuthorList"},{"id":"19092","name":"Grant Sanderson","__typename":"AuthorList"},{"id":"20557","name":"Howard Lee","__typename":"AuthorList"},{"id":"66","name":"Ingrid Daubechies","__typename":"AuthorList"},{"id":"85","name":"Ivan Amato","__typename":"AuthorList"},{"id":"37141","name":"Jake Buehler","__typename":"AuthorList"},{"id":"12170","name":"Janna Levin","__typename":"AuthorList"},{"id":"32","name":"Jeanette Kazmierczak","__typename":"AuthorList"},{"id":"51","name":"Jennifer Ouellette","__typename":"AuthorList"},{"id":"72","name":"John Pavlus","__typename":"AuthorList"},{"id":"16475","name":"John Preskill","__typename":"AuthorList"},{"id":"91","name":"John Rennie","__typename":"AuthorList"},{"id":"10351","name":"Jonathan Lambert","__typename":"AuthorList"},{"id":"31716","name":"Jonathan O'Callaghan","__typename":"AuthorList"},{"id":"1241","name":"Jordana Cepelewicz","__typename":"AuthorList"},{"id":"8463","name":"Joshua Roebke","__typename":"AuthorList"},{"id":"49","name":"Joshua Sokol","__typename":"AuthorList"},{"id":"67","name":"K.C. Cole","__typename":"AuthorList"},{"id":"37462","name":"Karmela Padavic-Callaghan","__typename":"AuthorList"},{"id":"87","name":"Kat McGowan","__typename":"AuthorList"},{"id":"36139","name":"Katarina Zimmer","__typename":"AuthorList"},{"id":"20556","name":"Katherine Harmon Courage","__typename":"AuthorList"},{"id":"90","name":"Katia Moskvitch","__typename":"AuthorList"},{"id":"27374","name":"Kelsey Houston-Edwards","__typename":"AuthorList"},{"id":"40","name":"Kevin Hartnett","__typename":"AuthorList"},{"id":"12570","name":"Laura Poppick","__typename":"AuthorList"},{"id":"23451","name":"Liam Drew","__typename":"AuthorList"},{"id":"79","name":"Liz Kruesi","__typename":"AuthorList"},{"id":"60","name":"Maggie McKee","__typename":"AuthorList"},{"id":"2333","name":"Mallory Locklear","__typename":"AuthorList"},{"id":"3569","name":"Marcus Woo","__typename":"AuthorList"},{"id":"414","name":"Mark H. Kim","__typename":"AuthorList"},{"id":"17147","name":"Matthew Hutson","__typename":"AuthorList"},{"id":"30953","name":"Max G. Levy","__typename":"AuthorList"},{"id":"32437","name":"Max Kozlov","__typename":"AuthorList"},{"id":"7186","name":"Melinda Wenner Moyer","__typename":"AuthorList"},{"id":"14093","name":"Michael Harris","__typename":"AuthorList"},{"id":"23","name":"Michael Moyer","__typename":"AuthorList"},{"id":"74","name":"Michael Nielsen","__typename":"AuthorList"},{"id":"19093","name":"Michele Bannister","__typename":"AuthorList"},{"id":"1472","name":"Moira Chas","__typename":"AuthorList"},{"id":"6476","name":"Monique Brouillette","__typename":"AuthorList"},{"id":"35407","name":"Mordechai Rorvig","__typename":"AuthorList"},{"id":"10","name":"Natalie Wolchover","__typename":"AuthorList"},{"id":"37605","name":"Nick Thieme","__typename":"AuthorList"},{"id":"37428","name":"Nima Arkani-Hamed","__typename":"AuthorList"},{"id":"19962","name":"Nola Taylor Redd","__typename":"AuthorList"},{"id":"24","name":"Olena Shmahalo","__typename":"AuthorList"},{"id":"1816","name":"Patrick Honner","__typename":"AuthorList"},{"id":"84","name":"Peter Byrne","__typename":"AuthorList"},{"id":"55","name":"Philip Ball","__typename":"AuthorList"},{"id":"31","name":"Pradeep Mutalik","__typename":"AuthorList"},{"id":"24011","name":"Puja Changoiwala","__typename":"AuthorList"},{"id":"100","name":"Quanta Magazine","__typename":"AuthorList"},{"id":"2784","name":"R. Douglas Fields","__typename":"AuthorList"},{"id":"26114","name":"Rachel Crowell","__typename":"AuthorList"},{"id":"9412","name":"Raleigh McElvery","__typename":"AuthorList"},{"id":"820","name":"Ramin Skibba","__typename":"AuthorList"},{"id":"1666","name":"Rebecca Boyle","__typename":"AuthorList"},{"id":"20950","name":"Richard Masland","__typename":"AuthorList"},{"id":"48","name":"Robbert Dijkgraaf","__typename":"AuthorList"},{"id":"80","name":"Roberta Kwok","__typename":"AuthorList"},{"id":"15681","name":"Robin George Andrews","__typename":"AuthorList"},{"id":"24577","name":"Rodrigo Pérez Ortega","__typename":"AuthorList"},{"id":"78","name":"Sabine Hossenfelder","__typename":"AuthorList"},{"id":"83","name":"Sarah Lewin","__typename":"AuthorList"},{"id":"35441","name":"Scott Aaronson","__typename":"AuthorList"},{"id":"76","name":"Sean B. Carroll","__typename":"AuthorList"},{"id":"15680","name":"Sean Carroll","__typename":"AuthorList"},{"id":"7239","name":"Shannon Hall","__typename":"AuthorList"},{"id":"65","name":"Siobhan Roberts","__typename":"AuthorList"},{"id":"5944","name":"Sophia Chen","__typename":"AuthorList"},{"id":"61","name":"Steph Yin","__typename":"AuthorList"},{"id":"63","name":"Stephanie Bucklin","__typename":"AuthorList"},{"id":"26311","name":"Stephanie DeMarco","__typename":"AuthorList"},{"id":"71","name":"Stephen Ornes","__typename":"AuthorList"},{"id":"17148","name":"Steve Nadis","__typename":"AuthorList"},{"id":"13356","name":"Steven Strogatz","__typename":"AuthorList"},{"id":"17150","name":"Susan D'Agostino","__typename":"AuthorList"},{"id":"2960","name":"Tara C. Smith","__typename":"AuthorList"},{"id":"14785","name":"Thomas Lewton","__typename":"AuthorList"},{"id":"3","name":"Thomas Lin","__typename":"AuthorList"},{"id":"54","name":"Tim Vernimmen","__typename":"AuthorList"},{"id":"88","name":"Tom Siegfried","__typename":"AuthorList"},{"id":"12964","name":"Vanessa Schipani","__typename":"AuthorList"},{"id":"53","name":"Veronique Greenwood","__typename":"AuthorList"},{"id":"86","name":"Virginia Hughes","__typename":"AuthorList"},{"id":"3244","name":"Viviane Callier","__typename":"AuthorList"},{"id":"89","name":"Wynne Parry","__typename":"AuthorList"},{"id":"15913","name":"XiaoZhi Lim","__typename":"AuthorList"}],"adBehavior":"everywhere","adUrl":"https://www.quantamagazine.org/gift-store","adAlt":"The Prime Number Conspiracy - The Biggest Ideas in Math from Quanta – Available now!","adImageHome":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/01/Ad_Default_250x342_2x_math_3.jpg","adImageArticle":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/01/Ad_Article_320x600_math.jpg","adImageTablet":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/01/Ad_Tablet_890x250_2x_math.jpg","adImageMobile":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/01/Ad_Mobile_250x200_2x_Math.jpg","trackingScripts":"rn"},"theme":{"page":{"accent":"#ff8600","text":"#1a1a1a","background":"white"},"header":{"type":"default","gradient":{"color":"white"},"solid":{"primary":"#1a1a1a","secondary":"#999999","hover":"#ff8600"},"transparent":{"primary":"white","secondary":"white","hover":"#ff8600"}}},"redirect":null,"fallbackImage":{"alt":"","caption":"","url":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif","width":1200,"height":600,"sizes":{"thumbnail":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-520x260.gif","square_small":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-160x160.gif","square_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-520x520.gif","medium":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif","medium_large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default-768x384.gif","large":"https://d2r55xnwy6nx47.cloudfront.net/uploads/2017/04/default.gif","__typename":"ImageSizes"},"__typename":"Image"}},"modals":{"loginModal":false,"signUpModal":false,"forgotPasswordModal":false,"resetPasswordModal":false,"lightboxModal":false,"callback":null,"props":null},"podcast":{"id":null,"playing":false,"duration":0,"currentTime":0},"user":{"loggedIn":false,"savedArticleIDs":[],"userEmail":"","editor":false},"comments":{"open":false},"cookies":{"acceptedCookie":false}},
env: {
APP_URL: 'https://www.quantamagazine.org',
NODE_ENV: 'production',
WP_URL: 'https://api.quantamagazine.org',
HAS_GOOGLE_ID: true,
HAS_FACEBOOK_ID: true,
},
}

Source link

RELATED ARTICLES