# The latest math stars: honeybees!

Understanding the concept of zero—I still remember climbing that mountain, so to speak. It took the teacher quite a while to convince me that representing ‘nothing’ as a zero was worthwhile. In fact, it took the combined efforts of both my parents and the teacher to convince me to use zeroes as I was prepared to go without. The battle is long since over and I have learned to embrace zero.

I don’t think bees have to be convinced but they too may have a concept of zero. More about that later, here’s the latest abut bees and math from an October 10, 2019 news item on phys.org,

Start thinking about numbers and they can become large very quickly. The diameter of the universe is about 8.8×1023 km and the largest known number—googolplex, 1010100—outranks it enormously. Although that colossal concept was dreamt up by brilliant mathematicians, we’re still pretty limited when it comes to assessing quantities at a glance. ‘Humans have a threshold limit for instantly processing one to four elements accurately’, says Adrian Dyer from RMIT University, Australia; and it seems that we are not alone. Scarlett Howard from RMIT and the Université de Toulouse, France, explains that guppies, angelfish and even honeybees are capable of distinguishing between quantities of three and four, although the trusty insects come unstuck at finer differences; they fail to differentiate between four and five, which made her wonder. According to Howard, honeybees are quite accomplished mathematicians. ‘Recently, honeybees were shown to learn the rules of “less than” and “greater than” and apply these rules to evaluate numbers from zero to six’, she says. Maybe numeracy wasn’t the bees’ problem; was it how the question was posed? The duo publishes their discovery that bees can discriminate between four and five if the training procedure is correct in Journal of Experimental Biology.

An October 10, 2019 The Company of Biologists’ press release on EurekAlert, which originated the news item, refines the information with more detail,

Dyer explains that when animals are trained to distinguish between colours and objects, some training procedures simply reward the animals when they make the correct decision. In the case of the honeybees that could distinguish three from four, they received a sip of super-sweet sugar water when they made the correct selection but just a taste of plain water when they got it wrong. However, Dyer, Howard and colleagues Aurore Avarguès-Weber, Jair Garcia and Andrew Greentree knew there was an alternative strategy. This time, the bees would be given a bitter-tasting sip of quinine-flavoured water when they got the answer wrong. Would the unpleasant flavour help the honeybees to focus better and improve their maths?

‘[The] honeybees were very cooperative, especially when I was providing sugar rewards’, says Howard, who moved to France each April to take advantage the northern summer during the Australian winter, when bees are dormant. Training the bees to enter a Y-shaped maze, Howard presented the insects with a choice; a card featuring four shapes in one arm and a card featuring a different number of shapes (ranging from one to 10) in the other. During the first series of training sessions, Howard rewarded the bees with a sugary sip when they alighted correctly before the card with four shapes, in contrast to a sip of water when they selected the wrong card. However, when Howard trained a second set of bees she reproved them with a bitter-tasting sip of quinine when they chose incorrectly, rewarding the insects with sugar when they selected the card with four shapes. Once the bees had learned to pick out the card with four shapes, Howard tested whether they could distinguish the card with four shapes when offered a choice between it and cards with eight, seven, six or – the most challenging comparison – five shapes.

Not surprisingly, the bees that had only been rewarded during training struggled; they couldn’t even differentiate between four and eight shapes. However, when Howard tested the honeybees that had been trained more rigorously – receiving a quinine reprimand – their performance was considerably better, consistently picking the card with four shapes when offered a choice between it and cards with seven or eight shapes. Even more impressively, the bees succeeded when offered the more subtle choice between four and five shapes.

So, it seems that honeybees are better mathematicians than had been credited. Unlocking their ability was simply a matter of asking the question in the right way and Howard is now keen to find out just how far counting bees can go.

I’ll get to the link to and citation for the paper in a minute but first, I found more about bees and math (including zero) in this February 7, 2019 article by Jason Daley for The Smithsonian (Note: Links have been removed),

Bees are impressive creatures, powering entire ecosystems via pollination and making sweet honey at the same time, one of the most incredible substances in nature. But it turns out the little striped insects are also quite clever. A new study suggests that, despite having tiny brains, bees understand the mathematical concepts of addition and subtraction.

To test the numeracy of the arthropods, researchers set up unique Y-shaped math mazes for the bees to navigate, according to Nicola Davis at the The Guardian. Because the insects can’t read, and schooling them to recognize abstract symbols like plus and minus signs would be incredibly difficult, the researchers used color to indicate addition or subtraction. …

Fourteen bees spent between four and seven hours completing 100 trips through the mazes during training exercises with the shapes and numbers chosen at random. All of the bees appeared to learn the concept. Then, the bees were tested 10 times each using two addition and two subtraction scenarios that had not been part of the training runs. The little buzzers got the correct answer between 64 and 72 percent of the time, better than would be expected by chance.

Last year, the same team of researchers published a paper suggesting that bees could understand the concept of zero, which puts them in an elite club of mathematically-minded animals that, at a minimum, have the ability to perceive higher and lower numbers in different groups. Animals with this ability include frogs, lions, spiders, crows, chicken chicks, some fish and other species. And these are not the only higher-level skills that bees appear to possess. A 2010 study that Dyer [Adrian Dyer of RMIT University in Australia] also participated in suggests that bees can remember human faces using the same mechanisms as people. Bees also use a complex type of movement called the waggle dance to communicate geographical information to one other, another sophisticated ability packed into a brain the size of a sesame seed.

If researchers could figure out how bees perform so many complicated tasks with such a limited number of neurons, the research could have implications for both biology and technology, such as machine learning. …

Then again, maybe the honey makers are getting more credit than they deserve. Clint Perry, who studies invertebrate intelligence at the Bee Sensory and Behavioral Ecology Lab at Queen Mary University of London tells George Dvorsky at Gizmodo that he’s not convinced by the research, and he had similar qualms about the study that suggested bees can understand the concept of zero. He says the bees may not be adding and subtracting, but rather are simply looking for an image that most closely matches the initial one they see, associating it with the sugar reward. …

If you have the time and the interest, definitely check out Daley’s article.

Here’s a link to and a citation for the latest paper about honeybees and math,

Surpassing the subitizing threshold: appetitive–aversive conditioning improves discrimination of numerosities in honeybees by Scarlett R. Howard, Aurore Avarguès-Weber, Jair E. Garcia, Andrew D. Greentree, Adrian G. Dyer. Journal of Experimental Biology 2019 222: jeb205658 doi: 10.1242/jeb.205658 Published 10 October 2019

This paper is behind a paywall.

# Are science cities London, Paris, New York and Tokyo losing prominence?

I am more accustomed to thinking about great art cities than great science cities but it appears I lack imagination if a Dec. 13, 2013 news item on Nanowerk is to be believed (Note: A link has been removed),

The world’s largest scientific centers are losing some of their prominence due to geographical decentralization at the global scale, according to a team of researchers from the LISST (Laboratoire Interdisciplinaire Solidarités, Sociétés, Territoires, CNRS / Université de Toulouse II-Le Mirail / EHESS) who conducted a systematic statistical analysis of millions of articles and papers published in thousands of scientific reviews between 1987 and 2007. Their project, whose results were recently published on the Urban Studies website (“Cities and the geographical deconcentration of scientific activity: A multilevel analysis of publications (1987–2007)”), was the first to focus on the geography of science in all the world’s cities.

Here’s an image illustrating the researchers’ work,

The Dec. 10, 2013 CNRS (France’s Centre national de la recherche scientifique) news release, [English language version] [en français]), which originated the news item, provides more details,

Geographic encoding, city by city, of all of the articles listed in the Science Citation Index (SCI) (1) between 1987 and 2007 shows that traditional scientific centers are not as prominent as they used to be: the combined share of the world’s top 10 science cities dropped from 20% in 1987 to 13% in 2007. Researchers at the LISST (Laboratoire Interdisciplinaire Solidarités, Sociétés, Territoires, CNRS /Université de Toulouse II-Le Mirail / EHESS), aided by two collaborators at the CIRST (Centre Interuniversitaire de Recherche sur la Science et la Technologie) in Montreal, concluded that this phenomenon is accompanied by a general trend toward decentralization worldwide, especially in emerging nations. China offers a good illustration: the main provincial capitals are playing a much stronger role than they did in the past, and the skyrocketing development of science in China goes alongside with a geographical realignment. Whereas Beijing and Shanghai together accounted for 52.8% of the articles published by Chinese researchers in the Science Citation Index in 1987, this percentage dropped to 31.9% in 2007. Turkey is another striking example of an emerging nation whose scientific system has seen very rapid growth. In terms of the number of articles published, the country rose from 44th to 16th place worldwide between 1987 and 2007. Over the same period, its two main scientific hubs, Ankara and Istanbul, lost some of their pre-eminence within the country. While these two cities represented more than 60% of Turkey’s scientific production in 1987, they now produce slightly less than half of the articles published by Turkish researchers. And, as in China, growth in scientific activity is accompanied by geographical decentralization: Turkey has more science hubs now than it did two decades ago, and its two traditional scientific capitals play a lesser role.

The US, which remains the world leader in terms of scientific production, is an exceptional case: the number of articles published by American researchers continues to rise steadily, but at a slower pace than in the emerging nations. Consequently, the country’s share of worldwide scientific production is lower than it used to be: in 1987, the US represented 34% of the SCI, but by 2007 this figure had fallen to 25%. Nonetheless, the American scientific scene remains quite stable geographically: the role of its main research centers has not evolved significantly because the US scientific establishment has always been one of the least centralized in the world, with research activities scattered across hundreds of cities of all sizes.

Does this development herald the decline of the great scientific centers? The fact that scientific activity is becoming more geographically decentralized on a worldwide scale does not imply that it is declining in large cities with a strong research tradition. The number of articles published in London, Paris, New York and Tokyo continues to rise every year. But the pace of growth in those traditional centers is slower than in others in the global scientific system. As more research is conducted in an increasing number of cities, the main scientific centers contribute a lesser share to the total.

The findings of this project, funded as part of an ANR program (2010-2013), challenge the assumption that scientific production inevitably tends to be concentrated in a few large urban areas, which therefore should be given priority in the allocation of resources.

(1) The Science Citation Index (or SCI) is a bibliographical database created in the US in 1964 for the purpose of documenting all scientific production worldwide. In its current version (SCI-Expanded), which is part of the Thomson Reuters Web of Science database (WoS), it registers more than one million scientific articles every year, encompassing the experimental sciences and sciences of the universe, medicine, the engineering sciences, etc., but not the humanities and social sciences, which are included in the SSCI. The SCI-Expanded records contain information on the content of each article (title, name of publication, summary, keywords), its author or authors (name, institution, city, country), and the list of references cited in the article.

This is especially fascinating in light of a recently published book claiming that the major city centres for art in the 21st century will shifting to some unexpected places. From Phaidon Press’ Art Cities of the Future webpage,

The volume profiles 12 global cities to watch for exciting contemporary art: Beirut, Bogotá, Cluj, Delhi, Istanbul, Johannesburg, Lagos, San Juan, São Paulo, Seoul, Singapore and Vancouver.

Thankfully, in both the old world and the new, commentators appear to agree. “It’s great to have a look around and discover truly interesting new work,” said Simon Armstrong, book buyer at Tate Modern and Tate Britain, in The Bookseller, “and there are some great examples of emergent artists here in this huge presentation of contemporary art from 12 cities on the fringes of the art map.”

Hannah Clugston, writing in Aesthetica concurred, describing the title as “brilliantly executed” with “stunning images,” and possessing an awareness “of the wider concerns behind the work.”

It appears that the geography of creative endeavours in the arts and the sciences is shifting. For those curious about the science end of things, here’s a link to and a citation for the paper about geography and scientific activity,

Cities and the geographical deconcentration of scientific activity: A multilevel analysis of publications (1987–2007) by Michel Grossetti, Denis Eckert, Yves Gingras, Laurent Jégou, Vincent Larivière, and Béatrice Milard. Urban Studies, 0042098013506047, November 20, 2013, doi:10.1177/0042098013506047

This paper is behind a paywall.