Honeybees can count to six


This 2014 video says about itself:

Honeybee‘s Counting Book Volume 6. Jeanette Vuuren

This is the audiobook for HONEYBEE’S COUNTING BOOK, Volume 6 of the Honeybee Series and consists of approximately 55 pages which include honeybee words, phrases, sentences and full-color illustrations. It is an educational book for ages 3 to 5, and provides the opportunity for readers to learn the basic honeybee words, at the same time practicing numbers names and symbols from one to ten. This book also includes extra practice for counting from one to ten, as well as Honeybee’s Silly Rhyme which includes the basic information about honeybees.

From the University of Cologne in Germany:

Bees recognize that six is more than four

March 2, 2020

Summary: A new study at the University of Cologne proves that insects can perform basic numerical cognition tasks. Their neuronal network can also be used to perform successful machine learning.

Writing in iScience, zoologists have shown that insects have the cognitive abilities to perform so-called numerosity estimation, allowing them to solve simple mathematical problems. Zoologist Professor Dr Martin Paul Nawrot and doctoral student Hannes Rapp from the ‘Computational Systems Neuroscience’ research group at the University of Cologne demonstrated these abilities in a computational model inspired by the honeybee.

‘Experiments showed that insects such as honeybees can actually “count” up to a certain number of objects. For example, bees were able to compare sets of objects and evaluate whether they were the same size or whether one set was larger than the other’, said Hannes Rapp, explaining the underlying question of what is known as numerical cognition. For example, the bee recognized that six diamonds are more than four circles.

So far, it has been unclear how the neuronal network for this cognitive ability is constructed. Earlier theoretical models had assumed a firmly implemented circular circuit with four involved neurons for the four arithmetical operations ‘equal to’, ‘zero’, ‘more than’ and ‘less than’, explained Professor Nawrot. ‘However, our computer model showed that not four, but only one neuron is sufficient. The action potential of a single neuron varies depending on the math problem — and this can be trained on the neuron. As a result, the researchers identified a comparatively simple model with which a neural network can learn to solve numerical cognition tasks.

According to Nawrot, this model also helps the neural networks of an artificial intelligence to learn: ‘A lot of money has already been invested into training artificial neural networks to visually recognize the number of objects. Deep learning methods in particular enable counting by the explicit or implicit recognition of several relevant objects within a static scene’, Nawrot added. ‘However, these model classes are expensive because they usually have to be trained on a very large number of patterns in the millions and often require cloud computing clusters. Our honeybee-inspired approach with a simple model and learning algorithm reduces this effort many times over.’

Many cities are introducing green areas to protect their fauna. Amongst such measures are flower strips, which provide support to flower-visiting insects, insect- and seed-eating birds. According to the first quantitative assessment of the speed and distance over which urban flower strips attract wild bees, one-year-old flower strips attract 1/3 of the 232 species recorded from Munich since 1997: here.

Bees can count, new research


This 11 August 2017 video says about itself:

Bees can count from four to zero. Found by scientists at RMIT University in Melbourne [Australia].

They trained the insects to count shapes on a platform. The bees were encouraged to fly towards a platform carrying fewer shapes than another one.

They recognise a platform with no shapes as a smaller number than one with some shapes. Then when the platform had no shapes on it the bees could also understand this concept of the number zero.

From the Queen Mary University of London in England:

Bees can count with small number of nerve cells in their brains, research suggests

Insect-inspired miniature ‘brain’ simulated on a computer with just four nerve cells

December 21, 2018

Bees can solve seemingly clever counting tasks with very small numbers of nerve cells in their brains, according to researchers at Queen Mary University of London.

In order to understand how bees count, the researchers simulated a very simple miniature ‘brain’ on a computer with just four nerve cells — far fewer than a real bee has.

The ‘brain’ could easily count small quantities of items when inspecting one item closely and then inspecting the next item closely and so on, which is the same way bees count. This differs from humans who glance at all the items and count them together.

In this study, published in the journal iScience, the researchers propose that this clever behaviour makes the complex task of counting much easier, allowing bees to display impressive cognitive abilities with minimal brainpower.

Previous studies have shown bees can count up to four or five items, can choose the smaller or the larger number from a group and even choose ‘zero’ against other numbers when trained to choose ‘less’.

They might have achieved this not by understanding numerical concepts, but by using specific flight movements to closely inspect items which then shape their visual input and simplifies the task to the point where it requires minimal brainpower.

This finding demonstrates that the intelligence of bees, and potentially other animals, can be mediated by very small nerve cells numbers, as long as these are wired together in the right way.

The study could also have implications for artificial intelligence because efficient autonomous robots will need to rely on robust, computationally inexpensive algorithms, and could benefit from employing insect-inspired scanning behaviours.

Lead author Dr Vera Vasas, from Queen Mary University of London, said: “Our model shows that even though counting is generally thought to require high intelligence and large brains, it can be easily done with the smallest of nerve cell circuits connected in the right manner. We suggest that using specific flight movements to scan targets, rather than numerical concepts, explains the bees’ ability to count. This scanning streamlines the visual input and means a task like counting requires little brainpower.

“Careful examination of the actual inspection strategies used by animals might reveal that they often employ active scanning behaviours as shortcuts to simplify complex visual pattern discrimination tasks. Hopefully, our work will inspire others to look more closely not just at what cognitive tasks animals can solve, but also at how they are solving them.”

Brain size matters a lot when it comes to bees. They have only one million nerve cells in total, so they have precious little brainpower, and must implement very efficient computational algorithms to solve tasks. In comparison, humans have 86 billion nerve cells which are responsible for receiving information and sending commands.

To model the input to the brain, the authors analysed the point of view of a bee as it flies close to the countable objects and inspects them one-by-one.

The results showed the simulated brain was able to make reliable estimates on the number of items on display when provided with the actual visual input that the bee is receiving while carrying out the task.

Professor Lars Chittka, also from Queen Mary University of London and leader of the team in which the study was performed, added: “These findings add to the growing body of work showing that seemingly intelligent behaviour does not require large brains, but can be underpinned with small neural circuits that can easily be accommodated into the microcomputer that is the insect brain.”

Researchers set out to test whether bees could do math, building on a groundbreaking finding that bees understand the concept of zero. The new study shows bees can be taught to recognize colors as symbolic representations for addition and subtraction, and use this information to solve arithmetic problems. The revelation that even the miniature brain of a honeybee can grasp basic mathematical operations has implications for the future development of AI: here.

Shark scales study helped by Alan Turing


This 1 July 2015 video from the USA says about itself:

The Math of Shark Skin

Emory math professor Alessandro Veneziani, an expert in fluid dynamics, draws inspiration from nature. The rough surface of shark skin, for instance, helps sharks move faster through the water. Mathematicians have developed an equation for how this roughness translates into less viscosity for a swimming shark. Veneziani has applied this knowledge to everything from swimsuit design to the study of human blood flowing through arteries, to help doctors devise the best strategies for treating aneurisms.

From the University of Sheffield in England:

Codebreaker Turing’s theory explains how shark scales are patterned

November 7, 2018

A system proposed by world war two codebreaker Alan Turing

The British government ‘rewarded’ Turing for helping to win the war against nazi Germany with homophobic persecution, killing him. Like they had done before to Irish author Oscar Wilde.

more than 60 years ago can explain the patterning of tooth-like scales possessed by sharks, according to new research.

Scientists from the University of Sheffield’s Department of Animal and Plant Sciences found that Turing‘s reaction-diffusion theory — widely accepted as the patterning method in mouse hair and chicken feathers — also applies to shark scales.

The findings can explain how the pattern of shark scales has evolved to reduce drag whilst swimming, thereby saving energy during movement. Scientists believe studying the patterning could help to design new shark-inspired materials to improve energy and transport efficiency.

Turing, forefather of the computer, came up with the reaction-diffusion system which was published in 1952, two years before his death. His equations describe how molecular signals can interact to form complex patterns.

In the paper, published today (7 November 2018) in the journal Science Advances, researchers compared the patterning of shark scales to that of chicken feathers.

They found that the same core genes underlying feather patterning also underlie the development of shark scales and suggest these genes may be involved in the patterning of other diverse vertebrate skin structures, such as spines and teeth.

Dr Gareth Fraser, formerly of the University of Sheffield and now at the University of Florida, said: “We started looking at chicks and how they develop their feathers. We found these very nice lines of gene expression that pattern where these spots appear that eventually grow into feathers. We thought maybe the shark does a similar thing, and we found two rows on the dorsal surface, which start the whole process.

“We teamed up with a mathematician to figure out what the pattern is and whether we can model it. We found that shark skin denticles are precisely patterned through a set of equations that Alan Turing — the mathematician, computer scientist and the code breaker — came up with.

“These equations describe how certain chemicals interact during animal development and we found that these equations explain the patterning of these units.”

Researchers also demonstrated how tweaking the inputs of Turing’s system can result in diverse scale patterns comparable to those seen in shark and ray species alive today.

They suggest that natural variations to Turing’s system may have enabled the evolution of different traits within these animals, including the provision of drag reduction and defensive armour.

Rory Cooper, PhD student at the University of Sheffield, said: “Sharks belong to an ancient vertebrate group, long separated from most other jawed vertebrates. Studying their development gives us an idea of what skin structures may have looked like early in vertebrate evolution.

“We wanted to learn about the developmental processes that control how these diverse structures are patterned, and therefore the processes which facilitate their various functions.”

Scientists used a combination of techniques including reaction-diffusion modelling to create a simulation based on Turing’s equations, to demonstrate that his system can explain shark scale patterning, when the parameters are tuned appropriately.

Mr Cooper added: “Scientists and engineers have been trying to create shark-skin inspired materials to reduce drag and increase efficiency during locomotion, of both people and vehicles, for many years.

“Our findings help us to understand how shark scales are patterned, which is essential for enabling their function in drag reduction.

Therefore, this research helps us to understand how these drag reductive properties first arose in sharks, and how they change between different species.”

Patterning is one important aspect that contributes to achieving drag reduction in certain shark species. Another is the shape of individual scales. Researchers now want to examine the developmental processes which underlie the variation of shape both within and between different shark species.

“Understanding how both these factors contribute towards drag reduction will hopefully lead towards the production of improved, widely applicable shark-inspired materials capable of reducing drag and saving energy”, added Mr Cooper.

Asian elephants and mathematics


This 2008 New Scientist video says about itself:

Asian elephant does arithmetic

A cunning Asian elephant bests a science reporter at a simple counting game.

Read more here.

From ScienceDaily:

Asian elephants could be the math kings of the jungle

Experimental evidence shows that Asian elephants possess numerical skills similar to those in humans

October 22, 2018

Asian elephants demonstrate numeric ability which is closer to that observed in humans rather than in other animals. This is according to lead author Naoko Irie of SOKENDAI (The Graduate University for Advanced Studies and the Japan Society for the Promotion of Science) in Japan. In a study published in the Springer-branded Journal of Ethology, Irie and her colleagues found that an Asian elephants‘ sense of numbers is not affected by distance, magnitude or ratios of presented numerosities, and therefore provides initial experimental evidence that non-human animals have cognitive characteristics similar to human counting.

Previous research has shown that many animals have some form of numerical competence, even though they do not use language. However, this numerical ability is mainly based on inaccurate quantity instead of absolute numbers. In this study, the researchers aimed to replicate the results of previous research that already showed that Asian elephants have exceptional numeric competence.

Irie and her colleagues developed a new method to test how well the animals can judge relative quantity. They successfully trained a 14-year old Asian elephant called Authai from the Ueno Zoo in Japan to use a computer-controlled touch panel. The programme was specifically designed to examine the cognition of elephants, so that any unintended factors potentially influencing the results could be ruled out. Authai was presented with a relative numerosity judgment task on the screen, and then had to indicate with the tip of her trunk which one of the two figures shown to her at a time contained more items. These ranged from 0 to 10 items, and contained pictures of bananas, watermelons and apples. The fruit were not all presented in the same size, to ensure that Authai did not make her choices purely on the total area that was covered with illustrations per card.

Authai was rewarded whenever she chose the figures featuring the larger number of items. This she did correctly 181 out of 271 times — a success rate of 66.8 per cent. Her ability to accurately pinpoint the figure with the most fruits on it was not affected by the magnitude, distance or ratio of the comparisons. Authai’s reaction time was, however, influenced by the distance and ratio between the two figures presented. She needed significantly more time to make her selection between figures where relatively smaller distances and larger ratios were presented.

“We found that her performance was unaffected by distance, magnitude, or the ratios of the presented numerosities, but consistent with observations of human counting, she required a longer time to respond to comparisons with smaller distances”, explains Irie. “This study provides the first experimental evidence that nonhuman animals have cognitive characteristics partially identical to human counting.”

According to Irie, this is not an ability that the Asian elephant shares with the two species of African elephants. She says that because the species diverged more than 7.6 million years ago, it is highly probable that each developed different cognitive abilities.

How zebrafish get their stripes


This video from the USA says about itself:

6 November 2014

In the clip, a 10-day-old zebrafish gets its stripes in this series of images taken one a day for 30 days. Credit required: D Parichy Lab/University of Washington.

From Cardiff University in Wales:

How do zebrafish develop their stripes?

Cardiff University mathematician discovers key aspect underlining distinctive patterns of the zebrafish

September 28, 2017

A Cardiff University mathematician has thrown new light on the longstanding mystery of how zebrafish develop the distinctive striped patterns on their skin.

In a new study, Dr Thomas Woolley has simulated the intricate process that sees the pigmented skin cells of the zebrafish engaged in a game of cat and mouse as they chase after each in the early developmental stages before resting to create a final pattern.

Dr Woolley discovered that a key factor is the angles at which the cells chase after each other, and these angles can determine whether a zebrafish develops its distinctive stripes, broken stripes, polka-dot patterns or sometimes no pattern at all.

The findings have been presented in the journal Physical Review E.

Rather than have a pattern ingrained in their genetic code, zebrafish start their lives as transparent embryos before developing iconic patterns over time as they grow into adults. As is often the case in nature, many possible mutations exist and this can dictate the pattern that develops in the zebrafish.

Several researchers have studied how and why these pattern form and have concluded that it’s a result of three types of pigment cells interacting with one other. More specifically, black pigment cells (melanophores), yellow pigment cells (xanthophores) and silvery pigment cells (iridophores), chase after each other until a final pattern is reached.

As hundreds of these chases play out, the yellow cells eventually push the black cells into a position to form a distinct pattern.

Dr Woolley, from Cardiff University’s School of Mathematics, said: “Experimentalists have demonstrated that when these two types of cells are placed in a petri dish, they appear to chase after each other, a bit like pacman chasing the ghosts. However, rather than chase each other in straight lines, they appear to be chasing each other in a spiral.

“My new research has shown that the angle at which the cells chase after each other is crucial to determining the final pattern that we see on different types of zebrafish.”

In his study, Dr Woolley performed a number of computer simulations that took a broad view of how cells move and interact when the zebrafish is just a few weeks old. Different patterns were then spontaneously generated depending on the chasing rules.

By experimenting with different chasing angles in his simulations, Dr Woolley was able to successfully recreate the different patterns that are exhibited by zebrafish.

A new type of zebrafish that produces fluorescent tags in migratory embryonic nerve precursor cells could help a Rice University neurobiologist and cancer researcher find the origins of the third-most common pediatric cancer in the U.S.: here.

Babylonians, world’s oldest trigonometrists discovery


This video says about itself:

Ancient Babylonian tablet – world’s first trig table

24 August 2017

UNSW Sydney scientists have discovered the purpose of a famous 3700-year old Babylonian clay tablet, revealing it is the world’s oldest and most accurate trigonometric table, most likely used by ancient mathematical scribes to calculate how to construct palaces, temples and stepped pyramids.

Read more here.

Plimpton 322, the most famous of Old Babylonian tablets (1900-1600 BC), is the world’s oldest trigonometric table, possibly used by Babylonian scholars to calculate how to construct stepped pyramids, palaces and temples, according to a duo of researchers from the School of Mathematics and Statistics at the University of New South Wales (UNSW), Sydney, Australia: here.

African American women at NASA


This video from the USA says about itself:

14 August 2016

Watch the new trailer for Hidden Figures, based on the incredible untold true story. Starring Taraji P. Henson, Octavia Spencer & Janelle Monáe. In theaters this January.

HIDDEN FIGURES is the incredible untold story of Katherine G. Johnson (Taraji P. Henson), Dorothy Vaughan (Octavia Spencer) and Mary Jackson (Janelle Monáe)—brilliant African-American women working at NASA, who served as the brains behind one of the greatest operations in history: the launch of astronaut John Glenn into orbit, a stunning achievement that restored the nation’s confidence, turned around the Space Race, and galvanized the world. The visionary trio crossed all gender and race lines to inspire generations to dream big.

In Theaters – January 6, 2017

From Science News:

Hidden Figures highlights three black women who were vital to the U.S. space program

Despite racism and sexism, female “computers” put John Glenn into orbit

By Emily Conover

6:00am, December 23, 2016

Hollywood space flicks typically feature one type of hero: astronauts who defy the odds to soar into space and back again. But now a group of behind-the-scenes heroes from the early days of the U.S. space program are getting their due. Black female mathematicians performed essential calculations to safely send astronauts to and from Earth’s surface — in defiance of flagrant racism and sexism.

These “computers” — as they were known before the electronic computer came into widespread use — are the subject of Hidden Figures. The film focuses on three black women — Katherine Johnson (played by Taraji P. Henson), Dorothy Vaughan (Octavia Spencer) and Mary Jackson (Janelle Monáe) — and their work at NASA’s Langley Research Center in Hampton, Va., during the run-up to John Glenn’s orbit of the Earth in 1962.

A mathematics virtuoso, Katherine Johnson calculated or verified the flight trajectories for many of the nation’s space milestones. The film showcases her work on two: the first American in space (Alan Shepard), and the first American to orbit the Earth (John Glenn). But Johnson also had a hand in sending the first men to the moon, during the Apollo 11 mission, and when the Apollo 13 astronauts ran into trouble, Johnson worked on the calculations that helped them get home safely.

Mary Jackson worked on wind tunnel experiments at Langley, where she tested how spacecraft performed under high winds. The film follows Jackson as she overcomes obstacles of the Jim Crow era to become NASA’s first black female engineer. Though the movie focuses on her triumphant rise, after decades in that role, Jackson grew frustrated with the remaining glass ceilings and moved into an administrative role, helping women and minorities to advance their careers at NASA.

Johnson and Jackson got their start under the leadership of Dorothy Vaughan, who led the segregated group of “colored computers,” assigning black women to assist with calculations in various departments. As electronic computers became more essential Vaughan recognized their importance and became an expert programmer. A scene where she surreptitiously takes a book from whites-only section of a public library — a guide to the computing language FORTRAN — is a nod to Vaughan’s prowess with the language.

Electronic computers were so unfamiliar in the 1960s that everyone from engineers to astronauts felt more confident when a human computer calculated the numbers. After a room-sized IBM mainframe spits out figures for his trajectory, John Glenn requests, “Get the girl to check the numbers” — meaning Johnson. In the film, that request culminates in Johnson running a frantic last-minute check of the numbers and sprinting across the Langley campus while Glenn waits. In reality, that process took a day and a half.

For spaceflight fans, Hidden Figures provides an opportunity to be immersed in a neglected perspective. The women’s stories are uplifting, their resilience impressive and their retorts in response to those who underestimate them, witty.

But viewers should be aware that, although the main facts underpinning the plot are correct, liberties have been taken. Some of the NASA higher-ups in the film — including Johnson’s supervisor Al Harrison (Kevin Costner) — are not real people. And presumably because number-crunching tends to be a bit thin in the suspense department, the filmmakers have dramatized some scenes — Johnson is pictured in Mission Control during Glenn’s flight, but in reality she watched it on television — which seems a shame because the contributions of these women don’t need to be exaggerated to sound momentous.