The projects that are helping Zambian women get better access to land

File 20180718 142435 s4bwq6.jpg?ixlib=rb 1.1
A female farmer in Zambia tends to her crops.
Margaret W. Nea/Bread for the World/Flickr, CC BY-NC-ND

Cynthia Caron, Clark University

When a woman has access to and control over land and its revenue streams, she and her family benefit. Multiple studies have shown how women invest their land-based earnings in the health, nutrition and education of family members.

But for this to happen, customs that favour granting land to men must be altered. This requires both structural change, through for example government policies, and socio-cultural change.

The Zambian government has worked with civil society organisations to create a gender equality and land governance framework. Civil society organisations have used their social networks and through capacity building programmes pursue gender equality in the allocation of land in customary tenure systems.

I set out to study some of these programmes. In a recent article, I documented how women gain access to land in areas of Zambia where access is governed by traditional leaders and local customs. I was specifically interested in the role that civil society organisations play in strengthening women’s land rights in these areas.

Civil society organisations and their donors engage in five key activities that help women get access to land. They build and maintain regional and national networks; they document customary land rights and they train chiefs about gender equality. They also support men and women to work collectively within the home, and empower women to work together on pieces of land.

These activities show how civil society can support and expand the space for women’s land rights. Working with inter-generational family networks also might expand women’s access to economically-productive resources such as land.

Women’s rights organisations in other countries might draw on the Zambian experience, tailoring it to the local socio-economic and historical context within which they work.

Customary law

Zambia has two categories of land, state land and customary land. State land includes land in urban areas and land used for mining or nature conservation.

Customary land is administered by traditional leaders, such as chiefs and headpersons, according to customary law that is unwritten and based on local customs. Customary law is valid under the Constitution. Any customary practice that contradicts the constitution is illegal.

Women in customary tenure systems have what are called secondary land rights. This is because Zambia’s 288 chiefs, and village headpersons, handle land issues and generally grant occupancy and use rights to men because they’re considered the head of household. A woman tends to get access by asking her husband, or another male relative, to use a portion of the allocated land.

Gender activists are working to increase the prevalence of women as primary land rights holders. Their work is being helped by the fact that Zambia has a supportive policy environment thanks to the 2016 Constitution and the government’s gender policy.

The policies, together with a network of women and gender-oriented civil society organisations, have created momentum for legal reform and new measures to promote gender equality in the land sector. Chiefs, court officials, and men and women at the grassroots level have access to new tools to reconceptualise how men and women might work, live and develop their communities together.

Documenting and training

Changing the land use pattern faces a number of challenges. One of them is that there isn’t proper documentation of boundaries, or even of who has rights to what.

For example customary land in Zambia is neither systematically mapped nor registered. This leaves boundaries between individual plots unclear.

International organisations are working with chiefs and community groups like the Zambia Land Alliance to create what are known as Traditional Land Holding Certificates. These recognise land rights at either the individual or household level. Certifications clarify rights, verify claims through boundary demarcation, and end with the issuance of a certificate. The certificates allow a woman’s name to be listed as the land’s “primary” rights holder.

The certificate is designed to reduce property grabbing and the common practice of expelling a woman from a piece of land after her husband’s death. Establishing a system that registers these certificates and makes rights public would mean that women have a better chance of being protected.

Another major gap is knowledge. Chiefs don’t always know what the country’s policies and laws entail. Civil society organisations routinely hold provincial-level training for chiefs to explain women’s land rights. This isn’t always easy. One chief stated that “men need a bigger area” of land to cultivate than women do.

Gender rights activists try to identify more progressive chiefs who are willing to change local practice and tell men not to deny their partners’ land.


Getting men and women to work together when it comes to land is also a valuable intervention.

In many communities, husbands instruct their wives where to plant their crops. And when the cropping season is over, a woman might not be allowed to cultivate that same plot again and the husband will take it for his own cultivation.

One civil society organisation brings husbands and wives together and encourages them to own land and cultivate together. Bringing men and women within the household rather than maintaining separate fields closes the gender gap in land.

Another type of programme works through village-level groups that promote women’s collective access to land. Groups might ask their chief for a piece of land for growing crops or other income generating activities such as pig or goat rearing. If a widow’s relatives grab the property after her husband’s death, group leaders can intervene and help her keep her house and then allow her to cultivate a plot on the group’s land.

The ConversationSome organisations offer training in financial management, legal awareness, and leadership. Women then use these skills to organise, to obtain and maintain control over land and to be less dependent on men. Access to resources is based on relationships. Sustainable land rights programming and gender-equality initiatives must change not only how women think and behave but men too.

Cynthia Caron, Assistant Professor, Clark University

This article was originally published on The Conversation. Read the original article.

Why I teach math through knitting

File 20180627 112628 1tr48e8.jpg?ixlib=rb 1.1
Math in yarn.
Carthage College, CC BY-SA

Sara Jensen, Carthage College

One snowy January day, I asked a classroom of college students to tell me the first word that came to mind when they thought about mathematics. The top two words were “calculation” and “equation.”

When I asked a room of professional mathematicians the same question, neither of those words were mentioned; instead, they offered phrases like “critical thinking” and “problem-solving.”

This is unfortunately common. What professional mathematicians think of as mathematics is entirely different from what the general population thinks of as mathematics. When so many describe mathematics as synonymous with calculation, it’s no wonder we hear “I hate math” so often.

So I set out to solve this problem in a somewhat unconventional way. I decided to offer a class called “The Mathematics of Knitting” at my institution, Carthage College. In it, I chose to eliminate pencil, paper, calculator (gasp) and textbook from the classroom completely. Instead, we talked, used our hands, drew pictures and played with everything from beach balls to measuring tapes. For homework, we reflected by blogging. And of course, we knit.

Same but different

One crux of mathematical content is the equation, and crucial to this is the equal sign. An equation like x = 5 tells us that the dreaded x, which represents some quantity, has the same value as 5. The number 5 and the value of x must be exactly the same.

A typical equal sign is very strict. Any small deviation from “exactly” means that two things are not equal. However, there are many times in life where two quantities are not exactly the same, but are essentially the same by some meaningful criteria.

Imagine, for example, that you have two square pillows. The first is red on top, yellow on the right, green on bottom and blue on the left. The second is yellow on the top, green on the right, blue on bottom, and red on the left.

The pillows aren’t exactly the same. One has a red top, while one has a yellow top. But they’re certainly similar. In fact, they would be exactly the same if you turned the pillow with the red top once counterclockwise.

Rotating two square pillows.
Sara Jensen

How many different ways could I put the same pillow down on a bed, but make it look like a different one? A little homework shows there are 24 possible colored throw pillow configurations, though only eight of them can be obtained from moving a given pillow.

Students demonstrated this by knitting throw pillows, consisting of two colors, from knitting charts.

A knitting chart for a throw pillow.
Sara Jensen

The students created square knitting charts where all eight motions of the chart resulted in a different-looking picture. These were then knit into a throw pillow where the equivalence of the pictures could be demonstrated by actually moving the pillow.

Rubber sheet geometry

Another topic we covered is a subject sometimes referred to as “rubber sheet geometry.” The idea is to imagine the whole world is made of rubber, then reimagine what shapes would look like.

Let’s try to understand the concept with knitting. One way of knitting objects that are round – like hats or gloves – is with special knitting needles called double pointed needles. While being made, the hat is shaped by three needles, making it look triangular. Then, once it comes off the needles, the stretchy yarn relaxes into a circle, making a much more typical hat.

Knitting to learn.
Carthage College, CC BY-SA

This is the concept that “rubber sheet geometry” is trying to capture. Somehow, a triangle and a circle can be the same if they’re made out of a flexible material. In fact, all polygons become circles in this field of study.

If all polygons are circles, then what shapes are left? There are a few traits that are distinguishable even when objects are flexible – for example, if a shape has edges or no edges, holes or no holes, twists or no twists.

One example from knitting of something that is not equivalent to a circle is an infinity scarf. If you want to make a paper infinity scarf at home, take a long strip of paper and glue the short edges together by attaching the top left corner to the bottom right corner, and the bottom left corner to the top right corner. Then draw arrows pointing up the whole way around the object. Something cool should happen.

Students in the course spent some time knitting objects, like infinity scarves and headbands, that were different even when made out of flexible material. Adding markings like arrows helped visualize exactly how the objects were different.

Different flavors

An infinity scarf.
Carthage College

If the things described in this article don’t sound like math to you, I want to reinforce that they very much are. The subjects discussed here – abstract algebra and topology – are typically reserved for math majors in their junior and senior years of college. Yet the philosophies of these subjects are very accessible, given the right mediums.

In my view, there’s no reason these different flavors of math should be hidden from the public or emphasized less than conventional mathematics. Further, studies have shown that using materials that can be physically manipulated can improve mathematical learning at all levels of study.

The ConversationIf more mathematicians were able to set aside classical techniques, it seems possible the world could overcome the prevailing misconception that computation is the same as mathematics. And just maybe, a few more people out there could embrace mathematical thought; if not figuratively, then literally, with a throw pillow.

Sara Jensen, Assistant Professor of Mathematics, Carthage College

This article was originally published on The Conversation. Read the original article.

Capturing the shadow of Saturn’s moon Titan from right here on Earth

File 20180720 142423 5iics4.jpg?ixlib=rb 1.1
NASA’s Cassini spacecraft captures Saturn’s largest moon, Titan, passes in front of the planet and its rings.
NASA/JPL-Caltech/Space Science Institute

David Coward, University of Western Australia

Titan is Saturn’s largest moon, and it is more like a planet than a moon in many respects.

It has a thick atmosphere as well as wind, rivers, lakes made of hydrocarbons such as methane, and a liquid water ocean. Understanding its atmosphere may help us in the search for life on other planets.

Hence the excitement this July when a rare opportunity was available to further study Titan, from right here on Earth. On July 18 at 11:05pm (WAST, Western Australian time) Titan passed in front of a faint star, as seen by observers across most of Australia.

Read more:
The secrets of Titan: Cassini searched for the building blocks of life on Saturn’s largest moon

This event, known as an occultation, lasted only a few minutes and about 2% of the star’s light was blocked by Titan’s atmosphere.

The effect was so small it required large telescopes and a special camera to record it. But the data gathered should have profound implications for our understanding of an atmosphere on another world.

Saturn’s moon Titan compared (by diameter) to the Earth and its Moon.
Wikimedia/The Conversation

Examining Titan’s atmosphere

Scientists have developed a very clever technique to examine Titan’s atmosphere using stellar occultations. As Titan enters and exits an occultation, the star’s light would illuminate the atmosphere from behind, but be blocked by the moon itself.

Scientists then record subtle changes in brightness of the star over a few minutes, which represents a profile of the atmosphere’s density with height.

This method was used to study Titan’s atmosphere before, during a stellar occultation in 2003.

Artist’s concept of Cassini’s June 4, 2010, flyby of Saturn’s moon Titan.

But in 2005, when Cassini’s Huygens lander arrived at Titan and descended to its surface, the atmospheric profile measured from its instruments did not match that derived from the 2003 occultation. This fuelled the question of how variable is the state of Titan’s atmosphere.

Composite of Titans surface taken by Huygens at different heights.
ESA/NASA/JPL/University of Arizona

Since the Cassini mission ended in 2017, NASA’s Karsten Schindler said there was keen interest in any new atmospheric observations from occultations:

Occultations remain the only means to study Titan’s upper atmosphere and its evolution for the foreseeable future.

Countdown to the July occultation

So how were the latest observations made, and how was the data gathered?

From the air, the plan was for the July 18 occultation to be recorded by a camera mounted on a telescope of the Stratospheric Observatory of Infrared Astronomy (SOFIA) on board a Boeing 747 aircraft.

SOFIA takes off from Christchurch International Airport in 2017.
SOFIA/ Waynne Williams

That’s right: a telescope mounted inside a modified passenger plane imaging an object more than 1 billion kilometres away! SOFIA would fly above the clouds between Australia and New Zealand.

From the ground, several facilities across Australia were to attempt to record the occultation.

The University of Western Australia’s Zadko Telescope, located about 80km north of Perth (see map, below), was identified by NASA as a ground facility sensitive enough to contribute to the project.

The most obvious deal breaker was the weather. July is one of the wettest months at the Zadko telescope site. But, as we found out, there were other unforseen challenges.

Three days to occultation

NASA’s Karsten Schindler arrived at the UWA research site, at Gingin, on Monday July 16, armed with a case filled with delicate cameras, cables and electronics.

The camera was the key to record the event. The current Zadko telescope camera cannot record fast enough to capture the rapid changes in brightness of the occulted star.

The Zadko Telescope was fitted out with a fast shooting (a frame every few seconds), NASA camera, more like a movie camera than a standard astronomical camera. After hours of installation, the new imaging system needed to be tested.

Ground occultation team: John Kennwell, Arie Verveer, Karsten Schindler with the Zadko Telescope in the background.

Unfortunately, the observatory roof would not open because of a faulty sensor. No Monday test, but hey, we still had Tuesday to test the system? Onsite engineers scrambled to fix the sensor ready for Tuesday.

Two days to occultation

On Tuesday, I received the following text message from the site.

11:07pm: Rain sensor working but clouded out … cheers Arie. So no chance testing the camera and weather forecast for Wednesday was bleak.

The day of occultation

Despite the cloud and nearly constant rain showers, team occulation (Karsten, Arie and John) were on site ready to start pointing the telescope and activate the imaging.

“Up to 10pm it was still raining,” Karsten told me the next morning. “Then a miracle happened.”

Less than an hour before the event, and he said the weather changed.

“The clouds seemed to vaporise away, leaving a totally cloudless sky with 100% visibility. I have never seen anything like it.”

The team swung into action, pointing the telescope at the target star, focusing the camera. At the designated occulation time 11:05pm, Karsten hit the image acquisition button, enabling the camera to take hundreds of images over a few minutes.

Read more:
What Cassini’s mission revealed about Saturn’s known and newly discovered moons

Eager to see if the data contained the signature of an occulation, the team performed a preliminary analysis within minutes. Yes, there was a clear occulation signature, a big dip in the brightness of the star at exactly the predicted time of the occulation.

Next morning I was informed that SOFIA had also captured the event.

The data recorded from the Australian ground stations and by SOFIA will be analysed over the coming weeks and published in peer reviewed journals.

The ConversationBut one thing the journals won’t highlight is the excitement of the observation, and the enormous effort by a few individuals who helped acquire this data that should hopefully give us a better understanding of the atmosphere of Titan.

David Coward, Associate professor, University of Western Australia

This article was originally published on The Conversation. Read the original article.

Free-falling dead stars show that a cornerstone of physics holds up

File 20180704 73300 r9wjec.png?ixlib=rb 1.1
Triple star system involving a pulsar suggests Einstein was right.
Kevin Gill/Flickr, CC BY-ND

James Geach, University of Hertfordshire

It may not be intuitive, but drop a hammer and a feather and – in the absence of air resistance – they will hit the ground at exactly the same time. This is a key principle of physics known as “universal free fall”, stating that all objects accelerate identically in the same gravitational field. In fact, it’s an important theme in Albert Einstein’s immensely successful theory of general relativity, which describes how gravity works.

But although we know it holds true for hammers and feathers, it’s been unclear whether the principle extends to extreme objects such as stars. Now a new study, published in Nature, has tested the principle using a remarkably extreme astrophysical environment: a triple star system containing two white dwarfs and a pulsar (a rotating neutron star that beams radio waves). These objects are the extremely dense remnants of dead stars.

Spoiler alert: It turns out Einstein is still right, and it is getting even harder to prove him wrong.

But let’s start with the basics. Hold an object in your hand. It doesn’t matter what it is – the object will have some mass. We can think of that mass in two ways. Isaac Newton taught us that if we apply a force to a body it will undergo an acceleration, and the size of that acceleration is directly proportional to the amount of force applied – and inversely proportional to the mass itself. Give a broken-down car a push and it won’t accelerate very quickly, but apply that same push to a shopping trolley and you’ll send it careering down the aisle. When thinking about the acceleration of an object due to a force exerted on it, we think about the “inertial mass” of the body.

Any two objects with mass are attracted to each other through the gravitational force. So the object you are holding in your hand is attracted to the Earth, and the size of the force pulling it down is dependent on the mass of the object. In this case, we think about the “gravitational mass”.

If you dropped it, the object you are holding would “free fall” – the force of gravity would accelerate it towards the ground. The size of the force pulling the object down depends on the gravitational mass, but the amount of acceleration depends on the inertial mass. But is there any difference between the two types of mass? To find out, we can write down an equation of motion linking the two types of mass: inertial mass on one side of the equation and gravitational mass on the other.

The equation predicts something we can test using an experiment: if inertial mass is equivalent to gravitational mass, then all objects should fall towards the Earth with an identical acceleration regardless of their mass. That often surprises people. This is called the “Equivalence Principle”.

Galileo first noticed that plummeting objects fall at the same rate, and you can do this experiment yourself by simultaneously dropping two objects of different mass. However one problem doing this on Earth is the presence of another force acting on the falling bodies, called air resistance. If you drop a hammer and a feather, the feather will tend to gently drift down to the ground, lagging behind – the objects aren’t strictly in free fall. But go to the moon and do that experiment, as astronaut David Scott did during Apollo 15, where there is no air resistance, and the Equivalence Principle is clear to see.

Now, it has been unclear whether the theory does a good job of describing gravity in all situations. There is a lot at stake – if general relativity breaks down for certain situations then we would need a revised or modified theory of gravity. In particular, scientists have been wondering whether the universality of free fall applies to objects that have strong “self gravity” – a significant gravitational field of their own. Indeed some modified theories of gravity predict that the Equivalence Principle might be violated for strongly self-gravitating bodies in free fall, whereas general relativity says it should be universal.

Dance of stars

Thanks to an extreme laboratory in space – a triple stellar system 4,200 light years away – the new study managed to test this. That name doesn’t do it justice: we’re talking about two white dwarfs and a more massive “millisecond” pulsar (a neutron star rotating about 366 times a second, and beaming radio waves like a lighthouse). One white dwarf and the pulsar are orbiting each other every 1.6 days. In turn they also orbit around the other white dwarf every 327 days.

A triple stellar system involving normal stars, similar to the sun.

The pulsar-white dwarf pair can be considered to be in free fall towards the other white dwarf, because an orbit is just the case of free fall without ever reaching the ground, like satellites around the Earth. Of course, the pulsar and white dwarf are very massive objects themselves, with strong self gravity. General relativity predicts that the accelerations of the white dwarf and pulsar, due to being in free fall towards the outer white dwarf, should be identical – despite differences in mass and self-gravity.

Combining observations that span six years of monitoring, the astrophysicists carefully modelled the orbits of the pair. They measured a parameter called Delta, which describes the fractional difference between the acceleration of the white dwarf and the more massive pulsar. If general relativity holds, then Delta should be equal to zero. The results indicate that, within the uncertainties of the measurements, the difference in accelerations is indeed statistically consistent with zero – we can say with 95% confidence that Delta is less than 0.0000026.

This new constraint is far better than anything previously measured. It provides valuable new empirical evidence that general relativity remains our best model of how gravity works, so we are unlikely to need any new or modified theories at this point. This come just weeks after general relativity was proven right on a galactic scale for the first time.

The ConversationWill we ever find a situation where general relativity breaks down? In a way I do hope so, because it would reveal new physics. But the continuing success of general relativity, first written down a century ago, must surely be celebrated as one of the most incredible intellectual achievements of our species.

James Geach, Royal Society University Research Fellow, University of Hertfordshire

This article was originally published on The Conversation. Read the original article.

Discovering dopamine’s role in the brain: Arvid Carlsson’s important legacy

File 20180706 122256 vkxk93.jpg?ixlib=rb 1.1
Swedish pharmacologist and Nobel laureate, Arvid Carlsson.
Vogler/Wikimedia Commons, CC BY-SA

Patrick Lewis, University of Reading

Arvid Carlsson, the Swedish neuroscientist and Nobel laureate, died on June 29, 2018 at the age of 95. He had devoted his life to understanding how the brain works and was awarded the Nobel for his research into dopamine – an important chemical found in the brain.

So what is dopamine, and why did finding out about it merit the Nobel Prize?

Dopamine is a simple chemical, made in the body from an amino acid called tryptophan. Despite its simplicity, it plays an important role as a neurotransmitter – chemicals that brain cells use to communicate with one another.

What Carlsson did was to reveal exactly how significant dopamine is to the function of the brain. Before his research, most people thought that dopamine was just a precursor of a brain hormone called noradrenaline. By decreasing dopamine levels in the brains of rabbits in his lab in Gothenburg, Carlsson was able to show that if you don’t have the right level of dopamine in your brain, the circuits that determine how the brain controls movement don’t work properly.

Although Carlsson was investigating basic neuroscience, it wasn’t long before scientists and doctors realised that there were similarities between the problems with movement that Carlsson had observed in rabbits and the symptoms of Parkinson’s disease.

Parkinson’s disease is a neurodegenerative disorder, a type of disease where increasing numbers of brain cells die over time, causing patients to develop problems with their movement, including uncontrollable shaking, slowed movement and sudden freezing.

Following on from Carlsson’s research, doctors soon realised that if they examined the brains of people with Parkinson’s there was much less dopamine than you would find in a healthy brain. This is because the cells that make and use dopamine in the brain, dopaminergic neurons, are the cells that die in Parkinson’s disease.

This led researchers to propose a simple solution. If the symptoms of Parkinson’s are caused by too little dopamine, why not boost these levels, with a dopamine pill or injection, to help the brain work again?


Unfortunately, this approach didn’t work, as dopamine isn’t able to cross from the bloodstream into the brain. But providing people with Parkinson’s a precursor to dopamine, a chemical called levodopa that can get into the brain and is converted into dopamine, did work and provided relief from many of the symptoms of Parkinson’s. This was immortalised in the book Awakenings, written by neurologist Oliver Sacks and later made into a film starring Robin Williams and Robert De Niro.

In Awakenings, patients with post-encephalitic Parkinsonism (a viral disease similar to Parkinson’s disease) who were treated with levodopa, had almost miraculous improvements in their symptoms.

The ConversationUnfortunately, levodopa, and other drugs that target dopamine levels in the brain, only treat the symptoms of Parkinson’s, they don’t slow down the loss of brain cells that underlie the disease. Despite this, and some serious side effects, they remain the frontline drug in our fight against the disease. But we wouldn’t have these frontline drugs if it wasn’t for the important work that Carlsson conducted in the 1950s, and for which he shared the Nobel Prize for Physiology or Medicine in 2000.

Patrick Lewis, Associate Professor in Cellular and Molecular Neuroscience, University of Reading

This article was originally published on The Conversation. Read the original article.

Whale sharks gather at a few specific locations around the world – now we know why

File 20180618 85830 qai2nq.jpg?ixlib=rb 1.1
A whale shark basking in the Maldivian shallows.
Melody Sky, Author provided

Joshua Copping, University of Salford and Bryce Stewart, University of York

The whale shark is the largest fish in the world, but much of its lifecycle remains shrouded in mystery. These gentle giants gather in just a handful of places around the globe – something which has long baffled scientists – but our new research has started to explain why. Better understanding of whale shark movements could help prevent further population loss in a species that has already experienced a 63% population decline over the past 75 years.

When swimming solo, the whale shark, which can grow up to 18.8 metres in length and 34 tons in weight, travels all over the world. Recently, a group of scientists tracked the remarkable journey of one whale shark across the Pacific from Panama to the Philippines. At more than 12,000 miles it proved to be one of the longest migrations ever recorded.

Yet whale sharks are known to come together at just a few specific locations around the world. Anything from ten to 500 whale sharks may gather at any one time in areas off the coasts of Australia, Belize, the Maldives, Mexico and more.

Face to face with the world’s largest fish.
Jil Kühne, Author provided

Approximately 20 hotspots have been identified – mere pinpricks in the vastness of the world’s oceans – but we don’t know what exactly attracts the whale sharks to them. In some cases the sites are linked to a specific biological phenomenon – such as the spawning of land crabs at Christmas Island in the Indian Ocean, which provides whale sharks with the seasonal equivalent of a Christmas feast. Our new research aimed to discover whether there was something else that united the places where these giants of the ocean hang out.

It’s all about bathymetry

The physical features of these spots – known as their bathymetry – have been shown to influence gathering points in other marine species. So in collaboration with the Maldives Whale Shark Research Programme, we decided to investigate whether it drives whale shark gatherings in the same way.

Our new global study shows that whale sharks congregate in specific areas of shallow water, next to steep slopes that quickly give way to areas much deeper water (usually between 200 metres and 1,000 metres).

We identified three main reasons. First, the deep water is used by whale sharks for feeding. Studies have shown the sharks diving to depths of almost 2 kilometres (1,928 metres to be precise) to feed on zooplankton and squid.


Second, the steep slopes are known to bring nutrients up to the surface from the deep, which in turn increases the abundance of plankton and attracts large numbers of filter feeding species. And finally, in shallow water, as well as feeding on coral and fish spawn, the sharks are able to thermoregulate, warming themselves back up after their dives into deep water which gets as cold as 4℃.

Valuable but vulnerable

If you’ve ever seen or swum with a whale shark, it was most likely in one of these relatively shallow aggregation areas. Knowing where these hotspots are has provided local communities with a windfall from ecotourism. In the Maldives alone, economic benefits from whale shark-related activities were estimated at US$9.4m per year. Whale sharks are worth a lot more alive than dead – and with many of these meeting points in developing countries, the income is invaluable.

But with the increasing pressures of tourism comes new dangers for the sharks. Crowds of snorkelers and tourist vessels are increasingly disturbing the whale shark’s waters, and – more worryingly – risk potentially fatal strikes by boats. To protect these beautiful creatures and continue to reap the rewards of ecotourism, we recommend that marine protected areas should be set up around whale shark gatherings and codes of practice be followed when interacting with them.

Whale sharks are imposing, but feed on krill and other plankton.
MWSRP, Author provided

Deep mysteries remain

These discoveries have narrowed down some of the key reasons why whale sharks congregate where they do, but many mysteries remain. Do individuals travel between these hotspots? Coastal gatherings are predominately made up of immature male sharks, usually still just four or five metres long. So where are all the girls? And where do whale sharks mate and give birth? Mating and pupping have never been seen in the wild – but, intriguingly, up to 90% of the whale sharks passing through the Galapagos marine reserve are female and thought to be pregnant.

The ConversationCould this be a key labour ward for the world’s whale sharks? Last year a BBC film crew at the Galapagos attempted to follow a pregnant female in a submersible to watch it give birth, but to no avail. That’s one secret that the depths are keeping for now.

Joshua Copping, PhD Candidate in Environmental Sciences, University of Salford and Bryce Stewart, Lecturer in Marine Ecosystem Management, University of York

This article was originally published on The Conversation. Read the original article.

Mathematics talent abounds in Indigenous communities


By Veselin Jungic, Simon Fraser University

On the occasion of National Indigenous Peoples Day, I would like to show how ubiquitous mathematics — and mathematics talent — is within Indigenous cultures. As a mathematician who immigrated to Canada, and who has worked at universities for most of my adult life, my teaching and learning experiences have shown me this first hand.

After attending the First Nations Math Education Workshop in Banff in 2009, I launched the Math Catcher Outreach Program at Simon Fraser University (SFU), which uses the model of the Indigenous storytelling as a tool to attract youth to the study of mathematics.

The main goal of the program is to encourage both Indigenous and non-Indigenous students to discover the joy and appeal of mathematics in the hope that they may better understand the presence of math and its importance in everyday life, and consider mathematics as a field of study and vocation.

Inspired by Indigenous storytelling traditions, the program has created animated films in several Indigenous languages. We also coordinate a volunteer tutoring activity between the Native Education College and SFU.

Small Number and the Basketball Tournament.

We regularly visit First Nation communities across B.C. and Alberta to hold workshops for students and teachers, or to collaborate with the community members on math-related projects.

Through the Math Catcher Program, I’ve had the privilege to interact with hundreds of Indigenous students and their parents, elders, teachers and community members, both in urban and rural settings. These interactions have made it clear to me that talent and interest in mathematics abound among Indigenous learners.

It has also become clear to me that there is a profound mathematical presence in various Indigenous traditions, from art to weaving patterns in cedar root and birch bark baskets, to canoe designs, the strategies of the salmon harvest and the ways of managing resources.

Mathematical presence in Indigenous traditions

A recent Math Catcher visit to Tla’amin Nation included a community event built around several hands-on mathematical activities. In one activity, we explored the properties of the Möbius strip, a surface with only one side and one edge.

In another, we examined a challenging puzzle that required making a braid with six crossings and with no free ends from a piece of paper with two slits. The underlying mathematics of both of these activities is quite complex.

Sosan, a young woman who came to the workshop with her two children was among the event participants. I told her how impressed I was with how quickly she grasped the activities and she answered with something that I regularly hear: “I was never good at math.”

The following morning, after a Math Catcher workshop in the neighbourhood school, a teacher handed me a small package from Sosan containing two objects.

One was a small Möbius strip masterfully woven from cedar inner bark. Sosan’s creation captured the true essence of the Möbius strip: It is impossible to find where the strip begins and where it ends.

The other was a solid braid with twelve crossings and no free ends made from a long piece of bark. To create this braid one needs a great deal of skill and ingenuity because solving this puzzle requires both braiding and unbraiding. Sosan had to process the bark to make it pliable, then braid it, and then return the bark back to its solid state.

Small Number and the Old Canoe.

As a longtime university math instructor, I felt almost certainly, that no one had considered that solution until that moment. What kind of knowledge, talent and inspiration were needed to find a method and to execute it so precisely by creating a model of a complex mathematical object?

I wonder when Sosan came up with the braid in bark problem? During our event? While driving back home? While putting her children to bed?

In my career as a mathematician, I have been fortunate to collaborate with some of the most talented mathematicians in my area of study, Ramsey theory. My encounter with Sosan’s creativity and her deep understanding brought back that same dizzying feeling of witnessing something very special when I had worked with some of the finest mathematical minds.

Sosan’s gifts are now two of my most valued possessions.

This experience also describes what I consider a great challenge for my teaching and academic communities. What can we do, collectively and as individuals, to further challenge ways of thinking about mathematics? How can we create and sustain an environment for learning mathematics in which Indigenous learners can share their knowledge and skills with the broader community?

In other words, we need an environment for learning mathematics where we, as part of the school system as a whole, will listen and learn from our Indigenous learners about mathematical forms and the applications of mathematics that may be outside of what the current math curriculum prescribes.

How can we urge and support Indigenous students to further explore and develop their talents in mathematics?

The ConversationFor me, for now, it is one Math Catcher event at a time.

Small Number and the Old Totem Pole in Sliammon.

Veselin Jungic, Professor, Simon Fraser University

This article was originally published on The Conversation. Read the original article.