The final episode of Tom Rocks Maths on Oxide Radio for 2018 goes out with a bang. We’ve got another million-dollar maths problem, a healthy dose of nakedness, and we try chopping up traffic cones with a saw. Plus, music from Jay-Z/Linkin Park, the Red Hot Chili Peppers and the Foo Fighters. This is maths, but not as you know it…
Bees are not only able to build fantastic hexagonal honeycombs they’re apparently also able to count! But do they deserve their reputation as nature’s mathematicians? Georgia Mills spoke to Srini Srinivasan from the University of Queensland to find out how they discovered counting bees…
- Bees were trained to fly down a tunnel with a reward of sugar water at the end, and a series of identical landmarks labelled 1, 2, 3, 4, etc. along the route.
- One of the landmarks contained the reward and the bees had to test each one to discover its location. This was repeated several times until the bees learned the location of the reward.
- The spacing of the landmarks was then changed, but the reward remained at the same landmark, and the bees had to find it once again.
- They were able to ‘count’ the number of landmarks and would go straight to the correct location bypassing the others that did not contain a reward.
- The highest number of sequential landmarks the bees were able to ‘count’ was 4.
- Four is a universal number as when briefly presented with an image containing a number of objects, the largest amount most animals can recognise accurately is 4-5. This process is called subitising.
- Counting to 4 is useful for bees when for example deciding whether or not to land on a flower to collect pollen. If there are 3-4 bees already there then it is probably not worth their effort.
- Counting has also been looked at in fish birds and chimpanzees, and in each case the number four keeps cropping up, suggesting universality.
- The tunnel experiment was actually designed to investigate how bees navigate and the corresponding ‘waggle dance’ that they use to communicate information.
You can listen to the full interview with the Naked Scientists here.
Arriving at St John’s in 2008 to begin my study of mathematics, I was certain that within 4 years I would be working in the city as an actuary or an investment banker. Whilst I loved my subject, I saw it as means to obtain a good degree that would set me up for a career in finance. I’m not sure I could have been more wrong…
My current journey began towards the end of my second year, where I found myself enjoying the course so much that I wanted to continue to do so for as long as possible. This led me to research PhD programmes in the UK and the US, and I was fortunate enough to be offered a place to study Applied Maths at the University of Cambridge in 2012. During my time at Oxford, I found myself straying further and further into the territory of applied maths, culminating in a fourth-year course in fluid mechanics – the study of how fluids such as water, air and ice move around. This ultimately led to my PhD topic at Cambridge: where does river water go when it enters the ocean? (If you’re interested to find out more I’ve written a series of articles here explaining my thesis in simple terms.)
As part of my PhD I conducted experiments, worked on equations and even took part in a research cruise to the Southern Ocean. It was on my return from 6 weeks at sea that I had my first taste of the media industry via a 2-month internship with the Naked Scientists. I would spend each day searching out the most interesting breaking science research, before arranging an interview with the author for BBC radio. It was great fun and I learnt so much in so many different fields that I was instantly hooked. Upon completion of my PhD I went to work with the Naked Scientists full time creating a series of maths videos looking at everything from beehives and surfing, to artwork and criminals. You can watch a short trailer for the Naked Maths series below.
My work with the BBC and the media in general ultimately led me to my current position as a Mathematics Tutor at three Oxford colleges: St John’s, St Hugh’s and St Edmund Hall. This may not sound like the media industry, but the flexibility of the position has allowed me to work on several projects, including launching my website and my YouTube channel @tomrocksmaths where I am currently running two ongoing series. In the first, Equations Stripped, I strip back the most important equations in maths layer-by-layer; and for the second series in partnership with the website I Love Mathematics, I answer the questions sent in and voted for by students and maths-enthusiasts across the world.
Alongside my online videos, I am also writing a book discussing the maths of Pokémon – Pokémaths – and have a weekly show with BBC radio called ‘Funbers’ where I tell you the fun facts about numbers that you didn’t realise you’ve secretly always wanted to know. I have also recently presented at conferences in the US and India and hold regular talks at schools and universities, including for the Oxford Invariants and the Maths in Action series at Warwick University where I faced my biggest audience yet of 1200.
Looking back at my time at St John’s, I never would have imagined a career in the media industry lay before me, but the skills, experience and relationships that I formed there have undoubtedly helped to guide me along this path. I think it just goes to show that Maths is possibly the most universal of all subjects and really can lead to a career in any industry.
In October 2017, Dr Tom Crawford joined St Hugh’s as a Lecturer in Mathematics. He has since launched his own award-winning outreach programme via his website tomrocksmaths.com and in the process became a household name across Oxford University as the ‘Naked Mathematician’. Here, Tom looks back on the past year…
I arrived at St Hugh’s not really knowing what I was getting into to be completely honest. I’d left a stable and very enjoyable job as a science journalist working with the BBC, to take a leap into the unknown and go it alone in the world of maths communication and outreach. The plan was for the Lectureship at St Hugh’s to provide a monthly salary, whilst I attempted to do my best to make everyone love maths as much as I do. A fool’s errand perhaps to some, but one that I now realise I was born to do.
The ‘Naked Mathematician’ idea came out of my time with the Naked Scientists – a production company that specialises in broadcasting science news internationally via the radio and podcasts. The idea of the name was that we were stripping back science to the basics to make it easier to understand – much like Jamie Oliver and his ‘Naked Chef’ persona. Being predominantly a radio programme, it was relatively easy to leave the rest up to the listener’s imagination, but as I transitioned into video I realised that I could no longer hide behind suggestion and implication. If I was going to stick with the ‘Naked’ idea, it would have to be for real.
Fortunately, the more I thought about it, the more it made sense. Here I was, trying to take on the stereotype of maths as a boring, dreary, serious subject and I thought to myself ‘what’s the best way to make something less serious? Do it in your underwear of course!’ And so, the Naked Mathematician was born.
At the time of writing, the ‘Equations Stripped’ series has received over 100,000 views – that’s 100,000 people who have listened to some maths that they perhaps otherwise wouldn’t have, if it was presented in the usual lecture style. For me that’s a huge victory.
Of course, not all of my outreach work involves taking my clothes off – I’m not sure I’d be allowed in any schools for one! I also answer questions sent in by the viewers at home. The idea behind this is very simple: people send their questions in to me @tomrocksmaths and I select my favourite three which are then put to a vote on social media. The question with the most votes is the one that I answer in my next video. So far, we’ve had everything from ‘how many ping-pong balls would it take to raise the Titanic from the ocean floor?’ and ‘what is the best way to win at Monopoly?’ to much more mathematical themed questions such as ‘what is the Gamma Function?’ and ‘what are the most basic mathematical axioms?’ (I’ve included a few of the other votes below for you to have a guess at which question you think might have won – answers at the bottom.)
The key idea behind this project is that by allowing the audience to become a part of the process, they will hopefully feel more affinity to the subject, and ultimately take a greater interest in the video and the mathematical content that it contains. I’ve seen numerous examples of students sharing the vote with their friends to try to ensure that their question wins; or sharing the final video proud that they were the one who submitted the winning question. By generating passion, excitement and enthusiasm for the subject of maths, I hope to be able to improve its image in society, and I believe that small victories, such as a student sharing a maths-based post on social media, provide the first steps along the path towards achieving this goal.
Speaking of goals, I have to talk about ‘Maths v Sport’. It is by far the most popular of all of my talks, having featured this past year at the Cambridge Science Festival, the Oxford Maths Festival and the upcoming New Scientist Live event in September. It even resulted in me landing a role as the Daily Mirror’s ‘penalty kick expert’ when I was asked to analyse the England football team’s penalty shootout victory over Colombia in the last 16 of the World Cup! Most of the success of a penalty kick comes down to placement of the shot, with an 80% of a goal when aiming for the ‘unsaveable zone’, compared to only a 50% chance of success when aiming elsewhere.
In Maths v Sport I talk about three of my favourite sports – football, running and rowing – and the maths that we can use to analyse them. Can we predict where a free-kick will go before it’s taken? What is the fastest a human being can ever hope to run a marathon? Where is the best place in the world to attempt to break a rowing world record? Maths has all of the answers and some of them might just surprise you…
Another talk that has proved to be very popular is on the topic of ‘Ancient Greek Mathematicians’, which in true Tom Rocks Maths style involves a toga costume. The toga became infamous during the FameLab competition earlier this year, with my victory in the Oxford heats featured in the Oxford Mail. The competition requires scientists to explain a topic in their subject to an audience in a pub, in only 3 minutes. My thinking was that if I tell a pub full of punters that I’m going to talk about maths they won’t want to listen, but if I show up in a toga and start telling stories of deceit and murder from Ancient Greece then maybe I’ll keep their attention! This became the basis of the Ancient Greek Mathematicians talk where I discuss my favourite shapes, tell the story of a mathematician thrown overboard from a ship for being too clever, and explain what caused Archimedes to get so excited that he ran naked through the streets.
This summer has seen the expansion of the Tom Rocks Maths team with the addition of two undergraduate students as part of a summer research project in maths communication and outreach. St John’s undergraduate Kai Laddiman has been discussing machine learning and the problem of P vs NP using his background in computer science, while St Hugh’s maths and philosophy student Joe Double has been talking all things aliens whilst also telling us to play nice! Joe’s article in particular has proven to be real hit and was published by both Oxford Sparks and Science Oxford – well worth a read if you want to know how game theory can be used to help to reduce the problem of deforestation.
Looking forward to next year, I’m very excited to announce that the Funbers series with the BBC will be continuing. Now on its 25th episode, each week I take a look at a different number in more detail than anyone ever really should, to tell you everything you didn’t realise you’ve secretly always wanted to know about it. Highlights so far include Feigenbaum’s Constant and the fastest route into chaos, my favourite number ‘e’ and its link to finance, and the competition for the unluckiest number in the world between 8, 13 and 17.
The past year really has been quite the adventure and I can happily say I’ve enjoyed every minute of it. Everyone at St Hugh’s has been so welcoming and supportive of everything that I’m trying to do to make maths mainstream. I haven’t even mentioned my students who have been really fantastic and always happy to promote my work, and perhaps more importantly to tell me when things aren’t quite working!
The year ended with a really big surprise (at least to me) when I was selected as a joint-winner in the Outreach and Widening Participation category at the OxTALENT awards for my work with Tom Rocks Maths, and I can honestly say that such recognition would not have been possible without the support I have received from the college. I arrived at St Hugh’s not really knowing what to expect, and I can now say that I’ve found myself a family.
Answers to votes (watch by clicking the links):
- What is the probability I have the same PIN as someone else?
- How does modular arithmetic work?
- What would be the Earth’s gravitational field if it were hollow?
- What are grad, div and curl? COMING SOON
On the 30th June 2015 an extra second was added to clocks across the world. Seeing as you now have all of this extra time, here’s everything you need to know about the leap second…
- The leap second arises because the atomic clocks that we use today are actually more accurate than the earth at time keeping – one million times more accurate to be exact.
- Changes in the Earth’s orbit are influenced by a number of factors: from an occasional wobble to a gradual slowing of its rotation. This causes the Earth to speed up and slow down unpredictably and is the reason why we need to add leap seconds.
- A total of 27 leap seconds have been added since 1972 when the idea was first introduced.
- The last leap second was added at midnight on December 31st 2016, but due to the unpredictability of the Earth’s orbit I can’t actually tell you when the next one will be!
- Don’t worry though, all electronic devices are updated automatically so long as they’re connected to the internet.
You can listen to the 2015 announcement with the Naked Scientists here.
We’ve seen many recent extreme weather events – from mudslides in Columbia to flooding in Australia – which scientists say are a consequence of climate change; but it’s not just the weather that is affected. The Earth’s atmosphere is made up of several layers of air which all flow around each other in patterns known as jet streams and an increase in temperature will cause these to speed up. This is bad news for air passengers, including the 1 million people currently airborne at this very instant, because an increase in the speed of the jet streams will cause more turbulence making flying less comfortable and potentially more dangerous. I spoke to atmospheric scientist Paul Williams…
- Climate change will cause a 59% increase in light turbulence, 94% increase in moderate turbulence, and 140% increase in severe turbulence.
- Turbulence is measured on a scale from 1 to 7 where 1 means light turbulence, 3 means moderate, 5 means severe, and 7 means extreme.
- Light turbulence is a slight strain against the seat belt, moderate turbulence causes unsecured objects to become dislodged and makes walking around difficult, and severe turbulence results in anything that isn’t strapped down being catapulted around the cabin.
- Turbulence is caused by wind shear – the higher you go up into the atmosphere the windier it gets – and instabilities within these layers of shear generate turbulence.
- As the atmosphere is heated, the temperature increase causes the jet streams to move faster, creating more wind shear and thus more turbulence.
- The researchers hope that results such as this will encourage us to think more carefully about our carbon footprint as there are likely many effects of Climate Change that we do not know about.
You can listen to the full interview for the Naked Scientists here.
How fast should an animal be able to move? And why are the biggest animals, which pack more muscle, not the fastest? That’s what Yale scientist Walter Jetz was wondering, so he and his colleagues looked at hundreds of animal species and have come up with a new theory that successfully puts a speed limit on most species…
- There is a theoretical maximum speed that is expected to increase with body size, however, in order to actually get to any speed you need to first accelerate, and larger animals take much longer to do so – much like a truck accelerating to 60mph compared to a motorbike or car.
- Large bodied animals simply do not have sufficient energy to reach their theoretical maximum speed.
- The general distribution is a ‘hump-shape’ as shown in the plots below. Maximum speed increases with size until we reach a critical mass beyond which the maximum speed reached starts to decrease.
- Data for over 450 species were included in the study, across land, air and water.
- The study provides insight into evolutionary trade-offs for different species as they evolve to increase their chances of survival.
You can listen to the full interview with the Naked Scientists here.
Image copyright Dawn Key
We are now just over a week into the new year, how are those resolutions going? If like me you felt bad for (at least) a week’s worth of pigging out over the holiday season, then maybe you’ve been on a detox? They are a quick easy way to get healthy right? Yeah about that…
Most people think of a detox as some form of cleanse that removes various toxins from the body, usually after a period of excessive eating and drinking. While not completely incorrect, the use, or misuse, of the word nowadays is the result of very clever marketing. The correct definition of a detox is a medical procedure that removes dangerous and often life-threatening levels of drugs, alcohol and poisons from the body carried out by a trained medical professional in a hospital or clinic. Not quite the same as drinking some carrot juice then. What we’re doing is more of a ‘cleanse’.
The idea of cleansing the body isn’t new, but the way we do it has changed dramatically. Go back 100 years and we were using therapeutic vomiting, blood-letting and a process known as ‘smuding’ where smoke from burning sage is waved around the energy field of a person to destroy negative energy. These days it’s all intestinal cleaning, foot sponges which supposedly draw out toxins and coffee enemas (yes you read that correctly). The question is does detoxing (or cleansing) really do anything?
Let’s take a simple example: a master cleanse diet favoured by a number of Hollywood celebrities. Begin the day with a litre of warm salt water, consume 2 litres of a concoction of water, lemon juice, maple syrup and cayenne pepper throughout the day and finish with 250ml of laxative in the evening. Do this for 10 days and you will gain energy, lose weight and relieve symptoms of chronic conditions such as arthritis. Except you probably won’t. There are no data on this diet in the medical literature and similar studies on fasts and extremely low-calorie diets actually result in rapid weight gain following their completion. You will of course lose weight during the diet as you are only consuming 600 calories a day, but this is mostly due to fluid loss. Furthermore, the diet is lacking in protein, fatty acids and other essential nutrients, with the daily laxative regime likely to cause dehydration. Just this week doctors in the UK issued a health warning about the potential harms of undertaking a radical new year detox, highlighting the example of a 47-year-old woman admitted to intensive care following a detox diet of herbal remedies and water, that left her with dangerously low levels of salt in her body.
A search of medical literature using the words ‘detox’ and ‘clinical trial’ returns nothing. Quite simply there is no credible evidence to demonstrate that detox kits do anything at all. Perhaps most importantly they have not been shown to offer any of the supposed health benefits claimed by manufacturers and promoters. This may seem a little doom and gloom for the new year, but don’t worry, your body has got you covered. The human body is the best detoxing solution available and here’s how it works.
Let’s pretend I’m one of these mysterious ‘toxins’ trying to enter your body, cleverly concealed in your favourite alcoholic beverage. First up, I pass through the stomach and into the intestines, where I am confronted with lymph nodes called Peyer’s patches. These guys screen out parasites and other foreign substances before they are absorbed into the blood along with nutrients. Well, what if I disguise myself as a nutrient? Now I’m in the blood and ready to do some damage. But what’s this? An army of cells and molecules sent by the immune system are here to fight me off. They are specifically designed to recognise foreign substances and eliminate them from the body, making me target number one. Okay, well, suppose I somehow survive the onslaught from the army of cells, things must surely start to look up? Afraid not. The blood is passed through the liver where proteins called metallothioneins act to neutralise harmful metals and enzymes process drugs. The job of the liver is basically to break down anything that can cause harm to your body, which is bad news for me as a ‘toxin’. If by some miracle there is anything left of me after the liver has worked its magic then I will enter into the kidneys. These are the body’s natural filtration system and remove any waste substances that remain. I think it’s safe to say I’m done for…
If after all of that you still think the so-called ‘toxins’ have a chance, then by all means please do try that coffee enema, but if it were up to me I’d trust my body. The best new year detox plan is simply to concentrate on giving your body what it needs to do its job. That means a healthy diet, regular exercise and sufficient sleep. It might be less exciting than that Colon Detox Pro yoga session you had planned, but it also might actually work…
You can listen to the full interview for the Naked Scientists here.
Growing a human heart from a single cell may seem like science fiction, but scientists at the Gladstone Institute at the University of California San Francisco, have taken a huge step forward, by producing the first three-dimensional, beating, human heart chamber. Previously, it had been possible to produce a two dimensional sheet of beating heart cells, but to really gain an understanding of heart formation in a developing foetus and perhaps more importantly, how drugs given to women during pregnancy may affect this development, a three dimensional structure was needed. By treating stem cells with drugs and then confining them to a very small spherical geometry, Bruce Conklin and his team have managed to grow their very own three dimensional model of a human heart, as he explains…
Bruce – the cells around the edge became fibroblasts – a particular type of cell that you use to heal wounds and then only in the very centre were cardiac cells that beat. What this is forming is more of a little organoid is what we call it, where there’s beating cells but there’s also multiple other cell types and that’s what makes it so interesting is that these cell types are somehow talking to each other and somehow collaborating in some way so that they can actually make this structure that we didn’t expect.
Tom – It’s almost like they’re trying to form a heart…
Bruce – That certainly is the impression. They’re heart cells, they’re forming cavities so it could be a model of how parts of human development occurs, but it certainly is not a real human heart in the sense that there’s probably many things that we’re missing. We just have a simplified version with just one chamber, but having it in a controlled way where it happens the same way over and over again we can start asking questions about ‘how do these cells talk to each other?’ So once you have a system which is reproducible you can do experiments to break it in some way or to enhance it in another way.
Tom – What are the applications of this work then?
Bruce – The most obvious application of the work is to study human development. How do cells actually form a heart is something of basic interest. And also, the most common form of birth defects is actually cardiac defects. But the other application is that we can expose these developing human micro-chambers to drugs which are thought to cause developmental defects, specifically of the heart, and in fact one of the key experiments in this study was to use the drug thalidomide which is notorious for causing birth defects. When we expose these cells to the thalidomide they had a dramatic change in the morphology so that you could see that it was altering the developmental process in this micro-chamber. Thalidomide was tested in rodents before it was tried in people and there were no cardiac defects in the rodents. I think that more and more we’re thinking how do we get tests which use real human cells so that we can actually make safer drugs. And in this case say you turn back the hands of time and you had this sort of test perhaps you would have discovered that thalidomide was dangerous before it had gone on to be given to people.
You can listen to the full interview with the Naked Scientists here.