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During my recent trip to Madrid to speak at the Residencia de Estudiantes, I was interviewed by national newspaper ‘El Mundo’ about my talk on the ‘Maths of Sport’ and my mission to popularise maths. The original interview can be found here.
Known as Tom Rocks Maths, the Oxford University scientist transforms boring formulas into fascinating models that he applies to sport to improve records and reduce errors.
MAR DE MIGUEL | Madrid
Football World Cup, 2018. 1-1 on the scoreboard. Spain plays its pass to the quarterfinals in the penalty round against Russia. Koke has failed one. Cheryshev is ready to throw. He scores. It’s up to Aspas. Expectation. Whistle. Launch and … Akinfeev stops it. We miss the game.
Could it have been avoided? The answer is Tom Crawford, l’ enfant terrible of numbers, a punkrocker in the court of mathematicians at the University of Oxford. And he explains it with a worn shirt, leather jacket, curled hair, piercing and tattoos. Because Crawford is not a common scientist. He is Tom Rocks Maths, an alternative researcher and communicator who transforms boring formulas into fascinating models that he applies to sports science, his second passion as a marathoner and a follower of Manchester United.
But, since all science is not exact, nor is Crawford a fortune teller, his predictions are based on data, taking into account all possible variables and, above all, on the highest probability of hitting. It is about getting ahead of the facts, of having all the necessary information to reduce errors and improve the records.
The mathematics of sport consist of “building models using data from the past to predict the future. When you don’t have them, you have to go to the field, contact the athletes and gather new information, ”explains Crawford in an interview with EL MUNDO after the talk he gave Tuesday in Madrid during the cycle of conferences ‘Mathematics in the Residence’, organized by ICMAT, the Student Residence and the Deputy Vice Presidency of Scientific Culture of the CSIC.
Win or lose penalties
The countries that best know how to throw penalties are Uruguay, Germany, Argentina and Brazil. Spain is not good, not bad. We are 50% among this list of experts and 50% of the worst, Mexico. We share media with France and Ireland. But how a team is better than another is not a matter of tradition or genetics, but numbers.
The first thing is to know how the players have responded before to the penalties, their statistics of failures and successes. According to Crawford, in the case of the 2018 World Cup, while Iniesta had four hits of five shots, Koke had zero of one and Aspas 16 of 17. The great surprise could have been given by Thiago, a substitute with a full in hits, four of four.
There is also a way to measure their stress responses with glasses that observe the movements of the eye. Footballers who are not immuted by pressure keep their eyes fixed and the most distracted move them. Knowing this in advance could decide the choice of a coach to choose the most focused players on those decisive penalties of a World Cup. “Football clubs now have entire teams of mathematicians and scientists who analyze all this data,” says Crawford.
But math doesn’t end there. In a goal you can make as many measures as your imagination, as Archimedes, to find the radius that indicates the exact area where you should place the ball without being stopped by the goalkeeper. It is called an insurmountable area and it depends, among other things, on the distance the goalkeeper moves in the shortest possible time from his position in the center. It looks like this: r2-2r(a+b+R)+a2+b2-R2. “These calculations are going to help you but they don’t guarantee that the penalty is perfect. In fact, the goalkeeper may also have trained against these formulas, ” Crawford alerts.
Roberto Carlos, the king of the Magnus effect
If penalties are a science, free kicks are not far behind. Defining its trajectory is one of Crawford’s favorite equations when the ball is given effect, as we have allways called it, which also has its scientific name: Magnus effect. “The ball that spins does not go in a straight line, because the rotation moves it to the side,” he said.
In this modality, for Crawford there is a master: Roberto Carlos, king of the Magnus effect in a match against France in 1997. It happened like this: he carefully placed the ball with his hands on the ground. He kicked. The ball passed over the barrier of players, turned in the air to the right, then to the left, hit a stick and entered as a stroke.
“I saw it when i was eight years old and I thought that it was impossible, that it was magic. But years later, using this equation to model Roberto Carlos’s shot, by entering the correct data (the speed of the ball, the distance to the door and the spin that applies to the ball) the formula accurately predicted that movement. It is still amazing. Although now I have an explanation that tells me that it did not break the barriers of physics.”
Marathon in less than two hours
In Tom Crawford’s mind there are not only favorite sport formulas but also graphics. And if there is one that drives him crazy it is the one that calculates, with a curve, when you will be able to run, with conventional methods, a marathon in less than 2 hours, something that it could happen between 2027 and 2035.
The record is owned by Kenyan Eliud Kipchoge, 2:01:39. He obtained it in Berlin in September 2018. In October of this year, the same athlete beat it at 1:59:40, but his feat was not accepted by the International Athletics Federation. “It has not been taken into account because they have broken the rules. As a new official mark, this record below two hours does not count, ”says Crawford.
How they did it? “Creating the perfect race,” says Crawford. And something else: a flat route in a straight line to go through the center of the track; a pair of shoes with carbon fiber that balances and saves 4% of energy; a tape on the leg with lumps (like golf balls) that create streams; a squad of escorts in V to cut the wind (called hares); a car that laser marks the ground so that these satellite corridors maintain the perfect position; a scanner that controls the muscle accumulation of carbohydrates and an enriched diet.
“Where you draw the line between what is due to the human element or an incredible shoe. What is the next? Putting rockets in our soles? ”Crawford wonders. We saw it in swimming a few years ago with high-tech swimsuits that reduce friction with water. They were even questioned for increasing buoyancy. With them, in some competitions 130 records were broken in just two years.
It is clear that mathematics helps to overcome tests and marks. However, in sports there are uncontrollable factors, such as the mental control of athletes, to disarm algorithms. “You can never add that factor to your models. You can never really predict a sport with total certainty. There are many unknown variables, ”reflects the English mathematician.
And, returning to the football game that we lost in 2018, would we have win if we knew the data in depth and having other players thrown the penalties that took us out of the World Cup? According to Crawford, we could have reduced the risk of losing, but this is something we will never know. What is highly certain is that their talks not only reinforce the devotion to sports, but also awake the mathematical vocation of the youngest students.
Tom “rocks” maths on the internet – lecturer from Oxford arouses enthusiasm with crazy ideas…
The graduate mathematician Tom Crawford not only has rock music as a hobby, but he also looks like a rock star with his tattoos and piercings. However, some of his tattoos are related to mathematics. For example, the first 100 decimal places of Euler’s number wind around his arm and the number pi has been encrypted as an infinite series. On his Youtube channel “Tom Rocks Maths” he presents science in a fun way – the clothes sometimes fly during a striptease: “I want to show that maths is not always only downright serious, but fun.”
The math lecturer from Oxford came as part of the Heidelberg Laureate Forum (HLF) in the Electoral Palatinate. Since there is no Nobel Prize in mathematics, the winners (Latin: laureates) of comparable awards are invited to the HLF. The best math and computer scientists in the world meet here for a week with junior scientists and journalists. Crawford was on the ground as a publicist and presenter, and took the opportunity to speak to some of the awardees. For example, Martin Hairer, who received the Fields Medal for his seminal studies, had an appointment for an interview. In the end, they played Tetris for an hour and talked about “cool math”: “Such a relaxed and profound conversation is only possible at the Heidelberg Laureate Forum,” the Brit enthuses about the inspiring atmosphere at the HLF.
Tom Crawford was already “packed” in the elementary school of mathematics: “When we were learning multiplication, I did not want to stop working on difficult tasks until late in the evening – it did not feel like work at all.” Even later in high school, he always did math tasks first and gladly. “I was a good student in my eleven subjects, but math was the most fun.” The satisfying thing is, “in maths a result is right or wrong, there is no need to discuss it.”
After studying in Oxford, he went to Cambridge to write his PhD in fascinating fluid dynamics. “We wanted to model how fluids move and interact with the world. I was excited about the prospect of being able to analyse experiments as a mathematician.” From this, models of reality were developed: what path does a river take when it flows into the sea? The findings help to understand the pollution of the oceans and possibly stop it. During his PhD he worked for the BBC in the science programme “The Naked Scientists”: this meant that the scientists liberated their theories from the complicated “clothes” and reduced them to a comprehensible basis. In this way, a layman will discover “naked” facts – in the sense of comprehensible ones. The radio broadcasts were a great success.”But you also have to visualize maths,” so he started to make his own videos and took the concept of the “naked mathematician” literally. In some lectures, he reveals the equations “layer by layer” and in each stage falls a garment – until Tom remains only in his boxer shorts. And then his tattoos are also visible, on whose mathematical background he will give a lecture in Oxford soon – with many guests guaranteed!
With unusual ideas, the only 29-year-old mathematician arouses the desire and curiosity for his subject. His original internet activities have now been honoured with an innovation prize. Even when attending school in Schwetzingen Tom Crawford had unusual questions: “In the stomach of a blue whale 30 kilos of plastic have been found: How much would that be if a person swallows just as much in relation to their own body weight?” The students calculated that in the human stomach, six (empty) plastic shopping bags would be located. Or, “How many table tennis balls are needed to lift the sunken Titanic off the ground?” And which example impressed him most in mathematics? “It is terrific how Maxwell’s equations, which deal first with electricity and magnetism, follow the wave property of light with the help of mathematics alone. Math is just fantastic! ”
The original article published in the Die Rheinpfalz newspaper (in German) is available here.
“30kg of plastic has been found in a blue whale’s stomach: how much would that be if a person swallowed just as much proportional to their own bodyweight?” Tom Crawford from Oxford began his guest lecture at Hebel-Gymnasium with this question. The students calculated that you’d find six (empty) plastic shopping bags in a human stomach. The other results worked out over the course of the entertaining presentation were also very impressive.
Tom Crawford doesn’t just have rock music as a hobby, rather with his tattoos and piercings, he looks like a rockstar too – though his tattoos are all to do with maths: since for example, the decimal places of “e” (Euler’s number) wind around his arm, the number pi is also encoded in an infinite series. On his YouTube channel “Tom rocks maths”, he presents science in an entertaining way – sometimes even pieces of clothing fly off during stripteases: “I want to show that maths isn’t always just super serious but it can also be fun.”
The mathematics lecturer is currently part of the Heidelberg Laureate Forum in Heidelberg. This is where the best maths and computer scientists in the world are meeting up with junior researchers and journalists. Crawford came to Schwetzingen at the invitation of maths teacher Birgit Schillinger. He brought along some exciting questions. The common theme was Tom’s favourite number, pi, which is used in so many formulas. How many ping pong balls are needed to lift the sunken Titanic off the ground? Which factors are involved when a footballer bends a ball so that it flies in an arc past the wall into the goal? When calculating the trajectory, several physical variables play a role. But how? Crawford studied the mathematics behind it. His doctoral thesis was on fluid mechanics: What path does a river take when it flows into the sea? The findings help us to understand sea pollution and possibly help to stop it.
At the end, the Hebelians made Platonic solids, of which, amazingly, there are only five. Strange? No, Tom explains this number by the sum of the angles at the corners – all very logical! Finally a student’s question, which example in mathematics has impressed Tom the most: “It is terrific how the wave characteristic of light follows from Maxwell’s equations, which deal with electricity and magnetism, with only the help of mathematics. Maths is just awesome!”
Thanks to Cameron Bunney for the translation.
The original article in Schwetzingen can be found here.
Episode 10 of Tom Rocks Maths on Oxide Radio sees the conclusion of the million-dollar Millennium Problem series with the Hodge Conjecture, a mischievously difficult number puzzle, and the answer to the question on everyone’s lips: how many people have died watching the video of Justin Bieber’s Despacito? Plus, the usual great music from the Prodigy, the Hives and Weezer.
Image credit: Lou Stejskal
Incredibly excited to be featured on the legendary Numberphile explaining the million-dollar problem that is the Navier-Stokes Equations…
More great music and great maths from Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station. Featuring special guest Yuxiao who explains the Monty Hall problem, tackles the infamous numbers quiz, and sets us not one, but THREE problems in a bumper edition of the weekly puzzle. Plus, music from ACDC, Gym Class Heroes and The Offspring. This is maths, but not as you know it…
Thanks to Alice Taylor for production assistance.
3rd year Oxford Maths student Dan talks about his decision to choose Maths at university and the role models that helped him to get there.