A short sneak preview of the full-length ‘Mandelbulbs’ video currently in production. A Koch Snowflake is an example of a 2D fractal with infinite perimeter but finite area. Full details of the calculation in the final video… COMING SOON!
As a new member of the BIG STEM Communicators Network I was very pleased to be featured in the member spotlight for spring 2019. (The original article is ‘members only’ so I’ve copied the text below.)
“As a new member of the BIG community I would like to introduce myself as the ‘Naked Mathematician’ (yes you did read that correctly). I am a Maths Tutor at the University of Oxford with a goal to reduce fear and anxiety towards maths. One of the ways in which I do this is to take my clothes off – what better way to emphasise that the subject is not as serious and intimidating as many people think than by teaching in my underwear! The concept began as a series of videos on my YouTube channel entitled ‘Equations Stripped’ where I strip back some of the most famous equations in maths (and myself) layer-by-layer so that everyone can understand, and has since evolved into a live performance now touring universities across the UK. My efforts to bring maths to a new audience have been recognised by the University of Oxford, where I was awarded first prize in the Outreach and Widening Participation category at the OxTALENT awards, and I have also been shortlisted for the Institute of Physics Early Career Communicator award.
The ‘Naked Mathematician’ is of course not appropriate for every audience and as such is only a small part of the work that I do to share my love of maths. My ‘Funbers’ series was broadcast throughout 2018 on BBC Radio, where in each episode I look at numbers more closely than anyone really should to bring you the fun facts that you didn’t realise you’ve secretly always wanted to know… I also try to involve my audience in the creative process as much as possible by issuing a call for questions on social media and then hosting a vote to decide the topic of my next video in the ‘I Love Mathematics’ video series. Finally, I combine my love of sport with maths in my popular ‘Maths v Sport’ talk which features a live penalty shootout on stage and an attempt to break a running world record (appropriately scaled of course!).
All of the material that I produce is available for free on my website tomrocksmaths.com and associated social media profiles @tomrocksmaths on Facebook, Twitter, Instagram and YouTube. I am very excited to have joined BIG and look forward to working with the community to help to share STEM subjects with the world!”
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.
On Wednesday March 13th I’ll be presenting my research to MP’s at the Houses of Parliament in the final of the STEM for Britain Competition. You can find my research poster on modelling the spread of pollution in the oceans here.
Dr Tom Crawford, 29, a mathematician at Oxford University hailing from Warrington, is attending Parliament to present his mathematics research to a range of politicians and a panel of expert judges, as part of STEM for BRITAIN on Wednesday 13th March.
Tom’s poster on research about the spread of pollution in the ocean will be judged against dozens of other scientists’ research in the only national competition of its kind.
Tom was shortlisted from hundreds of applicants to appear in Parliament.
On presenting his research in Parliament, he said, “I want to bring maths to as wide an audience as possible and having the opportunity to talk about my work with MP’s – and hopefully show them that maths isn’t as scary as they might think – is fantastic!”
Stephen Metcalfe MP, Chairman of the Parliamentary and Scientific Committee, said: “This annual competition is an important date in the parliamentary calendar because it gives MPs an opportunity to speak to a wide range of the country’s best young researchers.
“These early career engineers, mathematicians and scientists are the architects of our future and STEM for BRITAIN is politicians’ best opportunity to meet them and understand their work.”
Tom’s research has been entered into the mathematical sciences session of the competition, which will end in a gold, silver and bronze prize-giving ceremony.
Judged by leading academics, the gold medalist receives £2,000, while silver and bronze receive £1,250 and £750 respectively.
The Parliamentary and Scientific Committee runs the event in collaboration with the Royal Academy of Engineering, the Royal Society of Chemistry, the Institute of Physics, the Royal Society of Biology, The Physiological Society and the Council for the Mathematical Sciences, with financial support from the Clay Mathematics Institute, United Kingdom Research and Innovation, Warwick Manufacturing Group, Society of Chemical Industry, the Nutrition Society, Institute of Biomedical Science the Heilbronn Institute for Mathematical Research, and the Comino Foundation.
Is alien maths different from ours? And if it is, will they be able to understand the messages that we are sending into space? My summer intern Joe Double speaks to philosopher Professor Adrian Moore from BBC Radio 4’s ‘a history of the infinite’ to find out…
Are we alone in the universe? The possibility that we aren’t has preoccupied us as a species for much of recent history, and one way or another we need to know. The problem is, there is a lot of space, and only so fast you can move around in it, so popping over to our nearest neighbouring star for a quick look around is off the table. We simply don’t know how to communicate or travel faster than light. Nor have we picked up any signals which are identifiable as any sort of message from little green men.
Therefore, perhaps our best chance of making contact with an alien species is to announce ourselves to the universe. If we send out messages to promising-seeming parts of space in the hope that someone will be there to receive them, we might just get a response.
But supposing our signals reach alien ears (or freaky antenna things or whatever), what hope do we have of them being understood? Sure, we might make signals which are recognised as deliberate (and not mistaken for more literal ‘messages from the stars’), but how will they get anything across to aliens whose language is entirely unknown to us?
Scientists in the ‘70s were asking themselves these very questions, and the most promising approach they came up with to get around this problem was one which used maths. In fact, it used an ingenious trick dating back all the way to the Ancient Greeks. The fruit of their labour, broadcast in 1974, was called the Arecibo message.
So, what is it? First off, the Arecibo designers gave up on the hope of sending a written message the aliens could read. Better to stick with pictures – you have to assume aliens will be pretty low down on the reading tree. But this still leaves a conundrum.
When you’re sending a message to space, you have to send a binary signal – a series of ‘1’s and ‘0’s (aka bits) which you hope will start to mean something when it’s processed on the other end. This is precisely how sending pictures over the internet or between computers works too – your message is turned into bits, beamed to the other computer, and then turned back.
And herein lies the problem; the aliens receiving the binary signal won’t have any idea what they’re supposed to do with the bits or how to piece the message back together to make a picture again. You’ve posted them a Lego set but no instructions, and even though they’ve got the bricks there’s no way they’ll figure out whether it was supposed to be built into a race car or a yellow castle. After all, they might not even know what those are!
The way around this is to make the process for turning the message into a picture as simple as possible, so the aliens will be able to guess it. And the way you turn the bits into a picture really is very simple – just write them out in a 23×73 grid, and colour in any square with a ‘1’ in it. Below is what you get (with added colour-coding – see below for what the different parts mean).
White, top: The numbers 1 to 10, written in binary
Purple, top: The atomic numbers for the elements in DNA
Green: The nucleotides of our DNA
Blue/white, mid: A representation of the double helix of DNA. The middle column also says how may nucleotides are in it.
Red: A representation of a human with the world’s pointiest head, with the average height of a man to the left, and the population to the right.
Yellow: A representation of the solar system and the sizes of the planets, with Earth highlighted
Purple, bottom: A curved parabolic mirror like the one used to send the message, with two purple beams of light being reflected onto the mirror’s focus, and the telescope’s diameter shown in blue at the bottom.
Image credit: Arne Nordmann
But how, you might ask, are the aliens supposed to figure out the 23×73 dimensions of the grid? Here is where Ancient Greek maths comes to save us.
The Arecibo message is 1679 bits long. That sounds random, but it is anything but – 1679 is actually the product of two numbers, 23 and 73. Sound familiar? That’s the dimensions of the picture! It’s precisely the fact that 1679 equals 23 times 73 that lets you write out the 1679 bits in a 23×73 grid.
You might be wondering why we used such weird numbers for the sizing. Couldn’t we have chosen nicer, rounder numbers for the picture, like 50×100 say? No. If we did that, the aliens might make a mistake like writing out the bits in a 5×1000 grid or a 500×10 grid, and this would still work numbers-wise because 50×100 = 5×1000 = 500×10.
The key here is that unlike 50 and 100, 23 and 73 are prime numbers. Primes are numbers which can only be divided by one and themselves, like 3 and 5. And most importantly, any number can be split up into primes in a unique way – for instance, 15 is 3×5, and there is no other way to get 15 by multiplying together prime numbers. Likewise, there is no other way to get 1679 than as 23 times 73. So, it is impossible for the aliens to make a mistake when they have to draw out the grid. The Lego set you posted may have no instructions, but you were careful to include parts which can only go together the right way.
An Ancient Greek called Euclid knew this key fact, that numbers split uniquely into primes, over two thousand years ago. The Arecibo designers are banking on the aliens being at least as good with numbers as he was, to be able to decipher the message. Given these are aliens who are capable of picking up a radio signal from space, it seems like a pretty safe bet that they can manage better than an ancient society which believed women have fewer teeth than men because a . It’s a gamble, and it relies on assumptions that the maths we’re interested in is what all species will be interested in – but then what part of blindly shooting intergalactic friend requests into space in the hope someone we’d want to know finds them wasn’t going to be a gamble?
Would it be better if we all spoke the same language? Live debate with Oxplore – Oxford University’s digital outreach portal. Watch me try to convince some linguists that Maths is indeed a language and also our best bet of communicating with aliens…