Tom Rocks Maths Episode 07

The latest episode from Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station. Featuring pirates that can’t count, the best way to carry a bundle of sticks, and special guest Toby, who talks about his favourite part of maths, his taste in music and tries out one of the infamous Tom Rocks Maths quizzes! Not forgetting the usual maths puzzle and great music from the Arctic Monkeys, Paramore and All Time Low…

2018 Abel Laureate Robert Langlands

The Norwegian Academy of Science and Letters kindly provided me with a scholarship to attend the Abel Prize week in Oslo earlier this year where I interviewed the 2018 Abel Laureate Robert Langlands.

In the first of a series of videos documenting my experience, Robert describes how he came to do Mathematics at university…

Spring into action and get ahead of the competition

Wherever we look in the world, we see competition between different groups or beings. Whether it’s two animals trying to earn the right to a watering hole, people trying to assert their social influence, or simply two sports teams playing against each other, this sort of interaction appears in many different situations. As humans, we have a natural desire to rank things that are in direct competition: which is better? Who would win if they faced each other? How does their rivalry compare to others?

We want to know the answers to these questions because it makes us enjoy the competition more, and we feel that we learn more about it. Imagine being able to correctly predict who would win every football match for the rest of the season, you’d probably feel pretty pleased with yourself… But, apart from the inevitable bragging rights, being able to rank competing entities and predict outcomes is an extremely useful skill in many different areas of research, including sociology, economics and ecology.

Of course, you need a bit of maths if you’re going to rank things reliably; you can’t just trust a hunch! There are many different methods that have been used before for rankings, but a group of scientists at the Santa Fe Institute in the USA have come up with a new way of doing it using springs!

So, the ranking system is… a trampoline?! Not exactly. This ingenious method, called SpringRank, treats each interaction as a physical spring, so the model is a whole system of connected springs. Think of a football league: between each pair of teams there is a spring in each direction, and the force of each spring is determined by how many times they have beaten each other in the past. For example, Manchester United have played Liverpool 200 times, winning 80 matches and losing 65. In our spring system, this means that the spring connecting the two teams is biased towards Manchester United – it requires more force to move closer to Liverpool than it does to move towards Manchester United. With this setup, it turns out that the best ranking of the teams is found when you make the total energy in all of the springs as low as possible.

But why use springs? The bonus is that we’ve been studying springs for hundreds of years and so we know the physics behind how they work, which makes it easy to do the calculations. We can use the positions of the springs to work out the rankings of millions of different teams in just seconds! Not only is the maths simple, but it’s also very effective, especially compared to other methods currently used for ranking. In tests run by the researchers, SpringRank performed much better at ranking competitors, as well as predicting the outcomes of future clashes, than existing methods. The data set covered topics as varied as animal behaviour, faculty hiring and social support networks, demonstrating just how versatile the method can be.

This research is a wonderful example of how different areas of science can be combined to create a tool that can actually be put to use in the real world. When learning the subjects separately at school, it’s hard to imagine that you could take centuries-old ideas from physics, turn them into mathematical models, and stick them into a computer program! But here we are, able to work out who is likely to become friends (and enemies), which animals will make it through the heatwave, and whether it’s worth bragging about your favourite team before the game has even happened. So next time you’re challenged to guess the league winner, reach for SpringRank and jump ahead of the competition!

Kai Laddiman

Cocaine addiction leads to iron build-up in the brain

Cocaine used to be the drug of the rich and famous, but over recent years it has become cheaper and more readily available, and as a result more and more people are becoming addicted to this highly dangerous substance. A report last year from the UK Government Advisory Council found that 1 in 10 people between the ages of 16 and 59 had used the drug at some point. The current treatment for cocaine addicts is through therapy, but relapse rates remain high. Now a new study has linked cocaine addiction with a build up of iron in certain parts of the brain, and particularly areas known to control our inhibitions, although the team don’t yet know what the iron is doing there. I spoke with lead author Dr Karen Ersche…

  • Cocaine addiction leads to disruptions in the regulation of iron, with reduced levels in the blood and higher levels in the brain
  • Iron build-up in the brain is highly toxic and can be seen in other degenerative diseases such as dementia and Parkinson’s
  • Participants in the study had a brain scan which identified iron build-up in the area of the brain that controls inhibition
  • Possible explanations are that cocaine users have an appetite for fatty foods which hampers the absorption of iron, or that the cocaine weakens or destroys the blood-brain barrier causing iron to leak into the brain
  • The study also found a relationship between the amount of iron accumulation and the duration of cocaine use, but further work is needed to clarify its effect on brain cells
  • Understanding the relationship between cocaine addiction and iron regulation in the body could provide a new avenue for treatment in the future

You can listen to the full interview for the Naked Scientists here.

Funbers 19

The 1900’s saw inventions that made a BIG change to our lives. Aeroplanes in 1903 changed the way we travel, TVs in 1925 changed home entertainment, and Microwaves in 1946 changed the way we eat. Nineteen also played an important role in the British Civil War and was the title of Adele’s first album…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Getting tattooed for science…

Listen to me being tattooed whilst attempting to describe the process, and hear from my artist Nat on his experience as a tattooist…. all in the name of science.

You can also watch a short video below of the tattoo being done from the perspective of the artist.

Audio edited by Joe Double.

Funbers 18

Time to celebrate with a glass of bubbly as we’ve reached the number 18! The legal drinking age in most countries around the world, unless you’re the US, Saudi Arabia or Haiti. In fact, in Haiti you only need to be ‘of school age’ to get your hands on the devil’s nectar…

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.

Alien maths – we’re counting on it

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).

aricebo

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?

Joe Double

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