From aliens to bees via tattoos…

A short review of intern Joe Double’s work with Tom Rocks Maths over the summer of 2018. Written for the OUS East Kent branch who provided funding for the project. 

‘First of all, I must thank you again for the grant, and for the warmth and friendliness at your event; it was an absolute delight to give my presentation and talk to your members, as it has been interacting with you in general.

I had the opportunity to work with one of my tutors over the summer to produce pieces for a general audience about complex mathematical topics. Without the help of the OUS East Kent group, I couldn’t have taken up this opportunity – with their grant’s help, I was able to afford to live in Oxford through a large part of the summer, allowing me to work in close contact with my tutor and use his studio for creating the videos and audio pieces I worked on. The OUSEK grant can be put to use far more flexibly than those from bigger schemes (which always have preconditions to meet about how the project will apply to industry, say), so I couldn’t recommend applying more if you have an idea for a project for your time at Oxford which is on the unusual side!’

Pieces I produced during the project:

Why do Bees Build Hexagons? Honeycomb Conjecture explained by Thomas Hales

A video I edited of Tom (my tutor) interviewing Thomas Hales about the mathematics behind beehives.

Would Alien (Non-Euclidean) Geometry Break Our Brains?

My main video, written, filmed and edited by me, about demystifying non-Euclidean geometry.

Take me to your chalkboard

My main audio piece, where I interview Professor Adrian Moore (also of St Hugh’s) about what philosophy can tell us about how aliens might do maths.

Maths proves that maths isn’t boring

An article about Gödel’s incompleteness theorems, and how they show maths is always risky.

Getting tattooed for science…

An audio piece I edited about a tattoo Tom got of the Platonic solids.

Alien maths – we’re counting on it

An article about how we use the mathematics of prime numbers to send messages to the stars.

Play Nice!

An article about a game theory paper which could amongst other things help stop deforestation.

The original article was published on the OUS East Kent website here.

Would Alien (Non-Euclidean) Geometry Break Our Brains?

The author H. P. Lovecraft often described his fictional alien worlds as having ‘Non-Euclidean Geometry’, but what exactly is this? And would it really break our brains?

 

Produced by Tom Rocks Maths intern Joe Double, with assistance from Tom Crawford. Thanks to the Oxford University Society East Kent Branch for funding the placement.

Take me to your chalkboard

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…

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

Funbers 10

We’ve finally reached double figures in the form of the number 10! The reason that ten is the first number with two digits is precisely because we count in base 10. Computers count in base two (0 and 1’s) and 7-tentacled aliens probably count in base seven…

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

Tom Rocks Maths Episode 02

The second live episode of Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station. Featuring aliens, death by duel, Indiana Jones and the weekly maths puzzle for you to solve. Plus music from Rise Against, Good Charlotte and Asking Alexandria…

Would Aliens Understand Maths?

Maths is found everywhere in our daily lives and is often referred to as ‘the language of nature’, so the big question is would aliens be able to understand it? I spoke to Professor Ian Stewart from the University of Warwick…

  • Maths is not as accurate as you might think – it all depends on how accurate your measurements are in the real world
  • The maths that we use on Earth is likely to have evolved from the environment here on Earth – rigid shapes and lines are common to us, but for an alien living on a gas giant such as Jupiter, things would be very different as everything would flow
  • Counting likely evolved from the need to keep track of objects such as our belongings or livestock
  • Maths is probably more likely to be understood by aliens than things such as culture or language because it transcends the whole universe

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

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