Exploring mazes, inventing algorithms (part I) 

by Paul Curzon, Queen Mary University of London

A maze with mouse searching for cheese.
Image by CS4FN

Computer science research in part involves inventing new algorithms or improving new ones. But what does that mean. Let’s explore some mazes to explore algorithms.

What does computer science research involve? It is very varied: from interviewing people to find out what the real problems that need solving in their lives or jobs are; to running experiments to find out what works and what doesn’t; to writing programs to solve problems.

Improving algorithms

A core part of much research is coming up with new and better algorithms that solve particular problems. The kind of algorithm could be anything from a new more secure cryptographic protocol, or a better way to rank the results of a search engine, to a new more effective machine learning algorithm that is less likely to make things up, or perhaps can better explain how it came to its conclusions.

What does it mean to come up with a better algorithm though? Once a problem is solved, isn’t it solved? Let’s explore a simple problem to see. Let’s explore mazes. Solve the simple maze puzzle above before you go on. Find a route that gets the mouse to the cheese.

Wandering around mazes, finding algorithms

If you’ve ever been in a hedge maze in the garden of some stately home, or a corn field maze, the chances are you just dived in and wandered rather aimlessly. Perhaps you tried to remember which way you went at each junction, to avoid going down the same dead-ends more than once. How about solving the paper version of a maze puzzle like the one above? Now perhaps you looked ahead to spot dead-ends to avoid tracing wrong paths with your pencil.

Probably what you are doing is at least a little random. You could, in theory at least, end up going back over the same paths, never taking the right one and and never getting to the middle. Could we come up with an algorithm that guarantees to solve mazes? To be an algorithm it would need to guarantee you ended up finding a path to the centre of the maze if you followed the steps of the algorithm precisely. It should also work for any maze, or at least all mazes of a particular kind. Ideally, the algorithm gives you a path that can then be followed by anyone without them having to run the algorithm themselves. They can just follow the path generated by the algorithm for that maze.

Wall-following

In fact lots of maze algorithms have been invented. Perhaps the one most people have heard of, if they know of any maze algorithm, is called Wall-following. It is very simple to do, You just pick a wall at the entrance either to the left or right and then follow it, If in a garden maze, keep your hand on the hedge as you walk round. If doing a paper puzzle, draw the path sticking to the chosen wall. Try it on the following simple maze.

A simple maze with mouse and cheese.
Image by CS4FN

Simply connected

The wall-following algorithm will guarantee to get you to the centre of the maze, and back out again too, but only as long as the maze is what is called simply connected. That just means the maze is constructed from a single hedge (or one unbroken drawn line) not a series of unconnected hedges. If you look at both examples above you will see I created them by just drawing a single wiggly line.

If a maze is simply connected then it cannot have looping paths, so no going round in circles for ever. It will also only have one entrance/exit. That shows the first aspect of inventing algorithms that is important. They often only work for some situations, not all. You must be sure you know what situations they do and don’t work.

Often the earliest algorithms invented to solve a problem are like wall-following: they only work for simple situations. Other people then come along and find new algorithms that can cover more problems (here more mazes). Can you tweak the wall-following maze algorithm to work even if there are multiple exits from the maze, for example? As it stands our algorithm could just take you from the entrance straight out of another exit without exploring much of the maze at all! See the end for one simple way to tweak the algorithm. What if there are paths that take you round in circles? Can you come up with an algorithm to deal with that?

Some times the improvements invented just involve tweaking an existing algorithm as with dealing with multiple exits in a maze. Some times a whole new algorithm is needed.

Faster, higher, stronger?

Even for a simple constrained version of the problem, like simply connected mazes, people can invent better algorithms. What does better mean for a maze? Well one way you might have a better algorithm is if it is faster in coming up with a solution. Another is that the solution it comes up with is faster. For a maze that means a shorter (ideally the shortest) path to the centre. Wall following may get you in to the centre (and out again) but you probably will have discovered a very long path that takes you in and out of lots of dead-ends needlessly. You do find a path to the centre, but it may be a very long path. Can you come up with an algorithm that finds shorter paths?

We will explore an algorithm that does next.

More to come…

Some solutions

The result of wall following on our simple maze

A route for the mouse to follow that takes it to the cheese.
Image by CS4FN

One way to deal with multiple exits

To deal with a maze that has multiple exits, so multiple breaks in the outer wall, tweak the wall-following algorithm as follows. First mark the exit you use to enter the maze, so you know when you return to it. If you come to any other exit then pretend there is a gate there and keep following the wall as though it were unbroken and there were no exit.

More on …

Magazines …

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

Why the Romans were pants at maths

Paul Curzon, Queen Mary University of London

ROman numerals I II III IV V in blocks
Roman number blocks image by Clker-Free-Vector-Images from Pixabay

The Romans were great at counting and addition but they were absolutely pants at multiplication. It wasn’t because they were stupid. It was because they hadn’t invented a good way to represent numbers, and that meant they needed really convoluted algorithms.

The Roman system is based on an earlier really simple way of writing numbers. You just put a line for each thing you’ve counted. Its probably the way shepherds kept count of sheep, drawing a line for each sheep. Those lines turned into the Roman letter I. To add 1 to a number you just add another I. You count: I, II, III, and so on and it makes counting easy.

This system is called unary – whereas binary involves counting with two symbols, 1 and 0, in unary you only have one symbol to count with. Addition in unary is easy too at least for small numbers. Take the first number and add on the end all the Is for the second and you’ve got the answer number. This is exactly the way we all start doing addition on our fingers.To add 2+3, hold up 2 fingers (II) then hold up another three fingers (III) and you have the answer (IIIII).

This is fine for small numbers but it gets a bit tedious as the numbers increase (and you run out of fingers!) Comparing numbers is easy in principle – do you have the same number of Is, but hard in practice for large numbers. We can’t keep all those Is in our head so a large number is hard to think about. To get round this the Romans invented new letters to stand for groups of Is. This is what we do when we tally numbers making a crossbar for every fifth number we count. It helps us keep track of larger numbers. The Romans invented a whole bunch of symbols to help: so for example in the Roman numeral system, V stands for 5 (IIIII), X stands for 10, L for 50, C for 100, D for 500 and M for 1000. They had invented a new way to represent numbers.

Clock face with roman numerals XI XII
Image by Katie Rose from Pixabay

This makes it much easier to write and compare larger numbers. Now when counting and you get up to 5 you just replace all those Is with a V and then carry on adding Is: VI, VII, VIII, VIIII. Then you get to VIIIII (10) so replace it all with an X, starting again adding a new lot of Is: XI, XII, XIII, XIIII, XV, and so on. Counting large numbers is now a bit more involved – the algorithm involves more than just adding an I on the end, but it is much more convenient. The addition algorithm has now become more complicated, though it is still fairly simple too. Take any two numbers to add like VII and VIII and string them together: VIIVIII. Now group together the same letters: VVIIIII. Anywhere you have enough to replace symbols with the next character do so. VV can be replaced by X and IIIII can be replaced by V to give XV in the above. Keep making replacements until you can make no more. Put the symbols in order from largest to smallest symbol and you have your answer.

Now the Romans were obviously a bit lazy as bored with writing even four Is in a row they sometimes introduced a new set of abbreviations, so that IIII became IV and VIIII became IX. Putting a smaller symbol (like I) before a larger one (like X) instead of after meant subtract it to get the number. so IX means “one less than 10” or 9. Counting just got a tiny bit more complicated to get the advantage of writing fewer symbols. Addition now needs a more convoluted algorithm though. There are several ways to do it. The easiest is actually just to change the numbers to add to the simpler form (so IV goes back to IIII). You them do the addition that way, and convert back at the end. Addition just got that little bit harder, and all because of a change in representation.

Worse, doing any more complicated maths is even harder still using the Roman number representation. See if you can work out how to multiply Roman numbers. The Roman number system doesn’t help at all. The only really easy way is to just repeatedly add ( so III x VI is VI + VI + VI). That just isn’t practical for large numbers. Try it on XXIII x LXV1. There are other possible ways including one that is actually based on the binary multiplication algorithms computers use – multiplying and dividing repeatedly by 2. See if you can work out how to do it. Whatever way you do it, its clear that the number system the Romans chose made maths hard for them to do!

A good representation makes maths easy. A bad one makes it much harder to do

Luckily, Indian and Arabian scholars understood that the representation they used mattered. They invented, and spread, the Hindu-Arabic numbers and decimal system we use today. What is special about it is that rather than introducing new symbols for bigger and bigger numbers, the position of a symbol is used instead. As we go from nine to ten we go back to the start of our symbols, from 9 back to 0, but stick a 1 in a new 10s column to count how many 10s we have. Counting is still pretty easy but suddenly not only is the algorithm for addition straightforward but we can come up with fairly simple algorithms for multiplication and division too. They are the algorithms you learn at school – though as with any algorithm making sure you follow the steps exactly and don’t miss steps is hard for a human (unlike for a computer). That is why we tend to find learning maths hard at first and it gets easier the more we practice.

An abacus
Image by Hans from Pixabay

In fact Romans needing to do serious maths probably used a variation of an abacus representing numbers with stones. They would do a calculation on the abacus and then convert the answer back into the Roman number system. And guess what. The Roman Abacus uses columns to represent larger numbers in a very similar way to the Hindu-Arabic system. The Romans understood that representation matters too.

Sometimes things are hard to do just because we make them hard! The secret of coming up with good algorithms is often to come up with a good representation first. In programming too, if you come up with a good way to represent data, a good data structure, you can often then make it much easier to write an efficient program.

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

Beheading Hero’s mechanical horse

Pegasus image by Dorota Kudyba from Pixabay

An early ‘magical’ (nearly headless) automaton from Ancient Greece

Stories of Ancient Greece abound with myths but also of amazing inventions. Some of the earliest automatons, mechanical precursors of robots, were created by the Ancient Greeks. Intended to delight and astound or be religious idols, they brought statues of animals and people to life. One story holds that Hero of Alexandria invented a magical, mechanical horse that not only moved and drank water, but was also impossible to behead. It just carried on drinking as you sliced a sword clean through its neck. The head remained solidly attached to body. Myth or Mystery? How could it be done?

The Ancient Greeks were clever. With many inventions we think of as modern, the Greeks got there first. They even invented the first known computer. Hero of Alexandria was one of the cleverest, an engineer and prolific inventor. Despite living in the first century, he invented the first known steam engine (long before the famous ones from the start of the industrial revolution), the first vending machine, a musical instrument that was the first wind-powered machine, and even the pantograph, a parallelogram structure used to make exact copies of drawings, enlarged or reduced. Did Hero invent a magical mechanical horse? He did, and you really could slice cleanly through its robotic neck with a sword, leaving the head in place.

Magic, myth and mystery

Queen Mary’s Peter McOwan was fascinated by magic and especially Hero’s horse as a child, and was keen to build one. When TEMI, a European project was funded he had his chance. TEMI aimed to bring more showmanship, magic and mystery to schools to increase motivation. By making lessons more like detective work, solving mysteries, they can be lots more fun. The project needed lots of mysteries, just like Hero’s horse, and artist Tim Sargent was commissioned to recreate the horse.

If you’re ever in Athens, you can see a version of Hero’s horse, as well as many other Greek inventions at Kotsanas Museum of Ancient Greek Technology.

How does it work?

The challenge was to create a version that used only Ancient Greek technology – no electricity or electromagnets, only mechanical means like gears, bearings, levers, cogs and the like. It was actually done with a clever rotating wheel. As the sword slices through a gap in the neck, it always connects head and body together first in front, then behind the blade. Can you work out how it was done? See a video of the mechanism in action below, with Peter introducing it.

Paul Curzon, Queen Mary University of London

Watch …

Related Magazine …

ssue 26 of the CS4FN magazine which is a memorial issue for *Peter McOwan, who died in June 2019. Peter, along with Paul Curzon, was one of the co-founders of CS4FN.

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

How far can you hear? Modelling distant birdsong.


by Dan Stowell, Queen Mary University of London

Blackbird singing at sunrise to an orange sky
Sunrise blackbird image by No-longer-here from Pixabay

How do we know how many birds there are out there: in the countryside, and in the city? Usually, it’s because people have been sent out to count the birds – by sight but especially by sound. Often you can hear a bird singing even when it’s hidden from sight so listening can be a much more effective way of counting.

In the UK, volunteers have been out counting birds for decades, co-ordinated by organisations such as the British Trust for Ornithology (BTO). But pretty quickly they came up against a problem: you can’t always detect every bird around you, even if you’re an expert at it. Birds get harder to detect the further away they are. To come up with good numbers, the BTO estimates what fraction of the birds you are likely to miss, according to how far away you are, and uses that to improve the estimate from the volunteer surveys.

But, Alison Johnston and others at the BTO noticed that it’s even more complicated than that: you can hear some types of bird very clearly over a long distance, while other birds make a sound that disappears into the background easily. If a pigeon is cooing in the forest, maybe you can’t hear it beyond a few metres. Whereas the twit-twoo of an owl might carry much further. So they measured how likely it is that one of their volunteers will hear each species, at different distances.

They created mathematical models that took into account these factors. Implemented in programs the models can then adjust the reports coming in from the volunteers doing the counting. This is how volunteers and computers are combined in ‘citizen science’ work which gathers observations from people all around the country. Sightings and numbers are collected, but the raw numbers themselves don’t give you the correct picture – they need to be adjusted using mathematical models that help fill in the gaps.

You can perfect your own recognition of British birdsong with the audio clips here.

Related Magazine …

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

Threads & Yarns – textiles and electronics

At first sight nothing could be more different than textiles and electronics. Put opposites together and you can maybe even bring historical yarns to life. That’s what Queen Mary’s G.Hack team helped do. They are an all-woman group of electronic engineering and computer science research students and they helped build an interactive art installation combining textiles and personal stories about health.

In June 2011 the G.Hack team was asked by Jo Morrison and Rebecca Hoyes from Central Saint Martins College of Art and Design to help make their ‘Threads & Yarns‘ artwork interactive. It was commissioned by the Wellcome Trust as a part of their 75th Anniversary celebrations. They wanted to present personal accounts about the changes that have taken place in health and well-being over the 75 years since they were founded.

Flowers powered

Jo and Rebecca had been working on the ‘Threads & Yarns’ artwork for 6 months. It was inspired by the floor tiling at the London Victoria and Albert Museum and was made up of 125 individually created material flowers spread over a 5 meter long white perspex table. They wanted some of the flowers to be interactive, lighting up and playing sounds linked to stories about health and well-being at the touch of a button.

Central Saint Martins College Textile students worked with senior citizens from the Euston and Camden area, recording the stories they told as they made the flowers. G.Hack then ran a workshop with the students to show them how physical computing could be built into textiles and so create interactive flowers. Short sound bites from the recorded stories were eventually included in nine of the flowers.

The interactive part was built using an open source (i.e., free and available for anyone to use) hardware platform called Arduino. It makes physical computing accessible to anyone giving an easy way to create programs that control lights, buttons and other sensors.

The audio stories of the senior citizens were edited down into 1-minute sound bites and stored on a memory card like those used in digital cameras. Each of the nine flowers were lit by eight Light Emitting Diodes (LEDs). They are low energy lights so they don’t heat up, which is important if they are going to be built into fabrics. They are found in most household electronics, such as to show whether a gadget is turned on or off. When a button is pressed on the ‘Threads & Yarns’ artwork, it triggers the audio of a story to be played and simultaneously lights the LEDs on the linked flower, switching off again when the audio story finishes.

Smooth operators

The artwork had to work without problems throughout the day so the G.Hack team had to make sure everything would definitely go smoothly. The day before the opening of the exhibition they did final testing of the interactive flowers in their electronics workshop. They then worked with Central Saint Martins and museum staff to install the electronics into the artwork. They designed the system to be modular. This was both to allow the electronics to be separate from the artwork itself as well as to ease combining the two. On the day of the exhibition, the team arrived early to test everything one more time before the opening. They also stayed throughout the day to be on call in case of any problems.

Leading up to the opening of the exhibition were a busy few weeks for G.Hack with lots of late nights spent testing, troubleshooting and soldering in the workshop but it was all worth it as the final artwork looked fantastic and received a lot of positive feedback from people visiting the exhibition. It was a really positive experience all round! G.Hack and Central Saint Martins formed a bond that will likely extend into future partnerships. ‘Threads & Yarns’ meanwhile is off on a UK ‘tour’.

Art may have brought the textiles, history and health stories together as embodied in the flowers. It’s the electronics that brought the yarn to life though.

Paul Curzon, Queen Mary University of London, June 2011

G.Hack

G.Hack was a supportive and friendly space for women to do hands-on experimental production fusing art and technology at Queen Mary University of London. As a group they aimed to strengthen each other’s confidence and ability in using a wide range of different technologies. They supported each other’s research and helped each other extend their expertise in science and technology through public engagement, collaborating with other universities and commercial companies.

The members of G.Hack involved in ‘Threads & Yarns’ were Nela Brown, Pollie Barden, Nicola Plant, Nanda Khaorapapong, Alice Clifford, Ilze Black and Kavin Preethi Narasimhan.

Related Magazines

The Women Are Here annual
CS4FN Issue 23
EE4FN magazine

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

3D models in motion

by Paul Curzon, Queen Mary University of London
based on a 2016 talk by Lourdes Agapito

Wireframe mesh image by Gerd Altmann from Pixabay

The cave paintings in Lascaux, France are early examples of human culture from 15,000 BC. There are images of running animals and even primitive stop motion sequences – a single animal painted over and over as it moves. Even then, humans were intrigued with the idea of capturing the world in motion! Computer scientist Lourdes Agapito is also captivated by moving images. She is investigating whether it’s possible to create algorithms that allow machines to make sense of the moving world around them just like we do. Over the last 10 years her team have shown, rather spectacularly, that the answer is yes.

People have been working on this problem for years, not least because the techniques are behind the amazing realism of CGI characters in blockbuster movies. When we see the world, somehow our brain turns all that information about colour and intensity of light hitting our eyes into a scene we make sense of – we can pick out different objects and tell which are in front and which behind, for example. In the 1950s psychophysics* researcher Gunnar Johansson showed how our brain does this. He dressed people in black with lightbulbs fastened around their bodies. He then filmed them walking, cycling, doing press-ups, climbing a ladder, all in the dark … with only the lightbulbs visible. He found that people watching the films could still tell exactly what they were seeing, despite the limited information. They could even tell apart two people dancing together, including who was in front and who behind. This showed that we can reconstruct 3D objects from even the most limited of 2D information when it involves motion. We can keep track of a knee, and see it as the same point as it moves around. It also shows that we use lots of ‘prior’ information – knowledge of how the world works – to fill in the gaps.

Shortcuts

Film-makers already create 3D versions of actors, but they use shortcuts. The first shortcut makes it easier to track specific points on an actor over time. You fix highly visible stickers (equivalent to Johansson’s light bulbs) all over the actor. These give the algorithms clear points to track. This is a bit of a pain for the actors, though. It also could never be used to make sense of random YouTube or CCTV footage, or whatever a robot is looking at.

The second shortcut is to surround the action with cameras so it’s seen from lots of angles. That makes it easier to track motion in 3D space, by linking up the points. Again this is fine for a movie set, but in other situations it’s impractical.

A third shortcut is to create a computer model of an object in advance. If you are going to be filming an elephant, then hand-create a 3D model of a generic elephant first, giving the algorithms something to match. Need to track a banana? Then create a model of a banana instead. This is fine when you have time to create models for anything you might want your computer to spot.

It is all possible for big budget film studios, if a bit inconvenient, but it’s totally impractical anywhere else.

No Shortcuts

Lourdes took on a bigger challenge than the film industry. She decided to do it without the shortcuts: to create moving 3D models from single cameras, applied to any traditional 2D footage, with no pre-placed stickers or fixed models created in advance.

When she started, a dozen or so years ago, making any progress looked incredibly difficult. Now she has largely solved the problem. Her team’s algorithms are even close to doing it all in real time, so making sense of the world as it happens, just like us. They are able to make really accurate models down to details like the subtle movements of their face as a person talks and changes expression.

There are several secrets to their success, but Johansson’s revelation that we rely on prior knowledge is key. One of the first breakthroughs was to come up with ways that individual points in the scene like the tip of a person’s nose could be tracked from one frame of video to the next. Doing this well relies on making good use of prior information about the world. For example, points on a surface are usually well-behaved in that they move together. That can be used to guess where a point might be in the next frame, given where others are.

The next challenge was to reconstruct all the pixels rather than just a few easy to identify points like the tip of a nose. This takes more processing power but can be done by lots of processors working on different parts of the problem. Key to this was to take account of the smoothness of objects. Essentially a virtual fine 3D mesh is stuck over the object – like a mask over a face – and the mesh is tracked. You can then even stick new stuff on top of the mesh so they move together – adding a moustache, or painting the face with a flag, for example, in a way that changes naturally in the video as the face moves.

Once this could all be done, if slowly, the challenge was to increase the speed and accuracy. Using the right prior information was again what mattered. For example, rather than assuming points have constant brightness, taking account of the fact that brightness changes, especially on flexible things like mouths, mattered. Other innovations were to split off the effect of colour from light and shade.

There is lots more to do, but already the moving 3D models created from YouTube videos are very realistic, and being processed almost as they happen. This opens up amazing opportunities for robots; augmented reality that mixes reality with the virtual world; games, telemedicine; security applications, and lots more. It’s all been done a little at a time, taking an impossible-seeming problem and instead of tackling it all at once, solving simpler versions. All the small improvements, combined with using the right information about how the world works, have built over the years into something really special.

*psychophysics is the “subfield of psychology devoted to the study of physical stimuli and their interaction with sensory systems.”

This article was first published on the original CS4FN website and a copy appears on pages 14 and 15 in “The women are (still) here”, the 23rd issue of the CS4FN magazine. You can download a free PDF copy by clicking on the magazine’s cover below, along with all of our free material.

Another article on 3D research is Making sense of squishiness – 3D modelling the natural world (21 November 2022).

Related Magazine …

EPSRC supports this blog through research grant EP/W033615/1.

Frequency Analysis for Fun

Scrabble letters
Scrabble letters image by christopher Walkey from Pixabay

Frequency Analysis, a technique beloved by spies for centuries, and that led to the execution of at least one Queen, also played a part in the development of the game Scrabble, over a hundred million copies of which have been sold worldwide.

Frequency Analysis was invented by Al-Kindi, a 9th Century Muslim, Arabic Scholar, as a way of cracking codes. He originally described it in his “A Manuscript on Deciphering Cryptographic Messages“. Frequency analysis just involves taking a large amount of normal text written in the language of interest and counting how often each letter appears. For example in English, the letter E is the most common. With simple kinds of ciphers that is enough information to be able to crack them, just by counting the frequency of the letters in the code you want to crack. Now large numbers of everyday people do frequency analysis just for fun, solving Cross Reference puzzles.

The link between frequency analysis and puzzles goes back earlier. When the British were looking for potential code breakers to staff their secret code breaking establishment at Bletchley Park in World War II, they needed people with frequency analysis like skills and problem solving skills. They did this by setting up Crossword competitions and offering those who were fastest jobs at Bletchley: possibly the earliest talent competition with career changing prizes!

Earlier still, in the 1930s, Architect Alfred Mosher Butts, hit on the idea of a new game that combined crosswords and anagrams, which were both popular at the time. The result was Scrabble. However, when designing the game he had a problem in that he needed to decide how many of each letter the game should have and also how to assign the scores. He turned to frequency analysis of the front page of the New York Times to give the answers. He also did it an easy way – looking at how many of each letter the printers had – the more they had meant the more often the same letters were needed at once. He broke the pattern of his frequency analysis though, including fewer letter Ss (the second most common word in English) than there should be so the game wasn’t made too easy because of plurals.

Sherlock Holmes, of course, was a master of frequency analysis as described in the 1903 story “The Adventure of the Dancing Men”. Sir Arthur Conan Doyle wasn’t the first author to use it as a plot device though. Edgar Alan Poe had based a short story called “The Gold Bug” around frequency analysis in 1843. It was Poe who originally popularised frequency analysis with the general public rather than just with spymasters. Poe had discovered how popular the topic was as a result of having set a challenge in a magazine for people to send in ciphers – that he would then crack, giving the impression at the time that he had near supernatural powers. The way it was done was then described in detail in “The Gold Bug”.

Paul Curzon, Queen Mary University of London

More on ,,,

For younger kids we have some fun free kriss-kross puzzles – they’re like crosswords but you’re given the words and you have to fit them into the crossword shape. You need to think like a computer scientist and use logical thinking, pattern matching and computational thinking to complete them. (For even younger kids these can also be used as a way of practising spelling, phonics and writing out words).

EPSRC supports this blog through research grant EP/W033615/1.

Keeping secrets on the Internet – encryption keeps your data safe

Padlock over encrypted text
Computer encryption padlock image by OpenClipart-Vectors from Pixabay

How do modern codes keep your data safe online? Ben Stephenson of the University of Calgary explains

When Alan Turing was breaking codes, the world was a pretty dangerous place. Turing’s work helped uncover secrets about air raids, submarine locations and desert attacks. Daily life might be safer now, but there are still threats out there. You’ve probably heard about the dangers that lurk online – scams, identity theft, viruses and malware, among many others. Shady characters want to know your secrets, and we need ways of keeping them safe and secure to make the Internet work. How is it possible that a network with so many threats can also be used to securely communicate a credit card number, allowing you to buy everything from songs to holidays online?

The relay race on the Internet

When data travels over the Internet it is passed from computer to computer, much like a baton is passed from runner to runner in a relay race. In a relay race, you know who the other runners will be. The runners train together as a team, and they trust each other. On the Internet, you really don’t know much about the computers that will be handling your data. Some may be owned by companies that you trust, but others may be owned by companies you have never heard of. Would you trust your credit card number to a company that you didn’t even know existed?

The way we solve this problem is by using encryption to disguise the data with a code. Encrypting data makes it meaningless to others, so it is safe to transfer the data over the Internet. You can think of it as though each message is locked in a chest with a combination lock. If you don’t have the combination you can’t read the message. While any computer between us and the merchant can still view or copy what we send, they won’t be able to gain access to our credit card number because it is hidden by the encryption. But the company receiving the data still needs to decrypt it – open the lock. How can we give them a way to do it without risking the whole secret? If we have to send them the code a spy might intercept it and take a copy.

Keys that work one way only

The solution to our problem is to use a relatively new encryption technique known as public key cryptography. (It’s actually about 40 years old, but as the history of encryption goes back thousands of years, a technique that’s only as old as Victoria Beckham counts as new!) With this technique the code used to encrypt the message (lock the chest) is not able to decrypt it (unlock it). Similarly, the key used to decrypt the message is not able to encrypt it. This may sound a little bit odd. Most of the time when we think about locking a physical object like a door, we use the same key to lock it that we will use to unlock it later. Encryption techniques have also followed this pattern for centuries, with the same key used to encrypt and decrypt the data. However, we don’t always use the same key for encrypting (locking) and decrypting (unlocking) doors. Some doors can be locked by simply closing them, and then they are later unlocked with a key, access card, or numeric code. Trying to shut the door a second time won’t open it, and similarly, using the key or access code a second time won’t shut it. With our chest, the person we want to communicate with can send us a lock only they know the code for. We can encrypt by snapping the lock shut, but we don’t know the code to open it. Only the person who sent it can do that.

We can use a similar concept to secure electronic communications. Anyone that wants to communicate something securely creates two keys. The keys will be selected so that one can only be used for encryption (the lock), and the other can only be used for decryption (the code that opens it). The encryption key will be made publicly available – anyone that asks for it can have one of our locks. However, the decryption key will remain private, which means we don’t tell anyone the code to our lock. We will have our own public encryption key and private decryption key, and the merchant will have their own set of keys too. We use one of their locks, not ours, to send a message to them.

Turning a code into real stuff

So how do we use this technique to buy stuff? Let’s say you want to buy a book. You begin by requesting the merchant’s encryption key. The merchant is happy to give it to you since the encryption key isn’t a secret. Once you have it, you use it to encrypt your credit card number. Then you send the encrypted version of your credit card number to the merchant. Other computers listening in might know the merchant’s public encryption key, but this key won’t help them decrypt your credit card number. To do that they would need the private decryption key, which is only known to the merchant. Once your encrypted credit card number arrives at the merchant, they use the private key to decrypt it, and then charge you for the goods that you are purchasing. The merchant can then securely send a confirmation back to you by encrypting it with your public encryption key. A few days later your book turns up in the post.

This encryption technique is used many millions of times every day. You have probably used it yourself without knowing it – it is built into web browsers. You may not imagine that there are huts full of codebreakers out there, like Alan Turing seventy years ago, trying to crack the codes in your browser. But hackers do try to break in. Keeping your browsing secure is a constant battle, and vulnerabilities have to be patched up quickly once they’re discovered. You might not have to worry about air raids, but codes still play a big role behind the scenes in your daily life.

Ben Stephenson, University of Calgary

More on …

Related Magazine …

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

Composing from Compression

Recoloured Cranium head abstract image by Gordon Johnson from Pixabay

Computers compress files to save space. But it also allows them to create music!

Music is special. It’s one of the things, like language, that makes us human, separating us from animals. It’s also special as art, because it doesn’t exist as an object in the world – it depends on human memory. “But what about CDs? They’re objects in the world”, you might say and you’d be right, but the CD is not the music. The CD contains data files of numbers. Those numbers are translated by electronics into the movements in a loudspeaker, to create sound waves. Even the sound waves aren’t music! They only become music when a human hears them, because understanding music is about noticing repetition, variation and development in its structure. That’s why songs have verses and choruses: so we can find a starting point to understand its structure. In fact, we’re so good at understanding musical structure, we don’t even notice we’re doing it. What’s more, music affects us emotionally: we get excited (using the same chemicals that get us excited when we’re in love or ready to flee danger) when we hear the anthem section of a trance track, or recognise the big theme returning at the end of a symphony.

Surprisingly, brains seem to understand musical structure in a way that’s like the algorithms computer scientists use to compress data. It’s better to store data compressed than uncompressed, because it takes less storage space. We think that’s why brains do it too.

Even more surprisingly, brains also seem to be able to learn the best way to store compressed music data. Computers use bits as their basic storage unit, but we can make groups of bits work like other things (numbers, words, pictures, angry birds…); brains seem to do something similar. For example, pitch (high vs. low notes) in sequence is an important part of music: we build melodies by lining up notes of different pitch one after the other. As we learn to hear music (starting before birth, and continuing throughout life), we learn to remember pitch in ever more efficient ways, giving our compression algorithms better and better chances to compress well. And so we remember music better.

Our team use compression algorithms to understand how music works in the human mind. We have discovered that, when our programs compress music, they can sometimes predict musical structures, even if neither they nor a human have “heard” them before. To compress something, you find large sections of repeated data and replace each with a label saying “this is one of those”. It’s like labelling a book with its title: if you’ve read Lord of the Rings, when I say the title you know what I mean without me telling the story. If we do this to the internal structure of music, there are little repetitions everywhere, and the order that they appear is what makes up the music’s structure.

If we compress music, but then decompress it in a different way, we can get a new piece of music in a similar style or genre. We have evidence that human composers do that too!

What our programs are doing is learning to create new music. There’s a long way to go before they produce music you’ll want to dance to – but we’re getting there!

Geraint Wiggins, Queen Mary University of London

Related Magazine …

Subscribe to be notified whenever we publish a new post to the CS4FN blog.

This blog is funded by EPSRC on research agreement EP/W033615/1.

QMUL CS4FN EPSRC logos

Balls, beams and quantum computers – performing calculations with patterns of light

Photo credit: Galton Box by Klaus-Dieter Keller, Public Domain, via Wikimedia Commons, via the Wikipedia page for the Galton board

Have you played the seaside arcade game where shiny metal balls drops down to ping, ping off little metal pegs and settle in one of a series of channels? After you have fired lots of balls, did you notice a pattern as the silver spheres collect in the channels? A smooth glistening curve of tiny balls forming a dome, a bell curve forms. High scores are harder to get than lower ones. Francis Galton pops up again*, but this time as a fellow Victorian trend setter for future computer design.

Francis Galton invented this special combination of row after row of offset pins and narrow receiving channels to demonstrate a statistical theory called normal distribution: the bell curve. Balls are more likely to bounce their way to the centre, distributing themselves in an elegant sweep down to the left and right edges of the board. But instead of ball bearings, Galton used beans, it was called the bean machine. The point here though is that the machine does a computation – it computes the bell curve.

Skip forward 100 years and ‘Boson Samplers’, based on Galton’s bean machine, are being used to drive forward the next big thing in computer design, quantum computers.

“Stripes beams lights” image by David from Pixabay

Instead of beans or silver balls computer scientists fire photons, particles of light through minuscule channels on optical chips. These tiny bundles of energy bounce and collide to create a unique pattern, a distribution though one that a normal digital computer would find hard to calculate. By setting it up in different ways, the patterns that result can correspond to different computations. It is computing answers to different calculations set for it.

Through developing these specialised quantum circuits scientists are bouncing beams of light forwards on the path that will hopefully lead to conventional digital technology being replaced with the next generation of supercomputers.

Jane Waite, Queen Mary University of London

Watch…

Related Magazine …

*Francis Galton appears earlier in Issue 20, you can read more about him on page 15 of the PDF. Although a brilliant mathematician he held views about people that are unacceptable today. In 2020 University College London (UCL) changed the name of its Galton Lecture Theatre, which had been named previously in his honour, to Lecture Theatre 115.

EPSRC supports this blog through research grant EP/W033615/1.