SJC Inspire: how to design a successful video game

Very excited to announce the launch of the SJC Inspire digital magazine this week – a project I’ve been working on for the past few months in my role as Access and Outreach Associate for STEM at St John’s College, Oxford.

The first issues is ‘how to design a successful video game’ and features articles by researchers at St John’s, video interviews with students at the college, and practice puzzles set (and solved) by real Oxford tutors (myself included). I’ve highlighted some of my favourites below, but be sure to check out the full contents of the issue on the website here.

Maths in video games

My former tutorial partner, James Hyde, now works for Creative Assembly developing hit titles such as Halo Wars and Halo Wars 2. Here he explains how maths has helped him to land his dream job…

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Fun and games at the circus

Try out this maths puzzle set by St John’s maths tutor Dr David Seifert. If you send your answers in to inspire@sjc.ox.ac.uk you might even win a goodie bag!

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How to earn billions by giving something away for free

St John’s Economics tutor Dr Kate Doornik explains the pricing strategy behind the incredibly successful ‘Fortnite: Battle Royale’. Originally given away for free, it is expected to make over $3 billion in sales in 2018…

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Oxplore: Do we see colour the same?

Livestream debate with researchers at the University of Oxford discussing the BIG question: do we see colour the same? Featuring an incredible trick with colour perception, a multiple choice question for you to try at home, and a discussion of the dress – is it blue and black or white and gold?

Tom Rocks Maths S02 E01

Tom Rocks Maths is back on Oxide – Oxford University’s student radio station – for a second season. The old favourites return with the weekly puzzle, Funbers and Equations Stripped. Plus, the new Millennium Problems segment where I tell you everything that you need to know about the seven greatest unsolved problems in the world of maths, each worth a cool $1 million. And not to forget the usual selection of awesome music from artists such as Rise Against, Panic at the Disco, Thirty Seconds to Mars – and for one week only – Taylor Swift. This is maths, but not as you know it…

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…

Tom Rocks Maths Episode 08

The final episode in season 1 of Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station – with very special guests Jon and Nick discussing everything from the number of stickers needed to cover the Earth, to different types of infinity, via a new name for the world’s smallest number. Plus, a mammoth quiz to end the season in style and music from Nirvana and Soundgarden. This is maths, but not as you know it…

Maths proves that maths isn’t boring

If all the maths you’d ever seen was at school, then you’d be forgiven for thinking numbers were boring things that only a cold calculating robot could truly love. But, there is a mathematical proof that you’d be wrong: Gödel’s incompleteness theorem. It comes from a weird part of maths history which ended with a guy called Kurt Gödel proving that to do maths, you have to take thrill-seeking risks in a way a mindless robot never could, no matter how smart it was.

The weirdness begins with philosophers deciding to have a go at maths. Philosophers love (and envy) maths because they love certainty. No coincidence that Descartes, the guy you have to thank for x-y graphs, was also the genius who proved to himself that he actually existed and wasn’t just a dream (after all, who else would be the one worrying about being a dream?). Maths is great for worriers like him, because there’s no question of who is right and who is wrong – show a mathematician a watertight proof of your claim and they’ll stop arguing with you and go away (disclaimer: this may not to work with maths teachers…).

However, being philosophers, they eventually found a reason to worry again. After all, maths proofs can’t just start from nothing, they need some assumptions. If these are wrong, then the proof is no good. Most of the time, the assumptions will have proofs of their own, but as anyone who has argued with a child will know, eventually the buck has to stop somewhere. (“Why can’t I play Mario?” “Because it’s your bedtime.” “Why is it bedtime?!” “BECAUSE I SAY SO!”) Otherwise, you go on giving explanations forever.

The way this usually works for maths, is mathematicians agree on some excruciatingly obvious facts to leave unproved, called axioms. Think “1+1=2”, but then even more obvious than that (in fact, Bertrand Russell spent hundreds of pages proving that 1+1=2 from these stupidly basic facts!). This means that mathematicians can go about happily proving stuff from their axioms, and stop worrying. Peak boring maths.

But the philosophers still weren’t happy. Mostly, it was because the mathematicians massively screwed up their first go at thinking of obvious ‘facts’. How massively? The ‘facts’ they chose turned out to be nonsense. We know this because they told us things which flat-out contradicted each other. You could use them to ‘prove’ anything you like – and the opposite at the same time. You could ‘prove’ that God exists, and that He doesn’t – and no matter which one of those you think is true, we can all agree that they can’t both be right! In other words, the axioms the mathematicians chose were inconsistent.

Philosophers’ trust in maths was shattered (after all, it was their job to prove ridiculous stuff). Before they could trust another axiom ever again, they wanted some cast-iron proof that they weren’t going to be taken for another ride by the new axioms. But where could this proof start off? If we had to come up with a whole other list of axioms for it, then we’d need a proof for them too… This was all a bit of a headache.

The only way out the mathematicians and philosophers could see was to look for a proof that the new axioms were consistent, using only those new axioms themselves. This turned out to be very, very hard. In fact (and this is where Gödel steps in) it turned out to be impossible.

Cue Gödel’s incompleteness theorem. It says that any axioms that you can think of are either inconsistent – nonsense – or aren’t good enough to answer all of your maths questions. And, sadly, one of those questions has to be whether the axioms are inconsistent. In short, all good axioms are incomplete.

This may sound bad, but it’s really an exciting thing. It means that if you want to do maths, you really do have to take big risks, and be prepared to see your whole house of cards fall down in one big inconsistent pile of nonsense at any time. That takes serious nerve. It also means mathematicians have the best job security on the planet. If you could just write down axioms and get proof after proof out of them, like a production line, then you could easily make a mindless robot or a glorified calculator sit down and do it. But thanks to Gödel’s incompleteness theorem, we know for sure that will never happen. Maths needs a creative touch – a willingness to stick your neck out and try new axioms just to see what will happen – that no robot we can build will ever have.

Joe Double

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…

This robot is a ‘Cheetah’

Robots are developing at an incredible rate, with their ability to perform real-world tasks improving almost by the minute. Such rapid development doesn’t come without downsides, and there are many people who believe that artificial intelligence (AI) could become too powerful, leading to the possibility of robots taking our jobs, or perhaps even taking over the world! Whilst these fears might not be completely unjustified, let’s instead focus on the positives for the time being and marvel at the astonishing accomplishments being made in the field of robotics.

The Cheetah robot, developed by scientists at MIT, is roughly the same shape and size as a small dog, and has been designed to be able to walk across difficult terrains efficiently and effectively. Such a trait is particularly useful when we need to explore dangerous and hazardous environments that may be unsuitable for humans, such as the Fukushima nuclear power plant that collapsed in Japan in 2011. Like all robots, it uses algorithms to help it to navigate, stabilise itself, and ensure that its movements are natural. The latest version, the Cheetah 3, was unveiled in early July, and I think it’s fair to say that it wouldn’t look too far out of place in the animal kingdom!

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[Image courtesy of Sangbae Kim, MIT]

Perhaps the most impressive feature of the Cheetah 3 is that the strangely adorable hunk of metal performs the majority of its navigation without any visual input, meaning that it is effectively blind. The researchers at MIT believe that this is a more robust way to design the robot, since visual data can be noisy and unreliable, whereas an input such as touch is always available. Let’s imagine that you are in a pitch-black room; how would you find your way around? Your eyes are pretty much useless, but you can use your sense of touch to feel around the environment, making sure that you don’t bump into walls or obstacles. It’s also important to step carefully, so that you don’t misjudge where the floor is, or tread too strongly and break through something. The Cheetah 3 takes all of this into account as it gracefully glides across even the roughest terrain.

One of the key ideas that was addressed in the new model is contact detection. This means that the robot is able to work out when to commit to putting pressure on a step, or whether it should swing its leg instead, based on the surface that it is stepping onto. This has a massive impact on its ability to balance when it is walking on rough terrain, or one that is full of different obstacles; it also makes each step quicker and more natural. Going back to our dark room, you are likely to step quite tentatively if you can’t see where you are going as this will allow you to react to whatever surface you come into contact with, and adjust your motion as required. With the latest update, the clever ‘canine’ can make these adjustments by itself in a natural manner.

The Cheetah 3 also contains a new and improved prediction model. This can calculate how much pressure will need to be applied to each leg when it experiences a force, by estimating what will happen in half a second’s time. Returning once again to our pitch-black room, imagine how great it would be if you were able to predict what you’re about to step on and adjust your path accordingly – no more treading on sharp objects or stubbing your toe! The scientists tested the power of the new model by kicking the robot when it was walking on a treadmill. Using its prediction algorithm, the Cheetah 3 was able to quickly calculate the forces it needed to exert in order to correctly balance itself again and keep moving. Whilst I can confirm that no animals were harmed in the making of this robot, whether or not the robot itself felt harm is perhaps a question for another day…

The new and improved Cheetah 3 is certainly one of the more remarkable recent accomplishments in the field of robotics. Its natural movements and quick corrections mean that it excellently mimics animal navigation, and it is easy to see how such a robot would be extremely useful for exploring dangerous terrains. Such incredible progress in the study of robotics is as impressive and exciting as it is scary. While it is extraordinary that we are able to replicate animal movements so closely, it has rightly made many people slightly worried; will robots eventually be able to completely replace us? We can only cross our fingers that these critters have no plans for world domination just yet…

Kai Laddiman

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