Category: issue 15 – Does your computer understand you?

The invisible dice mystery – a magic trick underpinned by computing and maths

Red dice image by Deniz Avsar from Pixabay

The Ancient Egyptians, Romans and Greeks used dice with various shapes and markings; some even believed they could be used to predict the future. Using just a few invisible dice, which you can easily make at home, you can amaze your friends with a transparent feat of magical prediction.

The presentation

You can’t really predict the future with dice, but you can do some clever magic tricks with them. For this trick first you need some invisible dice, they are easy to make, it’s all in the imagination. You take your empty hand and state to your friend that it contains two invisible dice. Of course it doesn’t, but that’s where the performance come in. You set up the story of ancient ways to predict the future. You can have lots of fun as you hand the ‘dice’ over and get your friend to do some test rolls to check the dice aren’t loaded. On the test rolls ask them what numbers the dice are showing (remember a dice can only show numbers 1 through 6), this gets them used to things. Then on the final throw, tell them to decide what numbers are showing, but not to tell you! You are going to play a game where you use these numbers to create a large ‘mystical’ number.

To start, they choose one of the dice and move it closer to them, remembering the number on this die. You may want to have them whisper the numbers to another friend in case they forget, as that sort of ruins the trick ending!

Next you take two more ‘invisible dice’ from your pocket; these will be your dice. You roll them a bit, giving random answers and then finally say that they have come up as a 5 and a 5. Push one of the 5s next to the dice your friend selected, and tell them to secretly add these numbers together, i.e. their number plus 5. Then push your second 5 over and suggest, to make it even harder, to multiply their current number by 5+5 (i.e. 10 – that’s a nice easy multiplication to do) and remember that new number. Then finally turn attention to your friend’s remaining unused die, and get them to add that last number to give a grand total. Ask them now to tell you that grand total. Almost instantly you can predict exactly the unspoken numbers on each of their two invisible dice. If they ask how it you did it, say it was easy – they left the dice in plain sight on the table. You just needed to look at them.

The computing behind

This trick works by hiding some simple algebra in the presentation. You have no idea what two numbers your friend has chosen, but let’s call the number on the die they select A and the other number B. If we call the running total X then as the trick progresses the following happens: to begin with X=0, but then we add 5 to their secret number A, so X= A+5. We then get the volunteer to multiply this total by 5+5 (i.e. 10) so now X=10*(A+5). Then we finally add the second secret number B to give X=10(A+5)+B. If we expand this out, X= 10A+50+B. We know that A and B will be in the range 1-6 so this means that when your friend announces the grand total all you need to do is subtract 50 from that number. The number left (10*A+B) means that the value in the 10s column is the number A and the units column is B, and we can announce these out loud. For example if A=2 and B=4, we have the grand total as 10(2+5)+4 = 74, and 74 – 50= is 24, so A is 2, and B is 4.

In what are called procedural computer languages this idea of having a running total that changes as we go through well-defined steps in a computer program is a key element. The running total X is called a variable, to start in the trick, as in a program, we need to initialise this variable, that is we need to know what it is right at the start, in this case X=0. At each stage of the trick (program) we do something to change the ‘state’ of this variable X, ie there are rules to decide what it changes to and when, like adding 5 to the first secret number changes X from 0 to X=(A+5). A here isn’t a variable because your friend knows exactly what it is, A is 2 in the example above, and it won’t change at any time during the trick so it’s called a constant (even if we as the magician don’t know what that constant is). When the final value of the variable X is announced, we can use the algebra of the trick to recover the two constants A and B.

Other ways to do the trick

Of course there are other ways you could perform the trick using different ways to combine the numbers, as long as you end up with A being multiplied by 10 and B just being added. But you want to hide that fact as much as possible. For example you could use three ‘invisible dice’ yourself showing 5, 2 and 5 and go for 5*(A*2+5) + B if you feel confident your friend can quickly multiply by 5. Then you just need to subtract 25 from their grand total (10A+25+B), and you have their numbers. The secret here is to play with the presentation to get one that suits you and your audience, while not putting too much of a mental strain on you or your friend to have to do difficult maths in their head as they calculate the state changes of that ever-growing variable X.

Paul Curzon, Queen Mary University of London

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Bringing people closer when they’re far away

Two children playing with a tin-can telephone, which lets them talk to each other at a distance. Picture credit Jerry Loick KONZI, CC BY-SA 4.0, via Wikimedia Commons

This article was written before the Covid pandemic led to many more of us keeping in touch from a distance…

Living far away from the person you love is tough. You spend every day missing their presence. The Internet can help, and many couples in long-distance relationships use video chat to see more of each other. It’s not the same as being right there with someone else, but couples find ways to get as much connection as they can out of their video chats. Some researchers in Canada, at the University of Calgary and Simon Fraser University, interviewed couples in long-distance relationships to find out how they use video chat to stay connected.

Nice to see you

The first thing that the researchers found is perhaps what you might expect. Couples use video chat when it’s important to see each other. You can text little messages like ‘I love you’ to each other, or send longer stories in an email, and that’s fine. But seeing someone’s face when they’re talking to you feels much more emotionally close. One member of a couple said, “The voice is not enough. The relationship is so physical and visual. It’s not just about hearing and talking.” Others reported that seeing each other’s face helped them know what the other person was feeling. For one person, just seeing his partner’s face when she was feeling worn out helped him understand her state of mind. In other relationships, seeing one another helped avoid misunderstandings that come from trying to interpret tone of voice. Plus, having video helped couples show off new haircuts or clothes, or give each other tours of their surroundings.

Hanging out on video

The couples in the study didn’t use video chat just to have conversations. They also used it in a more casual way: to hang out with each other while they went about their lives. Their video connections might stay open for hours at a time while they did chores, worked, read, ate or played games. Long silences might pass. Couples might not even be visible to each other all the time. But each partner would, every once in a while, check back at the video screen to see what the other was up to. This kind of hanging out helped couples feel the presence of the other person, even if they weren’t having a conversation. One participant said of her partner, “At home, a lot of times at night, he likes to put on his PJs and turn out all the lights and sit there with a snack and, you know, watch TV… As long as you can see the form of somebody that’s a nice thing. I think it’s just the comfort of knowing that they’re there.”

Some couples felt connected by doing the same things together in different places. They shared evenings together in living rooms far away from each other, watching the same thing on television or even getting the same movie to watch and starting it at the same time. Some couples had dinner dates where they ordered the same kind of takeaway and ate it with each other through their video connection.

Designing to connect

This might not sound like research about human-computer interaction. It’s about the deepest kind of human interaction. But good computer design can help couples feel as connected as possible. The researchers also wanted to find out how they could help couples make their video chats better. Designers of the future might think about how to make gadgets that make video chat easier to do while getting on with other chores. It’s difficult to talk, film yourself, cook and move through the house all at the same time. What’s more, today’s gadgets aren’t really built to go everywhere in the house. Putting a laptop in a kitchen or propping one up in a bed doesn’t always work so well. The designers of operating systems need to work out how to do other stuff at the same time as video. If couples want to have a video chat connection open for hours, sometimes they might need to browse the web or write a text message at the same time. And what about couples who like to fall asleep next to one another? They might need night-vision cameras so they can see their partner without disturbing their sleep.

We’re probably going to have more long- distance relationships in the future. Easy, cheap travel makes it easier to move to faraway places. You can go to university abroad, and join a company with offices on every continent. It’s an awfully good thing that technology is making it easier to stay connected with the people who are important too. Video chat is not nearly as good as feeling your lover’s touch, but when you really miss someone, even watching them do chores helps.

Paul Curzon, Queen Mary University of London

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Delicious computing

Gestural computing with bananas and pizzas…

A photograph of ripening yellow bananas

Bananas image by Couleur from Pixabay

Imagine being able to pick up an ordinary banana and use it as a phone. That’s part of the vision of ‘invoked computing’, which is being developed by Japanese researchers. A lot of the computers in our lives are camouflaged – smartphones are more like computers than phones, after all – but invoked computing would mean that computers would be everywhere and nowhere at the same time.

The idea is that in the future, computer systems could monitor an entire environment, watching your movements. Whenever you wanted to interact with a computer, you would just need to make a gesture. For example, if you picked up a banana and held one end to your ear and the other to your mouth, the computer would guess that you wanted to use the phone. It would then use a fancy speaker system to direct the sound, so you would even hear the phone call as though it were coming from the banana.

Sometimes you might find yourself needing a bit more computing power, though, right? Not to worry. You can make yourself a laptop if you just find an old pizza box. Lift the lid and the system will project the video and sound straight on to the box.

At the moment the banana phone and pizza box laptop are the only ways that you can use invoked computing in the researchers’ system, but they hope to expand it so that you can use other objects. Then, rather than having to learn how to use your computers, your computers will have to learn how you would like to use them. And when you are finished using your phone, you could eat it.

– CS4FN team, Queen Mary University of London

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This article was originally published on CS4FN and can also be found on page 2 of CS4FN Issue 15, Does your computer understand you?, which you can download as a PDF. All of our free material can be downloaded here: https://cs4fndownloads.wordpress.com/

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

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

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Your own electrical sea

A silhouetted man holding up an umbrella as a lightning storm rages around him against a slate grey sky. He is holding a briefcase.
Image by Gerd Altmann from Pixabay

Sensing your movements

You can’t see them, but there are waves of electricity flowing around you right now. Electricity leaks out of power lines, lights, computers and every other gadget nearby. Soon a computer may be able to track your movements by following the ripples you make in your own electromagnetic sea. Scientists at Microsoft Research in the US have figured out a way to sense the position of someone’s body by using it as an antenna.

Why would you want a computer to do this? So that you could control it just by moving your body. This is already possible with systems like the Xbox Kinect, but that works by tracking you with a camera, so you have to stay in front of it or it loses you. A system that uses your body as an electric antenna could follow you throughout a room, or even a whole building.

First you need an instrument that can sense the changes you make in your own electrical field as you move around. In the future, the researchers would like this to be a little gadget you could carry in your pocket, but the technology isn’t quite small enough yet. For this experiment, they used a wireless data sensor that’s about twice the size of a mobile phone. The volunteers wore it in a little backpack. All the electrical data it picked up were transmitted to a computer that would run the calculations to figure out how the user was moving.

Get moving

In their first experiment, the researchers wanted to find out whether their gadget could sense what movements their volunteers made. To do this, they had the volunteers take their sensing devices home and use them in two different rooms: the kitchen and the living room. Those two rooms are usually different from one another in interesting ways. Living rooms are usually big open spaces with only a few small appliances in them. Kitchens, though, are often small, and cram lots of big electricals in the same room. The electrical sensors would really have to work hard to make sense through the interference.

Once the experiment was ready to go, each volunteer ran through a series of twelve movements. Their exercises included waving, bending over, stepping to the right or left, and even a bit of kicking and punching. The sensor would collect the electrical readings and then send them to a laptop. What happened after that was a bit of artificial intelligence. The researchers used the first few rounds of movements to train the computer to recognise the electrical signatures of each movement. Later on, it was the computer’s job to match up the readings it got through the sensor to the gestures it already knew. That’s a technique called machine learning.

One of the surprising things that made the sensor’s job tougher was that electrical appliances change what they are doing more often than you think. Maybe a refrigerator switches its cooling on and off, or a computer starts up its hard disk. Each of these changes means a change in the electrical waves flowing through the room, and the computer had to recognise each gesture through the changing noise.

Where’d you go?

The next step for the system was to see if it could recognise which room someone was standing in when they performed the movements. There were now eight locations to keep straight – two locations in one large room and six more scattered throughout the house. It was up to the system to learn the electrical signature for each room, as well as the signature for each movement. That’s pretty tough work. But it worked well – really well. The system was able to guess the room almost 100% of the time. What’s more, they found that the location tracking even worked on the data from the first experiment, when they were only supposed to be looking at movements. But the electrical signatures of each room were built into that data too, and the system was expert enough to pick them out.

Putting it all together

In the future the researchers are hoping that their gadgets will become small enough to carry around with you wherever you are in a building. This could allow you to control computers within your house, or switch things on and off just by making certain movements. The fact that the system can sense your location might mean that you could use the same gestures to do different things. Maybe in the living room a punch would turn on the television, but in the kitchen it would start the microwave. Whatever the case, it’s a great way to use the invisible flow of energy all around us.

– Paul Curzon, Queen Mary University of London

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This article was originally published on CS4FN and can also be found on pages 14-15 of CS4FN Issue 15, Does your computer understand you?, which you can download as a PDF. All of our free material can be downloaded here: https://cs4fndownloads.wordpress.com/

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

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

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