It is Red nose day in the UK the day of raising money for the comic relief charity by buying and wearing red noses and generally doing silly things for money.
Red noses are not just for red nose day though and if you ‘ve been supporting it every year, you possibly now have a lot of red noses like we do. What can you do with lots of red noses? Well one possibility is to count in red nose binary as a family or group of friends. (Order your red noses (a family pack has 4 or a school pack 25) from comic relief or make a donation to the charity there.)
Red nose binary
Let’s suppose you are a family of four. All stand in a line holding your red noses (you may want to set up a camera to film this). How many numbers can 4 red noses represent? See if you can work it out first. Then start counting:
No one wearing a red nose is 0,
the rightmost end person puts theirs on for 1,
they take it off and the next person puts theirs on for 2,
the first person puts theirs back on for 3,
the first two people take their noses off and the third person puts theirs on for 4
and so on…
The pattern we are following is the first (rightmost end) person changes their nose every time we count. The second person has the nose off for 2 then on for the next 2 counts. The third person changes theirs every fourth count (nose off for 4 then on for 4) and the last person changes theirs every eighth count (off for 8, on for 8). That gives a unique nose pattern every step of the way until eventually all the noses are off again and you have counted all the way from 0 to 15. This is exactly the pattern of binary that computers use (except they use 1s and 0s rather than wear red noses).
What is the biggest number you get to before you are back at 0? It is 15. Here is what the red nose binary pattern looks like.
Image by CS4FN
Try and count in red nose binary like this putting on and taking off red noses as fast as you can, following the pattern without making mistakes!
The numbers we have put at the top of each column are how much a red nose is worth in that column. You could write the number of the column on that person’s red nose to make this obvious. In our normal decimal way of counting, digits in each column are worth 10 times as much (1s 10s 100s, 1000s, etc) Here we are doing the same but with 2s (1s 2s 4s 8s etc). You can work out what a number represents just by adding that column number in if there is a red nose there. You ignore it if there is no red nose. So for example 13 is made up of an 8s red nose + a 4s red nose + a 1s red nose. 8 + 4 + 1 = 13.
Image by CS4FN
Add one more person (perhaps the dog if they are a friendly dog willing to put up with this sort of thing) with a red nose (now worth 16) to the line and how many more numbers does that now mean you can count up to? Its not just one more. You can now go through the whole original sequence twice once with the dog having no red nose, once with them having a red nose. So you can now count all the way from 0 to 31. Each time you add a new person (or pet*, though goldfish don’t tend to like it) with a red nose, you double the number you can count up to.
There is lots more you can do once you can count in red nose binary. Do red nose binary addition with three lines of friends with red noses, representing two numbers to add and compute the answer on the third line perhaps… for that you need to learn how to carry a red nose from one person to the next! Or play the game of Nim using red nose binary to work out your moves (it is the sneaky way mathematicians and computer scientists use to work out how to always win). You can even build a working computer (a Turing Machine) out of people wearing red noses…but perhaps we will save that for next year.
What else can you think of to do with red nose binary?
[OOPS did I do this in a confusing way given red noses look like a 0 and normal noses look like a 1!?!]
Paul Curzon, Queen Mary University of London
*Always make sure your pet (or other family member) has given written consent before you put a red nose on them for ethical counting.
There are several Pi Day’s (14 March: 3.14; 22 July: 22/7) so we should look at how on earth you compute a number like Pi (3.1.4159….). It has an infinite number of digits containing no repeating pattern so you can never tie it down exactly. One of my favourite ways for calculating pi was first devised by the Indian mathematician Mādhava of Sangamagrāma 600 years ago. He worked out an algorithm for working out Pi based on the maths of infinite series that he had also worked out.
Pi is one of the most useful numbers in all of maths. In school you come across it when working out the area or circumference of a circle, but it crops up all over the place including in practical computer science situations. Digital music, for example, relies on it deep down. Remember that the next time you stream your favourite music!
So how, 600 years ago did Mādhava manage to work out a much more accurate version of Pi than anyone before him? He had worked out that certain sequences of infinite numbers wouldn’t get bigger and bigger but would just get closer and closer to some specific number. In particular, he worked out one such sequence linked to pi.
π / 4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – …
Writing this a slightly different way it gives us a way of calculating pi itself
π = 4 – 4/3 + 4/5 – 4/7 + 4/9 – …
With an infinite number of terms, this gives an accurate value for pi. We can’t add an infinite number of numbers together though. Instead, we can use it to get a good answer. To get an approximation to pi we just follow an algorithm where we gradually add / subtract the next term. Each new calculation then gives us a better estimate of what pi is.
So to start with we just take the first term which says
π = 4 (very approximately)
That isn’t very good as it doesn’t get any digits right! Pi is closer to 3 than to 4. So its not looking hopeful! That doesn’t matter though as it is just a starting point. When we subtract the next term it gets a bit better
π = 4 – 4/3 = 2.6666…
Hmm. Now we have overshot the other way. However, we are closer to the real value of pi than we were. So don’t lose heart, keep going and add the next term
π = 4 – 4/3 + 4/5 = 3.46666…
And another term …
π = 4 – 4/3 + 4/5 – 4/7 = 2.895 …
And another term …
π = 4 – 4/3 + 4/5 – 4/7 + 4/9 = 3.339…
and so on.
The important thing to notice is that after each term included we get a more accurate answer, and we can keep adding terms for as long as we are happy to do the calculations. Mādhava (or his followers) obviously liked doing calculations so kept going until he had worked out pi accurate to 10 decimal places (3.1415926535…) : a new world record at the time beating the previous best of 6 decimal places by a Chinese astronomer Zhao Youqin using a different algorithm, That record had been set 80 years earlier but was smashed by 4 decimal places. This new record lasted for another 96 years. In doing these calculations Mādhava was acting as a ‘computer’ in the original meaning of the word: a human following an algorithm to do computation.
His algorithm is what computer scientists call an iterative algorithm. This kind of algorithm is used quite a lot by computer scientists as it gives a general way of getting a good enough (if not perfect) answer to a problem that otherwise is hard (or impossible) to get a perfect answer to in a reasonable time. You start with a good guess and then gradually refine the answer until you are happy that it is accurate enough. These algorithms can be straightforward to code as it is just running a loop doing calculations that refine the answer. Mādhava was happy with 10 decimal places of accuracy but he could have kept going. The trouble is this is a very slow algorithm. As we saw with the first few iterations above, it takes a long time even to home in on the first digit being 3! Every new digit took a lot of extra work to get right. When calculating machines and then computers were invented it became easier to use slow algorithms like this, but even with a faster computer it is still better to have a faster algorithm. Now far faster algorithms have been invented and the world record at the time of writing gives pi accurate to 105,000,000,000,000 decimal places!
Mādhava would have needed to really like doing calculations (and have discovered the secret to eternal life) to have calculated pi that accurately. 600 years ago his world record for pi was still an amazing achievement.
Scientific fraud is worryingly common, though rarely talked about. It has been happening for years, but now Artificial Intelligence programs could supercharge it. If they do that could undermine Science itself.
Investigators of scientific fraud have found that large numbers of researchers have manipulated their results, invented data, or even produced nonsensical papers in the hope that no one will look closely enough to notice. Often, no one does. The problem is that science is built on the foundation of all the research that has gone before. If we can no longer trust that past research is legitimate, the whole system of science begins to break down. AI has the potential to supercharge this process.
We’re not at that point yet, luckily. But there are concerning signs that generative AI systems like ChatGPT and DALLE-E might bring us closer. By using AI technology, producing fraudulent research has never been easier, faster, or more convincing. To understand, let’s first look at how scientific fraud has been done in the past.
How fraud happens
Until recently, fraudsters would need to go through some difficult steps to get a fraudulent research paper published. A typical example might look like this:
Step 1: invent a title
Fraudsters look for a popular but very broad research topic. We’ll take an example of a group of fraudsters known as the Tadpole Paper Mill. They published papers about cellular biology. To choose a new paper to create, the group would essentially use a simple generator, or algorithm, based on a template. This uses a simple technique first used by Christopher Strachey to write love letters in an early “creative” program in the 1950s.
For each “hole” in the template a word is chosen from a word list.
Pick the name of a molecule
Either a protein name, a drug name or an RNA molecule name
Next, the fraudsters create the text of the paper. To do this, they often just plagiarise and lightly edit previous similar papers, substituting key words in from their invented title perhaps. To try to hide the plagiarism, they automatically swap out words, replacing them with synonyms. This often leads to ridiculous (and kind of hilarious) replacements, like these found in plagiarised papers:
“Big data” –> “Colossal information”
“Cloud computing” –> “Haze figuring”
“Developing countries” –> “Creating nations”
“Kidney failure” –> “Kidney disappointment”
Step 3: add in the results
Lastly, the fraudsters need to create results for the fake study. These usually appear in papers in the form of images and graphs. To do this, the fraudsters take the results from several previous papers and recombine them into something that looks mostly real, but is just a Frankenstein mess of other results that have nothing to do with the current paper.
A new paper is born
Using that simple formula, fraudsters have produced thousands of fabricated articles in the last 10 years. Even after a vast amount of effort, the dedicated volunteers who are trying to clean up the mess have only caught a handful.
However, committing fraud like this successfully isn’t exactly easy, either: the fraudsters still need to come up with a research idea, write the paper themselves without copying too much from previous research, and make up results that look convincing—at least at first glance.
AI: Adding fuel to the fire
So what happens when we add modern generative AI programs into the mix? They are Artificial Intelligence programs like ChatGPT or DALL-E that can create text or pictures for you based on written requests.
Well, the quality of the fraud goes up, and the difficulty of producing it goes way down. This is true for both text and images.
Let’s start with text. Just now, I asked ChatGPT-4 to “write the first two paragraphs of a research paper on a cutting edge topic in psychology.” I then asked it to “write a fake results table that shows a positive relationship between climate change severity and anxiety”. I won’t copy the whole thing—in part because I encourage you to try this yourself to see how it works (not to actually create a fake paper!)—but here’s a sample of what it came up with:
“As the planet faces increasing temperatures, extreme weather events, and environmental degradation, the mental health repercussions for populations worldwide become a crucial area of investigation. Understanding these effects is vital for developing strategies to support communities in coping with the psychological challenges posed by a changing climate.”
As someone who has written many psychology research papers, I would find the results very difficult to identify as AI-generated—it looks and sounds very similar to how people in my field write, and it even generated Python code to analyse the fake data. I’d need to take a really close look at the origin of the data and so on to figure out that it’s fraudulent.
But that’s a lot of work required from me as a fraud-buster. For the fraudster, doing this takes about 1 minute, and would not be detected by any plagiarism software in the way previous kinds of fraud can be. In fact, this might only be detected if the fraudsters make a sloppy mistake, like leaving in a disclaimer from the model as in the paper caught which included the text
“[Please note that as an AI language model, I am unable to generate specific tables or conduct tests, so the actual resutls should be included in the table.]”!
Generative AIs are not close to human intelligence, at least not yet. So, why are they so good at producing convincing scientific research, something that’s commonly seen as one of the most difficult things humans can do? Two reasons play a big part: (1) scientific research is very structured, and (2) there’s a lot of training data. In any given field of research, most papers tend to look pretty similar—an introduction section, a method describing what the researchers did, a results section with a few tables and figures, and a discussion that links it back to the wider research field. Many journals even require a fixed structure. Generative AI programs work using Machine Learning – they learn from data and the more data they are given the better they become. Give a machine learning program millions of images of cats, telling it that is what they are, and it can become very good at recognising cats. Give it millions of images of dogs and it will be able to recognise dogs too. With roughly 3 million scientific papers published every year, generative AI systems are really good at taking these many, many examples of what a scientific report looks like, and producing similar sounding, and similarly structured pieces of text. They do it by predicting what word, sentence and paragraph would be good to come next based on probabilities calculated from all those examples.
Trusting future research
Most research can still be trusted, and the vast majority of scientists are working as hard as they can to advance human knowledge. Nonetheless, we all need to look carefully at research studies to ensure that they are legitimate, and we should be on extra alert as generative AI becomes even more powerful and widespread. We also need to think about how to improve universities and research culture generally, so that people don’t feel like they need to commit scientific fraud—something that usually happens because people are desperate to get or keep a job, or be seen as successful and reap the rewards. Somehow we need to change the game so that fraud no longer pays.
What do you think? Do you have ideas for how we can prevent fraud from happening in the first place, and how can we better detect it when it does occur? It is certainly an important new research topic. Find a solution and you could do massive good. If we don’t find solutions then we could lose the most successful tool human-kind has ever invented that makes all our lives better.
The theme for British Science Week 2024 is Time so here we’re going back in time to our archives to bring you this article about… time. Below are the instructions to find out your own personal time zone but be careful if you’re sharing your results with others, remember that your longitude (if combined with your latitude) can give away your location.
Andy Broomfield has given us the secret to figuring out your own personal time zone based on your longitude! Now you can figure out your time zone right down to the second, just like his gadget did.
Step one: find your longitude
First you need find out the longitude of the place you’re at. Longitude is the measure of where you are on the globe in an east-west direction (the north-south measurement is called latitude).
The best resource to do this is Google Earth, which will give you a very accurate longitude reading in degrees, minutes and seconds. Just find your location in Google Earth, and when you hover your mouse over it, the latitude and longitude are in the bottom right corner of the window.
There are alternatives to Google Earth online, but they tend to only work for one country rather than the whole world. If you can’t use Google Earth, try an internet search for finding longitude in your country.
If you’ve got a GPS system (e.g. on your phone), you can get it to tell you your longitude as well.
Step two: find your time zone
We’ll be finding your time relative to Greenwich Mean Time (GMT or UTC), the base for timekeeping all over the world. If your Longitude is west of 0° you’ll be behind GMT, and if it’s east then you’ll be ahead of it.
Longitude is usually measured in degrees, minutes and seconds. Here’s how longitude converts into your personal time zone: • 15 degrees of longitude = 1 hour difference; 1 degree longitude = 4 minutes difference. • 15 minutes of longitude = 1 minute difference; 1 minute of longitude = 4 seconds difference. • 15 seconds of longitude = 1 second difference, 1 second of longitude = 0.066(recurring) seconds difference.
The best way to find your personal time zone is to convert the whole thing into seconds of longitude, then into seconds of time. Do this by adding together:
(degrees x 3600) + (minutes x 60) + (seconds)
You’ll get a big number – that’s your seconds in longitude. Then if you divide that big number by 15, that’s how many seconds your personal time zone is different from GMT. Once you’ve got that, you can convert it back into hours, minutes and seconds.
An example
Let’s find the personal time zone for the President of the United States. The White House is at 77° 2′ 11.7″ West, so converting this all to seconds of longitude gives:
(degrees x 3600) + (minutes x 60) + (seconds) = (77 x 3600) + (2 x 60) + (11.7) = (277,200) + (120) + (11.7) = 277,331.7
Now we find the time zone difference in seconds of time:
277,331.7 / 15 = 18,488.78 seconds
This means that the President is 18,488.78 seconds behind GMT. Next it’s the slightly fiddly business of expanding those seconds back into hours, minutes and seconds. Because time is based on units of 60 rather than 10, dividing hours and minutes into decimals doesn’t tell you much. You’ll have to use whole numbers and figure out the remainders. Here’s how.
If you divide 18,488.78 by 3600 (the number of seconds in an hour), you’ll find out how many hours can fit in all of those seconds. The answer is 5, with some left over. 5 hours is 18,000 seconds (because 5 x 3600 = 18,000), so now you’re left with 488.78 seconds to deal with. Divide 488.78 by the number of seconds in a minute (60), and you get 8, plus some left over. 8 x 60 is 480, so you’ve got 8.78 seconds still left.
That means that the president’s personal time zone at the White House is 5 hours, 8 minutes and 8.78 seconds behind GMT.
If you’re using decimal longitude
Longitude is usually measured in degrees, minutes and seconds, but sometimes, like if you use a GPS receiver, you might get a measurement that just lists your longitude in degrees with a decimal. For example, the CS4FN office is located at 0.042 degrees west.
Figuring out your time zone with a decimal is simpler than with degrees, minutes and seconds. It’s just one calculation! Just take your decimal longitude and divide it by 0.004167.
The only problem with this simple calculation is that it’s not as accurate as the one above for degrees, minutes and seconds. Plus, if you get a large number of seconds you’ll still have to do the last step from the method above, where you convert seconds back into hours and minutes.
In school we learn about the maths that others have invented: results that great mathematicians like Euclid, Pythagoras, Newton or Leibniz worked out. We follow algorithms for getting results they devised. Ada Lovelace was actually taught by one of the great mathematicians, Augustus De Morgan, who invented important laws, ‘De Morgan’s laws’ that are a fundamental basis for the logical reasoning computer scientists now use. Real maths is about discovering new results of course not just using old ones, and the way that is done is changing.
We tend to think of maths as something done by individual geniuses: an isolated creative activity, to produce a proof that other mathematicians then check. Perhaps the greatest such feat of recent years was Andrew WIles’ proof of Fermat’s Last Theorem. It was a proof that had evaded the best mathematicians for hundreds of years. Wiles locked himself away for 7 years to finally come up with a proof. Mathematics is now at a remarkable turning point. Computer science is changing the way maths is done. New technology is radically extending the power and limits of individuals. “Crowdsourcing” pulls together diverse experts to solve problems; computers that manipulate symbols can tackle huge routine calculations; and computers, using programs designed to verify hardware, check proofs that are just too long and complicated for any human to understand. Yet these techniques are currently used in stand-alone fashion, lacking integration with each other or with human creativity or fallibility.
‘Social machines’ are a whole new paradigm for viewing a combination of people and computers as a single problem-solving entity. The idea was identified by Tim Berners-Lee, inventor of the world-wide web. A project led by Ursula Martin at the University of Oxford explored how to make this a reality, creating a mathematics social machine – a combination of people, computers, and archives to create and apply mathematics. The idea is to change the way people do mathematics, so transforming the reach, pace, and impact of mathematics research. The first step involves social science rather than maths or computing though – studying what working mathematicians really do when working on new maths, and how they work together when doing crowdsourced maths. Once that is understood it will then be possible to develop tools to help them work as part of such a social machine.
The world changing mathematics results of the future may be made by social machines rather than solo geniuses. Team work, with both humans and computers is the future.
– Ursula Martin, University of Oxford and Paul Curzon, Queen Mary University of London
The history of computational devices: automata, core rope memory (used by NASA in the Moon landings), Charles Babbage’s Analytical Engine (never built) and Difference Engine made of cog wheels and levers, mercury delay lines, standardising the size of machine parts, Mary Coombs and the Lyons tea shop computer, computers made of marbles, i-Ching and binary, Ada Lovelace and music, a computer made of custard, a way of sorting wood samples with index cards and how to work out your own programming origin story.
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This blog is funded by EPSRC on research agreement EP/W033615/1.
A jury is given misleading information in court by an expert witness. An innocent person goes to prison as a result. This shouldn’t happen, but unfortunately it does and more often than you might hope. It’s not because the experts or lawyers are trying to mislead but because of some tricky mathematics. Fortunately, a team of computer scientists at Queen Mary, University of London are leading the way in fixing the problem.
The Queen Mary team, led by Professor Norman Fenton, is trying to ensure that forensic evidence involving probability and statistics can be presented without making errors, even when the evidence is incredibly complex. Their solution is based on specialist software they have developed.
Many cases in courts rely on evidence like DNA and fibre matching for proof. When police investigators find traces of this kind of evidence from the crime scene they try to link it to a suspect. But there is a lot of misunderstanding about what it means to find a match. Surprisingly, a DNA match between, say, a trace of blood found at the scene and blood taken from a suspect does not mean that the trace must have come from the suspect.
Forensic experts talk about a ‘random match probability’. It is just the probability that the suspect’s DNA matches the trace if it did not actually come from him or her. Even a one-in-a-billion random match probability does not prove it was the suspect’s trace. Worse, the random match probability an expert witness might give is often either wrong or misleading. This can be because it fails to take account of potential cross-contamination, which happens when samples of evidence accidentally get mixed together, or even when officers leave traces of their own DNA from handling the evidence. It can also be wrong due to mistakes in the way the evidence was collected or tested. Other problems arise if family members aren’t explicitly ruled out, as that makes the random match probability much higher. When the forensic match is from fibre or glass, the random match probabilities are even more uncertain.
The potential to get the probabilities wrong isn’t restricted to errors in the match statistics, either. Suppose the match probability is one in ten thousand. When the experts or lawyers present this evidence they often say things like: “The probability that the trace came from anybody other than the defendant is one in ten thousand.” That statement sounds OK but it isn’t true.
The problem is called the prosecutor fallacy. You can’t actually conclude anything about the probability that the trace belonged to the defendant unless you know something about the number of potential suspects. Suppose this is the only evidence against the defendant and that the crime happened on an island where the defendant was one of a million adults who could have committed the crime. Then the random match probability of one in ten thousand actually means that about one hundred of those million adults match the trace. So the probability of innocence is ninety-nine out of a hundred! That’s very different from the one in ten thousand probability implied by the statement given in court.
Norman Fenton’s work is based around a theorem, called Bayes’ theorem, which gives the correct way to calculate these kinds of probabilities. The theorem is over 250 years old but it is widely misunderstood and, in all but the simplest cases is very difficult to calculate properly. Most cases include many pieces of related evidence – including evidence about the accuracy of the testing processes. To keep everything straight, experts need to build a model called a Bayesian network. It’s like a graph that maps out different possibilities and the chances that they are true. You can imagine that in almost any court case, this gets complicated awfully quickly. It is only in the last 20 years that researchers have discovered ways to perform the calculations for Bayesian networks, and written software to help them. What Norman and his team have done is develop methods specifically for modelling legal evidence as Bayesian networks in ways that are understandable by lawyers and expert witnesses.
Norman and his colleague Martin Neil have provided expert evidence (for lawyers) using these methods in several high-profile cases. Their methods help lawyers to determine the true value of any piece of evidence – individually or in combination. They also help show how to present probabilistic arguments properly.
Unfortunately, although scientists accept that Bayes’ theorem is the only viable method for reasoning about probabilistic evidence, it’s not often used in court, and is even a little controversial. Norman is leading an international group to help bring Bayes’ theorem a little more love from lawyers, judges and forensic scientists. Although changes in legal practice happen very slowly (lawyers still wear powdered wigs, after all), hopefully in the future the difficult job of judging evidence will be made easier and fairer with the help of Bayes’ theorem.
If that happens, then thanks to some 250 year-old maths combined with some very modern computer science, fewer innocent people will end up in jail. Given the innocent person in the dock could one day be you, you will probably agree that’s a good thing.
Paul Curzon, Queen Mary University of London (originally published in 2011)
Edie was a computer scientist whose marriage to another woman was deemed ineligible for certain rights provided (at that time) only in a marriage between a man and a woman. She fought for those rights and won.
Think of the perfect robot companion. A robot you can hang out with, chat to and who understands how you feel. Robots can already understand some of what we say and talk back. They can even respond to the emotions we express in the tone of our voice. But, what about body language? We also show how we feel by the way we stand, we describe things with our hands and we communicate with the expressions on our faces. Could a robot use body language to show that it understands how we feel? Could a robot show empathy?
If a robot companion did show this kind of empathetic body language we would likely feel that it understood us, and shared our feelings and experiences. For robots to be able to behave like this though, we first need to understand more about how humans use movement to show empathy with one another.
Think about how you react when a friend talks about their headache. You wouldn’t stay perfectly still. But what would you do? We’ve used motion capture to track people’s movements as they talk to each other. Motion capture is the technology used in films to make computer-animated creatures like Gollum in Lord of the Rings, or the Apes in the Planet of the Apes. Lots of cameras are used together to create a very precise computer model of the movements being recorded. Using motion capture, we’ve been able to see what people actually do when chatting about their experiences.
It turns out that we share our understanding of things like a headache by performing it together. We share the actions of the headache as if we have it ourselves. If I hit my head, wince and say ‘ouch’, you might wince and say ‘ouch’ too – you give a multimodal performance, with actions and words, to show me you understand how I feel.
So should we just program robots to copy us? It isn’t as simple as that. We don’t copy exactly. A perfect copy wouldn’t show understanding of how we feel. A robot doing that would seem like a parrot, repeating things without any understanding. For the robot to show that it understands how you feel it must perform a headache like it owns it – as though it were really theirs! That means behaving in a similar way to you; but adapted to the unique type of headache it has.
Designing the way robots should behave in social situations isn’t easy. If we work out exactly how humans interact with each other to share their experiences though, we can use that understanding to program robot companions. Then one day your robot friend will be able to hang out with you, chat and show they understand how you feel. Just like a real friend.
multimodal = two or more different ways of doing something. With communication that might be spoken words, facial expressions and hand gestures.
We have recently written about the AMPER project which uses a tablet-based AI tool / robot to support people with dementia and their carers. It prompts the person to discuss events from their younger life and adapts to their needs. We also linked this with information about the types of careers people working in this area might do – the examples given were for a project based in the Netherlands called ‘Dramaturgy for Devices’ – using lessons learned from the study of theatre and theatrical performances in designing social robots so that their behaviour feels more natural and friendly to the humans who’ll be using them.
Greg Michaelson is an Emeritus professor of computer science at Heriot-Watt University in Edinburgh. He is also a novelist and a short story writer. He wrote this story for CS4FN.
“Come on!” called Alice, taking the coat off the peg. “We’re going to be late!”
“Do I have to?” said Henry, emerging from the front room.
“Yes,” said Alice, handing him the coat. “Of course you have to go. Here. Put this on.”
“But we’re playing,” said Henry, wrestling with the sleeves.
“Too bad,” said Alice, straightening the jacket and zipping it up. “It’ll still be there when we get back.”
“Not if someone knocks it over,” said Henry, picking up a small model dinosaur from the hall table. “Like last time. Why can’t we have electric games like you did?”
“Electronic games,” said Alice, doing up her buttons. “Not electric. No one has them anymore. You know that.”
“Were they really digital?” asked Henry, fiddling with the dinosaur.
“Yes,” said Alice, putting on her hat. “Of course they were digital.”
“But the telephone’s all right,” said Henry.
“Yes,” said Alice, checking her makeup in the mirror. “It’s analogue.”
“And radio. And record players. And tape recorders. And television,” said Henry.
“They’re all analogue now,” said Alice, putting the compact back into her handbag. “Anything analogue’s fine. Just not digital. Stop wasting time! We’ll be late.”
“Why does it matter if we’re late?” asked Henry, walking the dinosaur up and down the hall table.
“They’ll notice,” said Alice. “We don’t want to get another warning. Put that away. Come on.”
“Why don’t the others have to go?” asked Henry, palming the dinosaur.
“They went last Sunday,” said Alice, opening the front door. “You said you didn’t want to go. We agreed I’d take you today instead.”
“Och, granny, it’s so boring…” said Henry.
They left the house and walked briskly to the end of the street. Then they crossed the deserted park, following the central path towards the squat neo-classical stone building on the far side.
“Get a move on!” said Alice, quickening the pace. “We really are going to be late.”
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Henry really hadn’t paid enough attention at school. He knew that Turing Machines were named for Alan Turing, the first Martyr of the Digital Age. And he knew that a Turing Machine could work out sums, a bit like a school child doing arithmetic. Only instead of a pad of paper and a pencil, a Turing Machine used a tape of cells. And instead of rows of numbers and pluses and minuses on a page, a Turing Machine could only put one letter on each cell, though it could change a letter without having to actually rub it out. And instead of moving between different places on a piece of paper whenever it wanted to, and maybe doodling in between the sums, a Turing Machine could only move the tape left and right one cell at a time. But just like a school child getting another pad from the teacher when they ran out of paper, the Turing Machine could somehow add another empty cell whenever it got to the end of the tape.
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When they reached the building, they mounted the stone staircase and entered the antechamber through the central pillars. Just inside the doorway, Alice gave their identity cards to the uniformed guard.
“I see you’re a regular,” she said approvingly to Alice, checking the ledger. “But you’re not,” sternly to Henry.
Henry stared at his shoes.
“Don’t leave it so long, next time,” said the guard, handing the cards back to Alice. “In you go. They’re about to start. Try not to make too much noise.”
Hand in hand, Alice and Henry walked down the broad corridor towards the central shrine. On either side, glass cases housed electronic equipment. Computers. Printers. Scanners. Mobile phones. Games consoles. Laptops. Flat screen displays.
The corridor walls were lined with black and white photographs. Each picture showed a scene of destitution from the Digital Age.
Shirt sleeved stock brokers slumped in front of screens of plunging share prices. Homeless home owners queued outside a state bank soup kitchen. Sunken eyed organic farmers huddled beside mounds of rotting vegetables. Bulldozers shovelled data farms into land fill. Lines of well armed police faced poorly armed protestors. Bodies in bags lay piled along the walls of the crematorium. Children scavenged for toner cartridges amongst shattered office blocks.
Alice looked straight ahead: the photographs bore terrible memories. Henry dawdled, gazing longingly into the display cases: Gameboy. Playstation. X Box…
“Come on!” said Alice, sotto voce, tugging Henry away from the displays.
At the end of the corridor, they let themselves into the shrine. The hall was full. The hall was quiet.
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Henry was actually quite good at sums, and he knew he could do them because he had rules in his head for adding and subtracting, because he’d learnt his tables. The Turing Machine didn’t have a head at all, but it did have rules which told it what to do next. Groups of rules that did similar things were called states, so all the rules for adding were kept separately from all the rules for subtracting. Every step of a Turing machine sum involved finding a rule in the state it was working on to match the letter on the tape cell it was currently looking at. That rule would tell the Machine how to change the symbol on the tape, which way to move the tape, and maybe to change state to a different set of rules.
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On the dais, lowered the Turing Machine, huge coils of tape links disappearing into the dark wells on either side, the vast frame of the state transition engine filling the rear wall. In front of the Turing Machine, the Minister of State stood at the podium.
“Come in! Come in!” he beamed at Alice and Henry. “There’s lots of space at the front. Don’t be shy.”
Red faced, Alice hurried Henry down the aisle. At the very front of the congregation, they sat down cross legged on the floor beneath the podium.
“My friends,” began the Minister of State. “Welcome. Welcome indeed! Today is a special day. Today, the Machine will change state. But first, let us be silent together. Please rise.”
The Minister of State bowed his head as the congregation shuffled to its feet.
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According to Henry’s teacher, there was a different Turing Machine for every possible sum in the world. The hard bit was working out the rules. That was called programming, but, since the end of the Digital Age, programming was against the law. Unless you were a Minister of State.
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“Dear friends,” intoned the Minister of State, after a suitable pause. “We have lived through terrible times. Times when Turing’s vision of equality between human and machine intelligences was perverted by base greed. Times when humans sought to bend intelligent machines to their selfish wills for personal gain. Times when, instead of making useful things that would benefit everybody, humans invented and sold more and more rarefied abstractions from things: shares, bonds, equities, futures, derivatives, options…”
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The Turing Machine on the dais was made from wood and brass. It was extremely plain, though highly polished. The tape was like a giant bicycle chain, with holes in the centre of each link. The Machine could plug a peg into a hole to represent a one or pull a peg out to represent a zero. Henry knew that any information could be represented by zeros and ones, but it took an awful lot of them compared with letters.
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“… Soon there were more abstractions than things, and all the wealth embodied in the few things that the people in poor countries still made was stolen away, to feed the abstractions made by the people in the rich countries. None of this would have been possible without computers…”
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The state transition unit that held the rules was extremely complicated. Each rule was a pattern of pegs, laid out in rows on a great big board. A row of spring mounted wooden fingers moved up and down the pegs. When they felt the rule for the symbol on the tape cell link, they could trigger the movement of a peg in or out of the link, and then release the brakes to start up one revolution of the enormous cog wheels that would shift the tape one cell left or right.
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“…With all the computers in the world linked together by the Internet, humans no longer had to think about how to manage things, about how best to use them for the greatest good. Instead, programs that nobody understood anymore made lightening decisions, moving abstractions from low profits to high profits, turning the low profits into losses on the way, never caring how many human lives were ruined…”
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The Turing Machine was powered by a big brass and wooden handle connected to a gear train. The handle needed lots of turns to find and apply the next rule. At the end of the ceremony, the Minister of State would always invite a member of the congregation to come and help him turn the handle. Henry always hoped he’d be chosen.
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“…Turing himself thought that computers would be a force for untold good; that, guided by reason, computers could accomplish anything humans could accomplish. But before his vision could be fully realised, he was persecuted and poisoned by a callous state interested only in secrets and profits. After his death, the computer he helped design was called the Pilot Ace; just as the pilot guides the ship, so the Pilot Ace might have been the best guide for a true Digital Age…”
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Nobody was very sure where all the cells were stored when the Machine wasn’t inspecting them. Nobody was very sure how new cells were added to the ends of the tape. It all happened deep under the dais. Some people actually thought that the tape was infinite, but Henry knew that wasn’t possible as there wasn’t enough wood and brass to make it that long.
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“…But almost sixty years after Turing’s needless death, his beloved universal machines had bankrupted the nations of the world one by one, reducing their peoples to a lowest common denominator of abject misery. Of course, the few people that benefited from the trade in abstractions tried to make sure that they weren’t affected but eventually even they succumbed…”
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Nobody seemed to know what the Turing Machine on the dais was actually computing. Well, the Minister of State must have known. And Turing had never expected anyone to actually build a real Turing Machine with real moving parts. Turing’s machine was a thought experiment for exploring what could and couldn’t be done by following rules to process sequences of symbols.
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“…For a while, everything stopped. There were power shortages. There were food shortages. There were medical shortages. People rioted. Cities burned. Panicking defence forces used lethal force to suppress the very people they were supposed to protect. And then, slowly, people remembered that it was possible to live without abstractions, by each making things that other people wanted, by making best use of available resources for the common good…”
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The Turing Machine on the dais was itself a symbol of human folly, an object lesson in futility, a salutary reminder that embodying something in symbols didn’t make it real.
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“…My friends, let us not forget the dreadful events we have witnessed. Let us not forget all the good people who have perished so needlessly. Let us not forget the abject folly of abstraction. Let the Turing Machine move one step closer along the path of its unknown computation. Let the Machine change its state, just as we have had to change ours. Please rise.”
The congregation got to their feet and looked expectantly at the Minister of State. The Minister of State slowly inspected the congregation. Finally, his eyes fixed on Henry, fidgeting directly in front of him.
“Young man,” he beamed at Henry. “Come. Join me at the handle. Together we shall show that Machine that we are all its masters.”
Henry looked round at his grandmother.
“Go on,” she mouthed. “Go on.”
Henry walked round to the right end of the dais. As he mounted the wooden stairs, he noticed a second staircase leading down behind the Machine into the bowels of the dais.
“Just here,” said the Minister of State, leading Henry round behind the handle, so they were both facing the congregation. “Take a good grip…”
Henry was still clasping the plastic dinosaur in his right hand. He put the dinosaur on the nearest link of the chain and placed both hands on the worn wooden shaft.
And turn it steadily…”
Henry leant into the handle, which, much to his surprise, moved freely, sweeping the wooden fingers across the pegs of rules on the state transition panel. As the fingers settled on a row of pegs, a brass prod descended from directly above the chain, forcing the wooden peg out of its retaining hole in the central link. Finally, the chain slowly began to shift from left to right, across the front of the Machine, towards Henry and the Minister of State. As the chain moved, the plastic dinosaur toppled over and tumbled down the tape well.
“Oh no!” cried Henry, letting go of the handle. Utterly nonplussed, the Minister of State stood and stared as Henry peered into the shaft, rushed to the back of the Machine and hurried down the stairs into the gloom.
A faint blue glow came from the far side of the space under the dais. Henry cautiously approached the glow, which seemed to come from a small rectangular source, partly obscured by someone in front of it.
“Please,” said Henry. “Have you seen my dinosaur?”
“Hang on!” said a female voice.
The woman stood up and lit a candle. Looking round, Henry could now see that the space was festooned with wires, leading into electric motors driving belts connected to the Turing Machine. The space was implausibly small. There was no room for a finite tape of any length at all, let alone an infinite one.
“Where are all the tape cells?” asked Henry, puzzled.
“We only need two spare ones,” said the woman. “When the tape moves, we stick a new cell on one end and take the cell off the other.”
“So what’s the blue light?” asked Henry.
“That’s a computer,” said the woman. “It keeps track of what’s on the tape and controls the Turing Machine.”
“A real digital computer!” said Henry in wonder. “Does it play games?”
“Oh yes!” said the woman, turning off the monitor as the Minister of State came down the stairs. “What do you think I was doing when you showed up? But don’t tell anyone. Now, let’s find that dinosaur.”
Our Turing Machine so far has an Infinite Tape, a Tape Head and a Controller. The Tape holds data values taken from a given set of 4×4 bricks. It starts in a specific initial pattern: the Initial Tape. There is also a controller. It holds different coloured 3×2 bricks representing an initial state, an end state, a current state and has a set of other possible states (so coloured bricks) to substitute for the current state.
Why do we need a program?
As the machine runs it changes from one state to another, and inputs from or outputs to the tape. How it does that is governed by its Program. What is the new state, the new value and how does the tape head move? The program gives the answers. The program is just a set of instructions the machine must blindly follow. Each instruction is a single rule to follow. Each program is a set of such rules. In our Turing Machines, these rules are not set out in an explicit sequence as happens in a procedural program, say. It uses a different paradigm for what a program is. Instead at any time only one of the set of rules should match the current situation and that is the one that is followed next.
Individual Instructions
A single rule contains five parts: a Current State to match against, a Current Value under the Tape Head to match against, a New State to replace the existing one, and a New Value to write to the tape. Finally, it holds a Direction to Move the Tape Head (left or right or stay in the same place). An example might be:
Current State: ORANGE
Current Value: RED
New State: GREEN
New Value: BLUE
Direction: RIGHT
But what does a rule like this actually do?
What does it mean?
You can think of each instruction as an IF-THEN rule. The above rule would mean:
IF
the machine is currently in state ORANGE AND
the Tape Head points to RED
THEN (take the following actions)
change the state to GREEN,
write the new value BLUE on the tape AND THEN
move the tape head RIGHT.
This is what a computer scientist would call the programming language Semantics. The semantics tell you what program instructions mean, so what they do.
Representing Instructions in Lego
We will use a series of 5 bricks in a particular order to represent the parts of the rule. For example, we will use a yellow 3×2 brick in the first position of a rule to represent the fact that the rule will only trigger if the current state is yellow. A blue 2×2 brick in the second position will mean the rule will also only trigger if the current value under the tape head is blue. We will use a grey brick to mean an empty tape value. The third and fourth position will represent the new state and new value if the rule does trigger. To represent the direction to move we will use a 1×2 Red brick to mean move Right, and a 1×2 yeLLow brick to mean move Left. We will use a black 1×2 brick to mean do not move the tape head (mirroring the way we are also using black to mean do nothing in the sense of the special end state). The above rule would therefore be represented in Lego as below.
A single instruction for a Lego Turing Machine. Image by CS4FN
Notice we are using the same colour to represent different things here. The representation is the colour combined with the size of brick and position in the rule. So a Red brick can mean a red state (a red 3×2 brick) or a red value (a red 2×2 brick) or move right (a red 1×2 brick).
Lego programs
That is what a rule, so single Turing Machine instruction, looks like. Programs are just a collection of such rules: so a series of lines of bricks.
Suppose we have a Turing machine with two states (Red and Orange) and two values on the tape (Blue or Empty), then a complete program would have 4 rules, one for each possible combination. We have given one example program below. If there were more states or more possible data values then the program would be correspondingly bigger to cover all the possibilities.
A 4 instruction Turing Machine Program for a Turing Machine with two states (Red, Orange) and two data values (Blue, Empty). Image by CS4FN
A Specific Turing Machine
Exactly what it does will depend on its input – the initial tape it is given to process, as well as the initial state and where the tape head initially points to. Perhaps you can work out what the above program does given a tape with an empty value followed by a series of three blue bricks (and then empty data values off to infinity (the blank value is the only value that is allowed to appear an infinite number of times on an initial tape) and the Head pointing to the rightmost blue brick value. The initial state is red. See the Lego version of this specific machine below.
A full Turing Machine ready to execute. Image by CS4FN
Note something we have glossed over. You also potentially need an infinite number of bricks of each value that is allowed on the tape. We have a small pile, but you may need that Lego factory we mentioned previously, so that as the Turing Machine runs you always have a piece to swap on to the machine tape when needed. Luckily, for this machine a small number of bricks should be enough (as long as you do not keep running it)!
What does this Turing Machine do? We will look at what it does and how to work it out in a future article. In the meantime try and work out what it does with this tape, but also what it does if the tape has more or less blue bricks in a row on it to start with (with everything else kept the same).
Note that, to keep programs smaller, you could have a convention that if no rule fits a situation then it means the program ends. Then you could have fewer rules in some programs. However, that would just be shorthand for there being extra rules with black new states, the tape being left alone, and the tape head moves right. In real programming, it is generally a good idea to ALWAYS be explicit about what you intend the program to do, as otherwise it is an easy way for bugs to creep in, for example, because you just forgot to say in some case.
Alan Turing invented Turing Machines before any computer existed. At the time a “computer” was a person who followed rules to do calculations (just like you were taught the rules to follow to do long multiplication at primary school, for example). His idea was therefore that a human would follow the rules in a Turing Machine program, checking the current state and value under the tape head, and changing the state, the value on the tape and the movement of the head. A person provides the power and equivalent of a robotic arm that follows the underlying Turing Machine algorithm: the Turing Machine algorithm that if followed causes each Turing Machine’s program to execute.
If a human animating the machine was good enough for Turing, it is good enough for us, so that is how our Lego Turing Machines will work. Your job will be to follow the rules and so operate the machine. Perhaps, that is exactly what you did to work out what the program above does!
Next we will look at how to work out what a Turing Machine does. Then it will be time to write, then run, some Turing Machine programs of your own…
EPSRC supports this blog through research grant EP/W033615/1, The Lego Computer Science post was originally funded by UKRI, through grant EP/K040251/2 held by Professor Ursula Martin, and forms part of a broader project on the development and impact of computing.
Have you ever heard a grown up say “I’d completely forgotten about that!” and then share a story from some long-forgotten memory? While most of us can remember all sorts of things from our own life history it sometimes takes a particular cue for us to suddenly recall something that we’d not thought about for years or even decades.
As we go through life we add more and more memories to our own personal library, but those memories aren’t neatly organised like books on a shelf. For example, can you remember what you were doing on Thursday 20th September 2018 (or can you think of a way that would help you find out)? You’re more likely to be able to remember what you were doing on the last Tuesday in December 2018 (but only because it was Christmas Day!). You might not spontaneously recall a particular toy from your childhood but if someone were to put it in your hands the memories about how you played with it might come flooding back.
Accessing old memories
In Alzheimer’s Disease (a type of dementia) people find it harder to form new memories or retain more recent information which can make daily life difficult and bewildering and they may lose their self-confidence. Their older memories, the ones that were made when they were younger, are often less affected however. The memories are still there but might need drawing out with a prompt, to help bring them to the surface.
Perhaps a newspaper advert will jog your memory in years to come… Image by G.C. from Pixabay
An EPSRC-funded project at Heriot-Watt University in Scotland is developing a tablet-based ‘story facilitator’ agent (a software program designed to adapt its response to human interaction) which contains artificial intelligence to help people with Alzheimer’s disease and their carers. The device, called ‘AMPER’*, could improve wellbeing and a sense of self in people with dementia by helping them to uncover their ‘autobiographical memories’, about their own life and experiences – and also help their carers remember them ‘before the disease’.
Our ‘reminiscence bump’
We form some of our most important memories between our teenage years and early adulthood – we start to develop our own interests in music and the subjects that we like studying, we might experience first loves, perhaps going to university, starting a career and maybe a family. We also all live through a particular period of time where we’re each experiencing the same world events as others of the same age, and those experiences are fitted into our ‘memory banks’ too. If someone was born in the 1950s then their ‘reminiscence bump’ will be events from the 1970s and 1980s – those memories are usually more available and therefore people affected by Alzheimer’s disease would be able to access them until more advanced stages of the disease process. Big important things that, when we’re older, we’ll remember more easily if prompted.
In years to come you might remember fun nights out with friends. Image by ericbarns from Pixabay
Talking and reminiscing about past life events can help people with dementia by reinforcing their self-identity, and increasing their ability to communicate – at a time when they might otherwise feel rather lost and distressed.
“AMPER will explore the potential for AI to help access an individual’s personal memories residing in the still viable regions of the brain by creating natural, relatable stories. These will be tailored to their unique life experiences, age, social context and changing needs to encourage reminiscing.”
Dr Mei Yii Lim, who came up with the idea for AMPER(3).
Saving your preferences
AMPER comes pre-loaded with publicly available information (such as photographs, news clippings or videos) about world events that would be familiar to an older person. It’s also given information about the person’s likes and interests. It offers examples of these as suggested discussion prompts and the person with Alzheimer’s disease can decide with their carer what they might want to explore and talk about. Here comes the clever bit – AMPER also contains an AI feature that lets it adapt to the person with dementia. If the person selects certain things to talk about instead of others then in future the AI can suggest more things that are related to their preferences over less preferred things. Each choice the person with dementia makes now reinforces what the AI will show them in future. That might include preferences for watching a video or looking at photos over reading something, and the AI can adjust to shorter attention spans if necessary.
“Reminiscence therapy is a way of coordinated storytelling with people who have dementia, in which you exercise their early memories which tend to be retained much longer than more recent ones, and produce an interesting interactive experience for them, often using supporting materials — so you might use photographs for instance”
Prof Ruth Aylett, the AMPER project’s lead at Heriot-Watt University(4).
When we look at a photograph, for example, the memories it brings up haven’t been organised neatly in our brain like a database. Our memories form connections with all our other memories, more like the branches of a tree. We might remember the people that we’re with in the photo, then remember other fun events we had with them, perhaps places that we visited and the sights and smells we experienced there. AMPER’s AI can mimic the way our memories branch and show new information prompts based on the person’s previous interactions.
Although AMPER can help someone with dementia rediscover themselves and their memories it can also help carers in care homes (who didn’t know them when they were younger) learn more about the person they’re caring for.
Suggested classroom activities – find some prompts!
What’s the first big news story you and your class remember hearing about? Do you think you will remember that in 60 years’ time?
What sort of information about world or local events might you gather to help prompt the memories for someone born in 1942, 1959, 1973 or 1997? (Remember that their reminiscence bump will peak in the 15 to 30 years after they were born – some of them may still be in the process of making their memories the first time!).
See also
If you live near Blackheath in South East London why not visit the Age Exchange and reminiscence centre which is an arts charity providing creative group activities for those living with dementia and their carers. It has a very nice cafe.
Related careers
The AMPER project is interdisciplinary, mixing robots and technology with psychology, healthcare and medical regulation.
We have information about four similar-ish job roles on our TechDevJobs blog that might be of interest. This was a group of job adverts for roles in the Netherlands related to the ‘Dramaturgy^ for Devices’ project. This is a project linking technology with the performing arts to adapt robots’ behaviour and improve their social interaction and communication skills.
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