Categorie: Wiskunde

The Birthday Problem

The Birthday Problem

At the World Cup in Brazil in 2014, in 16 out of the 32 teams two players shared the same birthday. Considering each of these selections consisted of 23 players and there are 365 days in a year (excluding February 29), it seems like an enormous coincidence that this was the case for 50 percent of the teams. However, this trivia fact isn’t such a coincidence at all. In fact, the odds of two people in a group of 23 sharing the same birthday is 50.7 percent. This is what we call the birthday problem […]

13 oktober • Door Casper de Vries Tijd om te lezen Estimated reading time: 4 minuten

The impossible program

Each year new computer systems are put into the market, featuring increased memory capacity, better screens but perhaps most importantly, stronger processors. More processing power results in handling more tasks per second or, in other words, less time per task.  A modern computer can carry out most operations in a fraction of a second, even though it took the most powerful computers minutes or even hours, 30 years ago. As computers get stronger, however, the tasks we ask them to perform get more complicated too. Whereas they once had to solve simple mathematical operations, they […]

15 september • Door Pieter Dilg Tijd om te lezen Estimated reading time: 4 minuten

Mathematical impossibilities

‘Nothing is impossible’ is one of the most used phrases to convince people that they can accomplish anything, no matter how hard you have to work for it. But to what extent is this phrase actually true? The word impossible is something that a lot of people already have big trouble with getting their head around. If you would ask me for an example of ‘what is impossible?’, the first thing that comes to my mind is teleportation. But the second after thinking that, a new thought comes up: ‘is it really impossible though?’. Ofcourse, […]

10 september • Door Lars Beute Tijd om te lezen Estimated reading time: 4 minuten
Mathematical magic

Mathematical magic

Many card tricks in this world involve some fancy hand movements. However, there are also many tricks that involve some mathematics. During these very busy times with exams, I present some card tricks to get your mind off studying and challenge your brain in a whole different way.   52 factorial The first mind-boggling property of a regular 52 card deck, is the number of different ways we can arrange such a deck. The top card can be any of the 52 cards, the next card can be any of the 51 other cards and […]

25 juni • Door Sam Ansari Tijd om te lezen Estimated reading time: 6 minuten
True randomness

What is true randomness?

The shuffle function on Spotify is an easy way to listen to music without having to pick some numbers. However, once in a while we all seem to recognize patterns in the numbers that we listen to. The shuffle function does not seem to be so random at all, so are these numbers truly randomly picked? This recognition of a sequence is partially caused by the functioning of our brain. It is very easy for the brain to distinguish patterns in seemingly random things like shuffled music or dice roles. Especially when these “processes” are […]

18 juni • Door Casper de Vries Tijd om te lezen Estimated reading time: 3 minuten

Counting cattle

In 1769, the Herzog August Library of Wolfenbüttel, Germany, appointed a new librarian. The main task of this librarian consisted of translating the many Greek and Latin manuscripts of the library. After a few years, the first batch was published, which included a Greek poem of forty-four lines that dazzled the mathematical community for over a century. This poem was about a arithmetical problem Archimedes proposes to Eratosthenes and asks the reader to find the size of the cattle in the herd of the god of the sun, Apollo. This is an interesting problem since […]

11 juni • Door Jochem Hak Tijd om te lezen Estimated reading time: 3 minuten
the math behind poker

The Math behind Poker

Shady men wearing sunglasses, sitting around a table, playing for big pots of money. That is what we often associate with poker when thinking about the game of bluffing. A game where most people think that the essence is to read your opponents, while leaving them clueless about your cards. In reality, this psychological part of the game turns out to be just a small asset of the qualities a good poker player needs to have. Of course, being able to read your opponents is a huge advantage when playing poker, but the use of […]

19 mei • Door Casper de Vries Tijd om te lezen Estimated reading time: 7 minuten

The Duisenberg Pranksters

Sometime in the future, when physical college lectures are once again allowed, one hundred students are attending a lecture of the Multivariate Calculus course. The students, after hearing multiple savvy jokes about their intellect and ability regarding calculus, decide to play a prank on the professor and his colleagues. They plan to boobytrap some of the one hundred doors on the 7-th floor of the Duisenberg building. However, knowing that the professors are quite brilliant, they need to allocate the boobytraps in a manner that is hard to figure out. Near the end of the […]

07 mei • Door Pieter Dilg Tijd om te lezen Estimated reading time: 3 minuten
Jigsaw puzzle

Don’t let this piece puzzle you

Since the start of the corona crisis, solving these has probably become one of your biggest hobbies. Webshops cannot cope with the growing demand and the largest warehouse for this product, located in Missouri (USA), has reported mind-boggling revenue growth of 2000%. We are, of course, talking about jigsaw puzzles. At the moment it is almost impossible to buy a new ‘Jan van Haasteren’ puzzle and Instagram and TikTok are full of stylized pictures and videos of puzzles being solved. At first, a jigsaw puzzle seems like a fairly easy task, you can do them […]

05 mei • Door Jochem Hak Tijd om te lezen Estimated reading time: 6 minuten

The math behind the coronavirus

At the moment we live in a big crisis, the corona crisis. Already more than one million people over the world are infected and more than 60,000 people died. A lot of countries are having big outbreaks and the health care is having capacity problems. This is also one the many articles which you probably have seen about the coronavirus. What distinguishes this article from the rest is that it will dive a lot deeper into the mathematical models which researchers use to forecast the spread of the coronavirus. It is of course extremely important […]

07 april • Door Stan Koobs Tijd om te lezen Estimated reading time: 6 minuten
Neural networks

Neural networks, the machine learning of the future

The human brain solves millions of problems daily. To do this, the brain first acquires the necessary information needed to solve any given problem. Then it uses and modifies this information to get a clear assessment of what the problem exactly entails. Once it knows all of this it is (in most cases) able to solve the problem at large. It is able to do so, because of the knowledge about similar problems it has already obtained. Neural networks, named after the neurons in the human brain, work in a very similar way. They consist […]

24 maart • Door David Anthonio Tijd om te lezen Estimated reading time: 5 minuten

Should we be scared of algorithms?

The word ‘algorithm’ can be quite a scary word if one does not know what it actually means. But should we be scared of it? Nowadays, the word is much more frequently used than it was in the past. This is because artificial intelligence (AI) has had a huge rise in the last decade. Algorithms are the building blocks of everything you’re using to read this article. 

One definition of an algorithm is a set of steps to accomplish a task. Hence, you might have an algorithm for getting from home to school, for baking a cake or finding the perfect dress for your evening in the store. In computer science, an algorithm is a set of instructions that take an input, A, and provide an output, B, that changes the data involved in some way. So, all that algorithms are, is a set of basic mathematical instructions.

These algorithms are becoming an indispensable part of our lives. However, some view this as dangerous. For example, Elon Musk (@elonmusk) wrote on 12 Augustus 2017,


“If you’re not concerned about AI safety, you should be. Vastly more risk than North Korea.”

Besides this, there are many stories about AI having negative consequences:  police profiling that reinforces racial stereotypes 21st-century discrimination , acceptance algorithms that deny access despite rightful requesters, unfair rating system algorithms optimized for commercial gain and many other systems that reinforce inequality.

However, to declare that algorithms rule the world is a bit hyperbolic, even though the algorithms are being used more and more every day. This is due to the fact we use computers, laptops and our smartphones so much that they are playing an increasingly more important role in many aspects of our lives. To make all of these devices do anything, you have to write a computer program in which you tell the computer, step by step, exactly what you want it to do. When you are commanding the computer what to do, you also get to choose how it is going to execute it. This is where the algorithms come in. The algorithm is the basic tool used to get the job done. Nevertheless, this is not how all computer algorithms are designed. In this instance, we have the version described above, with unsupervised learning. This involves data representing situations without independent variables. Because of this, there is no need to know the results of each scenario to use for training, and patterns are simply discerned from the data, where all the data is used for training. Besides that, some algorithms allow computers to learn on their own. This is called supervised learning, which involves having data, based on scenarios or historical events, with both dependent and independent variables. The model is trained using this data with both features (dependent variables) and expected results (independent variables). It is then trained by showing the model the scenario and its corresponding result.

Thus meaning, there are uses for machine learning, including data mining and pattern recognition. For example, these mathematical creations determine what you see in your Instagram feed, what movies Netflix recommends you and what ads you see in your Gmail.

But are these algorithms is some way good or evil? As mathematical equations, they are not. However, both people with good and bad intentions can use and have used algorithms. For this, AI models are trained using datasets. The person training the algorithms can select the events that are used to train the models, which is called Feature Engineering. This ‘Feature Engineering’ can be done for many reasons. For example, it can allow algorithms to be used with limited or incomplete data. Besides that, it can improve training by using less or only relevant data. This can improve the accuracy of a model or simplify the maintenance of the model. On the other side, Feature Engineering cannot only bring us good things. It can introduce a bias to the data, which will most likely happen unintentionally. This bias is introduced by the people who select the data, but the technology itself does not have any bias. 

 

To summarize this, one can say that algorithms and AI do not have either morals or ethics, which makes it neither good nor evil. However, since the algorithms are a tool used by people, it can be misused by people. To stop the misuse of AI technology, spreading awareness of how to use it ethically is needed. The reason for this is because it is the people who have biases, morals and ethics. So, should we be scared of AI? No, we should not, but we should be aware that there are people who can and most likely will misuse it.


This article is written by Deirdre Westenbrink

17 maart • Door Deirdre Westenbrink Tijd om te lezen Estimated reading time: 4 minuten

By Daniele Zedda • 18 February

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