Women in Mathematics Conference

On the 29th of August, the Women in Mathematics 2018 conference, hosted this year by the School of Mathematics and Statistics at University College Dublin took place. The event was an amazing experience, we got to meet up with interesting people across the mathematics field, and the audience was able to learn so much more about mathematics. At the beginning of the talk, Minister Mitchell O’Connor talked to us about the importance of bringing more girls into maths, and joy one can find in exploring the field of STEM. After the motivational talk, the audience gained amazing insight into the life and work of Sheila Tinney, an Irish mathematician, physicist and educator. She was also the first Irish woman to achieve a PhD. And there were also introductions from other women involved in mathematics about their work. Works involving the use of mathematics that ranges from health statistics to physics, including a project involving the building of a database for public libraries. An element of pure maths was introduced as well, which involves a bit of intuition and brain cells to understand, but awe-inspiring at the same time. It was fascinating to hear about where mathematics can take you across the world and across different branches of study.  It was very motivating to hear about their work, and for me, deeply reassuring. Being a girl dreaming about going into mathematics, to hear about the real-life achievements in mathematics of other wonderful women makes my choice seem less daunting to me.

I think there is a power in conferences and talks like this. It has a deep effect on the audience, whether they are involved in the field already or a member of the general public. It give insights into other people’s work, it opens up our eyes and can lead a change in our minds. Connecting with other people who have the same interest and passion, and clash your idea with them can spark creativeness and friendship you never expected to happen.

In the morning, there was a group of Transition Year students who caught an early train just to attend this conference. I think this was the best part of the conference, spreading dream of STEM in the hearts of students of the next generation…and who knows? The next Sheila Tinney might have been in the audience that very day.

BT Young Scientist Exhibition

BT Young Scientist Exhibition (henceforth abbreviated into BTYSTE) is a large scale science exhibition in Ireland, and it is a platform for high school students to innovate, create and explore. As the BTYSTE website described, it is an unforgettable experience of a lifetime for the students who take part. And I completely agree with in this statement, in the two times I participated, I went home each time with a completely different perspective to the STEM field, as well as the potential young people can have.

The exhibition has two parts, in the fist part students interested has to enter a one page proposal and some more information onto the website, and those projects that qualifies would be able to compete in the final round, where students would be able to display their project and have the opportunity of communicating with other students with their unique ideas.

In the preparation stage one has to write a project report (Hard work there! So time consuming and my experience is that it is even easier to do the project than writing out the report), a project diary and design a poster. The day before the exhibition, students go to the big exhibition arena to set up. The time is needed as some projects require large machines or different demonstration props. and then comes the hardest and most exciting part: the exhibition itself!

The most daunting part, of course, is the judging. There are at least three rounds of judging for each project, and the presentation of your project to the judges can have equal importance as your project report. The project book shows all the details and your scientific knowledge, but the presentation gives an outline and shows your passions. A good presentation can be absolutely crucial to the evaluation of the project, and I personally found it so much harder than I thought it would be because you will have no clue where to start and if you does not have it planned beforehand the result can be a quite disorganised speech!

The exhibition is also a test for persistence. I have chatted to a participant who, every day after returning home from the exhibition, would carefully analyse how he did in his presentation today, and consider if there are any flaws to his project and if there is room for improvement. Then he would do more research and add in more details to his project. He did this to the very last day, and his hard work also paid off in the end, he got home on the last day finally relieved and holding a wonderful prize.

Of course, the prizes aren’t everything, the most exciting part is to be able to chat with other people. I cannot describe the motivation I felt after talking to amazing people my age, seeing their ability, and getting to know what I can work towards. It is also eye-opening to hear about their creative ideas.

Talking to the people who came to visit is also a tremendous joy, there are all sorts of people who come around and ask you the most amazing questions. There are people who are experts in the field and would throw you off guard with a detailed technological inquiry. There are people who are genuinely interested and would listen to you talk without end, and there are people who understand you and would discuss in detail with you the potential of the project. It is wonderful to get your ideas heard and appreciated. Sometimes, even crazier things happen, such as a job proposal, or a trade of name cards. These conversations can sometimes lead to more amazing adventures, and for ambitious people like us, there’s nothing more thrilling!

All in all, it is a wonderful experience that leaves you smiling when you remember it, and it cracks opens doors into worlds you have never explored before. I cannot but think what a marvellous thing it is, for a high school student to be able to take part and experience such an event. It might just change a life or two.

4D Cube Explained-part 2

Hello again, this is the promised follow up, in which we dive deeper into the secrets of the 4D cube!

In the last chapter, we covered the basic ideas of a 4D cube as an introduction. In this chapter, we would explain further into the idea of 4D geometry, as well as answering the questions proposed in the last chapter.

https://scienceangles.wordpress.com/2019/01/04/4d-cube-explained-part-1/

So, we have derived what a 4D cube look like, and to view it from a 3D perspective, we have two ways of representing that image:

Graph 1
Graph 2

                                                                                  

Wait a sec, those two look quite different, are they both correct? What’s the difference?

As we can see, in Graph 1, the two 3D cubes that are supposed to be opposite each other are of different sizes. However, in Graph 2, the two 3D cubes opposite each other are the same sizes. In the previous chapter, we explained how to intercept Graph 2, but what about Graph 1? How do we understand Graph 1?

Let’s go back to the relationship between 3D and 2D. What is the 3D equivalent of Graph 1?

We get a picture like this:

Two opposite sides of a 3D cube are two squares. One is bigger, one is smaller. They are connected at all vertices, to create the picture above. Where have I seen this picture before? Think back on the museums you’ve visited, the Renaissance paintings you’ve seen. Think about the study of perspective. Or better yet, think about the room you are in. Go to one end of this room, place your back against the wall, and look across the room at the other end. You get a picture kind of like the one below.

Is it not exactly what we drew just then? When we place ourselves inside the 3D cube, Given a variable distance, we can see the two sides opposite each other at the same time, only of different sizes.

Artists know this. They use this skill to create realistic feeling of a 3D world on a 2D plane. Take a look at this painting, School of Athens. In this famous painting, the people far from us seem smaller, whereas the people near us seem bigger. This creates the feeling of 3D world on the 2D panel.

School Of Athens by Raphael

So, if we have a 4D cube that looks like Graph 1 it means that we are placing ourselves inside a 4D space, the smaller cube farther from us and therefore looking smaller, the bigger cube nearer us, looking bigger. I’m using the term ”farther” “nearer”, but these adjectives are the adjective of a new variable, a variable that does not exist in our dimension, the 4th variable in space. What might that be? It could be anything, colour, temperature…anything will do. But for our convenience let’s consider the 4th dimension as time, which is the easiest thing to understand in our 3D world, but the one thing that we cannot control. Ok, so now our variable is time, and the cubes are just two cubes through different time lapse. We are standing at a starting position “Now”, and the smaller cube we see in the distance is the exact same cube, labelled ”a year from Now”. That cube is considerably farther from us, so it seems smaller.

hat is how we interpret the difference between Graph 1 and Graph 2. Also, we gained a brand new understanding of a cube in 4th dimension. It is a cube, consisting of several 3D cubes that are spread across a time span, but also tangible at the same time.

Check out these photographs from photographer Steven Wilkins, showing the same landscape at different times on the same panel. In these pictures, the same thing at different times coexists. These pictures amazingly share the same idea as the structure of a 4D cube.

https://www.stephenwilkes.com/fine-art/day-to-night/52fa9a11-c5e8-4048-8071-0b560af4b6c2

So through these two articles, I hope I have given you a better understanding of a 4D world, and I would be very glad if you would be more fascinated in the mysteries of the higher dimensional space. There are endless magic to that topic and still a lot to explore!

The Math Olympian – Richard Hoshino

Rating: 9/10

Suitable for: Everyone

The Math Olympian is certainly one of a kind- a book about Olympiad maths, yet it is a fictional novel. The novel spans the three hour paper of the Canadian Mathematical Olympiad, which the protagonist, Bethany, is taking, detailing her thought process while answering the questions and using flashbacks to weave together a picture of her journey.

Hoshino succeeds in creating an engaging, relatable, entertaining and inspiring story of how creativity and persistence can allow you achieve your dreams. Bethany, the main character, is likeable yet imperfect. The hurdles she faces will be familiar to both girls in maths and anyone involved in olympiad maths. Bethany has to deal with being in a male dominated environment and with the various challenges that are part of olympiad maths.

I really liked how Hoshino described some of the difficulties young people who are training for maths olympiads face. Bethany learns to deal with failure, a vital lesson that mathematical olympiads teach you but a difficult one to learn. Other challenges Bethany faces include self-doubt, bullying and not fitting in.

Bethany’s love of learning and mathematics is infectious. Hoshino portrays mathematics as the subject it is, full of creativity, innovation, problem solving and beauty, relevant in every aspect of life. It illustrates how different maths is from how it is often perceived, dull, dry and boring, like it usually is in school.

From a mathematics point of view, I thoroughly enjoyed the descriptions of how Bethany solved the problems. It reminded me of the Thinking Out Loud articles from www.egmo2018.org. Hoshino himself solved these problems when he was training for mathematical olympiads, so the accounts are authentic, hence believable. The solutions are well explained, I had no trouble understanding them and I think that most people who have experience with school maths could get the main ideas of the problems.

My only criticism is I felt that Hoshino gave a bit too much attention to the issue of faith. For me it seemed a bit irrelevant to the rest of the storyline and too much time was spent on it. At first it was interesting but it drew on a bit, becoming a distraction and detracting from the book as a whole. This is only a minor issue that I personally didn’t really like but it didn’t have a large impact on my overall enjoyment of the book.


Overall The Maths Olympian is an insightful, inspiring and entertaining book that I would highly recommend. A must read for any young people (especially girls) who are interested in maths!

-Laura

View on Amazon: https://www.amazon.com/Math-Olympian-Richard-Hoshino/dp/1460258738

Thoughts From a Boring Dinner Party

It was Christmas season last month, so it meant endless boring dinner parties. One day I was just at such an event, so I had loads of time to think and daydream. During one of the conversations I suddenly had some thoughts in relation to the origins of languages and the more I thought the more intrigued I became.

Being a Chinese, one part of our culture that I absolutely love is the Chinese language. It is so absolutely amazing and different from any other languages that I have heard of. The words are not a permutation of a set of letters, like English, but rather a combination of different strokes in different positions. Sitting at the dinner table yesterday I thought about the short, stout, sad stone-age men struggling to start a fire and scratching in the sand to create the sparks of civilisation— How did they come up with these languages? And why are two branches of languages (Latin & Greek verses Asian & Chinese ) so radically different?

The Chinese words are pictures, literally. Originally they are basically pictures on the back of turtles that represent different things, one picture for one thing. For example: in the three characters shown above, the one on the left was the moon, the middle one was the mountain, and the one on the right was water. (Picture source: Wikipedia) Vivid, huh? These words slowly evolved to become 月, 山 and 水. So they are very much visual—pictures tell the story. I think the sounds must have come after because, in Chinese, there are often a handful of words of different meaning but sharing the same pronunciation. This shows the prominence of sight over hearing.

English (and all European languages, but I’ll just take English as the example), however, is a different story. The words themselves are just permutations of 26 letters and by themselves do not necessarily mean anything. Their form are not resembling any specific thing. And come to think about it, who decided that the linear permutations of letters seem like a good idea to create meanings? After a wonderful piece of apple pie, I decided that it must be that instead of visual, the Celts and the German creators of English were somewhat more auditory. In order to convey meanings, people used sounds rather than pictures. They used different pronunciations to represent different things, and as the sounds got more complex and abstract the need to change them into form emerged. However there are just a limited amount of sounds that humans can utter and they appeared repeatedly in different permutations, so in order to represent these sounds to our knowledge our ancestors developed the system of the alphabet, each having its own phonetic representation and its form brings out the auditory meaning.

Chinese is 2D, English is 1D. Chinese is pictures, English is sounds. My theory is that the Chinese ancestors probably relied more on sight, whereas the early Celts and Germans and Greeks rely more on hearing, and this different way of processing information led to different styles of languages. I can’t justify this biologically and geographically, my best guess is that this may be related to the agricultural activity (as it is the most important part of early humanity). For example, maybe one group of people relies on hunting more than the other, and therefore their auditory ability is more treasured, whereas the other focus more on farming and therefore sight would be required to make sense of the different crops?

Of course, this is just my hypothesis, but I am quite satisfied with it and it then led me to think— apart from auditory and visual, is there any other form of languages? To my imagination, the communicating by action probably has been attempted, but they are too time-costing and energy consuming, and would be hard to record, so in the end, these languages did not come into being.

I have always believed that languages are derived from a way of thinking, and languages form and shape our way of thinking from an early age. I think of Story of Your Life by Ted Chiang, a wonderful sci-fi short story which was later adapted into the film Arrival. In this story, alien creatures came to earth with no clear intentions and the governments sent a group of scientists to investigate. They were trying to understand their language and communicate. Their language are formed in such a way that it transcends the concept of order. All the components of a sentence are arranged in whatever permutation in one picture, with certain connections between them. The sentences can therefore go on and form paragraphs…all in one big character. You could write an entire book in one weird and complex drawing. This interesting characteristic was due to the fact that the biology of these aliens allows them to look into the future, and so in their world, there was no first, nor last, everything was just there. After learning their language, the lead linguistic professor found that her way of thinking was changed too, and she can now see into the future and see what will happen to hers and her daughter’s life. This story kept bugging me across the years because I think it is a vivid portrayal of how language is intertwined with our own thoughts. The possible forms of languages are confined by our physical properties and it can in turn change us. Boomerang!

The path just went further from there and gave me an insight into what might be the reason that we have not yet discovered any pattern in animal vocal sounds. Despite our dreams and endeavours, we still could not identify any pattern in the chirps and quakes of sparrows. Now if we agree that our ability to interpret languages are bound by our biology, then a possibility is that because we do not have the mechanism to make the sound birds can make, the fine details of bird-language are also inconceivable to us. Could it be that the birds actually have a complex language system—several language systems—but we just couldn’t tell the difference between their chirping words because our biology just doesn’t allow us to? What this implies is that—to break through the bonds of languages, we may need to break through the bonds of biology first.

So as you can imagine, I went home from the dinner party the other day very hyper and excited. I think that hypothesis though it is, this is an idea worth sharing and I would be very glad if this can give you a moment of aha and somethings to consider and chat about in your next dinner party.

-Ian

4D Cube Explained-part 1

When you look at the Dali painting, Corpus Hypercubus, what comes to your mind? Weird, bizarre structure? Eerie feeling? What is the secret behind the cubes arranged together in the shape of a cross?

The answer may shock you: It is a hidden picture of a 4D cube.

Huh, I heard you sneer. We don’t even know what a 4D cube look like, how can one draw one on a 2D plane, and how can you understand it?

Well, the best way to imagine a higher dimension is to think of the relationship between our dimension and a lower dimension, and then picture that relationship onto a higher dimension and our dimension. This is what we’ll do a lot in the understanding of the fourth dimension. Take a 3D cube first. We all know what a cube looks like, right? It looks like this:


The cube sonsists of 6 sides which are 6 identical 2D squares, with 2 squares opposite each other. And similarly, “cube” in 2D space, a square, consists of 4 identical sides of 1 dimension. Therefore we can imagine that a 4D cube should have been consisted of 3D cubes with two 3D cubes facing  each other on opposite sides. Grab a piece of paper, and draw down 2 3D cubes slightly apart, then we have the two opposite sides of the 4D cube. Now we connect the vertices together, we get a very curious picture below:

Now this is what a 4D cube look like from a 3D perspective. It consists of 8 cubes (count it yourself!). The cubes are a little deformed because they are connected in the 4D space, and we cannot draw that connection out in the Euclid Geometry. In the picture below, the orange part marked out by the marker is another cube that is created by connecting two 2D sides of the opposite cubes.

Now that we’ve pictured what a 4D cube looks like in out 3D vision, let’s try to change the cube into a 3D model that could very well represent the cube in 4D. Let’s get back to the relationship between 3D and 2D: what happens when we cut a 3D cube up into a 2D picture? We take a paper cube and cut it up along the edges. We get the picture on the left. If we print it out on a piece of paper and then cut it out, we can fold it up into a 3D cube.

Now, if we cut the 4D cube up, we get a 3D model. In order to visualize it better, I drew a different version of a 4D cube. The difference between this 4D cube and the 4D cube I drew before would be explained in Part 2.

Anyways if we take this cube, and cut it up along the edges, we can get a model in 3D that can be folded up into a 4D shape. What does this model look like? Wait for it…

Did you get it right? And, hey, that really look kind of similar! That’s the cross in Dali’s painting!

Secret revealed! The surreal artist used a 3D model painted on the 2D canvas to demonstrate a 4D cube. He is telling us that God and the divine powers are a form of energy in higher dimensions that we cannot perceive. We can only glimpse their power and glory from a fraction of 3D perspective. Dalí’s inspiration for Corpus Hypercubus came from his change in artistic style during the 1940s and 1950s. Around that time, his interest in traditional surrealism diminished and he became fascinated with nuclear science. Sparked by science, his imagination takes him to explore concepts of a higher dimension, and thus born this interesting picture.

So in Part 1, we explained the shape and form of a 4D cube, imagined in a 3D perspective, and hopefully gave you some understanding of 4D geometry. But we have this weird and mythical picture in front of us, does it actually mean anything? How can we understand the nature of the fourth dimension through a cube? Is there any other way of picturing a 4D cube? All this and more, we will explain in the next part!

The next part will be posted on the 15th of January. Before then, follow us!!

-Ian

Alex’s Adventures in Numberland – Alex Bellos

Rating: 9/10

Alex’s Adventures in wonderland conveys the fascinating beauty of mathematics in an accessible, entertaining way. The book is aimed at a general audience – no specialised mathematical knowledge is needed, yet it would still entertain and inform a mathematician.

Like the title suggests, this book is a journey through the world of maths – a journey I highly recommend you take. Bellos explores the history of mathematics, analysing how numbers and counting developed. He describes the Munduruku people, who live in the Brazilian Amazon and only have words to count up to five. He analyses what numbers actually mean to people, and to animals such as apes.

The book consists of eleven chapters, each discussing a different topic, such as counting, probability, sequences, geometry and infinity. He weaves anecdotes, entertaining stories and images into his explanation of the maths. He combines maths and history with his own experiences travelling the world and meeting some of the most fascinating people in mathematics in an enthralling way. I could not put this book down while reading it, in no place was it stodgy, boring or difficult to get through. It reminds me of a thriller rather than a non-fiction book – it is an exciting page-turner.

I thoroughly enjoyed reading this book. It was informative and thought-provoking yet it was all easy to understand. Bellos’ lively writing style entertains as well as educates, making it an appealing read for everyone, no matter what their mathematical level is. The book illustrates how maths is involved in every aspect of our lives and illustrates how beautiful and exciting a subject it could be. I would highly recommend that anyone with the slightest interest in maths reads this book- it is an adventure that will not disappoint you.

View On Book Depository

-Laura
















Welcome!

It’s new year! A brand new beginning, and especially for the Science Angles team because——we’re launching!
Here’s a brief introduction: Science Blog founded by high school girls passionate about science(that’s us!) and we create this site as a place we post articles on all things about science. These articles include reports on major events, interviews with people in the STEM field, book reviews and so much more! We aim at people with different levels of interest and knowledge in STEM and we promise there will be something here for you!

We aim to encourage young people to develop a similar passion for STEM, and show them that STEM is so much more than the often dry and boring school subjects. We will explore the fascinating beauty of maths and science, as well as discussing related topics, such as Olympiad maths. Join us on our never-ending journey to learn more about the fields of science and mathematics.