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!

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