Recent Fascination with a Non-Orientable Mathematical Surface – Mobius Strips

I have realised the last time I published a post was way back in November and that maintaining a blog is, in fact, tremendously difficult during preliminary exams period, which very fortunately just ended. It is not guaranteed that the general schedule for updates will be followed due to final year school workload at the moment but, I’ll no doubt try my best.

I have always enjoyed mathematics in school, whether it was the logic behind exam problems or solving tricky little mathematical puzzles. I had first become aware of the field of topology research after the announcement of the 2016 Nobel Prize in Physics, where pretzels, doughnuts and mugs were used to demonstrate topological properties considering the different number of holes each contains. In a sense, if two objects have the same number of holes, they are topologically equivalent, because they can be deformed into the same object without tearing or glueing or taping.

Klein Bottle

Now, I do not claim that I understand topology at the slightest, yes, the subject is way beyond me currently, but it’s always nice to read around some of its core ideas.

Black Holes #1 – Singularities and Hawking Radiation

The Black Hole from Interstellar

Black Holes seem like something that only exists in Science fiction, like Dark Matter and Energy, however, these astronomical objects are in fact at the heart of theoretical research within Cosmology. Research involving Black Holes may likely help us uncover more about the mysteries of Quantum Gravity, something Physicists believe to be the Theory of Everything.

In simple terms, a Black Holes is a region in which the gravitational influence is so strong that nothing, not even light, can escape its pull beyond the Event Horizon, which means that the Escape velocity is essentially greater than the speed of light. Escape velocity is the speed in which an object needs to travel at to escape a gravitational field, e.g. the Earth’s.

How Small Can You Go in Scale?

After the many ramblings I made regarding Dark Matter previously, I want to turn around and think about Baryonic Matter again. Ordinary Matter is something that physicists know much more about than the mysterious Dark Matter and Dark Energy, even though in reality they do make up more than 95% of our known Universe. We are more knowledgeable about Baryonic Matter because of its presence all around us, after all, it is everything we can see and detect: from forms of life, elements in the Earth’s crust and mantle, buildings, cars, the Earth, the Sun, all of the stars… you get the idea.

Now, the stuff that makes up the matter. Firstly what comes to our mind may be elements, which are a table of 100 odd substances that are often called the “primary constituents of matter”. These elements can be identified through their chemical properties and are placed in the Periodic table in order of increasing atomic number (the number of protons in its atom’s nucleus).

Atoms are another level down from the elements of the periodic table, which distinguishes different types of atoms. Atoms themselves is another study on its own. In the early 20th Century, Rutherford and a couple other physicists discovered an awful lot that directly correlates to our modern understanding of the atom through an experiment – firing alpha particles at a piece of gold leaf.

The Basics of Special Relativity

Einstein’s famous “Warping of Space and Time”

Einstein

Albert Einstein is probably the most popular scientific figurehead in modern culture with his iconic messy hair and white lab coat. His image has been deemed by many people to be the stereotypical scientist. He is one of the favourite picks by young children to dress up for Halloween and his name is also a synonym of words such as “genius”. Additionally the very recent announcement of the detection of gravitational waves once again awakened people’s admiration for , however despite his immense popularity, most of the public have no idea what pioneering contributions he had made in the field of physics. Einstein’s breakthrough came from his work on Gravitation through his developments of two successful theories: Special and General theory of Relativity, with General Relativity becoming one of the two great pillars of modern physics, the other being Quantum Theory. In this post I will attempt to cover the basic concepts of Special Relativity.

Enigmatic Cryptology

So I want to start off talking about the film “The Imitation Game”. These three words probably brings you back to the moment when you were fangirling over the actor Benedict Cumberbatch who played the role of protagonist Alan Turing. However the film not only depicts Turing as the Mathematical prodigy and war hero who was estimated to have saved the most lives in World War 2, it also demonstrated the manifestation which stemmed from his genius mind, “The Bombe”. It was the decryption device used by the British Army in Bletchley Park to crack the infamous German Enigma machine. Since warfare has less to do with physical killing but rather strategy, communications within both sides of the allies and the axis were encrypted in code.

My Vision on Four Dimensions

Many of you may have heard of an object called the Tesseract.

Being able to perceive a tesseract is clearly impossible, as we cannot see beyond the number of dimensions we live in. We as humans clearly are and live in a three-dimensional world and there are three coordinate axes x, y and z, so we perceive directions left/right, forwards/backwards and up/down.

For example, this cube

Imagining four spacial dimensions is very difficult so we can try something simpler with three-dimensional objects. Let’s imagine we were a two-dimensional species living in a two-dimensional world called Flat land, named by Edwin Abbott. We walk about in the two-dimensional space unaware of the other dimension which is the z-axis and that’s completely okay, just like how humans can live perfectly without knowing about the fourth dimension.