Tag: symmetry

Posted in Science & Nature

Natural Design

Posted on by Jinavie

We look around the world we live in and marvel in all its complexity and grandeur. But Mother Nature focusses on one thing when it comes to design: efficiency. That is to say, that nature strives to design things that will do the job best. For example, stars and planets are always round because a sphere is the most effective way to get all the mass as close to the planet’s centre of gravity as possible (a process known as isostatic adjustment). The wings of a bird have evolved to maximise the thrust generated at the least energy cost, while the sleek, teardrop body shape of fish allow for them to slip through water with minimal resistance. One of the best examples of nature coming up with the best design solution is beehives.

If you look closely at a beehive, you will find that it is made up of tiny hexagons. Each hexagon is a room that a bee can fit in and the walls are made from wax. The interesting thing about hexagons is that it has many properties that make it the ideal shape in construction.

Firstly, hexagons can fit together perfectly to tile a plane, meaning that bees can tile thousands of columns without wasting any space. The little columns even end in a unique pyramidal shape that allows them to tile up nicely with each other at the centre.

Secondly, a hexagon has 6 rotational symmetries and 6 reflection symmetries, making it very easy to tile as every bee will know what orientation to build their cell in using the side of any cell as a reference.

Lastly, in a hexagonal grid each line is as short as it can possibly be when tiling an area with the smallest number of hexagons. Therefore, bees can use much less wax when constructing hives, while achieving remarkable strength as hexagons gain lots of strength under compression. This design also allows for the maximum amount of honey stored in each cell.

Bees have mastered this architectural feat not through physics and mathematics, but through evolution – the driving force of nature. Over millions and millions of years, various types of bees will have experimented with square-celled hives or triangular-celled hives, but they could not survive as long as the hexagonal-celled bees because their hives were less efficient. This is exactly why nature is so good at coming up with the best solution to a problem. Because in nature, the best solution to the problem an environment offers is rewarded with survival.

Posted in History & Literature

Elements: Yin And Yang

Posted on by Jinavie

Yin-yang is a frame of thinking that can be considered a fundamental basis of Eastern philosophy. In ancient Far East Asia, people categorised everything of nature as yin or yang, including natural phenomenon such as human physiology. Yang(陽) is a masculine element, yin(陰) is a feminine element and the two represent the countless symmetries found in nature. Just as there is a sky for the earth, a sun for the moon, a man for a woman and strength for softness, every phenomena in human societies and the universe can be identified in relative terms. The concept of reducing these to a plus and a minus to explain natural events is the concept of yin and yang.

For example, consider a hill in the sunlight. The bright side is called the “yang place” and the opposite, dark side is called the “yin place”. Thus, light is yang, darkness is yin. That is not all. The air that is heated by sunlight becomes warm and rises, while cold air sinks because it is heavy. Yang symbolises heat, lightness and upward, active movement while yin symbolises cold, heaviness and downward, sluggish movement. But that does not mean that yin is bad and yang is good. The reason being, everything that counters each other in nature coexists and forms a balance. Also, as time passes, the sun will move from the east to the west, making the sunny place dark and the dark place sunny. Yin-yang is a law that shows the relativity of nature very well. It shows that everything is relative to each other even if they seem like opposites, forming a harmonious balance and cycle.

Balance forms harmony and nature always seeks harmony. For example, traditional Korean and Chinese medicine is based on the concept that the reason why diseases occur is because of the balance of yin and yang in the human body being broken. To restore the balance, acupuncture and herbal remedies are used, restoring good health. A broken harmony is due to one side being greater than the other as yin and yang form a zero-sum game. This means that as one side waxes, the other side wanes and vice versa, with the sum of the two being equal at all times. But this does not mean that yin and yang oppress and fight each other. Instead, the two rely on each other despite being opposites. In this world, there is no light without darkness. There is no forwards without backwards and no life without death. For instance, if there were only men (yang) in this world, the human race would be wiped out in one generation. But if yin and yang coexist to help each other and form a union, they give birth to a new generation. Nature always exists as a perfectly balanced coexistence of two polarities. When yin and yang form a balance they form something even greater than their sum, which is harmony.

1 + 1 = 3

(Image source: http://falynevarger.deviantart.com/art/Yin-Yang-Dragons-119779525)