What makes a city or town aesthetically pleasing? Places such as Prague, Florence and Santorini are famous for their picturesque cityscape. Instead of specific famous buildings or tourist spots, postcards from these areas could just show any part of the city and they would still be beautiful. What sets these places apart? How is it that despite all our technological development, modern cities can’t compare to the beauty of cities that are hundreds or thousands of years old?
Korean architect Yoo Hyun-Joon proposes a theory regarding two factors: material and shape. Consider the following matrix using the two:
Out of these four, the combination that we find the most beautiful is when a city has simple materials but complex shape. For example, Santorini is made only of stone buildings painted white and blue. But because it is built on a volcano, the ground is uneven and the building shapes differ to accommodate for this. Florence is almost entirely made of bricks. Traditional Korean houses were made only of wood. This is because in the old days, due to labour costs and poor logistics, cities were usually built with materials abundant in the surrounding area. Instead of varying materials, architects would challenge the limit of materials with varied shapes.
Nowadays, thanks to trade and globalisation, it is much easier to obtain materials from all over the world such as glass, concrete and steel. Furthermore, we can use industrial vehicles to change the terrain to flatten the ground and we use tall rectangular buildings to maximise space. Thus, we end up with the ugly, chaotic combination of many materials and simple shape.
The solution to making a beautiful city is simple then – create a building restriction that unifies the building material to one. A good example is Newbury Street in Boston, USA. This shopping district is famous for its classy red brick appearance, thanks to a building restriction that ensures every new shop built on the street must have the side of the building facing the street built using red bricks.
Of course, just unifying the building material to any one thing does not solve the issue. For example, cities made of only concrete rarely are as appealing. What is important is to use local materials that best represent the context of the city and the land it was built on.
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.
Another well-known substitution cipher is the “pigpen cipher” or “Freemason’s cipher”. As the name suggests, it was often used by Freemasons to encrypt their messages. However, as time has passed, it has become so well-known that it is not a very secure cipher at all.
The pigpen cipher does not substitute the letter for another letter, but instead uses a symbol that is derived from a grid-shaped key. The key is made of two 3×3 grids (#)(one without dots, one with dots) and two 2×2 grids (X)(one without dots, one with dots). The letters are filled in systematically so that each shape represents a certain letter (e.g. v=s, >=t, <=u, ^=v)
The cipher has many variations that attempt to throw off an attacker by rearranging the order of the grids or the letters. Thus, even if a cunning attacker picks up on the fact that the cipher is a pigpen cipher, they may use the wrong key and get a completely wrong message. Nonetheless, it is a useful skill to recognise the unique symbols of the pigpen cipher as it is a popular cipher used commonly in puzzles.
As with any substitution ciphers, frequency analysis and pattern recognition is the key to cracking the pigpen cipher.
The northern white-faced owl, found in the Sahara Desert of Africa, is a small, cute bird of about 22~24cm length. It is famous for a very unique defence mechanism. As shown in the photo, it normally has a round, puffy appearance, but when faced with a fearsome predator like a hawk, it undergoes a drastic transformation. The owl shrinks itself as much as possible to avoid the enemy’s attention, while looking like a sick bird that has lost a lot of weight. This appearance gives the predator the impression that the owl is not worth the effort of hunting and lowers the chance of it attacking. The ability to shrink to half its original width is achieved through elongating its body and pulling in its feathers as much as possible. Also, when assuming this shape, the owl always faces the predator and poses at an angle to minimise its exposure.
This transformation is only seen when the owl is placed in front of a large predator like a hawk or a much larger owl. When in front of a similarly-sized owl, it exhibits a different transformation where it flares up its wings to make itself look much larger, intimidating the opposition. But this behaviour is common in many other species of owls, whereas the shrinking performance is a rare behaviour only seen in the northern white-faced owl.
The reason is that a square or rectangle has a diagonal greater in length than a side, so it can fall through if misplaced. A circle has equal lengths at any angle and is perfectly symmetrical, thus will never fall through.