Posted in Science & Nature

## Cow Modelling

There is a farmer who is unhappy with the milk production from his dairy farm. To rectify this, he writes to the local university asking for advice. A theoretical physicist responds to the request and visits the farm. He then takes many measurements such as the size of the cow and proceeds to do some calculations. After finishing all of this, he tells the farmer: “I have a solution, but it only works for spherical cows in a vacuum.”

The point of the joke is that in science, models are frequently used to simplify reality. Because there are infinite amounts of variables, it is impossible to predict anything unless the scenario is simplified through certain assumptions and removal of factors. For example, many physics principles make assumptions such as not accounting for air resistance. Occam’s razor states that if you shave away all the complex details, the simplest answer remains. But perhaps we oversimplify some things?

Posted in Science & Nature

## Seven Bridges Of Konigsberg

The city of Königsberg (capital of Prussia, now Kaliningrad, Russia) has the Pregel River running through the middle, with islands at the centre of the river connected by seven bridges. Is it possible to cross all of these bridges while only crossing them only once each?

If you try to solve this problem, you soon discover that it is incredibly difficult not to cross the same bridge twice. But it is difficult to tackle this problem in a brute force manner. To calculate all of the permutations in the order of bridges, you use 7! = 7 x 6 x 5 x 4 x 3 x 2 x 1 = 5040, meaning that there are 5040 possible arrangements of bridges. Then how can you prove if the problem is solvable or not?

The great mathematician Leonhard Euler, upon being asked to solve the problem, is reported to have said that the problem is impossible to solve on the spot. In 1735, he proved his answer by modelling the seven bridges of Königsberg in a diagram of four dots connected by lines (representing the bridges).

By using this model, the problem is converted into a “draw in one stroke” problem, which is also called a Euler walk to honour Euler’s contributions. Euler discovered many properties and laws regarding such problems. If a certain point is the starting point, then the line must first leave the point, then even if it comes back to the point, it must leave again. Ergo, the starting point must have an odd number of lines connected to it. The opposite applies to the ending point, where a line must enter the point, and if it leaves the point it must come back to it. Ergo, the ending point must also have an odd number of lines connected to it. In the case of a Euler walk, the starting and ending points are identical, so the number of lines is the sum of two odd numbers, making it an even number. Thus, to find out whether a picture can be drawn using one line, use the following laws:

1. If there are no points of odd degree (odd number of lines), the starting and ending points are identical.
2. If there are two points of odd degree, the starting and ending points are different.
3. If there are one of more than two points of odd degree, it is impossible to draw using one stroke.

Thus, a Euler walk is only possible if there are 0 or 2 points of odd degree. Looking at the seven bridges of Königsberg problem, we can see that A is connected to 5 lines and B, C and D are connected to 3 lines each. As there are four points of odd degree, we have thus proved that it is impossible to draw a path that crosses all the bridges while not crossing any bridge more than once.

Posted in Science & Nature

## Typical Person

What is the typical look of a human being? The following is a character bio using data of the most common traits and average statistics from the world population.

The typical model of Earth is a 28 year old Han Chinese male called Mohammed Lee. His height is 1.75m, weight 80kg, he has black hair and brown eyes and he is right-handed. He speaks Mandarin Chinese and his religion is Christianity. He works in a factory earning less than USD\$12,000. He owns a cellphone but not a bank account. The following is the most typical face constructed using a composite of 190,000 faces of people fitting the above description.

Posted in History & Literature

## Michelangelo’s Model

There are few (intellectual) people who do not know the master artist of the Renaissance, Michelangelo. His works are well-known for powerfully expressing the beauty of the male body and the energy it contains. However, there is a secret that lies in many of his paintings.

The work that most obviously shows this is the famous ceiling of the Sistine Chapel. This giant painting features many characters from the Bible and Greek mythology, one of which includes the Sybils, or female prophets. In particular, the one called The Libyan Sybil shows a woman holding up the pages of a large book. However, on closer inspection it can be seen that she has a very muscular build and very large shoulders – features of the male anatomy. In fact, this feature is found in almost all of the Sybils and many other supposedly “female” characters.

The reason being, Michelangelo was a misogynist and admirer of the male form, thus he frequently (and almost exclusively) used male models for his paintings. For example, the model of The Libyan Sybil was one of his studio assistants. He believed that beauty of the human body peaked only in men, which combined with his talents for expressing vigour and energy in his art produced some of the most powerful, masculine paintings.

Of course, him being attracted to the nude male beauty both aesthetically and emotionally have given birth to many theories that he was a homosexual.