Posted in Science & Nature

Tip Of The Iceberg

Icebergs are deceptive things. You may see a small bump above the ocean surface, but beneath the surface hides a massive block of ice. Using Archimedes’ principle of buoyancy, we can calculate exactly what proportion of an iceberg lies under the surface. Pure ice has a density of about 920 kg/m³ and sea water has a density of 1025 kg/m³. Ergo, we can calculate that about 10% of the volume of an iceberg is above water. Therefore, whatever you see above the surface, there is nine times the volume hiding beneath it.

Tip of the iceberg” is a useful metaphor in describing many things. Our base instinct is to believe what we see at first glance. We rely on first impressions, we judge books on their covers and we tend to believe headlines before reading the full text of an article.

Although this is a useful way to process massive amounts of information that we are exposed to every day, it is certainly a flawed method because not only can we miss a vast quantity of information, also easily misinterpret or misunderstand things.

Take mental health for example. Because we cannot read minds, we take clues from people’s expressions, body language and what they tell us to gauge what is happening in their minds and hearts. We are reasonably good at gauging this, so we often make assumptions based on surface information.

We might assume our friend is happy because they are smiling, or that a couple’s marriage is harmonious because of cute photos on their social media. Conversely, we might assume that a stranger is rude to us because they are terrible people.

But the smiling friend may be suffering crippling anxiety and depression. The happy-looking couple may be at the brink of divorce because of relationship problems. The rude stranger may have lost a loved one just the day before. Things are not always what they seem and it makes an incredible difference to have the insight to see past the surface.

Another lesson to learn from the tip of the iceberg is that when we encounter a problem – whether it be with another person or even within ourselves – we should ask the question of what lies beneath. The problem we notice may just be the tip, with 90% of the issues hidden from plain sight.

For example, if you feel tense and easily triggered often, perhaps it is worth looking under the hood and going on an introspective journey to discover what past experiences and traumas may have caused the insecurities. If you keep feeling victimised, attacked or sensitive, examine what story your subconscious is telling you and try to correct the narrative, being the agent of your own story.

Avoid the fate of the RMS Titanic: look beyond the visible tip of the iceberg and be aware of the entire problem. You will be surprised how it changes your perspective of the world, the people you interact with and how you feel about yourself.

Image credit: https://www.smbc-comics.com/comic/hubris

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?

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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).

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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.

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Posted in Philosophy

Wolf And Sheep Problem

If two wolves and one sheep vote on what to eat, it could be called a democracy. However, the result would obviously be against the best interest of the sheep. This problem, known as the wolf/sheep problem, is caused by the misunderstanding of the principles of democracy and is abused by many countries. Under a democratic system, a government is able to steal from the minority groups and redistribute it to the majority. Can such a system be called democratic?

The correct definition for democracy is: “a system where the people have power and are able to voice their individual opinions”. But if the minority opinion is silenced and ignored by the majority as described above, then that goes against the true spirit of democracy. Many confuse democracy with the principle of majority rule, which is only one method used to integrate the people’s opinions with politics. Ergo, the government has a duty to protect the voice and rights of the minority. The three most important of such rights are the freedom of political expression, speech and the press.

A democratic government should be a government of the people, by the people and for the people. Unfortunately, so many governments violate the meaning of democracy just as the two wolves prey on the sheep.

A wise person would not leave their fate in the hands of such a system.

Posted in Life & Happiness

Why And How

When an obstacle blocks the way, the first response a person shows is thinking “Why did this happen? Whose fault is it?”. A person looks for the person responsible and ponders what appropriate punishment should be given.
In an identical scenario, an ant first thinks “How, and with whose help, can I solve this problem?”.
In the ant world, there is no concept of “crime”.

It is obvious that there is a great gap between people who ask themselves “Why didn’t this work?” and those that ask “How can I make it work?”.
In modern times, the world is dominated by people who ask “why”. However, in the future a day will come when the world is ruled by those that ask “how”.

(from The Encyclopaedia of Relative and Absolute Knowledge by Bernard Werber)

Posted in Life & Happiness

Dali Nap

The famous surrealist artist Salvador Dalí had a strange habit. When he could not solve a problem or had difficulty coming up with an idea, he chose to nap. However, he did not nap “normally” to say – he used a unique method.

First, find a comfortable sofa or armchair, a spoon and a large plate or pan. Sit in a comfortable way, flip the plate over and place it on the ground, then hold the spoon directly above it with only your thumb and index finger. While thinking about the problem you want to solve, fall asleep.

As soon as you enter REM sleep, all of your muscles will relax and so the spoon will fall onto the plate, making a loud clatter. As soon as you get woken up by this, you will not only feel well rested, but also discover the solution or idea you were looking for.

Posted in Life & Happiness

Feynman Problem Solving Algorithm

Richard Feynman is a world-renowned genius physicist, famous for his ability of solving some of the most difficult problems in physics. He said that his intelligence was all thanks to his unique yet “normal” problem solving method, which he used to solve most of his problems. Here is the algorithm:

    1.  Write down the problem.
    2.  Think very deeply.
    3.  Write down the answer.

If that does not yield the answer:

    4.  Sleep.
    5.  Wake up, then think deeply again.
    6.  Write down the answer.

Nothing is impossible.