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Probability: From Apple to Black Swan

Do you think universe is always chaotic, hardly predictable and "estimation" is not useful in practice?

Photo by Hemerson Coelho on Unsplash
Photo by Hemerson Coelho on Unsplash

Until the beginning of the 20th century, it was thought that the universe operated under certain rules. Most scientists defended the deterministic idea and thought everything was predictable. Many supportive ideas have been put forward on determinism that developed with Newton, which was perhaps never questioned until Einstein. One of them is a theory put forward by Pierre-Simon Laplace in the early 19th century.

Laplace says: "We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes".

To explain with an example; The tail or head of a coin is the assumption that it can be found taking into account all the variables it will come to. These variables are the height of the money from the ground, the flipping speed of the coin, the angle of rotation, the friction force in the air, the direction and force of the wind, etc. If thousands of variables are calculated, it can be known whether the money will come to a tail or head. This theory would later be called the Laplace’s demon. These types of thought were common and accepted until Einstein’s physics.

As the new theories that came with Einstein’s physics, Newtonian physics became obsolete, in a manner of speaking, determinist approaches moved away from the opinion that everything is predictable and probabilistic views began to spread. In Schrödinger’s experiment, he developed by supporting the probabilistic approach with the expression "quantum cat can be both alive and dead, and in two places at once" in his famous words. However, a new era has entered and the foundations of science have changed.

The opinion that predicting the future is impossible in determinist approaches, but that the future is predictable with probabilistic approaches, has started to prevail. Probabilistic approaches have been used in many sciences and it has started to live its heyday. Towards the middle and the end of the 20th century, new arguments against the probabilistic approach started to show themselves.

It is the chaos theory that we hear the name frequently. Chaos theory maintains that the universe has an irregular (chaotic) structure. It is thought that it has its own order in this disorder, but it is impossible to find this order. This theory is closely intertwined with the Butterfly Effect; "The things that really change the world, according to Chaos theory, are the tiny things. A butterfly flaps its wings in the Amazonian jungle, and subsequently a storm ravages half of Europe". It gained fame with this example.

The main point of chaos theory is that it tries to explain that the results may be unpredictable with very, very small deviations due to the probabilistic approach. He tries to point out that small mistakes that are ignored by the probabilistic approach are actually very important.

The book "The Black Swan: The Impact of the Highly Improbable" published by Nassim Nicholas Taleb in 2007, he strongly opposes the probabilistic approach and explains it with the example of the black swan. Until Australia was discovered, all swans were thought to be white. In short, the proposition that "all swans are white" was accepted. After the discovery of Australia, the proposition that all swans should be white, which had been accepted for centuries, was turned upside down. He argues that the future, which cannot be predicted with the past information, is completely uncertain. He wants to say that anything can happen at any moment, even the most improbable thing can happen. Of course, in doing so, he heavily criticizes the statisticians who develop the probabilistic approach and apply it to real-life problems, and even goes further, implying that there is no need for statisticians.

After making a general discussion from determinism to the black swan, I want to end with my own opinion. Of course, making a perfect forecast is statistically impossible. However, estimating approximate results is useful in practice. Because "life is the sum of similarities rather than identities, no observation alone is a perfect example of the general." Each observation has its own characteristics independent of each other. However, Statistics focus on similarities rather than differences and finds approximate results, in spite of a certain error.

Due to the future is uncertain and chaotic does not mean it cannot be predicted with acceptable error. In order to make some plans for the future, need to make a decisions from today. I want to end with a word of Isaac Asimov; "When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together ".


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