Roger Caillois' Scientific and Mathematic Developments

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18th May 2020 Mathematics Reference this

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Roger Caillois, polymath, philosopher, historian of science, was friend of Andre Breton and many surrealists. However, in 1934, Caillois’s mind was different from surrealist investigators. The conflict arose between Caillois and Breton when they were shown the Mexican Jumping Beans, which will jump into the air suddenly. Caillois speculated that there was a worm inside them, and he wanted to open one of them to confirm his hypothesis. But Breton disagreed with this experiment. He thought Caillois just interested in conclusion and explanation but refused the marvelous minds. For Breton and surrealists, chances and unpredictability disrupted the logical thing of explanations and were a representation of disorder. Caillois wanted “research and poetic” together. 

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Caillois insisted on opening a Mexican Jumping Bean to see what was inside them, because he has a strong motive to transform magic thinking to contemporary scientific discoveries rather than a simple human imagination. Caillois insisted on marvelous elements in scientific discoveries, for example, in his view, new discoveries in structure of atom has reflected all of marvelous thinking about nature before.

In seventeenth century, people found the hieroglyphic universe, and this become a new perspective for twentieth century scientific developments. And divining, as a great example of magical thinking of earlier society, has changed the form in modern society but still have that momentum. Divining process could be a great example to help us understand magical thinking. Firstly, because the goal of thinking is knowledge, magical thinking could overcome the human limits to let us know about something we could not explain by experiments with data available at that time.  Secondly, they make a new order for universe to explain all of the phenomena they had seen, no matter whether it is coincidence. This kind of system also appears in another kind of system, the network of natural correspondences. In other word, some people will represent god to communicate with people. For example, in Baudelaire’s famous sonnet, Nature is a temple where living pillars, Let sometimes emerge confused words… And this kind of belief derives to the third characteristic of magical thinking. Some gifted people are chosen to send specific messages.  This kind of messages raised a conflict about how to understand the certain message, in order to have a certain decipherment for certain message. However, science wanted the certain answer. There will be a stable field of meaning, which is not influenced by human minds and errors. So, even the scientists have thousands of hypotheses about certain phenomena, they still need mathematical calculation and experiments to prove their hypothesis. 

The young poet Paul Valery visited London in 1894, and he was so excited to see many new physical discoveries articles- especially James Clerk Maxwell’s Treatise on Electricity and Magnetism.

Maxwell has always studied and published some works about electricity and magnetism as early as 1855 in his paper” On Faraday’s lines of force”. In this paper, he explained a simple model of Faraday’s theory and how electricity and magnetism were related together. And he also simplified all of his works into 20 equations which documented in his book “On Physical Lines of Forces”, which published in 1861.

Around 1862, Maxwell found out that the speed of electromagnetic filed is same as the speed of light. He insisted that this should be not just a coincidence, commenting, “We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena.”[1]

After several times of calculation and works, Maxwell predicted that there was a kind of waves of oscillating electric and magnetic fields, when they passed through the empty spaces, the speed of waves could be calculated in lab. The velocity Maxwell calculated in la is 310,740,000 meters per second (1.0195×109 ft/s) [2]. In his paper in 1864 “A Dynamical Theory of the Electromagnetic Field”, Maxwell wrote, “The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws” [3].

At the same time, Maxwell also put forward his theory of the electromagnetic field, which is much similar with Faraday’s theory of force lines. At the time, Maxwell believed that when light passed through the spaces, it will need a kind of medium for the waves, called luminiferous aether[4]. However, this kind of medium which has occupied the whole spaces according to Maxwell has not been detected in any of the experiments. However, it still could be hypothesis about the empty spaces. These difficulties influenced Albert Einstein to establish his theory about special relativity.

Scientific discoveries in 19th century was changing the concept of physical world in our knowledge, like Maxwell’s magnetism theory. In this process, Valery recognized the potential power of imagination, which could find out some features that could not be explained with data available in at that time, it could provide a hypothesis about mystery. “The study of my imagination …” he wrote in his London notebook, “has led me to considerations of mechanics and geometrics, which is hardly astonishing or hypnotizing. It is sometimes possible. Role of time, of space, of mass.” [5]. This kind of thought by Valery, reflected the logic of the imagination which led human minds to think about features which are still invisible in ordinary life, such as sound waves, interior of the atom, etc.

Additionally, Maxwell also had plenty of researches on kinetic theory of gases. The original theory about gases’ kinetic was developed by Daniel Bernoulli, but there were still many doubts about the credibility of his theory. Maxwell who was well-known as an experimenter and mathematician developed the theory of gases a lot. [6] Between 1859 and 1866, Maxwell did lots of experiments about the kinetic theory, and prove that temperatures and heat just influence the movement of molecules rather that their speed. These data actually has been existed earlier, Maxwell just had made a better conclusion about experiment results. But in other hand, Maxwell’s research on thermodynamics inspired him to design a kind of thought experiment which is known as Maxwell’s demon. And in this model, Maxwell disagreed the second law of thermodynamics by establishing an imagined object which could be sorted by energy. [7]

 In this thought experiment, a small demon controls the door between two gas chambers. He could open the door to let gas pass through the door be into another chamber. And in this experiment, when individual gas molecules get close to the door, the demon opens and shuts the door really fast so that only the fast molecules could go to the other chamber. Because fast molecules are hotter, the demon’s activity cause one chamber be hot and the other cool down, which violated the second law of thermodynamics, because entropy decreases.

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The second law of thermodynamics explained that when two objects with different temperatures are brought into contact with each other, and isolated from other objects, they will go into the same temperatures, because entropy will never decrease. Maxwell described a thought experiments to show his theory:

… if we conceive of a being whose faculties are so sharpened that he can follow every molecule in its course, such a being, whose attributes are as essentially finite as our own, would be able to do what is impossible to us. For we have seen that molecules in a vessel full of air at uniform temperature are moving with velocities by no means uniform, though the mean velocity of any great number of them, arbitrarily selected, is almost exactly uniform. Now let us suppose that such a vessel is divided into two portions, A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower molecules to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics. [12]

In other words, in his experiment, he divided on container into two sections, A and B. Both sections are filled with same gases with same temperatures, all the same, and placed together. An imaginary demon is standing on between of two sections and controlling the door. When a molecule in A section whose speed is higher than average speed in A section comes to the door, the demon will let it go to the section B. And when a molecule in section B whose speed is lower than average speed in section B comes to the door, the demon will let it go to the section A. The average speed of section B has increased because of the high-speed molecule, as section A speed is decreasing. So, the temperature will increase in section B, but decrease in section A. This is different from the second law of thermodynamics. At the same time, a heat engine between section A and B could have useful work because of their temperature difference. And in this experiment, demon should let both sides of molecules to go through that door, or it will cause the high temperature and high pressure in section B.

Even later, many scientists argued that the second law of thermodynamics should be right according to the calculation. However, in 1960, Rolf Landauer argued that he realized some measuring process do not need to increase entropy and this could be used to sort molecules. [6][8][13] But this condition could not exist in real life. Because of the connection between information entropy and thermodynamics entropy, if you do not want to cause entropy increase, the demon in thought experiment cannot erase the data of molecules, because erasing the data will cause increase of entropy. But in real life, because of the limit of storage, demon should erase the data in order to sort new molecules. So, this thought experiment could not be established in real life. But the discussion has never stopped yet, as this theory will cause revolution in thermodynamic field.

And in 1874, Maxwell built a plaster thermodynamics visualization in order to research on phase transitions. [8]

 And in this process, thought experiments play an important role in his research. This kind of examples are pretty common in scientific discoveries. For example,  Schrödinger’s cat is a famous experiment which controlled a perfectly sealed environment to show quantum indeterminacy.

 John Witt-Hansen established that Hans Christian Orsted was the first person who use German term Gedankenexperiment, which means thought experiment. [9] Much later, Ernst Mach used this kind of thought experiment as a real physical experiment for his students. He asked students to provide an explanation why their experiment results are different from their imaginary result. [10] He also thinks that thought experiments are a necessary precondition for physical experiments. Scientists also use thought experiments to implement some experiments which are impossible to conduct, such as Einstein’s thought experiment of chasing a light line, which proves the credibility of special relativity, even could not prove directly, but led to a successful theory, and then proved by other methods many years later.

From 19th to 20th century, thought experiments are widely used in physics and other sciences. In thought experiments, we could find out a brand-new perspective to look at the problems. We could gain new information even from data which has been known much earlier. For example, in Galileo’s thought experiments, he reorganized the experiments which in his original idea consisted in bodies with different weight. [11] No matter, what they wanted to do by using thought experiments, all thought experiments form a certain way of thinking which established to allow us to explain some unknown events in a more productive way.


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