Essay on the relation of mathematics and reality

One of the many examples of this is undoubtedly Planck’s constant. Max Planck, German Nobel Prize in physics, after twenty years of work achieved his desired goal. He performed the following experiment: he warmed a hollow body to the incandescence, let out a ray of radiation through a small opening, a beam that he analyzed in an electroscope. The experiment repeated it multiple times and found that radiant energy is not a direct current. It is issued in integral quantities, or quanta, that can be expressed in integral numbers. In other words, the measure always provides multiple integrals of h v, where v is the frequency and h is a universal quantity, known as the Planck constant. The discovery has two achievements, one, its technical ability to measure the value of this constant and another, the most important in my view, to find that no radiation can be emitted unless it is that amount or an entire multiple of she. That is, a stove can not provide heat until it has accumulated at least that amount. The radiation from your heat will increase until it accumulates double the initial amount and so on.

I put this example, despite being little known by the common people, not only because it seems astonishing to me that the value of this constant is the same both in the laboratory, in the world and in the stars, which in itself Is extremely disturbing, and no doubt examples like this are in large quantities. But also from this discovery the principle of causality is challenged, a subject to which Planck himself dedicated much of his time, and which refutes the old belief that all processes follow the order causes effect, occurring A great break between how nature was thought to be governed and how it really was, and it is now even thought that in some future the effects may precede the causes and time to run in the opposite direction.
At present and for some time there is a great interest in physics among the public, because physics is the most vital expression of human thought today. In addition, the metaphysical content of the highest speculations of theoretical physics seems to be the favorite sustenance for the hunger of the soul which was formerly appeased with the ideals of art and religion.
This hunger for knowledge, for wanting to unravel the hidden fabric of the universe, to know the order of things, if it really exists, to have something concrete in our hands that indicates that we know our surroundings, is not something recent, no doubt .

Let us go back when Plato formulated his theory of ideas. It explained reality by saying that what we perceived were shadows, the product of molds or ideal figures that existed behind everything we saw around us. Already at that time there was curiosity to know the world of ideas that inhabited the world of the senses that was the one we perceived. Knowledge of the world of the senses was imperfect because it was achieved through these which were deceptive and distinct for each individual. So the achievement of certain knowledge could only be obtained in the world of ideas, through the use of reason.

The Greeks thought that this sure knowledge was provided by mathematics, because according to them mathematical relationships never changed. Even to be able to learn from philosophy it was necessary to know mathematics before, this is deduced from the poster fixed at the entrance of the intellectual center of that time, the prestigious Academy of Plato, which said “No one enters here if he ignores geometry.”

It is precisely from this branch of mathematics, when Euclid formulates the principles of his geometry in the book The Elements that he begins to think that the absolute truth of creation had been found, the laws that God had invented to govern nature. This discovery became one of the cornerstones of human thought from the early Greeks to the nineteenth century.


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