The idea that the universe has numbers is one of the main systems of modern thought. From physics to philosophy, equations are often taken to reveal reality itself. But what if this is a guess rather than a discovery? A physicist Martin Lopez Corredoira it invites us to think again, to question whether mathematics describes the world as it is, or as we are able to understand it.
There are two different methods of studying Nature, both of which are inherited from different ways of thinking in ancient Greece: the rationalist-deductive method and the empirical-inductive method. The rationalist-deductive method was invented by Pythagoras (about 570-490 BCE) and Plato (about 427-347 BCE), according to whom the pure mathematical relationships in arithmetic and geometry are the truth that cannot change after the change of appearance in the world of senses. We cannot reach the truth by observing the senses, they argued, but only by reason, which can investigate the invisible mathematical forms that govern the world. In this way of thinking, there are a lot of abstract concepts, and the mathematical model is the main one than the experimental and observational results. For Pythagoras and his followers in the 6th century BCE, the universe was not only explained by numbers, but actually used by numbers. Harmony in music, grammar, and the arrangement of the heavens were all manifestations of mathematical relationships.
Some historians think that the idea of a world ruled by numbers is related to the introduction of coins into the market in the society where Pythagoras lived. Anything could be reduced to abstract numbers: the value of a pot, a jug of oil, a field, or a slave could be expressed in a precise number of coins, just as the wealth and value of any citizen could be expressed.
Plato also emphasized that true knowledge comes only through reason, thus reducing the role of the senses and the world as a whole. In his interview TimaeusPlato creates a cosmology with a creator who creates matter into projections of these ideal forms to create a Universe governed by eternal laws of mathematics, laws that humans can create because of reason alone. These eternal laws of mathematics are the real truth, while the changing Universe that we see is only an appearance; natural expectation is therefore unreliable.
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Mathematical excellence cannot be physics due to lack of observational support.
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There is a good chance of success using the rationalist-deductive method. An example in modern science is Albert Einstein’s (1879-1955) General Relativity, which was based on aesthetic and/or logical principles at a time when observational data did not require a new theory of gravity. In fact, observational tests proved that this idea was successful.
Modern physics and cosmology are Pythagorean in that theory is established before vision. It is common among modern Pythagoreans to accept statements such as looking for beauty in a mathematical structure that describes reality, or the divine plan by which the creator created the Universe. The physicist-mathematician tries to achieve something close to the mystical, he tries to read the Mind of God. Also, similar to religion, this theoretical physics and cosmology can only be understood by elites who are able to think in four or more dimensions, or in other similar terms.
Quantum mechanics is built on linear algebra in abstract Hilbert spaces. Particles are defined by wave functions, which are probabilities for coding mathematical objects. The basic state of nature appears not to be a concrete matter but a mathematical relationship.
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