Did Plato play football?

Aharon Kantorovich writes a review of the book "Matter and Spirit: The Spiritual Basis of the Universe", by Yakir Shoshani, published by the Ministry of Defense, "University Mashhadar" library, 240 pages, NIS 48.

In his book "The Spiritual Foundation of the Universe" Yakir Shoshani deals with many and varied topics from the history of science, physics and philosophy, and focuses on the concept of matter. Much effort is invested in the explanation of a unique philosophical thesis of his thought, which he calls "Apriorica". This approach deals with the possibility of knowing the world in an a priori way, meaning through thinking and thinking, and not through observations and experiments as is customary in science.

The last chapter of the book corresponds with the name of the book and tries to explain the creation of the world as a transition from spirit to matter. The author begins by analyzing the problem of creation "from nothing" and offers his view, according to which before creation the elementary entities existed and of each of them only one copy existed. Creation began with the beginning of the multiplication of these entities, which made it possible to create complex entities from them in the form of "elementary particles" and complex physical systems. In my opinion, this is the most interesting chapter, although also the most enigmatic.

What did Thales mean by Miletus?

The book is divided into several chapters: in the first three, the author tries to clarify that the concept of matter is based on "spiritual essences" in the form of mathematical patterns and global natural laws. The fourth chapter discusses the concept of "spiritual being" but does not clarify what the difference is between it and "spiritual essence", if at all. The three chapters that follow include a multitude of philosophical topics (such as epistemology, the theory of consciousness, collective consciousness, scientific realism, body-mind duality, and more) on which entire libraries have been written.

Questions and problems emerge already in the first chapter, when Shoshani reviews the development of the concept of matter from Greek philosophy to Newtonian mechanics. He presents this development as a series of scientific theories. However, when Thales of Miletus says "everything is water", it is not meant that a marble statue is actually made of water, this metaphor cannot be treated as a scientific theory. Only in the transition to the Platonic Torah can one see signs of a scientific theory. Shoshani presents Plato's teachings as an early example of a priori, that is, a theory constructed in a systematic and logical way by Goth. Contrary to his opinion, it is quite reasonable to assume that this theory was built by using ideas and mathematical tools that were proposed by philosophers of Plato's time and were already found in his immediate environment, ready for use.

Plato worked within the Pythagorean tradition and in building his theory he used the foundations of the teachings of his predecessor Empedocles and his contemporary Democritus. According to Empedocles the world consists of four elements: fire, air, water and earth. Plato wanted to base his teachings on geometrical foundations. According to a finding by Theaetitus, there are five phaons (bodies whose faces are polygonal, equal sides) perfect convexes: pyramid, cube, octahedron, dodecahedron and icosahedron. Plato tried, in different explanations, to match the four elements to the four fauns, until he finally paired the ether - the limits of the universe - which is the fifth element, with the dodecahedron, which has 12 pentagonal faces. That is, Plato used a mathematical tool - the finding of Theaetetus - to build his theory. Only after the fact did he reproduce his findings as if he had arrived at them in a calculated and rational manner. I wasn't there, of course, but this is a possible and reasonable interpretation of Plato's way of working and thinking.

To make the point, historians of science Stephen Tolmin and John Goodfield (in their 1962 book The Architecture of Matter) describe Plato's pairing of the ether and the dodecahedron. They say that the proximity between the dodecahedron and the ball was known to the Greeks, since their football was sewn from 12 pentagons of leather. That is, they imply that Plato built his theory on the basis of casual knowledge, and did not arrive at it from rational reasoning. Whereas Shoshani tells us the standard story, that Plato was guided by "pure intelligence" as reflected in geometry.

like a violin string

From here the author jumps directly to the concept of mass in Newtonian physics, a leap in which he skips more than 2,000 years, and which he calls "a summary of the history of matter - from Thales to Newton". Shoshani describes the principles of Newtonian physics in a friendly way for readers who are not familiar with the intricacies of mathematical formulas. Instead of peppering his book with amusing anecdotes and illustrations, as popular science writers sometimes do (such as Dan Falk or Anthony Zee), the author embellishes physics with philosophical passages.

The description of elementary particles as vibrating strings demonstrates this approach. According to string theory, in particle physics (a theory that is still largely speculative) the multiplicity of particles and the forces between them are supposed to be explained with the help of one fundamental entity that can be likened to a very tiny string, in the form of a loop, vibrating at a certain frequency in an 11-dimensional space. Shoshani adds that "a space with more than three dimensions cannot be perceived intuitively, but it is mathematically well defined... the string can vibrate at several characteristic frequencies, similar to a violin string vibrating at its characteristic frequency, which is determined by its length and physical characteristics." After this explanation Shoshani connects the basic idea of ​​string theory with the concept of the Apeiron (Apeiron, or "the unlimited"), coined by the Greek philosopher Anaximander about 2,500 years ago. According to Anaximander, the world was created from only one element - the epiron - which is unlimited and infinite and without attributes. Shoshani asserts that the epiron is a spiritual entity, since it is not characterized by any property known to us from the world of phenomena, and the substances we know are created from its expansion and contraction. However, this claim contains an internal contradiction: if the aferon expands and contracts, this means that it has a spatial dimension, such as length or volume, and this is definitely a property known to us from the world of phenomena, and therefore it is not a spiritual entity according to Shoshani's own definition.

Swan's song

I will end with Apriorika, the philosophical thesis that is the result of Shoshani's exclusive development, which is not necessarily related to the rest of the book. Shoshani only gets to it in the eighth and ninth chapters and it takes a lot of effort to decipher it, since it involves the physics of the "elementary particles", but I will try to emphasize a few general points: as mentioned, this approach deals with the possibility of knowing the world in an a priori way. It will be shortened to describe here how the author reaches his conclusions; But one can at least observe the conclusions themselves. For example, the author deduces the number of elementary particles in the world a priori. And see it's a miracle, this is exactly the number determined by the theory that dominates today in particle physics - the "standard model". This number was determined after many studies and experiments, but according to Shoshani, it can be reached based on a priori considerations only.

The average reader will find it difficult to judge the theory of a priori, but even those readers who are not physicists or philosophers will be able to take into account the following reasoning against it: it is possible that in the future new facts will be discovered through observations or experiments, from which it will become clear that the number of elementary particles is different from the number determined by the standard model today. However, the number determined a priori cannot be changed following new discoveries, just as it is impossible to change a sentence in geometry following facts that seem to contradict it. No fact can contradict the sentence: diagonals in a rectangle cross each other. That is, the theorems of geometry are a priori.

But it is very hard to believe that the "standard model" will not change, because even though this theory is the best that exists today, it is far from perfect and will most likely be replaced by one theory or another, or at least undergo radical changes as happened to many scientific theories in the past.

In conclusion, I would like to express my regret that this book is one of three that are the swan song of the IDF Broadcasting University Library published by the Ministry of Defense, which is currently closing its doors. Within this library, over 300 books in various fields have been published to date, which have greatly contributed to the public The educated in Israel.

Dr. Aharon Kantorovich is a researcher at the School of Physics and Astronomy at Tel Aviv University

The article was published in the book supplement of Haaretz newspaper, 21/01/09 and is presented here with the permission of the author and Haaretz newspaper.