Zeno’s Paradoxes

Автор Андрей Беликов

The book is a collection of scientific articles on topics that are almost not discussed in the scientific community, but are always of great interest. What is time? How to explain the paranormal? Why is Einstein's theory of relativity incorrect? How can we get into the future? How can we learn to treat ourselves? You will find answers to these questions and other questions in this book.

• Язык: Русский
• Издатель: T/O "Neformat"
• Дата выпуска: 30 янв. 2020 г.
• ISBN: 9780463260432

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Annotation: The article describes the solution of Zeno's paradoxes.

Keyword: dichotomy, Achilles, turtle, arrow, Aristotle, law, step, distance.

Zeno's aporias are the philosophical puzzles of the ancient Greek philosopher Zeno, which came to us in Aristotle's retelling in his work ‘Physics’. What was the original text, and what was its meaning remains a mystery. But even in this form, aporias are of interest not only as food for thought, but also as a monument of ancient Greek thought, studying which we can imagine the logic of thinking, peculiar to people who lived in the distant past. The article discusses the three most famous aporias of Zeno: The dichotomy, Achilles, Arrow, and offers their solution.

Dichotomy

‘There are four arguments of Zeno about the movement, causing great difficulties to those who are trying to solve them. The first one is about the non-existence of motion, based on the fact, that the moving [body] must reach half of the distance before the end’ [1]. In other words, in order to overcome the distance, you must first overcome half of it, and to overcome half of it, you must first overcome also its half, and so on to infinity. Therefore, the movement will never begin.

The minimum distance, to which it can be divided, is equal to the distance between the particles, because, as is known, the world consists of particles [2]. The movement can always start. The body, commensurate in size with the size of the particles, must first overcome the distance between the two particles, then the way, twice as large, etc. In order for a person to start moving, he needs to put the heel of the left foot close to the toe of the right foot. An infinitely small path length is formed between them. It can be considered such as it is many times smaller than the whole distance. Then press the heel of the right foot tightly to the toe of the left foot, etc. As a result, a person will go all the path (Fig.1). You can shift two squares relative to each other (Fig.2). Zeno is wrong.

Fig.1 Human Movement

Fig.2 Shifting of squares

Achilles

‘...the slowest [being] can never be overtaken by the fastest in the race, for the chasing one must first come to the place from which the escaping one has already moved, so that the slower one must always be some [distance] ahead of the [chasing one].’ [1] Let’s take a turtle as a slow runner. Let's say, Achilles runs ten times faster than a turtle and is a thousand steps behind it. During the time that Achilles ran this distance, the turtle crawled a hundred steps in the same direction. When Achilles runs a hundred steps, the turtle will crawl another ten steps, and so on. The process will continue indefinitely, and Achilles will never catch the turtle. Is that so? Let us consider everything in more detail (Fig.3).

Fig.3 Movement in Zeno's aporia

Achilles runs 1000 steps. During this time, the turtle runs 100 steps. When Achilles runs 100 steps, the turtle crawls 10 more steps. From the point 3, the width of the steps of the turtle decreases. There comes a point 6 when the turtle stops because it can't move in smaller steps. The same thing happens to Achilles. The width of his steps from the point 4 decreases, and at the point 7 he stops with a small lag in time from the turtle. Zeno is wrong. Achilles will catch the turtle. But why in real life everything is different? When we move like Achilles and a turtle, one of us always overtakes the other. The fact is that under the conditions of aporia, the width of the steps of Achilles and turtle decreases, and in ordinary life the dimension of steps remains constant (Fig.4). At first everything happens, as in the aporia, Achilles approaches the turtle. Then he catches up with her. Further, during the time when the turtle crawls 1 step, Achilles runs 10 steps, when the turtle crawls 10 steps, Achilles runs 100 steps, etc. We see Achilles running away from the turtle, which is what happens in real life.

Fig.4 Movement in everyday life

Arrow

‘The third [argument] mentioned now [states] that the flying arrow is stationary. [This conclusion] follows from the assumption that time is composed of [separate] ‘now’ [1]. In other words, the flying arrow is motionless, because at every moment of time it is resting, and because it is resting at every moment of time, it is always resting.

Zeno is absolutely right. The arrow is stationary at every moment. We perceive these moments consistently, and it seems to us that the arrow flies, although in fact it is motionless. According to the ‘Law of the past, present and future existence’ [2], the arrow and the human body always rest in every dimension – the moment of life of the Universe. The human soul, flying through its physical bodies, perceives the image of an arrow. The illusion of an arrow flight due to stroboscopic effect is created in the soul (Fig.5).

Fig.5 Fly of the arrow

Zeno's aporias, which we examined and explained, are based on the knowledge of modern man. From today's perspective, it is easy to talk about the philosophical themes of ancient Greek civilization. But the thing is that the ancient Greeks were able to create their masterpieces at the dawn of scientific knowledge, when almost nothing was known about the world. They took the first steps in scientific knowledge of nature, and many of their ideas still excite people. Not only aporias, but also logical constructions of ancient philosophers formed the basis of many Sciences, astronomy, and mathematics. The solution of aporias is a tribute to the philosophers of antiquity and admiration for their brilliant talent. What value do Zeno's philosophical puzzles represent for modern science? The most important thing is that they teach a person to think outside the box, force him to abandon his knowledge for a while, to follow the philosopher's thought first to think and formulate the conditions of the problem, which are not expressed explicitly, in order to ultimately find a solution. The truth is often hidden behind an external paradox. You just have to learn to sense and feel it. Zeno's aporias develop not only logical thinking. When working with them, it is important to mentally imagine, and it is best to draw various solutions on paper. This can come in very handy in design work where essentially the same is required. Gymnastics of mind, purposefulness-this is not all that is required to solve aporias. We must love philosophy, be interested in its achievements and try to solve not only philosophical, but also applied problems that also require a lot of mental work. Zeno's aporias will never become obsolete. Each person can solve them in his own path. This is the genius of Zeno, who created these masterpieces of the ancient world.

Literature:

1. Aristotle. Physics. Book 6, Chapter 9 /electronic library Royallib.ru

2. Belikov A.V. Teleportation in time

February 14, 2018

Belikov Andrey Vladilenovich

Engineer

Russia, Sverdlovsk region, Lesnoy,

FSUE «Integrated Plant «Electrohimpribor»

Zeno's paradox

Annotation: The article describes the solution of Zeno's paradoxes.

Keyword: stadium, plurality, measure, place, bag, move, particle, circle, square.

Once on the road met two philosophers. One was coming from home, the other from the shop. They started a conversation.

- Greetings, Podkabluchid!

- Greetings,Skryagchit!

- I lost my donkey's tail today, didn't you find it? - Podkabluchid asked.

- No.

-So you're tailed, ' Podkabluchid said.

- I lost a lot of gold today. Didn't you find it? - Skryagchit asked.

- No.

- So you have it, then. Give it back.

Skryagchit took off his invisible tail,