Instead of preface

I suppose most  people who are interested in the fourth dimension have already got acquainted with the ihabitants of    Flatland - flat beings.
Edwin Abbot, an English writer, invented them and wrote a book "Flatland" published in 1880. The author was able to show how schematically and tentatively our comprehension as to tridimensional space is. He did it with humour and smart. He invented the whole world existing on the plane, where polygons, straight-line segments, circles lived. Those flat beings lived according to their own rules, they distinguished each other only by touching. They had got their own science which logically explained why the world is organised exactly like theirs - it's two dimensional. Once a Sphere visited Flatland. The Sphere was changing the size of its section while crossing the plane of that world. Naturally the inhabitants of Flatland could see only a circle but they couldn't understand its properties at all because it was able to grow and reduce in size, appear "from nothing" and disappe "to nowhere". Those categories: "nothing" and "nowhere" were  the third dimension. But the flat beings couldn't even imagine it. After the Sphere took one of them - a Square - to the third dimension he could understand everything. But further on Abbot wrote something that a reader might not understand. Here is a dialogue:

The Square:  Please take me to the second trip to the zone of the fourth dimension, from where I can look at                                             the Country of the third dimension and see everything which is hidden inside any tridimentional house,                                   to learn the secrets of the tridimensional Land.
The Sphere:  But where is this Country of the Fourth Dimension.
The Square:  I don't know but You, my learned Teacher, You must know it.
The Sphere:  I know nothing. Such Land doesn't exist. The very thought of it has no sense.
Abbot  wanted to say we all can't imagine the fourth dimension. But the analogy widened the realization of a two-dimensional personage and he understood that other different N-measured worlds can exist. The Sphere seemed not to understand it somehow. One can state: it doesn't matter whether you are a square or a tridimensional creature, The ability of thinking logically is important  in this case. Then, as one sage said :"Looking at the water drop one can come to the conclusion that The Great Ocean can exist somewhere".
Let's begin with clever one-dimensional beings : they look like lines or points. They live on a straight line and see everything crossing their world as a point only but they can measure the length of a crossing line. In other words they must know the notion of length!
 It's not necessary for two-dimensional creatures - squares- to acquaint each other by means of touching. It's quite possible to observe the object just by going round it. Why shouldn't they have two eyes? Then they even shouldn't go round the object. They could see lines, in addition they know the concept of measures and the forms of planes. Two-dimension beings are able to imagine tri-dimension space by analogy with one-measured space.
What About tri-measured creatures? Can they see planes only? Oh,no, they can easily see the solidity of the bodies with the help of their eyes. They can measure a body's shape and proportions. So they must think about the fourth dimension "by analogy". Let's think. Logic tells that every next dimension spreads somewhere and we can see the bodies of the fourth dimension in their tri-measured reflection. Can we see?  There is an alternative here:1) we don't see them ( if they do exist) because they don't cross our world. 2) we can see the existing bodies without undestanding where they are spreading.  In my opinion the fourth dimension is spreading inside the volume in the form of substance which fills the volume. Further on we'll talk about it in details. Are we able to penetrate in the fourth dimension? Please don't say "NO". For example we can dive into water. After all we are living inside the substance - in the air- and we ourselves are made of material .One hundred times we could watch how certain creatures and things appear in our fourth dimension from  another fourth dimension: A man from the fog, the fishes sprang over the water and so on.
Any substance is in motion. We learned how to measure it. This motion is called the fifth dimension.
I realize that my ideas are so simple that it's difficult to accept them. The Nature itself uses the minimum: all the elements in the Period of Mendeleev  though have many various properties differ from each other in a number of electrones only. And Time? I share the opinion of  those people who consider that Time as a physical category doesn't exist. Are you shocked? Once upon a time people were shocked by the idea that the Earth isn't flat.     

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