Instead of preface
I suppose most people who are interested in the fourth
dimension have already got acquainted with the ihabitants of
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
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
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
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.
Please go on reading.
But where is this Country of the Fourth Dimension.
I don't know but You, my learned Teacher, You must know it.
I know nothing. Such Land doesn't exist. The very thought of it has no
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
notion of length!
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
them ( if they do exist) because they don't cross our world. 2) we can
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
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