At present the term " fourth dimension" is used mostly by science
fiction writers. Some scientists only assume
hypothetic possibility of the fourth and even the fifth and so on
dimensions existing. But there is no authoritative and proved grounds
this assumption. It should be noted that speaking about the fourth and
so on dimensions their geometric-spatial version is
supposed. The notion of three dimensions: length, width, height (three
dimensional system of co-ordinates) is an axiom. There is no subject to
be discussed, but! Let's try to make some short analysis.
a) beginning of co-ordinates
It is infinitesimal point (nought) arranged in any point of
space. It means that we can always dispose it in such a way
body, process can be described in positive. (Mathematics in
physics "doesn't want" to work with negative numbers: mathematics: 2 -
5 = -3, it's O.Key. But in physics 2 bodies - 5 bodies = -3
bodies, it's absurdity).
b) first dimension
It is a straight line, rather a ray, originating from the point
the beginning of co-ordinates.(fig.1)
We take arbitrary length of a piece as a unit of measurement, for
example: a meter, an inch, a mile etc. This measurement
determines the length of pieces. Here mathematics is arithmetic.
c) second dimension
This ray originates from the point of the beginning of co-ordinates
angle-wise 90degrees to the ray of the first
(fig.2). We take the same unit of measurement like in the first
dimension, but it's not necessary. We
may take FOOT for example, it will be m x foot.
We may also take a unit
of area not in the form of
a square, but in the form of a parallelogram, a
hexagon and so on. It's important to understand that the unit
obtained is independent, non-derivative.
We may know nothing about
the first dimension. But if we take a certain area (a sheet of veneer,
for example); this sheet is an independent example of the
unit. A square meter isn't m x
m in the
least. It can be in the form of a rectangle with
0,5m and 2m, in the form of a triangle, in this case its
area must be equal to the above
mentioned example. In
general, multiplication of a meter by a meter
is similar to multiplication (or division) of a cow
by a cow. Such units as an
acre,a hectare and so on
should be used . Therefore with the help of the second
we can describe plane geometric figures and lines and their
mutual disposition in the plane. Mathematics here
planimetry and algebra.
d) third dimension
You have already understood that cubic
measure here can be
in the form of a parallelepiped, a pyramid and so
and can be named : a litre,a gallon,
etc. The obtained unit is independent.
With the help of the third dimension we can
describe solid figures, spatial
lines and their
mutual disposition. Here mathematics
is stereometry, algebra,
Here comes the analysis
It consists in successive comparison of each
the previous one and the searching for possible
regularities on this basis. Don't forget that
everything equals nought in zero dimension.
(linear) differs from zero dimension so that
when we add it we get the first independent
(non-derivative!) unit - the unit of length, scope
from 0 to infinity. This dimension
previous 0 dimension.
2.The second dimension(plane)
differs from the first one by appearance of a new independent
unit - the unit of area, range of measuring from 0 to
and this dimension includes all the previous dimensions.
3. In third
dimension(space) a new
independent unit appears again. The unit
of cubic content, range of measuring from 0 to infinity.
dimension includes all the previous ones.
Here we have such phenomenon as NEST-DOLLS.
it's very important to understand every
current unit is
independent. For example: your parents are
Mary, you may be called "the son of John and Mary" but you are a new
independent personality with your own characteristic features. You are
Steve. And your son should be called "the grandson of John
Mary plus another grandma, another granddad", and his son should be
called… It's not only because it's inconvenient , but
you I deal concretely with Steve, not with
I appreciate exactly your characteristics, but not the product of
ýour parents'characteristics. The same is with
of the unit of area : its characteristics are not
of the product of a meter by a meter .
during the analysis a certain regularity of consistency in dimensions'
construction was revealed:
1. Units of measuring are positive numbers in a
range from a zero to infinity.
2. Each following dimension
includes all the previous ones.
3. Every dimension creates a
new, independent unit of measuring..
regularity determines algorithm of consistency in
dimensions are depicted in fig.4. In order to construct fourth
dimension one more axis should be drawn. Drawing it
domain of these three dimensions doesn't have any sense. And
drawing it in the domain of negative numbers contradicts to algorithm.
It should be noted that Decart system of
axes at angle 90˚ ) isn't a dogma. For example, axes can have 60˚ as it
is shown in fig.5. To draw here the fourth axis seems quite possible .
Please try if you've got time. One needs to understand that
the dimensions are abstraction, created by ourselves for
describing something. There is objective reality: space, material
bodies, processes occurring in substance. We
have described space in
dimensions, it's time to describe substance.
Let's put everything in order:
a) First dimension
Here the unit
is - an agreed piece.
b) Second dimension
It can be represented in the form of one axis,
this dimension has already included the previous
the unit of measure is an agreed
c) Third dimension
It can also be represented
in the form of one axis. Here the unit of measure is an agreed cubic
/ The same order is
valid for the following dimensions /
d) Fourth dimension
order to describe substance which is characterised by density, let's
draw a corresponding axis. As a result we obtain a new
unit - mass. It is possible to accept: a kg., a pound, etc. By means of
four dimensions we can describe any body, its form, its disposition in
space and the disposition as to other objects.
is actually the fourth dimension. Properties of substance:
aggregation of matter ( for
structure,etc. is presented in Chemistry.
Let's proceed and create the
e) fifth dimension
to algorithm it must be the product of
what? As substance can move then obviously into the unit of
motion. We know that generally accepted unit in this case is velocity.
But it doesn't correspond to our algorithm because velocity is
derivative quantity V= s/t. That's why let's temporarily take
existence of an abstract
of motion as
a fact. As motion is always
directed then this unit has a vector. Let's denote it .
We know that maximum velocity of substance motion is velocity
light in vacuum. It means that our unit ()
must have limit , but it doesn't correspond to our
Have we come into the deadlock? Not at all. If we
take it not as a
dimensional unit but as a coefficient then everything will be put in
order. Let's name this unit - a coefficient
can take maximal value of a coefficient = 1 or for convenience =
300thousand (meaning the velocity of light is 300.000km/sec),
's not important, the
matter is this coefficient can
describe any motion without ambiguity.
For example, (Kmax = Klight): a car moves at the speed of
100km/hour - the coefficient here = 0.027, and the speed of
rocket = 2000km/hour, here the coefficient = 0.55 and so
aren't accustomed to it yet? But it's correct.
You'll make sure of it in the further account.
Product of mass into a vector coefficient gives a new independent unit
dimension. Let' denote it . The dimension range
is positive numbers from 0 to ∞.
How shall we call it? The correct name can be a pulse, but
exists already. Our unit has quite different meaning, that's
name it vector
In fifth dimension rectilinear
motion of a
body or several bodies , their possible interaction (
everything is going on in one line) is described.
We are on
the boundary between classic and quantum physics and have
entered the area of vector algebra. Algorithm of
dimensions' construction has been observed, we can start with a new
(By the way, those who would like to travel in 'other' dimensions, the
fifth one suits here well: make some steps - and you
f) sixth dimension
can move not only along a strait line but also in the plane.You'll get
convinced in it when you pour some water on any surface. We'll create
required dimension for describing such processes. I think
not necessary to explain what axis should be added. As a
we get a new independent unit which equals the
As you can see this is the product of two vectors.
but let me remind you: in vector algebra there are
The first one is scalar ?×b×cosφ,
in this case the product equals -0. We aren't going to
examine this version here, bit it should be pointed out that
formula is the basis for the unified field theory. We can discuss it if
'd like to.
is the vector product. This is a new vector with scalar
quantity which equals a×b×sinφ, we have k×i×sin90?
But its direction is perpendicular to the plane of co-ordinates .
Moreover, this vector is non-commutative. Simply speaking, it can be
directed to both sides. (fig.a). What does it mean? I am going to
explain it but at first let's transform this figure.
take one of two possible vectors - the lower one at
first. According to the rules of vector algebra we can
vector (preserving it being parallel). See figure b.
We have already mentioned a jet of water falling down on the
describe similar processes. The jet, when falling down, spread
out at the angle of φ =
but if we pour it in the corner of the room it will spread
the angle of 90°. Similar processes take
we take the second vector. Let's direct a jet of water up from a hose
(ignoring Earth's gravitation) .It concerns non-commutativity.
Please pay attention to the fact how clear the regularity of
dimension's presenting in the form of one axis is exhibited
We have created the next dimension, algorithm has been observed,but we
can't see a new unit of dimension. In fact multiplying
by a coefficient we will not get a new unit . But multiplying this
quantity by a vector
coefficient we get a new unit. This unit has different direction of a
vector. So algorithm has been observed. Here
is vector algebra and everything that we used
( Travelling in this
dimension is possible, but very undesirable).
g) seventh dimension
Substance can move not only along the straight line or in the plane but
also in the volume: sound, light,
explosion and so on.
It's not necessary to describe the construction of this dimension , it
is similar to the preceding dimension.
Let's talk of NEST-DOLLS. The last three dimensions exhibit
phenomenon explicitly: substance when moving "finds"
dimension itself depending on conditions. For example, a flying
stone as it struck the wall scatters - goes from fifth to sixth
dimension. Water running down by a hole from the surface -
from sixth to fifth dimension,
a gun shot - goes from seventh to fifth dimension, and a mere
explosion - goes from fourth to seventh
Now let me explain what sinφ
is. Shortly speaking this sinφ
forms wave gist in any motion.You can ask me a question: what
about rectilinear motion? Let's use vector
here. You know that two and more vectors in the plane or in
can be converged into one vector by means of adding together.
we can present one vector in the form of two or three ones.
Thus rectilinear motion is a particular case of
So the attempt to
explain "the fourth
dimension" has brought us to the creation of a certain
This system permits us
to answer many questions.
Some additional information and
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