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 to 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.

Point of departure

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 that any 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 of 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.

Fig.1.

c) second dimension

This ray originates from the point of the beginning of co-ordinates angle-wise 90degrees to the ray of the first

dimension. (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 triangle, 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 its sides 0,5m and 2m, in the form of a triangle, in this case its

Fig.2 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 dimension we can describe plane geometric figures and lines and their mutual disposition in the plane. Mathematics here is planimetry and algebra.

d) third dimension

Look at the figure.

You have already understood that cubic measure here can be in the form of a parallelepiped, a pyramid and so on

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, differential calculation.

Fig.3

Here comes the analysis itself.

It consists in successive comparison of each dimension with the previous one and the searching for possible regularities on this basis. Don't forget that absolutely everything equals nought in zero dimension.

1. The first 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 of dimension from 0 to infinity. This dimension includes the 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 infinity 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. This dimension includes all the previous ones.

Here we have such phenomenon as NEST-DOLLS.

Note: it's very important to understand

Conclusions: 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..

The obtained regularity determines algorithm of consistency in dimensions' costruction.

4.Fourth dimension.

Three dimensions are depicted in fig.4. In order to construct fourth dimension one more axis should be drawn. Drawing it in the 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 co-ordinates ( 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 all 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 three 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, because this dimension has already included the previous one. Here the unit of measure is an agreed area.

c) Third dimension

It can also be represented in the form of one axis. Here the unit of measure is an agreed cubic content.

/ The same order is valid for the following dimensions /

d) Fourth dimension

In order to describe substance which is characterised by density, let's draw a corresponding axis. As a result we obtain a new independent 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. Algorithm is observed.

It is actually the fourth dimension. Properties of substance: state of aggregation of matter ( for example: gas, liquid), atomic structure,etc. is presented in Chemistry.

Let's proceed and create the fifth dimension.

e) fifth dimension

According to algorithm it must be the product of mass… into 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 the existence of an abstract

For example, (Kmax = Klight): a car moves at the speed of 100km/hour - the coefficient here = 0.027, and the speed of the rocket = 2000km/hour, here the coefficient = 0.55 and so on. You 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 of 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 this term exists already. Our unit has quite different meaning, that's why let's name it vector mass ().

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 dimension.

(By the way, those who would like to travel in 'other' dimensions, the fifth one suits here well: make some steps - and you are there).

f) sixth dimension

Substance 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 the required dimension for describing such processes. I think it's not necessary to explain what axis should be added. As a result we get a new independent unit which equals the product ×. As you can see this is the product of two vectors. Sorry, but let me remind you: in vector algebra there are two multiplications:

The first one is scalar ?×b×cosφ, as φ=90

The second is the vector product. This is a new vector with scalar quantity which equals a×b×sinφ, we have k×i×sin90

We have already mentioned a jet of water falling down on the plane. Here we describe similar processes. The jet, when falling down, spread out at the angle of φ = 360°, but if we pour it in the corner of the room it will spread out at the angle of 90°. Similar processes take place if 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 here.

We have created the next dimension, algorithm has been observed,but we can't see a new unit of dimension. In fact multiplying quantity 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 mathematics is vector algebra and everything that we used before.

( 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 this phenomenon explicitly: substance when moving "finds" necessary 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 - goes from sixth to fifth dimension,

a gun shot - goes from seventh to fifth dimension, and a mere explosion - goes from fourth to seventh dimension and so on.

Now let me explain what

So the attempt to explain "the fourth dimension" has brought us to the creation of a certain system. This system permits us to answer many questions.

Some additional information and examples

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