THE DIMENSIONS WE LIVE IN

The concept of 'dimension' is something that is interesting to all of us. Thanks to many science fiction texts, the first association that comes to our minds is something that refers to parallel or alternate universes. It is something profound that communicates with us about the deep levels of our existence.

The shortest definition of 'dimension', according to the dictionary, is: "Dimension is a measurement of something in a particular direction, especially its height, length, or width; a part, feature or way of considering something."

The main synonyms for 'dimension' are often 'direction' and 'size'. In Physics, it can also mean any physical measurement such as length, time or mass.

The concept of 'dimension' is so important that famous mathematicians, scientists, philosophers, artists and literary figures have all shown interest in it. They have tried to study and discover the properties of three-dimensional shapes by taking into account one or two of their aspects.

The interest of scientists is more focused on the dimensions we experience in our lives on planet Earth than on comparing them with the dimensions of other objects in the wider universe. There are many questions that remain unanswered because the way we can explore the universe is so limited by our experiences here on Earth.

With the development of technology, it is interesting to see what answers scientists will find to questions such as these: How many dimensions do we live in? Do we live only in three dimensions, or are there others that we are not capable of seeing? Is the situation in the universe the same, or are there many more dimensions? What about time? Is time a different dimension, or do we consider only the physical ones that refer to the concept of space? If we consider time as a dimension, that changes our image of the world, both scientifically and linguistically.

There are many three-dimensional objects in nature.

For example, a point has no dimensions, only position. A point has no size. We show points as dots so that we can see where they are. If we allow a point to move in one direction, we get a line. We need only one value to locate a point on that line. A line is one-dimensional.

If we allow the point to move in a different direction, we get a plane. We need two values to locate a point on that plane. A plane is two-dimensional (2D). If we allow that point to move in another completely different direction, we have three dimensions. A solid is three-dimensional (3D).

In physics and mathematics, the dimension of a mathematical object is informally defined as the minimum number of coordinates needed to specify any point within it. Time is often referred to as the "fourth dimension", and this is one way to measure physical change. In physics, three dimensions of space and one of time are the accepted norm.

There are theories suggesting that there is more to space than we can see, but for now these theories have no experimental evidence to support them. Time is an additional dimension, and together with space it forms a four-dimensional entity called spacetime.

However, architecture, education and dictionaries tell us that space is three-dimensional: the dimensions of height, depth and width within which all things exist and move.

Unlike mathematicians, who have the freedom to experiment with ideas, physics is bound to nature and to material things. As we know, mathematics is useful for describing the world, and if mathematics allows more than three dimensions, how do we know that physical space is limited to only three?

Dimensions are simply the different facets of what we perceive to be reality. We are immediately aware of the three dimensions that surround us on a daily basis—those that define the length, width and depth of all objects in our universe (the x-, y- and z-axes).

Beyond these three visible dimensions, scientists believe that there may be many more. In fact, the theoretical framework of Superstring Theory proposes that the universe exists in ten different dimensions. These different dimensions are believed to govern the universe, the fundamental forces of nature and all the elementary particles contained within it.

The first dimension, as already noted, is that which gives an object length (the x-axis). A good description of a one-dimensional object is a straight line, which exists only in terms of length and has no other discernible qualities.

Add to it a second dimension, the y-axis (or height), and you get an object that becomes a two-dimensional shape (like a square).

The third dimension involves depth (the z-axis) and gives all objects a sense of area and cross-section. A good example is a cube, which exists in three dimensions and has length, width, depth and volume.

Beyond these three lie seven dimensions that are not immediately apparent to us but which can still be perceived as having a direct effect on the universe and reality as we know it.

Mathematicians explore dimensions from different perspectives. They study the properties of 3D shapes, their volume and their surface area. The world around us is full of both 2D and 3D shapes. While some shapes exist only on flat surfaces, others exist everywhere around us.

A 2D shape is a figure that has only length and height as its dimensions. Because 2D shapes lie on a flat surface, they are also known as plane figures or plane shapes. Although they have area, 2D shapes have no volume.

Three-dimensional (3D) shapes are solid shapes. Apart from length and height, a 3D shape also has width or depth as its third dimension. In mathematics and physics, a 2D figure is plotted on two axes, namely the x- and y-axes, whereas a 3D figure is plotted on three axes, namely the x-, y- and z-axes.

3D shapes have faces, edges and vertices and can be viewed from different perspectives. A face is a flat surface. An edge is where two faces meet. A vertex is a corner, or the point where edges meet.

Circle, triangle, square, rectangle and pentagon are some of the most common examples of 2D shapes. Cube, cuboid, sphere, ellipsoid, cylinder, cone, triangular prism, hexagonal prism, triangular-based pyramid, square-based pyramid and hexagonal pyramid are among the most common 3D shapes.

In mathematics, we can also work with higher dimensions as abstract mathematical objects.

Volume is the amount of three-dimensional space inside an object. The two most common measurements of volume are millilitres and litres. A millilitre is a very small amount of liquid. The word millilitre literally means one-thousandth ("milli") of a litre.

When we collect 20 drops of water, we have about 1 millilitre. One millilitre (ml) is also one cubic centimetre (cm³). In other words, one millilitre is exactly the same as a little cube that is 1 cm on each side. One thousand millilitres make up one litre.

Surface area is the total area of all the faces, or the sum of the areas of all the surfaces of a 3D shape. A cuboid has six rectangular faces. To find the surface area of a cuboid, add the areas of all six faces.

We can also label the length (l), width (w) and height (h) of the cuboid and use the formula:

SA = 2lw + 2lh + 2hw

to find its surface area.

Here are the properties of the most common 3D shapes.

Cube – It has 6 faces. Each face has 4 edges and is a square. It has 12 edges. It has 8 vertices (corner points), and at each vertex, 3 edges meet. Six-sided dice are in the shape of a cube, as is the Rubik's Cube.

Cuboid – A cuboid is a box-shaped object. It has six flat faces, and all angles are right angles. All of its faces are rectangles. It is also a prism because it has the same cross-section along its length. In fact, it is a rectangular prism. Cuboids are very common in our world, from boxes to buildings. We can even fit them inside other cuboids.

Cone – It has a circle at one end and a point at the other end, as well as one curved surface. The pointed end of a cone is called the apex. The flat part is the base. A cone is also like a pyramid with an infinite number of sides. A cone can be made by rotating a triangle.

Cylinder – It has a flat base and a flat top. The base is the same as the top. From base to top, the shape stays the same. It has one curved surface. A cylinder is like a prism with an infinite number of sides.

Sphere – It is perfectly symmetrical. All points on the surface are the same distance, r, from the centre. It has no edges or vertices (corners). It has one surface (not a face, as it is not flat). It has the smallest surface area for a given volume. The sphere appears in nature when a surface wants to be as small as possible. Examples include bubbles and water drops.

Square pyramid – It has 5 faces. The 4 side faces are triangles. The base is a square. It has 5 vertices (corner points). It has 8 edges.

Triangular prism – A prism is a solid object with identical ends, flat faces and the same cross-section all along its length. In a triangular prism, the cross-section is triangular.

Triangular pyramid – It has 4 faces. The 3 side faces are triangles. The base is also a triangle. It has 4 vertices (corner points). It has 6 edges.

Torus – It can be made by revolving a small circle (radius r) around a larger circle (radius R). It has no edges or vertices.

How does the concept of different dimensions apply to human life, and in how many dimensions do we live? In how many directions and dimensions do we operate every day? Do we live only in the dimension of our physical body?

Even if we answer "yes" to this question, it does not mean that we stop living in the other dimensions simply because we do not recognise them. Living within the dimensions of our physical body is important. In fact, this is the only way we can see each other with our eyes.

But if we concentrate only on our visible presence and develop only this part of ourselves, there will be so much that we miss in life. Mainly because, if we do not develop in other directions, we will not be able to see them. This is the basic thing that places us on one level with the animals.

What makes us different? What makes us human?

These are the other dimensions of our existence: the dimension of our heart, of our mind and of our soul. They are equally important. If we stop developing one of them, our wholeness as human beings will suffer.

That is why, from our earliest years, we should try to educate not only our brains, which are led by ambition and ego most of the time. We should also educate our hearts and our souls.

There are no words to describe the significance of these two dimensions of our existence. Together, they create our own little personal cosmos, a space with such great power that no physical body is strong enough to conquer the power of the heart.

The way we feel the world is what makes us happy. The purpose of life is not only to know that you are alive, but to feel that you are alive.

This is possible only by regularly nourishing our heart and our soul. We need to nurture these dimensions constantly. So, when we go to the shop to buy food for our body, we should not forget that our heart and our soul need food as well.

Everything that inspires us and gives birth to positive emotions within us is food for them. There is a great variety of this kind of nourishment, and most of it is free.

There is contact with nature—our home—which brings us harmony and peace. There is beautiful art and the therapeutic effect it has on us. The more often we spend time observing different kinds of art, the more we will feel the power of human creativity and the way it transforms divine energy into dimensions that are easy for us to perceive.

There are kindness, care and respect for one another. These three have a profound impact on us, making us better and greater human beings.

There is the practice of cultivating inner peace and silence so that we can hear the other dimensions within us. This, too, is food for our heart and soul.

But above everything stands the dimension of love. This is the most important direction that gives meaning to our lives. Without love, nothing in this world makes sense. Love makes us feel important, noble and needed. Love should be the main nourishment that allows all our dimensions to blossom and develop.

Our health is something very complex. There are six main aspects of personal health: physical, emotional, social, environmental, spiritual and intellectual. These are six dimensions that we need to take care of if we want to consider a person to be in good health.

Each of these dimensions is connected with particular human needs. When these needs are not fulfilled, we suffer, and if this suffering becomes unbearable, we deny that dimension or part of it. Together, they represent both our inner and our outer world, equally important for our well-being.

The spiritual dimension is understood as the need for meaning, purpose and fulfilment in life, as well as hope, the will to live, belief and faith.

The intellectual dimension is the direction that allows us to apply our intellectual abilities, talents, creativity and skills. This leads us towards a life filled with passion and purpose.

The social dimension is the direction of our place in society and our relationships with other people.

The emotional dimension is about being able to express and share love and optimism. This is what strengthens our self-esteem.

The environmental dimension is about developing a higher consciousness. It concerns the way our personal habits, ideas and emotions affect the health of the planet, giving us a sense of collective care and responsibility.

Gravity is a natural force that attracts objects regardless of their position or dimensions, and it is something that should be taken into account.

Emotional gravity is what brings us together. Collective human gravity is an unbeatable force. We should all concentrate on building bridges between these dimensions so that we can connect more easily with one another.

Here are some activities for you:

Activity 1: Can you make a list of all the 3D shapes that you can see around you? They could be objects from nature, from the environment you live in, or even something you have bought from a shop. Can you name these objects using their mathematical names? If you can, now try to describe their properties.

Activity 2: Think about boxes. Which particular 3D shapes can boxes have? Give some examples.

Activity 3: Can you choose two 3D shapes from your list and try to calculate their volume and surface area?

Activity 4: If you had to choose the dimensions in which to live, what would they be? Would you choose four dimensions or even five? Can you explain what the world around us would look like in 4D or 5D? Draw a picture of these dimensions.

(E. S. Lyubenova, LoveMaths Story for My Students)