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 with something that refers to parallel or alternate universes. It is something profound that communicates to us about our deep levels of 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; part or feature or way of considering 'something'.

As main synonyms of ‘dimension’ often are used ‘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 people have shown interest in it. They have been trying to study and to find the properties of three-dimensional shapes by taking into account one or two aspects of theirs. The interest of the scientists is more about the dimensions we experience in our life on the planet Earth than comparing it with what we know of the dimensions of other objects in wider space. There are many questions that stay without answers 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 the scientists will get about it - How many dimensions do we live in? Do we live only in three dimensions, or are there others which 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, the scientific and the linguistic one. There are many three dimensional objects in nature.

But for example, a point has no dimensions, only position. A point has no size. We show them as dots so we can see where they are. If we allow the point to move in one direction we get a line. We need only one value to find 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 find 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 are 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 that there is more to space than we can see, but for now, those 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. But the architecture, the education and the 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 to describe the world and if mathematics allows more than three dimensions, how do we know that physical space is limited to three?

Dimensions are simply the different facets of what we perceive to be the 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 universes (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 the Superstring Theory posits that the universe exists in ten different dimensions. These different aspects are what govern the universe, the fundamental forces of nature, and all the elementary particles contained within.

The first dimension, as already noted, is that which gives it 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 2-dimensional shape (like a square).

The third dimension involves depth (the z-axis) and gives all objects a sense of area and a cross-section. A good example of this is a cube, which exists in three dimensions and has a length, width, depth and volume. Beyond these three lies the seven dimensions which 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 are exploring the dimensions from different perspectives. They study the properties of the 3D shapes, their volume and surface area. The world around us is full of shapes of 2D and 3D shapes. While some shapes exist only on flat surfaces, others exist everywhere else.

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. While they have areas, 2D shapes have no volume.

3-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 the 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 points.. A face is a flat surface. An edge is where two faces meet. A vertex is a corner, or 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 the most common 3D shapes.

In mathematics, we can have more dimensions, as artificial objects.

Volume is the amount of 3-dimensional space inside. 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. 1 millilitre (ml) is also 1 cubic centimetre (cc). In other words, 1 millilitre is exactly the same as a little cube that is 1 cm on each side (1 cubic centimetre). 1000 millilitres make up 1 litre.

Surface area is the total area of all the faces, the sum of the areas of all faces (or surfaces) in a 3D shape. A cuboid has 6 rectangular faces. To find the surface area of a cuboid, add the areas of all 6 faces. We can also label the length (l), width (w), and height (h) of the prism and use the formula, SA=2lw+2lh+2hw, to find the 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) at each vertex 3 edges meet. 6-sided dice are in the shape of a cube as well as the Rubik’s cube.

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

Cone - It has a circle at one end and a point at the other end. And a curved side. The pointy 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 side. 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 isn't flat). It has the smallest surface area for a 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) along a line made by a bigger circle (radius R). It has no edges or vertices

How does the concept of different dimensions apply to our human life and in how many dimensions do we live? In how many directions and sizes do we operate every day in? Do we live only in the dimensions of our physical body? Even if we say yes to this question it doesn’t mean that we will stop living in the other dimensions only because we don’t recognise them. Living in the size and direction of our physical bodies is important. Actually, this is the only way we can see each other, through our eyes. But if we concentrate too much only on our visible presence and if we develop only this part, there will be so much that we will miss in our life mainly because if we don’t develop in other directions, we will not be able to see them. This is the basic thing that puts 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 our soul. They are equally important. If we stop developing one of them, our wholeness as humans will suffer. That’s why since the early years we should try to educate not only our brains, which are led by our ambitions and by our ego most of the time. We should try to educate our hearts and our souls. There are no words to describe the significance of these two dimensions of our existence. They both create our little personal cosmos, space which has such a great power that there is no physical body with such a strength able to conquer the power of the heart. The way we feel the world is what makes us happy. The purpose of this life is not only to know that you are alive but to feel that you are alive. This is possible to happen only by giving regular food to our heart and to our soul. We need to constantly nurture this dimension. 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 inside of us is food for them. There is a variety of this kind of food and most of it is free. There is contact with nature - our home that harmonises us and makes us peaceful. This is the beautiful art and the therapeutic effect that 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 how it transforms the divine energy into dimensions which are easy for us to perceive. This is the kindness, the care and the respect for each other. These three have a huge impact on us, making us better and bigger. The exercise to activate inner peace and silence inside in order to hear the other dimensions in us, this is food for them as well. But above everything stays the dimension of love. This is the most important direction that gives meaning to our life. Without love, nothing makes sense in this world. Love makes us feel important, noble and needed. Love should be the main food for all our dimensions to blossom and to develop.

Our health is something very complex. There are six main aspects of personal health: physical, emotional, social, environmental, spiritual, and intellectual. And these are six dimensions to take care of if we want to consider the individual to be in good health. Each of the dimensions is connected to special needs. When these needs are not fulfilled, we suffer and if this suffering becomes unbearable, we deny the dimension or a part of it. They represent the internal and the external world, equally important for our wellbeing.

The spiritual dimension is described and is interpreted as the need for meaning, purpose and fulfilment in life, hope and 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 will lead us to a life filled with passion and purpose. The social dimension is the direction of our place in society, our relationships with others. The emotional dimension is about being able to express and to share love and optimism, this is what will improve our self-esteem. The environmental dimension is about developing higher consciousness. About how 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 to attract objects regardless of their position and dimensions, it is something that should be taken into account. Emotional gravity is what brings us together. Collective human gravity is an unbeatable force. And we all should concentrate on building bridges between the dimensions so we connect easily with others.

Here are some activities for you: Activity 1: Can you make a list of all 3D shapes that you can see around yourself? They could be objects from nature or in the environment you live, or even something bought from a shop in that shape. Can you name these objects using the mathematical names for them? If you did this, now try to describe their properties. Activity 2: It is about boxes - what particular 3D shape could the boxes be? Give examples. Activity 3: Can you choose two 3D shapes from your list and to try to calculate their volume and surface area? Activity 4: If you have to choose in what dimensions to live, what it would be? Would it be four dimensional or even five dimensional? Can you explain how the world around would look like in 4D or 5D shapes? Make a picture of these dimensions.

(E. S. Lyubenova; Lovemaths Story for my students)