INFINITY

The purpose of my texts  is not to try to say everything about the topic, not at all, mainly because this is not possible. Even a book, for example, about Infinity will not be able to say everything, in a book you always choose what to present and what to leave for the next book. My main purpose is to make you think not only about the specific topic but to try to find the connection between everything in real life, where there are no limitations and borders of our imagination and knowledge. So let’s challenge ourselves, this is the only way to develop ourselves more and more. There is no limit of development. Remember what I said: Thinking (together with Love) is one of the best joys we can experience. This is actually a good example of Infinity - human curiosity. 

The topic of Infinity is so interesting and bigger that I will need a lot of paper and time to say what  I would like to say about it. Don’t worry, I will try to keep it short. 

Infinity is not really a strictly a Maths topic, although in Maths there are examples of the idea of infinity. Remember, we said that mathematical language reflects real life and the life of nature and tries to find an abstract way with symbols to express it so later we can use its tools to carry on exploring life. It is like a circle. There is no beginning and end, everything is one. The idea of infinity is applied in nature, in human life, in  religion, in human languages (there is vocabulary about infinity), in art, in philosophy, in science and in Maths language as well.

The idea of infinity is not about something that is big, huge, large, enormous. No, because if we say that something is big that means that there is something that is bigger, things in life exist in pairs and we could compare them. The concept about  Infinity is about something that is endless. There is a sign that represents infinity and it is the number 8 but in a horizontal way. Our human brain is designed in a way that we know what are limitations, so we can measure things, count them and visualise them. Only then we feel calm that we are in a kind of control. Our human brain struggles with the idea of infinity and even feels like panicking. Mainly because we cannot visualise the infinity, we cannot touch it, we cannot measure or count it. Basically, we cannot control the infinity, it is a real cause for panicking.

Let’s try to find the presence of infinity in Maths first. Infinity is actually simpler than things which do have an end. Because when something has an end, we have to define where that end is. Remember the number ‘Pi’? This is a good example of an infinite chain of numbers.  In Geometry a Line has infinite length. A Line goes in both directions without end (Not a Ray and Line segment, which have end, beginning and directions!). The sequence of natural numbers, never ends and is infinite. Recurring numbers   represent the idea well. There are infinite points in a Line. Even a short line segment has infinite points. There are some really impressively big numbers. And there are even larger numbers that need to use "Power Towers" to write them down. But none of these numbers are even close to infinity, they are finite, we could eventually ‘get there’. Infinity does not behave as a real number. We can add numbers to infinity and we will get infinity at the end. We can carry on looking for mathematical infinity in sets theory for example. Infinity is not a number, it is an idea. 

Since the time of the ancient Greeks, the nature of infinity was the subject of many discussions among philosophers. In the 17th century (1655) was  the first introduction of the infinity symbol ('lemniscate', means 'ribbon' in Latin) by John Wallis, an English mathematician. Ancient cultures had various ideas about the nature of infinity. But they did not define infinity in precise formalism as does modern mathematics, and instead approaches infinity as a philosophical concept. 

In nature - there are many processes that repeat themselves for ever and they look infinite - growing, expanding, rebirth of nature, but even in these cases they have an end. 

In religion - people applied the idea of infinity into the idea of God. God is somebody, who created everything  visible and invisible. But He is much more than that. His powers are infinite, at least in our human understanding. Every culture and every human civilisation they had and they have their own applications of the idea of infinity. 

In our little material human lives everything has an end. The material world, built by people, is highly mortal. And here it comes something that is close to infinity - immortality. For us as humans maybe the best way to imagine infinity is to imagine that we are immortal, that people don’t have an end and they live forever. This is so close to the idea of God, the Creator of everything we see, feel, think, of everything which is invisible for human eyes. Is infinity the God Himself? Probably, we don’t know. But because our human brain is built in a way that has to be in control, for everything that is out of this control we feel sad and powerless. Yes, our human power is so limited. 

Infinity does not grow. It does not do anything, it just is. It is not a real number, it is an idea, a concept. Even these faraway galaxies can't compete with infinity. The space and its vast possibilities to include things is something that humans think is infinite. But even the space keeps growing and changing. The infinity does not change because the change requires the image of the beginning and end of something. Ok, my brain is starting to panic already. I am too small to embrace this vast idea. 

Cosmologists have long sought to discover whether infinity exists in our physical universe: Are there an infinite number of stars? Does the universe have infinite volume? Does space ’’go on forever’’?  This is an open question not only for cosmology.   

I have two  activities for you:

1) Activity 1: Can you make a list of things which are infinite to you? Make a list with things which you think in nature and in Maths are infinite? 

2) Activity 2: If you have some kind of superpower what would you make to last forever and to be infinite? Is it our human life or something else? Please name at least 5 things.

In our everyday life we see countless examples of infinite kindness, good, support,  love, intelligence, courage, curiosity. We cannot imagine our life without these wonderful signs of human nature. Life would be a sad and cold place. The important thing is not to be sad that our life is not endless. No, we know that the infinity for our physical life is not possible. But let’s imagine that we try to fill our days with countless nice gestures to the others. Let’s imagine that we fill our heart with the love we want. Let’s imagine that we fill our mind with the peace and calm we want. Let’s imagine all this, especially now when everybody is isolated from the others and everybody is like an island. The important thing now is to build the net of kindness so we don’t forget how to be kind. So we don’t forget how to love and how to think. Even  kind gestures online to others could make a big difference for them. Now when outside nature is on its way to show its colorful beauty for endless time and we cannot be closer to admire it. When outside is so quiet in an unusual way, it is important to remember what makes us humans. Love and thinking. This is what makes us more special species. There should not be limitations of sharing this. 

Make your days infinite with a lot of signs of love and thinking!

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