INFINITY

The purpose of my texts is not to try to say everything about a topic—not at all—mainly because that is impossible.

Even a whole book, for example, about infinity will never be able to say everything. In a book, you always choose what to present and what to leave for the next one.

My main purpose is to make you think not only about the specific topic, but also to try to find the connections between everything in real life, where there are no limitations or borders to our imagination and knowledge.

So let us challenge ourselves. This is the only way to continue developing.

There is no limit to development.

Remember what I said: Thinking (together with love) is one of the greatest joys we can experience.

Human curiosity is actually a wonderful example of infinity.

The topic of infinity is so interesting and so vast that I would need a great deal of paper and time to say everything I would like to say about it.

Don't worry—I will try to keep it short.

Infinity is not really a strictly mathematical topic, although mathematics contains many examples of the idea of infinity.

Remember, we said that the language of mathematics reflects real life and the life of nature. It tries to find an abstract way, using symbols, to express reality so that we can later use its tools to continue exploring life.

It is like a circle. There is no beginning and no end. Everything is one.

The idea of infinity appears in nature, in human life, in religion, in human languages (there is vocabulary related to infinity), in art, in philosophy, in science and in the language of mathematics as well.

The idea of infinity is not about something that is big, huge or enormous. No, because if we say that something is big, then there is always something bigger. Things in life often exist in pairs, and we can compare them.

The concept of infinity is about something that is endless. There is a symbol that represents infinity. It looks like the number 8 turned on its side. Our human brain is designed in such a way that it understands limitations.

That allows us to measure things, count them and visualise them. Only then do we feel calm because we have a sense of control. Our human brain struggles with the idea of infinity and may even begin to panic.

Mainly because we cannot visualise infinity. We cannot touch it. We cannot measure it or count it.

Basically, we cannot control infinity. And that is a real reason for panic. 

Let us first try to find the presence of infinity in mathematics. Infinity is actually simpler than things that do have an end. Because when something has an end, we have to define exactly where that end is.

Remember the number π (pi)?

It is a good example of an infinite sequence of digits.

In geometry, a line has infinite length.

A line extends endlessly in both directions. (Not a ray or a line segment, which have beginnings, ends and directions!)

The sequence of natural numbers never ends and is therefore infinite.

Recurring decimals also represent the idea of infinity very well.

There are infinitely many points on a line.

Even a short line segment contains infinitely many points.

There are some truly astonishingly large numbers.

And there are even larger numbers that require the use of "power towers" to write them down.

But none of these numbers is even close to infinity.

They are all finite.

Eventually, we could reach them.

Infinity does not behave like a real number.

We can add numbers to infinity, and the result is still infinity.

We could continue looking for mathematical infinity in set theory, for example.

Infinity is not a number.

It is an idea.

Since the time of the ancient Greeks, the nature of infinity has been the subject of many discussions among philosophers.

In 1655, the infinity symbol (called the lemniscate, meaning "ribbon" in Latin) was first introduced by the English mathematician John Wallis.

Ancient cultures had various ideas about the nature of infinity.

However, they did not define infinity with the precise formalism of modern mathematics.

Instead, they approached infinity as a philosophical concept.

In nature, there are many processes that seem infinite because they repeat themselves endlessly—growth, expansion and the continual renewal of nature.

Yet even these processes eventually come to an end.

In religion, people have applied the idea of infinity to the idea of God.

God is the One who created everything visible and invisible.

But He is much more than that.

His powers are infinite, at least from our human perspective.

Every culture and every civilisation has had—and still has—its own understanding and application of the idea of infinity.

In our little material human lives, everything has an end. The material world, created by people, is highly mortal. And here comes something that is close to infinity—immortality. For us as human beings, perhaps the best way to imagine infinity is to imagine that we are immortal, that people have no end and live forever. This comes very close to the idea of God, the Creator of everything we see, feel and think, and of everything that is invisible to human eyes. Is infinity God Himself? Probably. We do not know. But because our human brain is built in such a way that it needs to be in control, we feel sad and powerless whenever something lies beyond that control. Yes, our human power is very limited.

Infinity does not grow. It does not do anything. It simply is. It is not a real number; it is an idea, a concept. Even those distant galaxies cannot compete with infinity. Space, with its vast capacity to contain things, is often thought of as infinite. But even space continues to expand and change. Infinity does not change, because change implies the existence of a beginning and an end. Well, my brain is already beginning to panic. I am too small to embrace such a vast idea.

Cosmologists have long tried to discover whether infinity exists in our physical universe. Are there infinitely many stars? Does the universe have infinite volume? Does space go on forever? These remain open questions, not only in cosmology but in science as a whole.

I have two activities for you.

Activity 1: Can you make a list of things that are infinite to you? Can you make a list of things in nature and in mathematics that you believe are infinite?

Activity 2: If you had some kind of superpower, what would you choose to last forever and be infinite? Would it be human life, or something else? Please name at least five things.

In our everyday lives, we see countless examples of kindness, goodness, support, love, intelligence, courage and curiosity. We cannot imagine our lives without these wonderful qualities of human nature. Life would be a sad and cold place without them. The important thing is not to be sad that our lives are not endless. No, we know that infinity is not possible for our physical lives. But let us imagine filling our days with countless acts of kindness towards others. Let us imagine filling our hearts with the love we long for. Let us imagine filling our minds with the peace and calm we seek.

Let us imagine all this, especially now, when everybody is isolated from others and each person feels like an island. The important thing now is to build a network of kindness so that we do not forget how to be kind, how to love and how to think. Even small acts of kindness online can make a big difference to other people.

Now, while nature outside is preparing to reveal its colourful beauty once again, and we cannot be there to admire it, when everything outside is unusually quiet, it is important to remember what makes us human.

Love and thinking.

These are what make us a special species.

There should be no limits to sharing them.

Make your days infinite with countless signs of love and thoughtful reflection!

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