From morning to night,
From dusk to light?
That Thing,
Like a foreboding shadow,
A shadow that brings terror and fright,
Threatening to engulf the sunlight,
That Thing,
Like the cloak of darkness,
That comes with the frosty night,
Hiding everything nice from sight.
That Thing,
Like the screen of gold,
That hides the darkness and pity
Of the dying leaves in autumn,
That Thing.
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| by Suzanne Zahr |
With a rustle,
With a creak,
The wind sweeps through
The shaking shrub.
Swirls playfully,
And worries the tree,
Like a child bouncing on granny’s knee.
A few golden leaves flutter,
And fall to the floor,
Like old grey hairs,
From an old man’s scalp.
The wind tugs off a few more,
And picks them up tenderly,
So that they, the dead,
Can come and dance
Among the folds of Autumn’s lively dresses.
* * *
Новата ми книга 'LoveMaths Stories' може вече да се намери в Амазон.
Here is the link:
What makes a good person?
The idea of patterns has accompanied human life since the early years of human civilisation. It is an abstract and very powerful idea which holds human life in order and gives it good structure. Everything we do in life is subject to rules, models and repetitions. Since we were born, this has been the only way to discover the world around us, by following certain patterns.
In every area of our work or personal life, we obey some models, examples and rules. This is the only way to learn new things by investigating and identifying the forces that cause the patterns. We learn by repeating knowledge in a certain way, following certain patterns.
A pattern is a way in which something is done or organised, or in which something happens. We can talk about weather patterns, behaviour patterns, shape patterns, colour patterns and many other types of patterns depending on the nature of the activities we are involved in.
The idea of patterns is an abstract philosophical one with great applications in every aspect of human life. Whatever we do, we instinctively organise ourselves in a way that repeats itself again and again throughout space in an identical but not random way. Especially if the patterns are a good model and show progress and development, we tend to keep them for the next time as well.
A lack of everyday patterns that we could follow is a signal to our brain of chaos and can cause mental health problems. We will feel lost and frustrated, as if something is not right. We naturally like patterns and recognise them; it is part of our human intelligence. We cannot imagine our lives separated from patterns because the ability to organise ourselves in a specific way and to maintain this way is what makes us human as well. Pattern recognition is what allows us to do everything from recognising individuals and people's emotional states to solving jigsaw puzzles and sensing when a storm is about to come.
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| Marc Chagall, The blue bird |
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.
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| Lucy Pittaway 'The Joy Of Spring' |
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| Vassily Kandinsky 'Squares with Concentric Rings' |
For centuries, people have been fascinated by circles. Many scientists, philosophers, mathematicians, artists and religious thinkers have worked with the symbol of the circle, giving it different meanings according to its applications in real life.
There is one great reason for this interest. Above us in the sky, every day, we can see the great and magical solar circle. People depend on the Sun in so many ways. It gives us warmth and light, and it is always up there like a loyal friend. People throughout the world have regarded the solar circle as a very important symbol in their cultures.
In mythology, the Sun is usually a symbol of the divine and of a supreme God. It is full of mysterious power. The shape of the Sun is circular. For centuries, people have felt both great respect and fear towards it. Even people in ancient cultures realised that the Sun was something they could not control and that its behaviour could not always be predicted, so they could not ignore the giant circle. It was like a great ball that could bring either life or destruction.
All the changes happening to that giant circle affected human lives in many ways. Solar eclipses, for example, were seen as very bad signs, warning people of God’s punishment. Therefore, in many cultures, the Sun represented God Himself.
The circle is a universal symbol with many meanings. It represents totality, wholeness, original perfection, the Self, infinity, eternity, timelessness and all cyclical movement. As a symbol of God, the circle has no visible boundary. Or perhaps it is simply beyond human power to find and calculate the circumference of the circle when it is understood as a symbol of God. Its circumference is everywhere; there are no limits. From a spiritual point of view, God is also the centre.
The symbol of the circle also implies the idea of movement. It symbolises the cycle of time, the motion of everything that moves, the planets’ journeys around the Sun, the circle of the zodiac and the great rhythm of the universe. The circle is also represented by zero in our number system and symbolises potential or the embryo. It has magical value.
In this short reflection of ours, we are not going to write about the characteristics of a good teacher; we will do this separately. Here, we will try only to defend the student's right to have a good teacher.
Every student deserves a good teacher who will make him want to fly.
Education is a two-sided process - teaching and learning. There should be an equal effort and an equally honest attitude towards the process in order to achieve something.
Teachers are the most important people in schools. Together with the students, they create the image of education. But if the students still have a more dependent role, the teachers' role is the leading one. The quality of teaching and learning depends on the teachers. And although there are plenty of brilliant professionals in schools, and they make up maybe 90% of the teachers, there is still a percentage of teachers who are simply not fit for the role.
The role of the teacher is extremely demanding and challenging but, on the other hand, extremely rewarding. The teacher should not only be a brilliant expert in their subject but also a great communicator and a big fan of the students. To be a teacher means that you have a passion and love in your heart for the students. To be a good teacher means that you will always do what is right for the students, no matter how hard this is for you. It means that you have almost angelic patience. You will need a lot of patience.
Teachers create the students' memories, and the care for the students' well-being and learning should always come first. All that means that you have to embrace in your heart the philosophy of Humane Pedagogy, not the philosophy of Authoritarian Pedagogy.
Time and space are the two main features that describe our existence. Every second of our lives, we are located somewhere. We cannot describe our activities separately from time and space. After the question "When?" comes immediately the question "Where?"
Time remains one of the most mysterious aspects of the world in which we live. It connects our existence with the past, the present and the future in one continuous process. Many philosophers and scientists are still trying to define the concept of time.
Time is so fundamental to our lives that we cannot imagine our everyday existence without measuring it, as if life were one continuous process. The human brain is designed in such a way that it feels more comfortable and secure when everything is structured and organised. Without time, there would be great chaos. We need time to plan our lives and make them more organised.
Time management is important in our daily lives. We tend to think that we can manage time. Yet time moves only forwards, never backwards.
Don't lie to children so that they can learn to be honest.
Love children so that they can learn to love.
Talk to children so that they can learn to communicate.
Listen to children so that they can learn to listen.
Be patient with children so that they can learn patience.
Trust children so that they can learn to trust others.
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| Ramona Matei Art |
Money has had a long journey through human societies. It has gone through barter deals and the exchange of goods, metal coins, copper coins, gold and silver coins, paper notes, debit and credit cards, before transforming into something we call electronic money.
Today, we live in societies in which money is almost invisible. It has a discreet but powerful electronic presence.
But what is money?
I am sure we all know the answer to this question and, even more, that we all have some kind of connection with money itself or with the idea of money.
Writing about money can take many different directions. In this text, we will look at the historical development of money, how money is used in mathematics, and the influence of money on our lives.
Money is best described as a medium of exchange. The concept of money has been around since the dawn of human civilisation. Money allows individuals to trade what they have for what they need or want.
What has been considered money has varied throughout the ages and has included many different items. Currently, there are over 150 currencies used worldwide. Seventy per cent of the world's monetary value is denominated in the U.S. dollar, the euro, the U.K. pound, the Japanese yen and the Chinese yuan.
Money has been part of human history for almost 3,000 years. From the origins of bartering to modern money, this is how the system has evolved.
At the dawn of humanity, bartering was used instead of money to obtain goods. One of the earliest forms of barter included cattle, sheep, vegetables and grain.
The first known currency was created by King Alyattes in Lydia, now part of modern-day Turkey, around 600 BC. The first coin ever minted featured a roaring lion. Coins later evolved into banknotes around AD 1661. The first credit card was introduced in 1946.
Money is a means of exchanging wealth indirectly, rather than directly through barter. It is a mechanism that facilitates this process. Money may take a physical form, such as coins and banknotes, or it may exist as an electronic or written record.
People are always interested in their future, and what will happen tomorrow is sometimes more important to us than what is happening today. Tomorrow is like compensation and a gentle form of revenge for us. Most people are fascinated by tomorrow. What will our life look like? Am I going to be richer and prettier? It is like an escape from today, because today is always guilty of something.
That is why we often try to predict the future. Sometimes our predictions are based on what we know, and we have several possibilities to choose from. In this case, we simply use techniques and methods to determine which possible events are more likely than others. This kind of predictability is the subject of mathematics.
When our predictions are not based on real facts, it is difficult to decide which event has a greater chance of occurring in the future. In this case, it is like playing a blind game with no certain rules.
In this short text, it will not be possible to describe everything that is somehow related to probability. We will simply try to open the door and allow curiosity to come in.
There are many situations in real life where we have to take a chance or a risk. Based on certain situations, the likelihood of a particular event occurring can often be predicted. In simple words, the chance of a particular event occurring is what we study in probability.
Здравей, мой малки приятелю!
Отново ти пиша аз, врабчето Рошко! Надявам се, че си бил послушно дете, докато очакваше следващото ми писмо! Много е важно да слушаш родителите си, защото те знаят кое е най-добре за теб и много те обичат! Надявам се, че вече си се настанил удобно, защото имам да ти разказвам разни неща за големи приключения.
Пиша ти в момента от Средната английска земя. Правилно си се досетил, че тя се намира по средата на страната Англия. Тук е родното място на един голям английски поет – Уилям Шекспир. Ще научиш повече за него, когато станеш голям и тръгнеш на училище.
В градчето Уорик пък се намира един от най-старите средновековни замъци на Англия – той така и се нарича: „Замъкът Уорик“. Потрепервам само при споменаването му, защото тук ми се случи нещо, което бих искал по-скоро да забравя. Но ще побързам да ти го разкажа, защото, ако първо аз го забравя и не го разкажа на никого, няма да има кой да помни доброто, което дойде след ужасното приключение.
My short LoveMaths text this time is about Roman numerals. Roman numerals are very interesting for many historical and cultural reasons, and it is a pity that they have such limited use today and are almost forgotten.
Roman numerals are the numbers that the ancient Romans used. This is just a short reminder about these beautiful numerals, which are still very much alive on some occasions, although they have limited and more specific uses.
One of their greatest disadvantages is that they form very long strings of letters.
Rome was the capital of the vast Roman Empire, which encompassed almost the entire continent of Europe, along with Mediterranean territories in Asia and Africa.
The Roman Empire was one of the most powerful empires of the ancient world. Historians believe that the earliest Roman settlements began in 753 BC.
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| (Blenda studio) |
Mathematics is the universal language of our environment, helping people to explain and create.
"When am I ever going to use maths?" Students often wonder if, when and how they will ever use maths in real-life situations.
The truth is that we use maths all the time!
But how well do we know, and how well do we remember, the language of mathematics?
Let us try to answer this question.
If we know the language of mathematics relatively well, do we use it in our everyday lives?
Everybody uses the language of mathematics to some extent in their daily life. We are often so used to this language that we do not even think about how grateful we should be to mathematics for developing its symbolic language, which serves us in so many ways.
Let us try to remember and summarise some of the applications of maths that we all use without being mathematicians.
The language of mathematics is part of human civilisation. In fact, it has helped to shape human civilisation and culture.
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.
Writing about symmetry is both a great challenge and a great joy. It is a challenge because, like the topic of infinity, it is all around us, yet it is so profound and deep that there is a great risk that, by trying to say something, we may fail to say very much at all. I am willing to take this risk, mainly because I am not trying to achieve the impossible—to say everything. No, that would require much more research and much more knowledge than I have at the moment.
I will simply try to lift the curtain on the topic and make connections, on the one hand, with the mathematical language of symmetry and how it reflects real life in order to develop practical tools for describing and working with symmetry. On the other hand, as we have mentioned many times, mathematical language developed from people's practical needs to solve practical problems, so we also need to make connections with other areas.
Symmetry is one of the most fundamental ways in which nature structures itself. It is one of the laws of nature that we humans simply imitate in our everyday activities. We are naturally attracted to symmetry.
When you hear the words symmetry and symmetrical, what is the first association that comes to your mind? Is it something beautiful? And what about asymmetrical? Are your associations less positive? If so, don't worry—you are not alone.
The idea and the principles of symmetry lie at the very foundation of how we see, perceive and understand the world. Symmetry is what holds different parts of the world together and makes them more pleasing to the eye. Everything is in harmonious proportion when it is symmetrical. Nature itself is governed by the principle of symmetry, which creates balance rather than chaos. In many ways, symmetry represents order—a beautiful, peaceful and well-ordered world. It helps us make sense of the world around us.
The Language of Love Is Silent
You're trying to speak to me in your language, but I don't understand you. You make awkward gestures, trying to show me what your words fail to convey. I listen to hear, to understand, to feel, to ease your awkwardness, to shorten the distance between us. We speak different languages, but it is the sparkle in our eyes that brings us closer. Desperate because your words do not reach me, you sink into silence, and only your eyes look at me intently. They look at me as though I am the one who lights the fire within them. And then I understand everything. You become so excited that you spontaneously embrace me as a sign of apology and humility. And suddenly everything is clear without words. Because you speak the language of love.
But today you are different, and I do not understand the language of your silence. Today you are different, and you speak to me in the language of indifference. You change every day, and I fail to learn your language, to understand your heart and the way it expresses itself.
One day you are yourself, and the next you dissolve into everything, living and inanimate. I want to learn to understand you, to find you. You want to learn to understand me so that you do not lose me.
Езикът на любовта е мълчалив.
Ти се опитваш да ми говориш на своя език, но аз не те разбирам. Правиш някакви конфузни жестове, опитвайки се да ми покажеш онова, което думите ти не успяват да предадат. Аз цялата съм слух, за да те чуя, да те разбера и да те усетя, да направя твоето смущение по-малко, да скъся разстоянието помежду ни. Ние говорим на различни езици, но блясъкът в очите ни е това, което ни сближава. Отчаян, че думите ти не достигат до мен, потъваш в тишина и само очите ти напрегнато ме гледат. Гледат ме така, все едно аз съм онова, което запалва огъня в тях. И тогава разбирам всичко. А ти си толкова развълнуван, че спонтанно ме прегръщаш като знак на извинение и смирение. И така всичко е ясно – без думи. Защото ти говориш на езика на любовта.
Но днес ти си различен и аз не разбирам езика на твоето мълчание. Днес ти си различен и ми говориш на езика на безразличието. Ти се променяш всеки ден, а аз не успявам да науча твоя език, за да разбирам твоето сърце и начина, по който то се изразява.
Един ден ти си себе си, а след това се разтваряш във всичко живо и неживо. Аз искам да се науча да те разбирам, за да те намеря. Ти искаш да се научиш да ме разбираш, за да не ме изгубиш.
Let us ask ourselves: why do we learn mathematics? For calculations and applications. And for inspiration. The connection between mathematics and nature is inspiring and makes us think. Mathematics teaches us how to think. It is not just about solving for x. It is also about discovering how and why.
The Fibonacci sequence is one of the most famous patterns in mathematics. It has been part of human knowledge for centuries. It proves once again that we cannot draw a line separating one field of knowledge from another. If we do so, it is only for practical reasons, such as educational subjects and examinations. More often than not, we borrow knowledge and theories from different disciplines in order to gain a better understanding of our own.
The Fibonacci numbers show us that the whole universe is interconnected—the fabric of space itself, the galaxies, nature and human knowledge, all striving to understand the bigger picture. The Fibonacci sequence entered mathematics through observations of the natural world and inspired ancient mathematicians to find logical and practical explanations for natural phenomena that everyone could observe.
From the Fibonacci sequence, we can calculate the Golden Ratio, and from the Golden Ratio comes the spiral. The spiral can be seen throughout the natural world and across the universe. We encounter this pattern everywhere. The spiral is both a mathematical and a spiritual symbol of life, energy and rebirth. It is like the thread that holds everything together. It is like God's signature, reminding us that everything—from immense galaxies to the smallest fingerprints—has been created according to the same spiral design. It is the spiral that keeps everything in the universe connected and in order.
I will try to compare natural human languages and mathematical language in an attempt to answer the question: "Is Maths really a language?"
This is a very big question that would require a great deal of writing. My purpose, however, is not to make you feel bored, but to spark your curiosity about the topic so that you will continue exploring it on your own. That is why I will make this comparison only briefly.
Mathematics is very often called a language, and it is true that it is used as a tool in many other areas of human knowledge. Think of engineering, science, geography and almost every other discipline—they all use mathematics in one way or another. It seems that the language of mathematics exists to serve other fields by offering them a wide range of tools: arithmetic, statistics, graphical methods of representing knowledge, probability for risk assessment, geometry for construction and engineering, and algebra, which is sometimes so annoying with its constant effort to find x in our lives.
But this is exactly what we do very often in our own lives—we become detectives trying to solve our own little mysteries. So we can agree that mathematics is present in every aspect of our personal and professional lives.
What is a natural human language, then? By natural, I mean languages that are spoken by people and have developed over many centuries. They may be official national languages or dialects, which are spoken locally and do not have official status. There are more than 6,000 languages in the world, and many of them are disappearing, mainly because of migration. Some languages are spoken by hundreds of millions of people, such as English, Arabic, Russian and Spanish. Others are much smaller, and some are even micro-languages.
