Can you see what is not yet written?
We are living in a time when the human being, the human form and the world is being rewritten. The speed of progress for the last 100 years has been amazing. A world is dying, and a new one will emerge. You should listen to the talk of Leonard Brody and look at these videos.
We cannot teach and learn as it was done before with the classical methods of learning. We need to find ways to develop a growth mindset and be able to understand the framework that is being built right now in the world.
we need cross-fertilization and all our curiosity to explore and understand. We have to read what is written to guess what is not yet written.
We should start the adventure by creating an intimate space for freedom. The first condition for developing creativity is to protect a 'freedom soft spot' within yourself. This is preliminary work, an incubation period. For this part, I suggest a few keys requirements as silence, solitude and meditation, but recognize these are very personal and may take different forms for different people.
The second condition is based on a requirement that is fundamental for everyone: movement. This is also why I created walking seminars. Artists, poets, writers, philosophers and scientists have used it for centuries to stimulate their creativity and develop their thinking process. Now comes the third element; Learning to see.
The history of science and mathematics is a wonderful odyssey that teaches us lessons that we should always keep in mind. Learning to see is certainly one of the most important. The first scientific approach began with the observation of the relationship between heaven and earth... From astronomy to writing, through to counting, many things were invented quickly 5000 years ago. The Sumerians, our ancestors, began a scientific approach, trying to understand the links between heaven and earth. The sky was their reference, they watched it carefully, seeking answers to their questions.
Numbers are a beautiful adventure. From the invention of the zero, as a placeholder in the absence of a quantity, in India and China via Persian and Arab scholars through to hesitation in choosing the most convenient base: 12, 60 (of which there are traces in the months of the year or the angles) and then finally 10.
THEY WERE DOING THE IMPOSSIBLE.
WHO DARED TO INVENT THE ZERO?
WHO DARED TO INVENT THE IRRATIONAL NUMBERS?
Irrational number were an early confrontation with infinity, and, with good reason, caused a stir among mathematicians.
Human beings have imagination; there is absolutely no doubt about that! In their day, those who invented the zero, irrational numbers and imaginary numbers were pretty audacious and creative, don't you think?
In 2011, one of my favorite places for contemporary art in Paris, La Fondation Cartier pour l'Art contemporain presented an extraordinary exhibition on Mathematics for their thirtieth birthday and invited famous artists and scientists to share their points of view. The curator was the movie director, David Lynch. If you can read French, here is the post I wrote on the topic at that time. The exhibition was inspirational and very poetic.
Among the stories this one is very pecular and extraordinary:
"For Vanuatu Islands people, for example, patterns drawn in the sand play a very important role in social life: sometimes almost ordinary messages, sometimes works of art or expression of myths and sacred rituals. Their complexity points to the theory of entrelacs, idealized objects created by mathematicians, but for which the people of Vanuatu had developed a kind of classification," explained Jean-Pierre Bourguignon.
Just by observing very carefully, we can learn and discover so many things. Jean-Pierre Bourguignon also wrote in the exhibition catalogue:
"Free creation may be the shortest path to solve a persistent mathematical problem on which so much attention has been put on that we don’t realize the existence of a missing link that could lead us to the solution. Often a radical shift in the way of thinking is needed for a solution to appear. This shift could happen by chance in a sharing context. It is not possible to program it. This context will be easier to create if the protagonists are not too specialized, and if external advice is systematically required. Seeking this sudden shift is as valid for engineers as for scientists." Jean-Pierre Bourguignon, chief scientist, IHÉS, Polytechnique School in Paris in MATHEMATICS, A BEAUTIFUL ELSEWHERE
STRIDING INTO THE FIELD OF MATHEMATICS
This exhibition showed how mastering the infinite, infinitely large or infinitely small, was one of the great achievements of the seventeenth century, first in Japan by Skei Takakazu, then in Europe by Leibniz and Newton.
"It was then possible to speak of limits and thus instantaneous speed, the rate of infinitesimal increase of the position, and acceleration, a gigantic conceptual leap which helped formulate the fundamental law of dynamics.
In the same vein, Isaac Newton constructed a mathematical model of the incredible efficiency of celestial mechanics, a major challenge posed to humans, which was finally resolved with definitive precision if we ignore the influence of two formed by the Sun and a planet.
These advances have accompanied the operational formulation of major theories of physics, leading to evolving equations. Therefore mechanics, physics and mathematics have constantly fertilized each other; issues arising from conceptual advances of the first two being so many challenges for the third, and conceptual advances in mathematics opening new possibilities for physics and mechanics, as was the case with Einstein's general theory of relativity.
What is also very impressive is to discover the things that they accomplished even before the theory existed, for example the Alhambra in Granada.
Exploring other patterns… famous tilings found in the architectural and decorative jewel in the Islamic tradition: the Alhambra in Granada. A mathematical theorem prohibited the existence of more than 17 different kinds of motifs. This reflects the inventive and methodical genius of Moorish artists of the fourteenth century.
Cross-fertilization between cultures allowed the development of universal and productive thinking tools
Almost all conceptual advances have given rise to various calculations:
- calculus (XVIe S.)
- logarithms (by John Neper, XVIIe S.)
- differential calculus (Newton and Leibniz)
- numerical calculus
- symbolic calculus (imposed by physicists to mathematicians, Laurent Schwartz)
- stochastic calculus (Kiyoshi Itô (decisive for finance)
- binary calculus (by which computers handle literals of a size that would render them inaccessible by humans exploration)
The role of these methods is to make effective and usable concepts by many engineers and scientists. The Result: Many fields become accessible as models to simulate complex systems, weather, climate, the behaviour of an aircraft wing in a flow of air, the activity of a molecule to test a new drug…
It took boldness to those who have dared to imagine these theories may seem absurd at first, the great lesson we learned from the history of science: We need to keep an open mind... What seems so improbable can become possible. It's not new that cross-fertilization is a great source of innovation, the crossing of disciplines and fields is often an enrichment.
DO WE INVENT THINGS?
DO WE DISCOVER THEM?
The famous periodic tilings of the plane that is found in the architectural and decorative jewel of Islamic tradition that is the Alhambra in Granada. There are exactly 17 really different kinds, and there can be more of a mathematical theorem prohibited. But the theorem was not invented yet when the Moorish artists achieved this masterpiece!
These are just some examples presented at this superb exhibition, Mathematics, A Beautiful Elsewhere. where six famous scientists and six famous artists were invited to work together. The purpose was to let mathematics and mathematicians speak out by giving them the opportunity to brainstorm with major artists from the world of contemporary art. The catalogue was conceived as a discussion forum for the mathematicians and artists, an opportunity for them to exchange ideas and share their thoughts on the most important questions relating to mathematics.
A combination of written texts, questionnaires and portraits, the catalogue also illustrates the diversity of mathematical thoughts—as expressed by the scientists as well as the artists—and emphasizes the importance of creativity in this field. Among the scientist invited, Cedric Villani shared his excitement to explore the complexity of the word. If you haven't listened to his Ted Talk yet, he is a great storyteller don't miss it.
Learning to see is the job of any good scientist and artist. And this observation is driven by an insatiable curiosity. One that best embodies this is Leonardo da Vinci. You can read my post: In The Mind of a Genius.
Leonardo studied spirals and swirls of water. This inspires a revolutionary theory - questionable for the time - in which the movement of water is comparable to the movement of the hair, which can move in two ways depending on the weight of the hair or the orientation of the loops. It analyzes the water in terms of lines of force. Another unlikely combination.... in connection with intense observation.
Please share your comments. How curiosity led you to a discovery in the past?