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Where do mathematics come from? It is a question with which some of the most eminent mathematical minds have been discussed.
Some believe that we discover them, others that we invent them; some think that they are both discovered and invented, while others confess that they do not know.
The jury is very divided.
But there is something that all parties had to take into account before taking sides: the ideas of Plato, one of the most important figures of ancient Greece.
What the famous philosopher has said remains to this day the basis of what many scientists think of the origin of mathematics.
Fundamental but separate
In ancient Greece, there was no doubt that everything seemed to indicate that mathematics was something we discovered.
For Pythagoras and his disciples, they were a window on the world of the gods.
But there is more: although they are a fundamental part of the world in which we live, they are, in a way, strangely separated from it.
Trying to make sense of this apparent paradox is a crucial point the dilemma on the origin of mathematics.
And that's what Plato did.
In another kingdom
The philosopher was fascinated by the geometric forms that could be produced according to the rules of mathematics, which he believed to come from divinities.
To understand what he said, let's use a flat, closed curve in which all points are equidistant from the center.
Better said, a circumference.
It is likely that you have already had to draw one, that you have tried to make yourself look good and that it has worked for you, although not quite perfect.
Thus, you have access to the most accurate computer in the world, the circumference that you trace would not be perfect either.
Approach sufficiently and any physical circumference, as well as the circle that determines, will have bumps and imperfections.
According to Plato, this is because circumferences and flawless circles do not exist in the real world; the perfect circle lives in a divine world with perfect forms, a kind of heaven where you can find all the math, but only if you are a true believer.
5 objects
The philosopher was also convinced that everything in the cosmos could be represented by 5 solid objects called the platonic solids.
So, the Earth was the solid rock cube. The fire was the very pointed tetrahedron. The air was the octahedron, while the icosahedron, with its 20 triangular sides, represented the water.
The last platonic solid, the dodecahedron, encapsulated the entire universe.
Platonic solids have something special. These are the only objects in which all sides have the same shapeand there are only five.
Whatever your efforts, you will never find another object with these unique mathematical qualities.
Plato believed that all these forms existed in a world of perfect forms beyond our reach: mere mortals, a place we call the platonic world.
Although these ideas may seem a little crazy, many people believe in them, and these people seem to be healthy in spirit.
"The platonic solids, for me, are an excellent example that mathematics is discovered instead of inventingsaid Max Tegmark, professor of physics and mathematics at the Massachusetts Institute of Technology (MIT).
"When the ancient Greeks discovered their existence, they were able to invent their names." The man with the twelve faces called the dodecahedron. But the pure dodecahedron itself was already there to discover, "says Tegmark.
"I have Platonic vision that there are triangles, numbers, circles," says physics philosopher Eleanor Knox. they are part of this mathematical landscape I am exploring. "
But not everyone believes in this Platonic world of mathematical truths.
"I believe that the Platonic world is in the human head", says astrophysicist Hiranya Peiris," it's a product of our imagination, "he adds.
"I understand people who really believe in this other realm of reality and, in particular, they spend their days and nights thinking and doing research in this area," says Brian Green, professor of physics and mathematics at Columbia University.
"That's not to say that it's real", decrees.
Plato would have disagreed.
He encouraged us to believe in this other world where all mathematics could be found, and do not be fooled and to think that the world around us is all that exists.
What we perceive as a reality, he warned, is nothing but a shadow.
Two millennia later …
More than 2,000 years ago, Plato took shape geometry as proof of God's influence, ideas limited to the senses and the imagination.
Today & # 39; hui, Geometry is at the forefront of science.
New technologies have allowed us to look at the world beyond our senses and, again, it seems that the natural world is actually written in mathematical language.
This is a virus model.
Immediately, you will notice its geometric shape: it's one of the platonic solids.
Reidun Twarock, professor of mathematics at York University, his colleagues designed a computer simulation that places the mathematician at the center of the virus.
"What we are trying to understand is how this virus is formed and for that, we create the illusion of being inside the virus, where the material normally lies. genetics, "he told BBC Reidun.
So they discovered that the virus takes advantage of the power of mathematics to build its outer wall in the fastest and most efficient way possible.
With this knowledge, Reidun is trying to find a way to prevent the spread of viruses such as hepatitis B and even the common cold.
That's what makes this search so exciting.
Revealing the mathematics that allow the virus to form its envelope can give us the means to interrupt it. Without an outside wall, there is no virus; no virus, no infection.
Discovered or invented?
Beyond the reach of the human senses, it seems that the Universe knows somehow mathematics.
Actually it's amazing how often these trends seem to emerge. They are in plants, they are in marine life, even in viruses.
And each time we add more things we can explore and exploit using the mathematics we have.
All of this suggests that there is a natural order that supports the world around us and that we are only discovering mathematics.
But maybe we looked for models in the wrong places.
If everything is in our heads, the brain could be a good place to look.
Next week: Is there any evidence in the brain that mathematics is an invention of human spirit?
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