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Where exactly do mathematics come from? It is a question with which some of the most eminent mathematical minds have been discussed.
Some people think that we discover them, others that we invent them; some think they are both discovered and invented, while others confess that they do not know it.
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.
Try to make sense of that. to appear the paradox is a crucial point of the problem of the origin of the mathematics .
And that's what Plato did.
In another kingdom
The philosopher was fascinated by geometric forms that could be produced according to mathematical rules, which he believed to come from deities.
To understand what he said, let's use a flat, closed curve in which all his 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 beautiful and that everything is going well, without being perfectly perfect.
Thus, you would have access to the most accurate computer in the world, the circumference to be plotted would not be perfect either.
Get close enough and any physical circumference, as well as the circle that it will determine, will have protuberances and imperfections.
According to Plato, it is because circumferences and impeccable circles do not exist in the real world; the perfect circle lives in a perfect-form divine world a kind of paradise where all mathematics can be found, 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 known as the Platonic Solids .
So, 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 about them. These are the only objects in which all the faces have the same shape and there are only 5.
So difficult it is, you will never find another object presenting these unique mathematical qualities.
All these forms, Plato believed, existed in a world of perfect forms that were beyond our reach – mortal simulations – a place we call the Platonic world .
These ideas may seem a little crazy, there are many people who believe in them and who look like strings.
"Platonic solids, for me, are an excellent example of discovering mathematics instead of inventing it ," says Max Tegm ark, professor of physics and mathematics at the Mbadachusetts Institute of Technology (MIT ).
"When the ancient Greeks discovered that they existed, they were able to invent their names, the 12-sided one called it the dodecahedron. But the pure dodecahedron itself was already there said Tegmark
"I have the Platonic view that there are triangles, numbers, circles," says physics philosopher Eleanor Knox – All are all part of this mathematical landscape that I am exploring. "
] But not everyone believes in this Platonic world of mathematical truths.
"I believe the Platonic world is in the human head ," says astrophysicist Hiranya Peiris. "This is a product of our imagination"
"I understand people who truly believe in this other realm of reality and, in particular, if they spend their days and nights thinking and doing things. research in this area, "said Brian Green, professor of physics and mathematics at the University of California. Columbia University
" That does not mean it's real ," he says.
Plato would not have agreed.
He encouraged us to believe in this other world where all mathematics could be found, and to not let us add and think that the world around us is everything what exists.
What we perceive as a reality, he warned, is nothing but shadows.
Two millennia later … …
Over 2,000 years ago, Plato took shape geometry as evidence of God's influence, ideas limited to the senses and to the imagination .
Today, Geometry is at the forefront of science
New technologies have allowed us to look at the world beyond our senses and, again, seems that the natural world is really written in mathematical language.
This is a virus model.
You will immediately notice its geometric shape: it is one of the Platonic solids.
Reidun Twarock, professor of Amathematics at York University, his colleagues devised 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 creates the illusion of being inside the virus., In the position where is normally found genetic material, "he told BBC Reidun.
They discover that the virus exploits the power of mathematics to build its outer wall in the fastest way possible. and effective as possible.
With this knowledge, Reidun is trying to find a way to prevent can develop viruses like hepatitis B and even colds.
That's what makes this research so exciting.
The virus forming 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 realm of the human senses, it seems that the Universe knows mathematics one way or another.
Really is surprising. frequency with which these models seem to emerge . They are in plants, they are in marine life, even in viruses.
And whenever we add more things we can explore and exploit using the mathematics we have.
All this suggests that there is a natural order that feeds the world around us and that we are only discovering mathematics.
But perhaps we looked for models in the wrong places .
If everything is in our heads, then the brain could be a good place to look.
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