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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 that they are both discovered and invented, while others confess that they do not know.
The jury is very divided.
But all parties had to take into consideration before taking sides: the ideas of Plato, one of the most important figures of ancient Greece. A renowned philosopher stated that it remained to this day the basis of what many scientists think of the origin of mathematics.
Fundamental but Separated
In ancient Greece, there was no doubt that everything seemed to indicate that mathematics was something we discovered.
For Pythagoras and his followers, 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 in the problem of the dilemma of the origin of mathematics .
And that's what Plato did.
In another kingdom
The philosopher was fascinated by the geometric shapes that could be produced following the rules of mathematics, from the pseudo they came from the deities.
To understand what he said, let's use a flat, closed curve where 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 beautiful and that it has worked for you, although not quite perfect.
If you had access to the most accurate computer in the world, the circumference you traced would not be perfect either.
Do not stray from the circumstance, as well as more specific information. 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 called the platonic solid .
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 about them. These are the only objects in which all faces have the same shape and there are only 5.
Despite all your efforts, you will never find another object with these qualities unique mathematics.
All these forms, Plato believed, existed in a world of perfect forms and out of our reach – simulacra of mortals – a place we call the platonic world [1945900] ]. 19659002] Although these ideas may seem a little crazy, many people believe in them and seem to be healthy in spirit.
"Platonic solids, for me, are an excellent example of mathematics discovered in Instead of Inventing Them ," says Max Tegmark, professor of physics and mathematics at Mbadachusetts Institute of Technology (MIT) .
"When the Greeks of the day discovered that they existed, they were able to invent their names, the dodecahedron .. But the dodecahedron itself was already to be discovered ," says Tegmark.
"I have the Platonic view that there are triangles, numbers, circles Eleanor Knox, philosopher in physics, all of them are part of this mathematical landscape that I am currently working on. to explore. "
But not everyone believes in this platonic world of mathematical truths. The Platonic world is in the human head "says astrophysicist Hiranya Peiris. It is a product of our imagination, "he adds.
" I understand people who truly believe in this other realm of reality and in particular, if you spend your days and nights thinking about and do research in this area, "says Brian Green, professor of physics and mathematics at Columbia University.
" That's not to say it's real ] ", decree.
Plato would have disagreed.
He encouraged us to believe in this other world where all mathematics can be found, and not to be fooled and to think that the world around us is everything, what is there
Two Millennia Later …
More than 2,000 years ago, Plato considered the geometry of forms as a proof of the influence of God, the senses and the imagination
Today, geometry e 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 immediately notice its geometric shape: it is one of the platonic solids.
Reidun Twarock, a professor of mathematics at the University of York, 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 we create for it the illusion of being in the virus, in the position where the genetic material is normally found ", he explains to BBC Reidun.
that the virus exploits the power of mathematics to build its outer wall in the fastest and most efficient way possible.
Armed with this knowledge, Reidun is looking to find a way to prevent the development of viruses such as hepatitis B and even the common cold.
This is what makes this research so interesting.
Revealing the calculations allowing the virus to form its envelope can give us a way 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 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 gives weight to the idea that there is a natural order that supports the world around us and that we do not do. more than the discovery of mathematics.
But perhaps we looked for reasons in the wrong places .
If everything is in our head, the brain could be a good place to look.
Next week: Is there any evidence in the brain of these mathematics to be an invention of of the human spirit ?
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