[ad_1]
Copyright of the Image
Getty Images
We Wondered if Mathematics was Invented or Discovered .. Today, we give the word to Plato.
Where 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 Separate
In ancient Greece, there was no doubt because everything seemed to indicate that mathematics was something we discovered.
Copyright image
Getty Images
Will they be in a world apart?
For Pythagoras and his disciples, they were a window on the world of the gods.
- Why the Greeks of Antiquity thought that mathematics was a gift from 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.
Trying to make sense of this apparent paradox is a crucial point in the problem of the dilemma relating to the origin of mathematics .
And that's what Plato did.
Copyright of the Image
Getty Images
Plato had the answer.
In Another Realm
The philosopher was fascinated by the geometric shapes that could be produced according to the mathematical rules, which he thought came from deities.
To understand what he said, let's use a flat curve. and closed in which all its 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.
Thus, you would have access to the world's most accurate computer and the circumference to be plotted would not be perfect either.
Copyright picture
Getty Images
Very good! But not perfect.
Get close enough and any physical circumference, as well as the circle that determines, will have bumps 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 divine world of perfect forms 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, 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 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.
The tetrahedron, the cube (or hexahedron), the octahedron, the dodecahedron and the icosahedron are also called perfect solids, platonic polyhedra and cosmic bodies, among others.
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 .
Although these ideas may seem a little crazy, there are many people who believe in them, and these people look like strings.
"Platonic solids, for me, are an excellent example of discovering mathematics instead of inventing ", Max Tegmark, professor of physics and mathematics at the Institute of Mbadachusetts Technology (MIT).
"When the ancient Greeks discovered that they existed, they were able to invent their names, the twelve-sided one called the dodecahedron." The pure dodecahedron itself already existed said Tegmark.
"I have the Platonic view that there are triangles, numbers, circles," says physics philosopher Eleanor Knox – "All ". ] are part of this mathematical landscape that I am exploring. "
Copyright
Getty Images
All mathematicians know the existence of this Platonic world in which live perfect forms, but do not believe all of them.
But not everyone believes in this Platonic world of mathematical truths.
"I think 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.
" This does not mean that it is real ", decrees.
Plato would have disagreed.
He encouraged us to believe in this other world where we could find all the mathematics, and to not be fooled and to think that the world around us is all that There is.
What we perceive in reality, he warned, are only shadows.
Two Millennia Later …
More than 2,000 years ago, Platon considered geometry of forms as proof of God's influence. the senses and 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, it seems that the Natural world is actually written in mathematical language.
This is a virus model.
Recognized geometric form virus.
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 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 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.
If you know how viruses use mathematics to create their geometric shapes, you can find a way to stop them.
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 mathematical calculations that allow 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 one way or another about mathematics.
Really surprises the frequency with which these models seem to emerge . They are in plants, they are in marine life, even in viruses.
- Mathematics … do we invent them or discover them? A Millennial Debate Without Solution
And whenever we add more things we can explore and exploit with the help of the mathematics we have.
All this reinforces the idea that there is a natural order that supports the world around us. and that we are only discovering mathematics.
But perhaps we looked for reasons in the wrong place .
If everything is in our head, the brain could be a good place to look.
Next week: Is there any evidence in the brain that mathematics be an invention of human mind ?
Do not forget that you can receive notifications from BBC News World. Download the new version of our application and activate them to not miss our best content.
Source link
