Wednesday , January 20 2021

Why is the divine world of Plato where mathematics is still so important? BBC News



Where do math come from? It is a matter with which some of the most eminent mathematical minds were discussed.

Some believe that we discover them, others that we invent; some think that they are part open pie and part invented, while some confess that they do not know it.

The jury is very divided.

But there is something that all sides had to consider before taking part: the ideas of Plato, one of the most important figures of ancient Greece.

What the famous philosopher said has remained until this day based on what many scientists think about the origin of mathematics.

Fundamental but separate

In ancient Greece, there was no doubt because everything seemed to indicate that mathematics is something we discover.

Figure not sky
Will they be in a separate world?

For Pythagoras and their followers, they were a window in the world of gods.

But there are 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.

Plato
Plato had the answer.

In another kingdom

The philosopher was fascinated by the geometric shapes that could have been produced following the rules of mathematics, which he believed were from deities.

To understand what he said, we will use a flat and closed curve in which all points are at the same distance from the center.

Better said, a circumference.

It is likely that he would have to draw one at a time, that he tried to look good and that surely worked for you, even if it is not perfect.

So, he had access to the world's most accurate computer, the circumference he draws would not be perfect either.

Circles
Very good! But it is not perfect.

Proper approach and any physical circumference, as well as the circle that determines, will have bumps and imperfections.

According to Plato, it is because circumferences and immaculate circles do not exist in the real world; The perfect circle lives in a divine world in perfect forms, a kind of sky where you can find all the mathematics, but only if you are a true believer.

5 objects

The philosopher was also convinced that everything in the cosmos could be represented by five solid objects known as o platonic solids.

Thus, the Earth was the solid stone cube. The fire was the very pointed tetrahedron. The air was the octahedron, while the icosahedron, with its 20 triangular sides, represented water.

The last platonic solid, the dodecahedron, encapsulated the entire Universe.

There is something special about platonic solids. They are the only objects in which all sides have the same shapeand there are only five.

No matter how hard you try, you will never find another object with these unique mathematical qualities.

the tetrahedron, the cube (or the hexahedron), the octahedron, the dodecahedron and the icosahedron
The tetrahedron, the cube (or hexahedron), the octahedron, the dodecahedron and the icosahedron are also called perfect solids, platonic polyhedrons and cosmic bodies, among others.

All these forms, considered Plato, existed in a world of perfect forms beyond our reach: mere mortals, a place we call the platonic world.

Although these ideas seem a bit crazy, there are many people who believe in them and those people seem to be well.

"Platonic solids are for me A great example of mathematics are discovered instead of inventing"says Max Tegmark, professor of Physics and Mathematics at the Massachusetts Institute of Technology (MIT).

"When the ancient Greeks discovered that they existed, they could invent their names." The man of 12 factions was called a dodecahedron. But the very pure dodecahedron was already there to be discovered, "says Tegmark.

"I have the platonic vision that there are triangles, numbers and circles around," says the philosopher of physics Eleanor Knox. They are part of this mathematical landscape I'm exploring. "

platonic solids
All mathematicians know about this platonic world in which the perfect forms live, but not everyone believes in it.

But not everyone believes in this Platonic world of mathematical truths.

"I think that the Platonic world is in the human head"says the 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, spend their days and evenings thinking and investigating that field," says Brian Green, professor of physics and mathematics at Columbia University.

"That does not mean it's real", decrees.

Plato would not agree.

He encouraged us to believe in this other world where all the mathematics could be found, and do not be fooled And think that the world around us is everything there is.

What we perceive as reality, he warned, is nothing more than shadows.

Two millennia later …

More than 2,000 years ago, Plato took the geometry of forms as evidence of the influence of God, ideas that were limited to the senses and the imagination.

Today, Geometry is at the forefront of science.

New technologies allow us to observe the world beyond our senses and, once again, it seems that the natural world is really written in the language of mathematics.

This is a virus model.

virus
A virus with a recognized geometric shape.

Immediately, you will notice its geometric shape: it is one of the platonic solids.

Reidun Twarock, professor of mathematics at the University of York, colleagues designed a computer simulation that puts the mathematician at the center of the virus.

"What we try to understand is how this virus is formed and for that we create the illusion of being within the virus, in the position where the genetic material is normally," explains BBC Reidun.

Then they discovered that the virus takes advantage of the power of mathematics to build its exterior wall the fastest and most efficient way possible.

Viruses
If you know how viruses use mathematics to make their geometric shapes, you can find a way to stop them.

Armed 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.

This is what makes this research so exciting.

Revealing the maths that allow the virus to form its envelope can give us the way to interrupt it. Without outer wall, there is no virus; No viruses, no infection.

Discovered or invented?

Beyond the reach of human senses, it seems that the Universe knows in some way mathematics.

Really The frequency with which these patterns appear is surprising. They are in plants, they are in marine life, even in viruses.

And every time 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 sustains the world around us and that we do not do anything but discover mathematics.

But maybe we were looking for patterns in the wrong places.

If everything is in our heads, then the brain could be a good place to look.


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