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


Where does math come from? It is a question with which some of the most eminent mathematical minds have been discussed.

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

The jury is very divided.

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

What the famous philosopher said remains to this day the basis of what many scientists think about the origin of mathematics.

Fundamental but separate

In Ancient Greece there was no doubt, for everything seemed to indicate that mathematics is something we have discovered.

Figure in the sky
Will they be in a world apart?

For Pythagoras and his followers, they were a window into the world of the gods.

But there is more: although they are a fundamental part of the world in which we live, they are, somehow, strangely separated from it.

Trying to make sense of this seeming paradox is a crucial point. the dilemma about the origin of mathematics.

And that's what Plato did.

Plato had the answer.

In another kingdom

The philosopher was fascinated by the geometric forms that could be produced following the rules of mathematics, which he believed to come from divinities.

To understand what he said, let's use a closed flat curve in which all points are equal to the distance from the center.

Or rather, a circumference.

It is likely that you have already had to draw one, that you have tried to look good and that it has worked well for you, although it is not perfect.

So you had access to the most accurate computer in the world, the circumference you draw would also not be perfect.

Very well! But not perfect.

Approaching a lot and any physical circumference, just like the circle that determines, will have bumps and imperfections.

According to Plato, this is because flawless circumferences and circles do not exist in the real world; the perfect circle lives in a divine world of perfect forms, a kind of heaven where you can find all 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 known as O platonic solids.

Thus, 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 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'll never find another object with these unique mathematical qualities.

the tetrahedron, the cube (or 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 polyhedra and cosmic bodies, among others.

All these forms, Plato believed, 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 these people seem to be sensible.

"Platonic solids, for me, are a great example of how mathematics is 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 were able to invent their names." The 12-sided man was called a dodecahedron. But the pure dodecahedron itself was already there to be discovered, "says Tegmark.

"I have the Platonic view that there are triangles, numbers, circles around," says physics philosopher Eleanor Knox. they are part of this mathematical landscape I'm exploring. "

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

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," is a product of our imagination, "he adds.

"I understand the people who really believe in this other realm of reality and, in particular, spend their days and nights thinking and researching about that realm," says Brian Green, a professor of physics and mathematics at Columbia University.

"This does not mean it's real"he decrees.

Plato would have disagreed.

He encouraged us to believe in that other world where all mathematics could be found, and not to be deceived and to think that the world around us is all that exists.

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

Two millennia later …

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

Nowadays, Geometry is at the forefront of science.

New technologies have allowed us to look at the world beyond our senses and, once again, it seems that the natural world is actually written in the language of mathematics.

This is a model of a virus.

A virus with a recognized geometric shape.

Immediately, you will notice its geometric form: it is one of the Platonic solids.

Reidun Twarock, a professor of mathematics at York University, designed a computer simulation that puts 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, in the position where genetic material is normally found," he told the BBC Reidun.

Then they discovered that the virus harnesses the power of mathematics to build its outer wall as quickly and efficiently as possible.

If you know how viruses use math to create their geometric shapes, you may 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.

That's what makes this research so exciting.

Revealing the math that allows the virus to form its envelope can give us the way to stop it. Without outer wall, there is no virus; no virus, no infection.

Discovered or invented?

Beyond the reach of human senses, it seems that the universe somehow knows math.

Really It is amazing how often these standards seem to arise. They are in plants, they are in marine life, even in viruses.

And every time we add more things we can explore and explore using the math 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 nothing but discover the mathematics.

But we may have looked for patterns in the wrong places.

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



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