Did humans create mathematics or is it an essential part of existence?

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Many believe that mathematics is a human invention. For this way of thinking, mathematics is like language: it may describe things that are real in the world, but they do not “exist” outside the minds of the people who use them.

But the Pythagorean school of thought in ancient Greece had a different view. Its proponents believe that reality is fundamentally mathematical.

More than 2,000 years later, philosophers and physicists began to take this idea seriously.

As Sam Barron, associate professor at Australian Catholic University, argues in a new paper, mathematics is an essential component of nature that gives structure to the physical world.

– Hexagon honeybee

In the hives, bees produce a hexagonal honeycomb. Why?.

According to the “honeycomb conjecture” in mathematics, hexagons are the most effective form of tiling a plane. And if you want to cover an entire surface with tiles of uniform shape and size, while keeping the overall perimeter length to a minimum, hexagons are the shape to use.

Charles Darwin concluded that bees evolved to use this form because they produce the largest cells to store honey for the smallest input of energy to produce wax.

The honeycomb conjecture was first proposed in antiquity, but was only proven in 1999 by the mathematician Thomas Hals.

Here’s another example: There are two subspecies of periodic cicadas (cicadas) in North America that live most of their lives on land. Then, every 13 or 17 years (depending on the subspecies), cicadas appear in large swarms for about two weeks. Why is she 13 and 17 years old?

One explanation calls for the fact that 13 and 17 are prime numbers. Imagine that cicadas have a group of predators that also spend most of their lives in the land. And cicadas need to get off the ground when their predators are asleep.

Suppose there are predators with life cycles of 2, 3, 4, 5, 6, 7, 8 and 9 years. What is the best way to avoid them all?

Compare a 13-year life cycle with a 12-year life cycle. When the cicada with a 12-year life cycle comes out of the ground, the predators of 2, 3 and 4 years will also be extraterrestrial, because 2, 3 and 4 are all equally divided into 12.

When a cicada with a life cycle of 13 years leaves the Earth, none of its predators will leave the Earth, because none of 2, 3, 4, 5, 6, 7, 8, or 9 is evenly divided into 13 and the same is true for 17.

These cicadas seem to have evolved to exploit basic facts about numbers.

Creation or discovery?

Once we start looking, it’s easy to find other examples. From the shape of soap discs, to the design of gears in engines, to the location and size of gaps in Saturn’s rings, mathematics is everywhere.

And if mathematics explains a lot of the things we see around us, then it is unlikely that mathematics is something we invented. The alternative is to discover mathematical truths: not only by humans, but by insects, soap bubbles, combustion engines, and planets.

What did Plato think?

The ancient Greek philosopher Plato had an answer, as he believed that mathematics describes things that already exist.

For Plato, these objects included numbers and geometric shapes. Today, we may add more complex mathematical objects such as groups, classes, functions, fields, and loops to the list.

Plato also asserted that mathematical objects exist outside space and time. But this view only deepens the mystery of how mathematics explains anything.

Interpretation involves showing how one thing in the world depends on another. And if mathematical objects exist in a world apart from the world in which we live, they do not appear to be able to relate to anything physical.

– Pythagoras

The ancient Pythagoreans agreed with Plato that mathematics describes a world of things. However, unlike Plato, they did not believe that mathematical things exist outside of space and time.

Instead, they believed that physical reality is made of mathematical things in the same way that matter is made of atoms.

And if reality is made of mathematical objects, it is easy to see how mathematics can play a role in explaining the world around us.

In the past decade, two physicists have put forward important defenses of the Pythagorean position: Swedish-American cosmologist Max Tegmark and Australian physicist Jane McDonnell.

Tegmark argues that reality is just a great mathematical object. And if that sounds weird, think about the idea that reality is a simulation, a computer program, a kind of mathematical thing.

McDonnell’s view seems even crazier. She believes that reality is made of mathematical objects and minds. And mathematics is how the conscious universe defines itself.

Barron advocates a different view: the world has two parts, mathematics and matter. Mathematics gives matter its shape, and matter gives mathematics its essence. Mathematical objects provide a structural framework for the physical world.

The future of mathematics

It makes sense to rediscover the Pythagoreans in physics.

In the last century, physics has become more and more mathematical, turning to seemingly abstract fields of research such as group theory and differential geometry in an attempt to explain the physical world.

With the blurring of the boundaries between physics and mathematics, it becomes difficult to determine which parts of the world are physical and which are mathematical.

But it is strange that philosophers neglected the Pythagoras for a long time. And it’s time for the Pythagorean revolution, a revolution that promises to fundamentally change our understanding of reality.