Pythagoras’ Revenge: Humans Didn’t Invent Mathematics
Many individuals believe that mathematics is a human invention. In this way of thinking, mathematics is like a language: it may define actual things on the planet. However, it does not “exist” outside the minds of the people who utilize it.
However, the Pythagorean school of thought in ancient Greece held a different sight. Its advocates believed reality is fundamentally mathematical.
More than 2,000 years later, physicists and philosophers are beginning to take this idea seriously.
Sam Baron, an associate professor at Australian Catholic University, suggests in a brand-new paper that mathematics is a crucial component of nature that offers structure to the physical world.
Hexagons and honeybees
Why do bees build hives in a hexagonal honeycomb?
According to the “honeycomb conjecture” in mathematics, hexagons are the most practical shape for tiling the plane. Suppose you wish to completely cover a surface utilizing tiles of uniform size and shape while maintaining the overall size of the perimeter to a minimum. In that case, hexagons are the shape to utilize.
Because it produces the biggest cells to hold honey for the smallest input of power to generate wax, Charles Darwin reasoned that bees have actually evolved to utilize this form.
The honeycomb conjecture was first proposed in ancient times. However, it was only validated in 1999 by mathematician Thomas Hales.
Cicadas and prime numbers
Here is another example. There are two subspecies of North American periodical cicadas that live most of their lives in the ground. After that, every 13 or 17 years (depending on the subspecies), the cicadas emerge in huge swarms for around two weeks. However, why is it 13 and 17 years, and not 12 and 14, or 16 and 18 years?
One explanation leans to the fact that 13 and 17 are prime numbers.
Picture the cicadas have a variety of predators that also spend a lot of their lives in the ground. When their predators are lying inactive, the cicadas need to come out of the ground.
Presume there are predators with life cycles of 2, 3, 4, 5, 6, 7, 8, and 9 years. What is the most effective method to avert them all?
Compare a 12-year life cycle and a 13-year life cycle. When a cicada with a 12-year life cycle appears on the ground, the 2-year, 4-year, and 3-year predators will additionally be out of the ground since 2, 3, and 4 all divide uniformly into 12.
When a cicada with a 13-year life cycle emerges from the ground, none of its predators will undoubtedly be out of the ground because none of 2, 3, 4, 5, 6, 7, 8, or 9 divides evenly into 13—the exact same holds for 17.
It seems these cicadas have actually evolved to exploit basic facts about numbers.
Creation or discovery?
It is easy to find other examples once we begin looking. From the shape of soap films to gear design in engines to the location and dimension of the spaces in the rings of Saturn, mathematics is all over the place.
It is not likely that mathematics is something we have created if mathematics explains so numerous things we see around us. Alternatively, mathematical facts are discovered: not just by people, but by insects, soap bubbles, combustion engines, and planets.
What did Plato think?
However, if we are finding something, what is it?
Plato, the ancient Greek philosopher, had an answer. He assumed mathematics defines objects that truly exist.
For Plato, these objects included numbers and geometric shapes. Today, we may add more complex mathematical objects such as groups, categories, fields, rings, and functions to the listing.
Plato likewise maintained that mathematical objects exist outside of space and time. However, such a view only deepens the mystery of how mathematics explains anything.
The explanation includes showing how one thing on the planet depends upon another. If mathematical objects exist in a sphere apart from the world we stay in, they do not appear to connect to anything physical.
Enter Pythagoreanism
The ancient Pythagoreans agreed with Plato that mathematics describes a world of objects. However, unlike Plato, they did not assume mathematical objects exist beyond space and time.
Instead, they thought physical fact is made from mathematical objects like matter is made of atoms.
It is very easy to see how mathematics could play a role in describing the globe around us if reality is made of mathematical objects.
Two physicists have placed significant defenses of the Pythagorean position in the last decade: Swedish-US cosmologist Max Tegmark and Australian physicist-philosopher Jane McDonnell.
Tegmark suggests reality just is one huge mathematical object. Consider the idea that reality is a simulation if that appears odd. A simulation is a computer program, a type of mathematical object.
McDonnell’s view is more radical. She believes reality is made from mathematical objects and minds. Mathematics is exactly how the Universe, which is aware, comes to know itself.
Baron defends a different perspective: the world has two parts, mathematics and matter. Mathematics gives matter its type, and matter offers mathematics its substance.
Mathematical objects offer a structural framework for the physical world.
The future of mathematics
It makes good sense that Pythagoreanism is being found in physics.
In the past century, physics has become increasingly more mathematical, resorting to relatively abstract fields of inquiry such as group theory and differential geometry to describe the physical world.
As the limit between mathematics and physics blurs, it becomes more challenging to state which parts of the world are physical and mathematical.
However, it is weird that Philosophers have overlooked Pythagoreanism for so long.
Baron believes that will change. The moment has arrived for a Pythagorean revolution, one that promises to modify our understanding of reality substantially.
Read the original article on The Conversation.
