(ORDO NEWS) — Many people believe that mathematics is a human invention. In this approach, mathematics is like a language: it can describe real things in the world, but it does not “exist” outside the minds of the people who use it.
However, the Pythagorean school of thought in ancient Greece took a different view. Its proponents believed that reality is fundamentally mathematical.
More than 2,000 years later, philosophers and physicists are starting to take this idea seriously.
As I argue in my new work, mathematics is an essential component of nature, giving structure to the physical world.
Honey bees and hexagons
Bees in hives produce hexagonal combs. Why?
According to the “honeycomb” mathematical hypothesis, hexagons are the most efficient shape to cover a plane. If you want to completely cover the surface with tiles of the same shape and size, while maintaining a minimum perimeter length, then hexagons are the shape to use.
Charles Darwin suggested that bees evolved to use this form because it allows for the largest honey storage cells at the lowest energy cost to produce wax.
The honeycomb hypothesis was put forward in antiquity, but was only proven in 1999 by the mathematician Thomas Hales.
Cicadas and prime numbers
Here is another example. There are two subspecies of the North American periodic cicada that live most of their lives in the ground. Then, every 13 or 17 years (depending on the subspecies), the cicadas appear in huge flocks for a period of about two weeks.
Why is it 13 and 17 years old? Why not 12 and 14? Or 16 and 18?
One explanation has to do with the fact that 13 and 17 are prime numbers.
Imagine that cicadas have a range of predators that also spend most of their lives in the ground. Cicadas need to come out of the ground when their predators are dormant.
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 13 year life cycle and 12 year life cycle. When a cicada with a 12-year life cycle comes out of the ground, two-year-old, three-year-old and four-year-old predators also come out of the ground, because 2, 3 and 4 are divisible by exactly 12.
When a cicada with a 13-year life cycle emerges from the ground, none of its predators will emerge from the ground, because none of 2, 3, 4, 5, 6, 7, 8 or 9 is evenly divisible by 13. Ditto the most true for the number 17.
It looks like these cicadas have evolved to use the basic facts about numbers.
Creation or discovery?
Once we start looking, it’s easy to find other examples. From the shape of a soap film, to the design of gears in engines, to the location and size of gaps in Saturn’s rings, mathematics is everywhere.
If mathematics explains so many of the things we see around us, then it is unlikely that mathematics is something we have created.
The alternative is that mathematical facts are discovered not only by people, but also by insects, soap bubbles, internal combustion engines and planets.
What did Plato think?
But if we discover something, then what exactly?
The ancient Greek philosopher Plato had an answer. He believed that mathematics describes objects that actually exist.
For Plato, these objects included numbers and geometric figures. Today, we can add to this list more complex mathematical entities such as groups, categories, functions, fields, and rings.
Plato also argued that mathematical objects exist outside of space and time. But such a view only deepens the mystery of how mathematics explains anything.
Explanation involves showing how one thing in the world depends on another. If mathematical objects exist in a realm other than the world we live in, then they cannot be associated with anything physical.
The ancient Pythagoreans agreed with Plato that mathematics describes the world of objects. But, unlike Plato, they did not believe that mathematical objects exist outside of space and time.
Instead, they believed that physical reality was made up of mathematical objects in the same way that matter is made up of atoms.
If reality is made up of mathematical objects, then it is easy to see how mathematics can play a role in explaining the world around us.
Over the past decade, two physicists have come out with strong defenses of the Pythagorean position: the Swedish-American cosmologist Max Tegmark and the Australian physicist-philosopher Jane McDonnell.
Tegmark argues that reality is just one big mathematical object. If this seems strange, consider that reality is a simulation. A simulation is a computer program that is a kind of mathematical object.
McDonnell’s view is more radical. She believes that reality is made up of mathematical objects and the mind. Mathematics is how the universe, which has consciousness, knows itself.
I defend a different point of view: the world consists of two parts – mathematics and matter. Mathematics gives form to matter, and matter gives mathematics content.
Mathematical objects provide the structural framework for the physical world.
The future of mathematics
It is quite logical that Pythagoreanism is rediscovered in physics.
In the last century, physics has become more and more mathematical, turning to seemingly abstract areas of study such as group theory and differential geometry in an attempt to explain the physical world.
As the line between physics and mathematics blurs, it becomes increasingly difficult to tell which parts of the world are physical and which parts are mathematical.
But it is strange that Pythagoreanism has been ignored by philosophers for so long.
I believe this will change soon. The time has come for a Pythagorean revolution that promises to radically change our understanding of reality.”
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