Seashells display a Golden Spiral
Nature is an unstoppable force, and a beautiful one at that. Everywhere you look, the natural world is laced with
stunning patterns that can be described with mathematics. From bees to blood vessels, ferns to fangs, math can explain how such beauty emerges.
Math is often described this way, as a language or a tool that humans created to describe the world around them, with precision.
But there's another school of thought which suggests math is actually what the world is made of; that nature follows the same simple rules, time and time again, because mathematics underpins the fundamental laws of the physical world.
This would mean math existed in nature long before humans invented it, according to philosopher Sam Baron of the Australian Catholic University.
"If mathematics explains so many things we see around us, then it is unlikely that mathematics is something we've created," Baron
writes.
Instead, if we think of math as an essential component of nature that gives structure to the physical world, as Baron
and others suggest, it might prompt us to reconsider our place in it rather than reveling in our own creativity.
© Westend61/Getty Images
A world made of mathThis thinking dates back to Greek philosopher
Pythagoras (around 575-475 BCE), who was the
first to identify mathematics as one of two languages that can explain the architecture of nature; the other being music. He thought all things were made of numbers; that the Universe was 'made' of mathematics, as Baron
puts it.
More than two millennia later, scientists are still going to great lengths to uncover where and how mathematical patterns emerge in nature, to answer some big questions - like why cauliflowers look
oddly perfect.
"We spent many hours frantically dismantling [cauliflower] florets, counting them, measuring angles between them,"
writes University of Nottingham mathematician Etienne Farcot, who studied cauliflower growth in an effort to understand these "mysterious cabbages."
Fractals are exquisite, self-repeating patterns which, besides some cauliflowers, are also found in fern fronds, branching blood vessels, and the rings of Saturn. Fractals are geometrical shapes made up of smaller and smaller copies of themselves, creating a mesmerizing 'self-similarity' that is infinitely deep.
© Wolfgang Beyer/Wikimedia, CC BY-SA 3.0Mandelbrot set (black) in a continuously colored environment.
Although only mathematical or computer-generated fractals are truly perfect fractals, nature comes pretty close.
"These repeating patterns are everywhere in nature,"
says mathematician Thomas Britz of the University of New South Wales in Sydney, Australia. "In snowflakes, river networks, flowers, trees,
lightning strikes - even in our blood vessels."
© VerboseDreamer/Wikimedia CommonsFern fronds
Part of the charm of fractals is that they help to explain how complexity is born out of simplicity. As Benoît Mandelbröt, the Polish-born mathematician who coined the term fractal,
said in 2010: "Bottomless wonders spring from simple rules which are repeated without end."
Branching river systems also carve
near-perfect fractal patterns in the landscape.
So persistent are these patterns that in one instance, archaeologists looked for
missing fractals to deduce ancient Egyptians might have modified river channels when building pyramids nearby.
© NASA Earth ObservatoryLake Erepecu and Trombetas River in Brazil.
Insects appear to follow mathematical principles, too.
Whether they know it or not, bees build hexagonal honeycomb in a way that produces the most storage space using the least materials - a theory known as the 'honeycomb conjecture' which was
finally demonstrated by American mathematician Thomas Hales in 1999.
Some species of cicadas also have a life cycle geared towards prime numbers. Swarms of two North American species emerge from their subterranean burrows
every 13 or 17 years, a trick which scientists think
helps cicadas avoid predators with more regular rhythms.
© Meggyn Pomerleau/UnsplashHoneycomb is a natural tessellation
Let's not forget nature's 'favorite' numbers,
Fibonacci numbers, where each number in the sequence is the sum of the previous two. Fibonacci numbers are seen in
sunflower seeds,
pine cones and pineapples.
Spiral galaxies and
nautilus shells also mimic so-called
golden spirals by growing in a logarithmic ratio with every quarter turn.
But even though mathematical patterns are everywhere to be seen in nature, recent discoveries suggest the connection between math and nature runs deeper still, in ways we're only just beginning to appreciate.
© James L. Amos/Getty Images
Earlier this year, researchers discovered what they described as a previously unknown
law of nature: a growth pattern which describes how pointed shapes form again and again in nature - from shark teeth and spider fangs to bird beaks and
dinosaur horns.
"The diversity of animals, and even plants, that follow this rule is staggering," evolutionary biologist Alistair Evans from Monash University in Australia
said at the time they discovered the mathematical formula, dubbed the 'power cascade'.
"We found it almost everywhere we looked across the kingdoms of life - in living animals, and those extinct for millions of years."
Back in 2015, scientists were also delighted to find a classic formula for Pi - the ever-constant ratio between a circle's circumference and its diameter - lurking in
hydrogen atoms.
In a roundabout way, that discovery leads us back to the idea that mathematics provides a structural framework for the physical world. It's an interesting idea to entertain - so long as your head doesn't explode.
Nature is not there to be tamed by mathematics, its there to be marvelled at.