Numbers in Nature: A Look at the Philosophy of Nature
Numbers: The World’s Language
People recognized early on that natural phenomena could be described with astonishing precision using numbers and mathematical laws. Mathematics, the language of numbers, became the key to understanding our world this way (see also the article “Numbers in Mathematics and Geometry”). Even Pythagoras suspected a hidden order behind everything we perceive, one that had to exist independent of any divine hand. That laid the groundwork for a scientific study of the laws of nature, one that runs through thinkers like Archimedes, Galileo, Newton, and Darwin, all the way to Albert Einstein, and shows up in countless achievements of the modern world. This view was a core part of natural philosophy from early on, a field that still asks about the basic principles behind everything we see today. Today, mathematics applies to the very smallest scales, quarks, atoms, and molecules, all the way up to the very largest: the motion of galaxies, the expansion of the universe, and the structures of the cosmos.
Numbers, certain ones especially, have always played a central role in this. That’s how we discovered constants in nature: numerical values that are universal and unchanging. Among the first was the circle constant pi (π), which the ancient Egyptians most likely already knew (see also the article “Numbers in the Egyptian Pyramids”). Others followed later, like Euler’s number e, the fine-structure constant alpha, or the speed of light c. Constants like these form the foundation of the laws of physics, regardless of place or time. They’re objectively rooted in nature and hold true everywhere in the universe. Today we know that even the tiniest shift in one of these constants, in the force of gravity, say, would produce a completely different world, maybe even one where life couldn’t exist at all.
With numbers and the relationships between them, people could finally start to know these connections, not just believe in them. Numbers made nature calculable, and with that, understandable.
Nature’s Love of Geometry
Nature’s fondness for geometric shapes stands out in particular. One of the simplest, and at the same time most perfect, is the circle: it shows up everywhere, in the iris of the eye, in the sun, in the cross-section of a tree trunk, in a drop falling onto water. Because it appears so universally, because of its simplicity, and because of the mysterious-seeming circle constant pi that describes it, the circle was considered the original, divine proportion in many wisdom traditions and religions.
Another fundamental geometric form in nature is symmetry. Symmetry means an object can be mapped onto itself through reflection, rotation, or translation. We run into it in living things, in the bilateral symmetry of the human body, in flowers, butterflies, and animals, but also in inorganic structures like snowflakes, rainbows, or crystals.
Figure: Symmetry in Nature
The earliest philosophers and scientists already made this observation. The obvious connection between number and message was likely what led Pythagoras to his thesis “All is number.” He was already connecting numbers to the phenomenon of beauty: his theory of harmony showed that certain musical intervals could be defined mathematically, and that harmony arises from numerical ratios (see also the article “Numbers in Music”).
„Why do apple blossoms always have five petals? Only children ask such questions. Adults pay little attention to such things; they take them for granted.“
(György Doczi)
The Beauty of Nature in Numbers
Early researchers recognized similar properties in another famous geometric proportion: the golden ratio. They discovered that proportions in this ratio are experienced as especially beautiful. Later, the findings around the golden ratio went much further. It became clear that the golden ratio runs deep through nature and its growth patterns. Researchers found it, along with the Fibonacci sequence tied to it, in the development and structure of countless plants, animals, and even humans.
Newer Geometries
Later, researchers discovered many new geometric patterns that seem to play a significant role in nature. Fractals, above all, became well known: self-similar patterns that repeat across different scales. These weren’t studied in real depth until the 20th century; the best-known example is the Mandelbrot set. In nature, you find fractals in broccoli, in blood vessel networks, in the branching of lungs, or in coastlines. Today, fractal geometry gets used in computer graphics, data compression, and describing chaotic processes in physics.
„To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.“
(William Blake)
„Almost all of the networks that sustain life are approximately self-similar fractals. […] What’s especially fascinating is that the number 4 shows up in all of these exponents.”
(Geoffrey West)
(More on the meaning of the number 4.)
All Matter Is Built on Numbers
One especially striking example of how deeply numbers are rooted in nature is the periodic table of the elements. No other system describes and sorts the basic building blocks of all matter the way it does. It’s worth noting that neither the elements it contains nor their arrangement are human inventions. That arrangement follows directly and necessarily from the structure of the elements, and that structure is purely numerical. The different elements that make up all matter differ only in number: the count of protons, neutrons, and electrons they carry. Pure number determines an element’s properties. Put another way: quality follows quantity. Here too, numbers aren’t just quantities. They’re directly tied to specific properties. Carbon, the essential element of life, has six protons, for instance, while plutonium has ninety-four. Number alone decides whether an element sustains life or kills it outright. Quality follows quantity here in the most direct way possible.
Numbers in Nature: More Than Mere Quantities
It’s remarkable that nature shows such a preference for numbers, not just because numbers describe and calculate what happens in nature so well, but especially because certain numbers, proportions, and geometries necessarily come bundled with certain properties. Numbers, then, aren’t pure quantities. They always carry qualities too. That view isn’t popular today, since we try to strictly separate the calculating, formal side of numbers from a qualitative one tied to meaning. To modern scientists, connecting the two perspectives looks unscientific. A philosophy of numbers no longer exists. And yet the examples above show that this split, between form and content, quantity and quality, matter and mind, looks artificial. Reality itself doesn’t recognize that split. Maybe it’s time to take up a more holistic view again: one where knowledge and wisdom don’t exclude each other, but complete each other.
Find out more in the book Verlorene Weisheit.
Image Credits:
iStock.com/ChaoticMind75 (snowflake), iStock.com/Daniela Korn (yellow blossom), iStock.com/Avilika (butterfly), iStock.com/Racide (sunflower), canva.com/dariolopresti (snail shell), iStock.com/Trifonov_Evgeniy (galaxy), iStock.com/Queserasera99 (Romanesco broccoli), iStock.com/hlehnerer (Mandelbrot set), iStock.com/LagartoFilm (numbers on a green background)