Welcome back to Defender’s Voice. This is Dr.Paul. Thank you for joining us today. Please send your questions to firstname.lastname@example.org. Visit our website www.doctorpaul.org to learn about our ministry. You can also subscribe to our podcast.
Today’s question is: The numbers in nature. What is their significance?
Excellent question. I really love the mathematics of nature. That is why this video is going to be a long video because you tapped into my favorite subject. One of the great mysteries of nature is the presence of hidden mathematics underlying its structures.
First thing in mathematics is pattern recognition. Mathematics is simply the study of patterns. You go out and walk in a garden. You see different plants with different flowers. Some flowers with 4 petals, some with 5 petals, some with 6 petals. You start to notice those patterns in plants. That is the birth of botany. Not just botany, every branch of science starts with pattern recognition. That is how mathematics was born and all other sciences were born.
In the patterns, first I would like to talk about the Golden Ratio. The name says it all. It is a ratio. In a ratio, you compare and contrast two things and find out their relationship. It is one of nature’s most common ratios. Two numbers are in the golden ratio if the ratio of the sum of the numbers divided by the larger number is equal to the ratio of the larger number divided by the smaller number.
Let us take a and b. A is the larger number and B is the smaller number.
A + B/A= A/B
Don’t get confused here. A + B/A = A/B. That is the golden ratio.
It is approximately 1.618…… I said, dot.dot.dot, because it is an irrational proportion. It is represented by the Greek letter phi.
The Greeks knew the golden ratio. Pythagoras, famous for the Pythagorean theorem, observed it and used it to design Greek temples. You can see the golden ratio on the Parthenon. The Egyptians used it in their monuments. The Great Pyramid of Giza. The largest pyramid and the largest man-made structure in the world. It was built in the 26th century BC. It was built based on the Golden ratio.
We see the golden ratio in human body proportions. Index finger…from its first to its second knuckle is in golden ratio; from the full finger to wrist…is in golden ratio. from hand to forearm..is in golden ratio. Divide the length from your shoulder to the tip of the index finger by the length from your elbow to the wrist…you get the golden ratio. Not just fingers and joints. Even our internal organs show a golden ratio.
Not just humans..bears, peacocks, dolphins..their anatomy shows golden ratio.
Leonardo da Vinci (1452 – 1519) was an Italian genius. He drew the famous drawing called Vitruvian man. In that drawing, you will see a man in two superimposed positions stretching his arms and legs within a square and circle. Da Vinci’s aim was to show us an ideal human body in mathematical proportions. Da Vinci believed that by understanding the proportions of the human body we can understand the proportions of the universe. He was proved right. You can see the golden ratio in the solar system and the star studded galaxies.
Modern engineers also take inspiration from the golden ratio. Car manufacturer Aston Martin said, ‘Golden ratio sits at the heart of every Aston Martin’. It helps to achieve a great shape, function, balance and weight bearing to a car. If you look at their sports car Rapide S, it draws your attention to its shape and ‘ready to roll’ kind of feeling. That is the magic of Golden Ratio.
At this juncture, we should also talk about another Leonardo. Not Leonardo Da Vinci, but Leonardo of Pisa. He is also known as Fibonacci. A mathematical sequence named after him is the Fibonacci sequence. It is a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers. Easy. Just add the previous two numbers and you will get the next number in this sequence. Any kid can do that. But here is the interesting part. As you go on in this sequence, the ratio of sequential Fibonacci numbers approaches the golden ratio.
610/377 = 1.618
377/233 = 1.618
233/144 = 1.618
Dividing Fibonacci sequence brings us to the Golden Ratio. I find that mind-blowing. You see the Fibonacci sequence in nature. Pineapples, artichokes, sunflowers, leaves of plants, the sides of an unpeeled banana, the ridges on a peeled banana.
Yes, bananas have a Fibonacci sequence. Ray Comfort argues that bananas are intelligently designed by God. Richard Dawkins mocked him as ‘banana man’. But bananas have Fibonacci sequences in them. Something to think about.
Golden ratio and Fibonacci sequence became a staple of many great architects. Le Corbusier was a great French architect. He is considered one of the pioneers of modern architecture and urban planning. He prepared the master plan for the city of Chandigarh in India. He developed an architectural model called ‘Modulor’. It is based on the Golden Ratio and Fibonacci numbers. He believed that these proportions create harmony among the buildings, starting from door handles to entire cities.
next we should talk about spirals. What are spirals? They are curves that start from a center point and get further and further away as they circle around that point.
Nature has so many spirals. You can see a spiral in a nautilus shell, in the arrangement of leaves on a stem, in bighorn sheep, in a sunflower, in a pineapple,in a hurricane and in a galaxy. From the shell in your hand to a galaxy in outer space – objects are arranged in the form of a mathematical spiral.
Next, we should also see the relationship between a spiral and the golden ratio. If you put Fibonacci numbers as squares and progress in the sequence, you will get a spiral. If take a nautilus shell, the distance between each turn of the spiral progressively gets larger than the one before it. This is a logarithmic spiral. You can fit a logarithmic spiral in a golden ratio.
The interconnectedness of the golden ratio and spirals via Fibonacci numbers. Another mind-blowing truth we see in the numbers of nature. Recently I was visiting the Rocky Mountains in Colorado. We stopped to see some beautiful ponderosa trees. My son Jacob picked up a pine cone and showed it to me. ‘Dad, see this pinecone. The scales are arranged in spirals. Do they show the Fibonacci sequence?’ He is a kid, 10 years old. He could see numbers in those cones. The seeds of sunflowers and pine cones twist in opposing spirals of Fibonacci numbers.
Pinecones: You see 8 spirals going one way; 13 going the other. 8 and 13. Take a look at the sequence. They are Fibonacci numbers
Sunflower: You see 34 spirals go in one direction; 55 the other. 34 and 55. Take a look at the sequence. They are Fibonacci numbers.
Artichoke: You see the oldest leaves are on the outer ring and the newest at the center. The spiral of its leaves show Fibonacci numbers
These spirals not only give great beauty to these flowers but also pack the seeds efficiently over the available surface area.
Next, we should talk about Voronoi patterns. In these patterns, you will see polygons arranged in the available space. Let us say I threw some ‘seeds’ into that space and the seeds fell into different polygons. In a Voronoi pattern, every point inside a polygon is closer to the ‘seed’ inside that polygon than it is to any other seed outside that polygon.
Voronoi patterns got their name from their creator, Russian mathematician Georgy Voronoi. You can see its uses in diverse fields.
If you want to divert a plane to a nearest airf field, during its flight plan, consider using a Voronoi pattern
As you drive over a road, your cell phone connects to a local transmission tower using a Voronoi pattern
You want to find the nearest hospital using the shortest path. Your map will use a Voronoi pattern
You got an infection. How did it start? The public health expert might use a Voronoi pattern to trace it’s source.
There is an interesting story about it. In 1854 a cholera epidemic was destroying thousands of lives in the city of London. Physician John Snow used a Voronoi diagram over the locations of water pumps and identified the source of infection. He counted deaths in each polygon and considered the water pump in the area as a possible source of infection.
Mathematicians are delighted to find the usefulness of Voronoi patterns in diverse human activity. But nature has already been using voronoi patterns.
the irregular brown spots on the fur of a giraffe
the veins on a dragonfly’s wings
the bony scales of a turtle shell
the epithelial cells in human body
the hexagonal cells in a honeycomb.
Honeycomb is a three-dimensional Voronoi pattern. Each angle measures about 120 degrees, the angle gives the largest volume with the smallest surface area.
The next pattern we should look at is fractals. Fractals look similar at any scale and repeat themselves. Zoom in or zoom out, you will see the shape repeating infinitely.
Earlier we have seen how the Fibonacci sequence produces spirals. As you go, those spirals become fractals. The Golden spirals are self-similar. Another mind-blowing aspect of numbers in nature.
Mathematicians studied the fractals. In fact, the word ‘fractal’ was coined by a mathematician named Benoit Mandelbrot. He developed a theory of ‘roughness and self-similarity’ in nature.
Many things look ‘rough’, ‘chaotic’ and ‘disorderly’ to our eyes. But if you zoom in, you will see beautiful fractal patterns in them. Mandelbrot’s work became fundamental to computer graphics and animation. He also showed the mathematics of fractals could be applied to nature, because nature is full of fractals.
If you wander in a desert and look at the sand dunes, you will see fractals created by the wind over the sand
Take a look at the Amazon river from above, it branches and branches into tiny streams.
Look at a city map, so many big roads and small roads, they show a fractal pattern
If you go to a forest, you will find fractals from seeds to branches and leaves and to plants and trees throughout the forest. They divide, divide and divide
Madagascar reminds us of beautiful Baobab trees. Their branches show fractal patterns.
Observe flowers. Growth spirals on a flower often show fractal patterns in Fibonacci sequence
Observe leaves. They show fractal patterns
Observe ice crystals. They show fractal patterns
Observe Romanesco broccoli. It shows fractal patterns
Observe the filaments of a sea fan coral. It shows fractal patterns
Observe a cloud in the sky. It shows fractal patterns
Observe a mountain range. It shows fractal patterns
Observe an anthill. Its network of tunnels shows fractal patterns
Fractal patterns reveal the simplicity that underlies nature’s complexity. Sometimes you will see fractals arranged in spirals like the spirals of pine cone seeds. If you cut a cabbage vegetable, you will see thick leaves surrounding other leaves. You will see a fractal branching in these leaves. The leaves are arranged in spirals in the Fibonacci sequence. Spirals, fractals and Fibonacci sequence – coming together in cabbage. This nice interconnectedness helps to deliver water and nutrients efficiently.
Our human body is also full of fractals
Observe the lungs. The bronchial tree branches and branches showing a fractal pattern.
Observe the brain. The nervous tissue shows a fractal pattern.
Every organ and every cell in our body needs a continuous supply of oxygen and nutrients. The fractal branching helps the circulatory system to reach even the smallest cell in our body. For every tiny cell, there will be a tiny capillary in its neighborhood.
Golden ratio, spirals, Fibonacci sequence, Voronoi patterns, fractals…they point us to the mathematical genius of God, who created nature. By studying nature, we can understand some attributes of God.
We read in Romans 1:20
For his invisible attributes, namely,
his eternal power and divine nature,
have been clearly perceived,
ever since the creation of the world,
in the things that have been made.
So they are without excuse.
When we see the nature around us, when we observe the creation of the world, we can see the invisible attributes of God.
In Greek, Apostle Paul wrote,
aorta autou apo ktiseos kosmou tois poiemasin nooumena kathoratai
Aorata…the invisible qualities of God
kathoratai….are clearly seen
nooumena….are clearly understood
Richard Dawkins mocked Ray Comfort calling him ‘banana man’. That is not right. The fibonacci sequence in a banana clearly points us to the mathematical genius of God.
When you see the numbers in nature, you can easily see and understand the invisible qualities of God. They point us to God, our Creator. They point us to our Lord Jesus Christ, who created this universe.
Come to Jesus, confess your sins, accept his salvation and invite him into your life as your Lord and Savior. Thank you.