What does this number sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765…
have to do with the nautilus shell pictured above? Or with these other images from nature?
All of the images have a spiral to them. The spirals increase in size incrementally with each turn. Those increments just happen to match the numerical sequence above. Let me explain.
The Fibonacci Sequence
The pattern is called the Fibonacci sequence, after the mathematician who pointed it out to the western world in the 13th century (although it had been mentioned in ancient texts hundreds of years earlier). Each step is the sum of the two previous steps:
0 plus 1 = 1;
1+1=2;
1+2=3;
2+3=5;
3+5=8;
5+8=13;
8+13=21,
13+21=34,
21+34=55,
34+55=89,
55+89=144
…
The pattern can continue infinitely. Within the sequence, the ratio from one number to the next is very consistent at approximately 1:1.61803. For instance, 21 divided by 13 is 1.615; 89 / 55 = 1.618; and 6765 / 4181 = 1.618. This proportion is known as the “Golden Ratio”. Mathematicians find other patterns within the Fibonacci sequence, also. An example is that every third number after two is a multiple of 2; every fourth number after three is a multiple of 3; every fifth after five is a multiple of 5; and so on.
The Fibonacci pattern can be used to draw a spiral using a series of squares, such as graph paper. Each succeeding square is a block measured by the next Fibonacci number: 1X1, 2X2, 3X3, 5X5, 8X8, etc. This image gives a demonstration:
Click here for a good article describing the Fibonacci sequence, the Golden Ratio, and the resulting spiral.
Fibonacci in Nature
While the math alone is fascinating, it is even more intriguing to note how often these numbers and the Golden Ratio appear in nature. The images above are good examples. Scroll through these on unsplash.com to see many more ways that artists have captured this phenomenon.
Fibonacci numbers and the Golden Ratio also appear throughout the human body. One example is right there in your hand: The proportions between the length of the three bones in each finger match that ratio, as does the proportion between the hand and forearm. You can see it yourself: Just make a fist, and see the spiral that it forms.
That proportion, or those numbers, can be found in many places in our bodies, even down to spirals in the DNA molecule! See this article (from a site dedicated to describing the Fibonacci concepts) for diagrams showing a body full of Fibonacci. 🙂
Why the Pattern?
Why is it that numbers can be formed into a pattern like this? We take it for granted that math “works”. But why does it do so? In a completely random world, existing for no reason with no intelligence involved in its design, there is no excuse to expect anything to be consistent or related. Even an abstract concept such as math would make no sense. It depends on logic, and random evolution — by definition — is not logical.
Even in a reality where math makes sense, why would so many biological and natural phenomena incorporate that math? There’s no natural reason why DNA, sunflower seeds, nautilus shells, and galaxies should all fall into spiral patterns, include the same series of numbers, or repeatedly make use of the same ratio.
Try to completely take the idea of God or any Intelligent Designer out of the equation. How could these numbers and proportions exist at all, much less show up in so many disparate places?
People try to leave God out. In this article, after extensively studying the way that trees have branches and leaves arranged in Fibonacci patterns that best capture sunlight with the least shading, the author decided that “Evolution chose the Fibonacci pattern to help trees track the Sun moving in the sky and to collect the most sunlight even in the thickest forest.” How could impersonal, un-directed Evolution choose anything? 1
Here is a thread on quora.com with posters who argue that patterns in nature are not anything to get excited about. Of course, they exist; why wouldn’t they? That’s just the way things are. One of those posters says “Any naturally evolving system will have an optimal configuration built into it which requires the least amount of energy to operate…The Fibonacci Series / Spiral is an outcome of a process of nature which is waiting to be discovered.“
Oh, OK, that explains it…..
Because God Said So
I can’t come up with any non-intelligent, non-designed explanation. Trying to do so requires the contortions mentioned above.
It’s much simpler and more logical to think “That’s a beautiful, intricate design. The Designer liked it enough to re-use it frequently in His creation.“
I’ll go with that one…and with that One!
How great are Your works, O LORD!
Psalm 92:5, 104:24, 111:2, 139:14, 145:5
Your thoughts are very deep.
…
O LORD, how many are Your works!
In wisdom You have made them all;
The earth is full of Your possessions.
…
Great are the works of the LORD;
They are studied by all who delight in them.
…
I will give thanks to You, for I am fearfully and wonderfully made;
Wonderful are Your works,
And my soul knows it very well.
…
On the glorious splendor of Your majesty
And on Your wonderful works, I will meditate.