THE GOLDEN RATIO & THE FIBONACCI SEQUENCE
The once secret code hidden throughout life and creation.
The Golden Ratio, also known as The Golden Section, or The Golden Mean, is a special number equal to approximately 1.618 that can be seen in the geometry of the Fibonacci Spiral and is reflected throughout the proportions of the human body, animals, plants, atoms, DNA, music, The Bible, The Universe, as well as in ancient art and architecture. Almost everywhere we look, we can see the Golden Ratio.
The Golden Ratio is a mathematical ratio based upon the following.
Look at this illustration. This is the Golden Section which can be easily explained using a single line. Section ‘a’ of the line is equal to 1.618 and section ‘b’ of the line is equal to 1. This creates the Golden Mean ratio of ‘1: 1.618’.
If we write this as a mathematical formula, it would be written as follows:
This is the Greek letter, known as ‘Phi’, which is used to represent the Golden Ratio / The Golden Mean / The Golden Section, that corresponds to the number 1.618033988749895…which is a number that goes on to infinity.
To understand how the Golden Ratio appears in nature we need to understand the following illustration, which is known as the Fibonacci Spiral, which relates to the Fibonacci Sequence and The Golden Ratio.
THE FIBONACCI SEQUENCE AND THE FIBONACCI SPIRAL
The Golden Ratio can be found reflected within the Fibonacci Sequence and the Fibonacci Spiral.
The Fibonacci Spiral is a spiral shape that contains The Fibonacci Sequence and The Golden Ratio within its design. Let’s look at the following rectangles so you can understand how Phi is reflected in the Fibonacci Spiral.
The first illustration is a rectangle that has The Golden Ratio incorporated into the design. The ‘y’ and ‘x’ axis’s are in a ratio of ‘1: 1.618’. Now, if you make a perfect square within this rectangle, you will have the following image:
Now we have a perfect square on the left, and a new rectangle on the right. This square and rectangle are in proportion to each other according to The Golden Ratio, by ‘1: 1.618’.
If we continue to repeatably apply The Golden Ratio formula to each new rectangle created on the right, by adding another perfect square within the left of each new rectangle, we will eventually get the following illustration, with progressively smaller squares.
Each of the squares and rectangles we continue to create contain The Golden Ratio and relate to one another by a ratio of ‘1 to 1.618.
So how does the Fibonacci Spiral fit into this?
The Fibonacci Spiral is created from the Fibonacci numbers, or from what is commonly called the Fibonacci Sequence. The Fibonacci Sequence is (0,) 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,…and continues to infinity.
Starting from number 0, The Fibonacci Sequence is created by adding together the two preceding numbers in the sequence. The 2 is found by adding together the two numbers before it, (1+1). The 3 is found by adding together the two numbers before it, (1+2). The 5 is found by adding (2+3), and so on to infinity.
If we look at the following illustration, we can see that the Fibonacci Sequence of numbers corresponds to the Phi ratio, ‘1: 1.618’.
As we can see, every Fibonacci number from the Fibonacci sequence perfectly reflects The Golden Ratio, ‘1: 1.618’. We can add together 1+1 box to find 2 boxes. We can add together 2+1 boxes to find 3. We can add together 3+2 boxes to find 5, and so on.
Now, if we draw a spiral shape in these boxes, starting from the smallest box and continuing into the bigger boxes, we get the following spiral.
This is what we call the Fibonacci Spiral, which is a spiral shape that curves outwards in direct proportion to the Fibonacci Sequence, which reflects The Golden Ratio.
“Contrary to popular belief, The Fibonacci Sequence was not invented by the Italian mathematician, Leonardo Fibonacci.”
This number sequence was named The Fibonacci Sequence in the 19th century after Fibonacci used the mathematical principle in his publication ‘Liber Abaci’, in 1202. This book was written to help tradesmen make a financial calculation to track profit, loss, remaining balances, and so on.
The original Fibonacci Sequence, before it was given that name, was found in ancient Sanskrit texts, that used the Hindu-Arabic numerical system, which predates Leonardo Fibonacci by centuries.
If we look for real-world examples, we can see this same Fibonacci Spiral, reflecting The Golden Ratio, throughout the physical world, from the smallest microcosm to the largest macrocosm.
THE GOLDEN RATIO & THE FIBONACCI SPIRAL IN NATURE
We can see The Golden Ratio and The Fibonacci Spiral reflected throughout nature.
If we look around us, we can see the Golden Ratio is reflected throughout the physical world, in plants, flowers, animals, shells, Galaxies, and Hurricanes.
If we look at the physical human body, we can see The Golden Ratio reflected from DNA to faces.
The DNA molecule measures 34 angstroms long by 21 angstroms wide, for each cycle of its double helix spiral. The numbers 21 and 34 are two number found in the Fibonacci Sequence, which is a reflection of the Golden Ratio. So The Golden ratio is encoded into your DNA.
We can also see The Golden Ratio appearing in our faces.
When our eyes fall upon someone who’s facial symmetry is closer to the Golden Ratio, we naturally find that face more beautiful and attractive. So it would seem that, on a psychological and instinctual level, we are naturally primed to recognise The Golden Ratio and to respond accordingly.
As we humans are naturally primed to recognise beauty when we see the proportions of The Golden Ratio, artists and architects have been incorporating this ratio into their buildings and works of art for thousands of years.
THE GOLDEN RATIO IN ART & ARCHITECTURE
The Golden Ratio can be found in many ancient temples and buildings.
The Golden Ratio is evident in many temples and buildings throughout the ancient world and humanity has been reflecting The Golden Ratio in buildings for at least 4,000 years, while some argue much longer. One example we can see is in Greek architecture and how the Parthenon was built.
We can see in this example that the Golden Ratio was used to determine the relationship between the width of the building and its height, and was used to position the supporting columns.
We can also see The Golden Ratio is used throughout ancient Greek sculptures, such as The Venus de Milo, carved by Greek sculptor Alexandros.
Leonard da Vinci was famous for incorporating the Golden Ratio in his paintings, and he made many beautiful works of art using this same ratio. One of which was The Last Supper, that shows Jesus perfectly placed in the middle of the painting and the people and the background painted in perfect Phi ratio.
This list could go on and on because almost everywhere we look, we can see The Golden Ratio reflected at us.
There is, however, something much deeper which many intellectuals have pondered over for centuries. Why did humans throughout the ages paint, draw, sculpt, and build using The Golden Ratio?
Why are so many people throughout human history drawing our attention to the Golden Ratio?
THE GOLDEN RATIO SUGGESTS AN INTELLIGENT CREATOR
Known as a 'Cosmic Constant', The Golden Ratio suggests an intelligent origin to life.
For hundreds of years, mathematician, scientists, philosophers and scholars have suggested that the Golden Ratio, which exists throughout creation in perfect symmetry, is not a sign of a random Universe, but instead, a sign of intelligent design.
Proponents of intelligent design claim, that because the same pattern underlies creation, from the smallest DNA to the largest of galaxies, that there is an inherent code that exists which directs nature. In so many unrelated phenomena, both living and non-living, we can see the Golden Ratio, which suggests a deeper level of design in the Universe.
The Golden Ratio is said to represent a “cosmic constant”, that appears in the curl of an elephant tusk, hurricane spirals, the spirals of galaxies, DNA structure, the distribution of planets in the solar system, the growth of many plants, the Periodic Table of the Elements, spiral shells, the stability of atomic nuclides, and topology of space-time, and that’s only for starters.
Professor Francis Thackeray, a palaeontologist at Wits University’s Evolutionary Studies Institute, and Jan Boeyens, a former professor at Wits University, present their research titled ‘Number theory and the unity of space’, and quotes:
We suggest that there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time….
Apart from the Golden Ratio, a second common factor among this variety of structures is that they all represent spontaneous growth patterns. The argument that this amazing consilience (‘self-similarity’) arises from a response to a common environmental constraint, which can only be an intrinsic feature of curved space-time, is compelling. - https://www.sajs.co.za/article/view/4033/5864
Professor Francis Thackeray concludes:
“The time has come to recognise that relativity and quantum theories can be integrated, and linked numerically to the value of a mathematical constant — whether in the context of space-time or biology.” - https://www.sajs.co.za/article/view/4033/5864
What these two professors have shared is that The Golden Ratio appears in physics, chemistry, biology, the topology of space-time, relativity, and quantum mechanics. The Golden Ratio, it appears, is evident throughout creation.
This has led many scientists to claim the existence of an intelligent creator of the Universe. We can see the Golden Ratio at the root of so much in our Universe, including the fabric of space-time itself. This shows us there is an underlying code which connects our DNA and bodies to nature, the Universe and the fabric of space-time.
The scientific evidence of an intelligent creator becomes all the more convincing when we analyze our DNA a little deeper.
OUR DNA SUGGESTS AN INTELLIGENT CREATOR
Modern day science and geneticists have explored our DNA and found evidence of intelligent design.
With the in-depth knowledge we have today about DNA and genetics, scientists can make increasingly deeper observations into the code that underlies life on Earth. What this research has revealed to many scientists, is evidence of intelligent design.
In 1953 when Watson and Crick elucidated the structure of the DNA molecule, they made a startling discovery. The structure of DNA allows it to store information in the form of a four-character digital code. Strings of precisely sequenced chemicals called nucleotide bases store and transmit the assembly instructions — the information — for building the crucial protein molecules and machines the cell needs to survive.
Francis Crick later developed this idea with his famous “sequence hypothesis” according to which the chemical constituents in DNA function like letters in a written language or symbols in a computer code. Just as English letters may convey a particular message depending on their arrangement, so too do certain sequences of chemical bases along the spine of a DNA molecule convey precise instructions for building proteins. The arrangement of the chemical characters determines the function of the sequence as a whole. Thus, the DNA molecule has the same property of “sequence specificity” that characterizes codes and language.
Moreover, DNA sequences do not just possess “information” in the strictly mathematical sense described by pioneering information theorist Claude Shannon. Shannon related the amount of information in a sequence of symbols to the improbability of the sequence (and the reduction of uncertainty associated with it). But DNA base sequences do not just exhibit a mathematically measurable degree of improbability. Instead, DNA contains information in the richer and more ordinary dictionary sense of “alternative sequences or arrangements of characters that produce a specific effect.” DNA base sequences convey instructions. They perform functions and produce specific effects. Thus, they not only possess “Shannon information,” but also what has been called “specified” or “functional information.”
Like the precisely arranged zeros and ones in a computer program, the chemical bases in DNA convey instructions by virtue of their specific arrangement — and in accord with an independent symbol convention known as the “genetic code.” Thus, biologist Richard Dawkins notes that “the machine code of the genes is uncannily computer-like.” Similarly, Bill Gates observes that “DNA is like a computer program, but far, far more advanced than any software we’ve ever created.” Similarly, biotechnologist Leroy Hood describes the information in DNA as “digital code.”
After the early 1960s, further discoveries revealed that the digital information in DNA and RNA is only part of a complex information processing system — an advanced form of nanotechnology that both mirrors and exceeds our own in its complexity, design logic, and information storage density.
Where did the information in the cell come from? And how did the cell’s complex information processing system arise? These questions lie at the heart of contemporary origin-of-life research. Clearly, the informational features of the cell at least appear designed. And, as I show in extensive detail in my book Signature in the Cell, no theory of undirected chemical evolution explains the origin of the information needed to build the first living cell.
Why? There is simply too much information in the cell to be explained by chance alone. And attempts to explain the origin of information as the consequence of pre-biotic natural selection acting on random changes inevitably presuppose precisely what needs explaining, namely, reams of pre-existing genetic information. The information in DNA also defies explanation by reference to the laws of chemistry. Saying otherwise is like saying a newspaper headline might arise from the chemical attraction between ink and paper. Clearly something more is at work.
Yet, the scientists who infer intelligent design do not do so merely because natural processes — chance, laws, or their combination — have failed to explain the origin of the information and information processing systems in cells. Instead, we think intelligent design is detectable in living systems because we know from experience that systems possessing large amounts of such information invariably arise from intelligent causes. The information on a computer screen can be traced back to a user or programmer. The information in a newspaper ultimately came from a writer — from a mind. As the pioneering information theorist, Henry Quastler observed, “Information habitually arises from conscious activity.”
This connection between information and prior intelligence enables us to detect or infer intelligent activity even from unobservable sources in the distant past. Archaeologists infer ancient scribes from hieroglyphic inscriptions. SETI’s search for extraterrestrial intelligence presupposes that information embedded in electromagnetic signals from space would indicate an intelligent source. Radio astronomers have not found any such signal from distant star systems; but closer to home, molecular biologists have discovered information in the cell, suggesting — by the same logic that underwrites the SETI program and ordinary scientific reasoning about other informational artefacts — an intelligent source.
DNA functions like a software program and contains specified information just as computer software does. We know from experience that software comes from programmers. We know generally that specified information — whether inscribed in hieroglyphics, written in a book, or encoded in a radio signal — always arises from an intelligent source. So the discovery of such information in the DNA molecule provides strong grounds for inferring (or detecting) that intelligence played a role in the origin of DNA, even if we weren’t there to observe the system coming into existence.” - https://evolutionnews.org/2018/04/yes-intelligent-design-is-detectable-by-science/
The geneticists of today are adamant they have detected evidence, in the form of a sophisticated code, written into the fabric of our DNA that proves we have an intelligent creator.
For the world to come into existence somehow, there must be a First Cause. The mathematical regularity we observe in the cosmos, which we see coded within The Golden Ratio and our DNA, suggests the presence of an intelligent Creator as being that First Cause.
In time, and as knowledge advances, perhaps science will one day witness what wise men have experienced throughout the ages. That the intelligent creator, whom many call God, is evident within us.