Golden Ratio, Phi, Divine Proportion: Math or Esotericism?
Throughout the history of humanity, certain mathematical concepts have stood out from others through their philosophical messages, their operational effectiveness or quite simply their beauty.
The golden ratio, sometimes simply called phi, is one of the best examples.
Discovered in ancient Greece by some of the greatest minds of all time, this number contains mathematical secrets, yes, but also esoteric and occult ones.
From Pythagoras to Euclid, including Renaissance scientists like the Italian Leonardo of Pisa or the famous Johannes Kepler, the list of discoveries made about the golden ratio has benefited from the work of true geniuses.
Today we are going to share some of these discoveries with you.
Contents :
The golden ratio from a mathematical point of view
The golden ratio from a mathematical point of view
Sometimes also known as the "golden ratio", "proportion of the gods" or "divine proportion", the golden ratio is decidedly a unique animal in the world of mathematics (a world nevertheless populated by oddities and differences). 'strangeness).
From an algebraic point of view, it corresponds to the ratio between 1 + √5 (square root) and 2, which gives a result approximately equal to 1.618.
Approximately, yes, because the golden ratio is an irrational, to understand a number having an infinity of digits after the decimal point, digits which also seem to have no logical sequence and to follow one another in an astonishing chaos.
In this sense, the number phi has many similarities with another well-known number, the number pi.
In short, how were we able to find the value of this famous golden number, you ask me?
In fact, it is the limit term (on which the sequence converges) of the Fibonacci sequence, the famous sequence where each term is the sum of the two previous ones (1, 1, 2, 3, 5, 8, 13, etc.). Famous suite, yes, because artists and architects and artisans have long known the capabilities of this suite to create beauty wherever it is found.
Another interesting mathematical property of the number phi is that it is “itself its reciprocal less than 1. Concretely, dividing 1.618 by 0.618 gives 1, which is precisely the result of the difference between the two numbers.
Now, we understand a little better what mathematicians were able to find in our famous golden ratio... but that tells us nothing about its esoteric or spiritual meaning !
Pythagoras, the Greeks and the golden ratio
If our dear phi presents mathematical particularities unique to the world, it is we, humanity, who have decided to give it such a place in our imagination.
His epic journey began several millennia ago, in ancient Greece.
There, a genius mathematician known as Euclid first described this relationship, which he saw as "the division of a line into extreme and middle reason." Already therefore, the golden ratio was well associated with a geometric, and therefore aesthetic, relationship.
Some time later, Pythagoras and his esoteric movement, the Pythagoreans, also looked into the case of the number phi, which they (re)discovered and saw it as the particular relationship found inside one of the figures the most important of sacred geometry: the pentagram.
Better known as the “five-pointed star”, the pentagram is this famous geometric pattern associated with occultism, the devil (for Christians at least), witchcraft and schools of magic in general.
For anyone who knows a little about esotericism or the occult arts, it will be “fun” to find this symbol here...
But after all, what if there was nothing surprising about it?
The golden ratio in nature
If the golden ratio has been present in the minds of men since the dawn of time, it is also present in that of nature...
In any case, this is what certain observations that we can all make suggest.
As images are better than sometimes too long speeches, here is a list of some natural phenomena where our numbers are found:
- Numerous flowers form rows of petals respecting the Fibonacci sequence, and therefore its divine proportion.
- Pine cones have their pinions forming spirals according to the ratio of the golden ratio.
- The sunflower has hundreds of seeds in its center, which grow in such a way as to form spirals whose numbers in both directions always give two successive numbers of the Fibonacci sequence.
- Most trees have particular leaves, because the ratio between the width of the veins and the spacing between two of them presents a ratio worth precisely phi.
- Most animal species have the golden ratio connecting certain bones in their skeletons. In humans, it is often said that the ear presents a spiral of its own following the Fibonacci sequence, or that the size of the foot, the cubit and the width of the hand are linked by our number.
- Some crystals also seem to be arranged according to the golden ratio.
A trace to our DNA
We could have mentioned this strangeness in the previous point, but something as important as our own DNA, the code that constitutes us and makes us who we are, deserves a little more attention.
It's no secret that DNA is made up of a sort of double helix, modeled on two wires wound together and connected by a kind of small bridge between them.
Where things get more complicated is when scientists point out that the length and width of a complete cycle of this double helix are respectively 34 and 21 angstroms (a unit of measurement based on nanometric emissions).
In short, hold on, the ratio between these two numbers... gives us precisely phi.
Dr. Leonard Horowitz, a world-renowned scientist, was able to demonstrate that human DNA continually emits and receives photons. An idea then emerged that our DNA is literally what links us to the world, to the universe and, for the most religious, to God.
In fact, it would be a bit as if part of the universal light was found in each of us through our DNA.
When we also know the importance of the golden ratio in the construction of our world, some of the most curious have put forward a theory according to which we all have more or less occurrence of this famous divine ratio in our genetic code, and that it would be this concentration (or not) which would influence our psychic abilities, and our ability to perceive the hidden reality beyond things.
The golden ratio in the arts
Basically, nature is the first artist, and even brilliant men can only be inspired by it.
It is therefore not surprising that the golden ratio is found in so many brilliant works universally recognized as beautiful.
In particular, painters, sculptors and architects have included this divine proportion quite consciously in their works, aware that it could bring them balance and harmony.
One of the most famous examples and undoubtedly the famous “Vitruvian Man” by Leonardo Da Vinci, which he created with the desire to place as many times as possible what he then called the “sectia aurea”, or golden section.
This work expressed the spirit of its time, the Renaissance, where many thinkers looked again at the hidden secrets of the golden ratio, such as for example the mathematician Luca Pacioli, who even went so far as to dedicate a book to it in 1509, soberly named “ De Divina Proportione ”.
According to the archaeological discoveries of our last centuries, however, all this was only a rediscovery of knowledge formerly known to past civilizations.
Coincidence or not, the fact is monuments around the world include the golden ratio in their designs. From megaliths found all over the world, to the architecture of pre-Columbian America, and including Chinese and Japanese art: the use of our report is a constant.
Among all the monuments in the world, however, there is one that may interest the curious and open-minded more than the others: the Great Pyramid of Giza.
Without going into the details of this marvel, objectively far too ahead of its time, you should know that the phi number is found there almost systematically.
Ratio of lower and upper rooms, base divided by height and size of corridors are just a few examples.
For further
Here we have discussed some themes linked to mysteries and esotericism... and that's good, our site specializes in just that!
In particular, here are some collections of symbols, weird objects and lucky charms that you might like:
- That linked to Greek culture, because some of the greatest mathematicians (and esotericists also for that matter) came from there.
- That specific to ancient Egypt, because there is undoubtedly something to look for in that area too.
- That linked to meditation, because the golden ratio can be a means of accessing certain spiritual truths.
Here are also some external resources that you can consult if some of the topics we have covered have left you wanting more:
- More information on the Fibonacci sequence, very linked to our phi.
- A description of the Pythagorean school, halfway between mathematics and occultism.
- A list of mathematical observations made on the Pyramids of Gizet.
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