For Plato, the universe we inhabit is merely a reflection of a higher truth, a divine principle.
This higher dimension consists of what he described as ideal forms – the perfect triangle or circle for instance – which are a blueprint for the world in which we live. The imperfect variations of these ideal forms make up the material realm around us, one which aspires towards a perfection that is always out of reach.
It’s impossible to create a perfect circle, either by drawing it or even by using a computer. The decimals of the number Pi (which is the ratio of a circle’s circumference to its diameter) continue to infinity so we cannot have an exact value for it. While the idea of the perfect circle exists within mathematics, even a computer is limited by pixels and as such we can only ever generate a very close approximation of it at best. Pi is an irrational number, and is infinite.
Plato understood that mathematics is the key to the clockwork of a universe which, by its very limitations, opens the gate to the plane of ideal forms.
While it is known in mathematics that a triangle or a circle drawn by a draughtsman will always be an approximation, the imagination is still stirred. In this, Plato said that the mind of the mathematician is thereby drawn towards the realm of perfect forms. Here, too, we can see one of the key aspects of sacred geometry and its practical work. The concept of inspiring the mind towards the divine.
The relatively new study of fractal patterns has gone some way towards proving Plato right in his view of the physical realm. It also provides an interesting insight into the created universe.
While mathematician Benoit Mandelbrot coined the term ‘fractal’ in 1975, the study of these patterns began in the 17th century with notions of recursion, essentially recurring patterns in nature.
These recurring geometric patterns exhibit similar – although not exact – patterns at increasingly smaller scales, such as we see in a leaf. In their expanding symmetry throughout nature we have a cycle of recurrence, continuing variations of ideal geometric forms.
You could say that these patterns of nature continue infinitely, potentially even through multiple universes. This is akin to the idea of the Ouroboros, or the corporeal realisation of it at least, of nature continually eating and giving birth to itself.
Recurring patterns can be found in the microcosms and macrocosms of the universe.
We can see the shape of a shell echoed in that of a spiral galaxy, both incorporating the Fibonacci sequence.
In geometry a Fibonacci spiral is a logarithmic spiral whose growth factor approaches the Golden Ratio (1.618 etc). Various approximations of the Golden Ratio can be found throughout nature, in our own bodies too.
As the Golden Ratio is another irrational (or perhaps ideal) number represented by an infinite sequence, the closest approximation of it that we can give form to is the Fibonacci sequence. Here, each number is added to the previous to create the sequence (0,1,1,2,3,5,8,13 etc).
If you take any two successive Fibonacci numbers, their ratio is close to the Golden Ratio. As the numbers get higher, the ratio becomes closer still but is always imperfect as the Golden Ratio is an infinite number. Within this imperfection we find variation, the variation we see in the universe around us.
It is this lack of perfection, in a sense, that gives the universe physical form.
So we can say that the perfect circle is a concept that exists beyond form, because when we try to give it form we limit it by the parameters of the physical realm and make it imperfect. It is, as Plato says, “an ideal”. An infinite number by its very nature cannot be given physical form.
This applies to the Golden Ratio too, hence our usage of the Fibonacci. Through mathematics we can say that both the perfect circle and Golden Ratio exist, even though they’re intangible to us. We can see their altered reflections in the world around us though they themselves are beyond form.
In all this, we can find close allusions to the teachings of great mystics such as Meister Eckhart.
Eckhart described this universe as a fragment of reality. For him, as with Plato, the material world is a reflection of a higher truth. God is both fully transcendent and fully immanent, entirely beyond the corporeal realm and yet completely entwined with it as the groundless essence of all.
This is the Panentheistic view (“All in God, God in All”) of many great mystics who see the world and God as distinct, but the world as being comprehended by and existing through God, who Himself is mind, and who dwells in all.
Plato, an initiate of the Egyptian mystery schools, was well aware of the path tread by mystics such as Eckhart; one of detachment from the polarised material realm, inner purification and focus upon the divine. In this sense the initiate is both in the world and not of the world.
Although God is beyond even ideal forms Plato understood that these concepts can help attune our mind towards higher principles of the divine ground within us.
“He who has followed the path of love’s initiation in the proper order will on arriving at the end suddenly perceive a marvelous beauty, the source of all our efforts,” – Plato.