What do you mean Infinity?

When we think of infinity we often turn out attention to the infinite space of the universe. But infinity is much more than that..


There are some concepts where the word that describes it does not do justice to the phenomena. For example, the word Science, provides us with an idea, but if we did a little deeper we find that there are many different kinds of science. Physic, Chemistry and biology are just three examples, but each of these is divided still into further specialisations.

The same can be said of infinity. Whilst initially the word might spark an intuition, an idea of a never ending something, in fact there are many different types of infinity that can be demonstrated mathematically, and geometrically.

One of the first to challenge the mainstream view of infinity was George Cantor, who fathered new fields of mathematics, including infinite sets, chaos theory, and fractal geometry. All of these came out of a revolution in our understanding of infinity, which have gone on to change the way we perceive the world. From computer software and technology, to modelling the behaviour of natural systems, all come out of our understanding of infinity and how it works.

Different types of infinity

Yet, today, many people still consider infinity to be the expanse of the universe, that extends out toward deep space. Yet this is just one type of infinity, we call Infinity OUT. Let’s outline a few other types of infinity before we describe them in more detail:

  1. Infinity OUT
  2. Infinity IN
  3. Infinite Rotation (clockwise and anti-clockwise.)
  4. Infinity with in boundary

Each of there types of infinity play a very particular role in the functioning of universe, and it exhibited in specific 2D shapes.

Infinity OUT

This infinity is most common to people. Between the stars we find the blackness of space, a void that goes on, potentially to infinity. When we consider the natural numbers, we can count in series, but where will it end. No one has ever found the last number, as you can always add another one to the last to form the next greater numbers. At first the infinity out seems to be unbounded, incalculable, and unreachable. Many spiritual teaching and scriptures relate infinity to the nature of God, who holds wisdom and intelligence beyond the capabilities of man.

When we practice the Art of compass construction, This is the first type of infinity that flows naturally out of the circle. By placing a series of circles of the same size a central circle we create an image called the Seed of life.

We can add more circle to the nodes where the circle meet to increase the size of the outer circle, to create the next image called the Flower of Life.

Now we can clear see that the outer circle is expanding in discreet steps, with each step comprised of an ever increasing number of circles. This procedure can be continued on into infinity. Using compass construction, the circle naturally wants to expand in infinity; the infinity OUT

Infinity IN

Everything in the Universe tends to have an opposite. Therefore, wherever and infinity big thing exists, so must there be an infinity small thing. This concept is so intrinsic to life as it creates the phenomena of scale. The scale is the size, amount or quantity of one thing to another. For example. Imagine a box that you can hold in your hand. It has a side length of about 3cm. Now imagine that you shrink in size, by being zapped be a ray gun, like in the movie ‘Honey, I shrunk the Kids’. Now the box is big enough for you to walk inside of. Instead of 3cm the box now measure 3m. The box did not change, only your perception of it. If you shrink the box grows and if you grow the box shrinks. Though this notion, we can extend the current scientific notion of relativity to include the dimension of scale. The modern relativistic model, put forward by Einstein at the beginning of the last century, includes concepts of length contraction and time dilation.

What is not so commonly considered is the scale of the observer. The human concept of a meter appears very different to an ant, as does the time it takes for each to traverse it. When we observe the universe we do so from a particular scale of existence. Objects on the Earth only grow to a certain size. Similarly the smallest objects we can see are insects, that look take on the form a the seed of life.

Yet beyond this veil is a whole world of activity we call the CELLULAR DIMENSION. This dimension of existence is contained within all living entities in some form. Under the microscope cells look like tiny dots. Yet with the advent of electron microscopes we are able to penetrate even deeper into the fabric of reality, where we find cells are made up of atoms.

In fact the whole universe is made of just 81 stable atoms. These form the periodic table, which is the foundation of all chemistry. Inside the atom we reach the limit of our observational capacity, and so there are many questions that begin to arise beyond that point. At this scale matter reveal itself as mainly empty space, with a tiny nucleus made of protons and neutron that in turn are made out of interactions with Quarks and other bosons.

What lies beyond this? Maybe we shall never know as it may well go on into infinity.

That is the Infinity IN.

Infinity Around

If you ever had the feeling that you are going round in circles, well that’s because you are! In fact the notion of rotation is found as every scale of the universe. From the atom to the galaxy, the whole universe is in motion. We derive our denomination of time from the rotation of the earth, as it traverses its orbit around the sun. Just as we use infinity IN and OUT to determine scales of SPACE, we use Infinity AROUND to qualify time.

To help clarify this important point, let’s consider a table with three apples people sat in a room, large, medium and small. We can identify each one simultaneously, and form a judgement about their spacial qualities; i.e. size. Now if we ask one of them to stand up and turn around 10 times, and then sit back down. If you observe the person in action then to will be able to count the number of rotations. If someone were to walk in during the process and begin counting then they will witness a fewer number of turns, and so their result will be different to yours. After the person sits back down then there is no indicating that anything change from the previous state. A new observer entering the room would be none the wiser. From this we can begin to understand that space is a type of infinity, that passes through a moment of time.

Time is unified and space is differentiated!

We can only exist in our own space, at any particular time and we cannot exist in the same place as another object. As the moments shift, so space get rearranged into a new configuration, completely unique to itself.

This concept lies at the heart of quantum physics, and is expressed in Feynman diagrams that depict the possible interactions between electrons, photons and other particles. As an infinite number of these interaction occur, so the atomic fabric of reality is recreated in the next fraction of time. This time is also quantised into discreet length, call Planck Time, that is governed by the nature of the quantisation of the photon.

Infinity in a boundary

The final type of infinity is an expression of fractal geometry. Whereas infinity IN and Out convey the notion of scale and therefore the idea of space, and Infinity AROUND complete cycles that we can ascribe to time, Infinity within a boundary can produce the complexity of forms found through the universe.

The two most popular forms of Infinity within a boundary come out of the triangle and the square. The Koch Curve was developed at the start of the 1900’s, and describes a triangle that has its sides divided into 3. An additional three triangles are place on the mid section of each side, to form a six pointed star. The process can be repeated on into infinity, adding smaller and smaller triangles at each step, yet the overall form will never exceed the initial boundary of the hexagon. The same can be said of a square, that produces another outer square rotated at 45° to the first. This form of fractal geometry is expressed through a process we call inverse geometry that you can learn about in our course and teachings.

This infinity also finds an expression between the circles placed inside a square. In each of the 4 corners a small square can be placed that fills the space between the circle and the square. We can continue adding more and more smaller square around this initial square and fill the space on into infinity, without ever crossing the circumference of the circles or side of the square. Eventually the difference becomes imperceptible. If you think about a circle that is generated on a computer screen it looks pretty perfect, yet under close examination we see it is comprised of small square pixels.

Reality is similar in many respects. A classic example, posed at the inception of fractal geometry, asked, “what the length of the coastline of Britain?”. From space we can see the island in its entirety, and predict a certain value in km. However, as we move closer we more details become apparent. This adds more length to overall coastline. Closer still, and we realise that the waves are washing up and down against the shore. This means the coastline is actual shifting from one moment to the next. We call this a fuzzy boundary, and it is used to explain why life acts in a chaotic manner whilst at the same time behaves in constancy with scientific observation.

This concept of fractal infinity can be used to explain all kinds of natural phenomena, and we only briefly introduce the concept here. However in our courses and teaching materials you will find a lot more details and explanation, as well as methods for drawing fractals using just a compass and straight edge.


There are different types of infinity that has expressions found in different regular shapes. Infinity IN and Out determine the universal scales, or spacial existence. Infinity ROUND can also be applied in clockwise and anticlockwise rotations, and is akin to time. These infinity work together to produce, and maintain the foundation of reality, time, and space.

The third type of infinity is related to fractal geometry, that is able to fill a space between two types of form. This type of infinity creates the appearance of nature, through mathematical iteration, that is able to produce an infinity diversity, whilst maintaining an adherence to a generalised structure. Whilst each tree, cloud, rick, flower, animal, human being, solar system or galaxy are different, we are still able to recognise each for what it is.

Infinity is in action all around us, at every second of time, and every corner of space, and within everything we are able to experience.

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