Why God is a Topologist

god_geometry_bigSometimes I am getting very frustrated when I read spiritual books. I am getting frustrated because those books are a very complicated mixture of many other books that are also very complicated mixtures of other books.

The most complicated spiritual books are the books that use mathematical or physical theories to proof they are Right. The main reason is of course that mathematics and physics is complicated stuff to understand.

Mathematics contains the essence of Physics. You have to understand a little bit of mathematics to understand elementary Physics. The essence of Mathematics is Geometry. When you understand Geometry the rest of mathematics is just calculation (Algebra).

Geometry started as a very practical science concerned with navigation in space and the measurement of all kinds of forms. Soon the old scientists discovered interesting and unexplainable patterns. They discovered a hidden, sacred, structure behind reality and started to find ways to proof their intuiton was right.

It was not for nothing that Einstein believed God was a Geometer. Much earlier the Mystic School of Pythagoras tried to find the Sacred Geometry behind the Numbers to understand the Whole. At this moment Geometry has advanced a lot in relation to the old days of Pythagoras and even Einstein. Geometry is now called Topology, the Science of Spaces. In terms of Einstein, God was a Topologist.

To proof the theorems of Geometry the concept of congruency was used. Two figures are congruent if they have the same shape and size, but are in different positions or in more difficult language,  if they can be transformed by a combination of translation, rotation and reflection. When two figures are congruent they are “the same” and when things are “the same” you are able to prove theorems.

During the Renaissance to understand perspective drawing, two things are considered the same if they are both views of the same object. In the Renaissance the perspective, looking from a different angle, was added as a “the sameness”. Circles and ellipses became part of one class.

A “the sameness” has a lot to do with Identities and Wholes. When your view on “the sameness” changes you are able to identify a different whole. The new concept of the Perspective made is possible to “see” the Sun as a persistent object instead of an ever changing object.  

During the Renaissance the Sun became the Center of the Whole. The highly confusing worldview of the Middle Ages where something was the same when it really was the same object in reality slowly faded away. The external world became the world of the Eye, the microscope and the telescope.

Topology changed this view dramatically. In topology, any continuous change which can be continuously undone is allowed. So a circle is the same as a triangle or a square, because you just pull on parts of the circle to make corners and then straighten the sides, to change a circle into a square.

In the View of Topology the Sun is nothing but a small part of an ever expanding and contracting Universe. Topology transformed the external World of the Eye into the Internal World of Moving Water, Waves and the Emotions, the Felt Sense.  Topology is the Science that prepares the Way for the Water Bearer, Aquarius.

Topology is just like Geometry not only the science of space. It is also the science of transformation and transformation is also the essence of spirituality.

The major issue of Topology is the Contraction and Expansion of forms and again the essence of spiritual transformation is the Breath of God, the Holy Spirit. Topology has also a lot to do with Harmony or Symmetry and again Realizing Harmony is one of the major issues in Spirituality.

The interesting part of Topology is that you are able to do research on a huge scientific mathematical domain by exploring just one structure which is a representative of all the other structures.

ouroboros

The first object of interest are the Circle and The Line. It is not possible to transform a Circle into a Line without cutting the Cycle in one Point, Infinity.

In a circular, moving world, Infinity is non existent or every Point of the Circle corresponds with Infinity. 

This is an  interesting insight because  almost nobody doubts about the fact that the space we live is a Circular Rotating Space. In the World of the Circle  The very Small and the very Big are the Same.

 

monster

According to the Physicists our Space is a much stranger Space than a Circular Space.

Our Universe is highly dimensional because the complicated symmetry of our Universe simply does not fit in a lower dimensional space.

The most symmetric object, strangely called the Monster, uses 196,884 dimensions.

We, the Humans, travel a small part of the Monster, because we are not able to see enough perspectives. A perspective is a dimension.

One of the most interesting subjects is Self-Reference. The most simple Self-Referential structure is a Circle.

Topology contains very special Self-Referencial Structures like the Moebius Ring and the Klein-Bottle. The Moebius Ring is a Space without an Outside. It is closed in Its Self. You always travel the same surface.

klein bottle

A Klein Bottle is even stranger. Its surface is Closed in Itself but it has no Inside and no Outside. It simply IS. 

A Moebius Ring exists in our 3-dimensional space.

A Klein Bottle needs 4-dimensional space. The Klein Bottle has a lot in common with a very old concept, the Ouroburos, the Snake who eats Himself. The Snake is a symbol for the Kundalini, the Force of Enlightment.

knotMore complicated topological structures are Knots and to give you a quick insight, the Universe is a Web that was never Woven, a beautiful Veil that is difficult to See when you are travelling a small part of it.

I know this small blog will not help to get an insight but I assure you that when you start to explore Topology You will encounter new Concepts (or Paradigms) that will surprise You.

Topology will  give You a still small but highly extended perspective on the Creation of the One that expanded in so many Harmonic structures.

LINKS

The History of Topology

About our Limited Perspective and the Limits of Reasoning

About the Topology of Art, a Short Introduction to Bahktin

About Free Will, Time and the Monster

About the Moebius Ring and the Klein Bottle in Philosophy

About Self-Reference in Physics

About Knots in Philosophy

About the Klein Bottle

About the Hyperdiamond

The Monster
The Hyperdiamond

The beauty of our Universe is highly related to what mathematicians call symmetry. A structure is symmetric when it is possible to find a function that maps the structure unto itself.

A simple example is mirror-symmetry. In this case the structure looks the same when it is reflected in a mirror. Another example is rotational symmetry. The structure returns when it is rotated.

The symmetries can be combined to create more complex symmetries. For more than a century mathematicians are trying to create a periodic table of elements of all the possible symmetries called symmetry groups.

The “classification theorem” of such groups, also known as the “enormous theorem” (requiring over 15,000 pages to “prove”), states that the periodic table can be classified completely into 5 groups.

In two dimensions the symmetry-group contains 17 types of symmetrical transformations. All of them are visible around the walls of the Alhambra.

One of the five groups is made up of exceptions to the regularity of the others. These exceptional sub-groups are known as sporadic groups.

Attention has long been focused on these 26 exceptional sporadic groups. The largest of these, incorporating 20 of the others, has been named the Monster — the most exceptional finite symmetry group in mathematics.

bolletjes
Packing spheres

It is a giant (hyper)Diamond in 196,884 dimensions composed of more elements than there are supposedly to be elementary particles in the universe (approx. 8 x 10**53).

The Monster is something special but what makes the Monster spectacular is that it showed a strange connection (called Moonshine) with a very different part of Mathematics called Number Theory.

Recently I read a book about this subject by Mark Ronan called Symmetry and the Monster.

Kissing-3d
The maximum of 12 spheres can be packed in the 3rd dimension

Mathematics and especially Number- and Group theory are very hard to understand even for mathematicians. It is a very special specialization.

Number Theory was one of the most important issues in the Mystical Schools of the Old Scientists.

Pythagorus and of course the mystics in the East were very interested in the patterns behind the Beauty of the Universe. Number was the unifying concept necessary for understanding everything from planetary motion to musical harmony.

They believed the Universe was based on integer numbers (1,2,3,..) and the Monster shows that this could be the case.

One of the magic numbers that would have exited Pythagoras is 24. It is a magic number because the sum of the square-roots of all the numbers 1 to 24 is equal to the square of 70.

The sequence of 1 to 24 is part of a 26-dimensional Lorenz-space that is highly connected to the monster and moonshine. A Lorenz-space is an extension of the space Einstein used called Minskowski space. This space connects space with time. The Monster suggests that we could live in a space of 24 dimensions instead of 3.
24-cell
The kissing number in 4 dimensions is 24. The cells can be connected to the 24d hyperdiamond.

The interpretation of all this in normal language can be found by the relationship of the Monster to a special surface called the Leech Lattice. The Leech Lattice is created when we package spheres.

The Leech Lattice has the highest Kissing Number. This number is 12 in 3 dimensions. In the third dimensions we are able to package spheres that touch other spheres at 12 places.

The Monster connected by Moonshine to Physics (String Theory) shows that our Universe consists of an enormous amount of Bubbles called Quantum Foam. We live in the Universe where the bubbles are touching with the highest kissing number possible. 

LINKS

About the Universe of Bubbles

About the Symmetry of the Sri Yantra