Dynamic Symmetry – Phylotaxis – Oleh Bodnar

The term dynamic symmetry was for the first time applied by the American architecture researcher J. Hambidge to a certain principle of proportioning in architecture . Later this term independently appeared in physics where it was introduced to describe physical processes that are characterized by invariants. Finally, in the given research the term dynamic symmetry is applied to regularity of natural form-shaping that in terms of origin also appears not to be connected with Hambidge’s idea, and, moreover, appearance of this term in physics. However, all the three variants are deeply interconnected in terms of their meaning which we are going to show.

At first, we point out strategic similarity of Hambidge’s and our researches. This is a well-known historical direction which in the field of architecture and art is motivated by the search for harmony regularities and, thus, is aimed at studying the objects of nature. Usually architects take interest in the structural regularities of natural form-shaping and, particularly, in the golden section and Fibonacci numbers which are regularities standing out by their intriguing role in architectural form-shaping. It is not accidentally that architects who do researches so frequently pay attention to botanical phenomenon phyllotaxis which is characterized by these regularities.

DYNAMIC SYMMETRY IN NATURE AND ARCHITECTURE

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Softology – DLA – LBM – Snowflake – Cellular Automata
















Number and Magnitude

We have lost the relationship between Number and Form or Number and Magnitude as the Ancient Greeks called their Forms.

Article

A few years ago a Revolution in Mathematics and Physics has started. This revolution is caused by Geometric Algebra.

In Geometric Algebra the Ancient Theories of Euclid and Pythagoras are reevaluated.

Numbers are Scalar (Quantum) Movements of Geometric Patterns and not Static Symbols of Abstractions that have nothing to do with our Reality.

Movements and not Forces are the Essence of Physics.

The basic rule Movement = Space/Time (v=s/t) shows that  Time and Space are two Reciprocal 3D-Spaces. Our Senses Experience Space and not Time.

The Simple Rule N/N=1/1=1 balances the Duals of Space and Time. One Unit Step in Space is always Compensated by One Unit Step in Time.

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Caroline Series – Hyperbolic Geometry, Perspective and Time

Medieval Perspective

Introduction

When we Look with our Eyes and not with our Mind we can See that Space looks very different from what we Think it is. In Our Space Parallel Lines meet at Infinity.

Around 1400 during the Renaissance Painters started to look at Space with their own Eyes and discovered the Rules of Perspective Drawing.

Between 1600-1800 Perspective Theory changed from a Theory of Art to a Theory of Mathematics called Projective Geometry.

It took 400 Years before a few Mathematicians realized that Projective Geometry was the Foundation of Mathematics and it took another 100 years before Projective Geometry started to influence Physics.

In 1908 Hermann Minkowski discovered that Einstein’s Theory of Special Relativity could be analysed using Projective Geometry. Minkowski created a 4D Space-Time Metric Geometry in which he added one Time Dimension.




Many experiments now show that 4D-Space-Time  is not sufficient to incorporate what Time Really is.

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