Research :: Geometry
 


 

 


 
 

 

 

Geometry

Patterns generated by the CymaScope instrument often receive praise for their beauty, but beyond their obvious symmetrical perfection what do they mean? Do they convey information? Contemplating these and related questions is the purpose of this section in which we begin to investigate cymascopic images for what they can teach us.

The building blocks of matter, whether gas, liquid, solid or plasma, consist of vibrating atoms and / or molecules. Mother Nature does not assemble her building blocks randomly or chaotically; harmony exists at all levels, even extending to the orbital motions within the atoms and molecules themselves. To help understand this principle, imagine freeze-framing the motion within a single atom. Where orbital paths cross, vertices become evident and when these points are connected by straight lines, Euclidean geometry becomes apparent: virtual geometric structures interacting with space. The twin graphic on the right hand side of this page demonstrate this principle1 , showing the arcing dynamics, generated by spin and rotation. Therefore, in a very real sense, matter is geometry in motion.

Just as the microscope and telescope brought unseen vistas into view, the CymaScope reveals the once hidden realm of sound, providing a window into the heart of sonic vibrations. It does so by transcribing the periodicities in a given sound to periodic wavelets on the surface and sub-surface of water. The structures created by sound's imprint on water are quasi-3D in nature and may be considered analogs of the vibrational data within the sound. In a sense the images represent a slice through the spherical propagation of that particular sound. Since the CymaScope uses water of a few millimetres depth, straight line measurements within the imagery approximate the gentle arcs in the dynamics, revealing ratios that can be used to create 3D geometric models.

It is important to note that, in general, single frequency sounds create simple imagery and complex harmonic sounds, such as music, create complex imagery. There are some exceptions to this general rule, the Mereon Prime Frequency pattern being an important example in which a single sinusoidal frequency exhibits complex imagery, for reasons still being explored. More about Mereon can be read in the Mereon section of this web site.


In the geometry gallery a series of CymaScope images are presented in which sound has given rise to a sequence of periodic structures. Examine the images closely and their quasi-3D nature will be evident. The images in the far left column of the gallery are un-retouched CymaGlyphs -- the name given to a sound image -- while in the columns to the right we've delineated a particular mathematical ratio within each image. As this section develops you will see a coherent relationship between the sound of a star, a single cell, a human heart beat and the harmonious sounds from a musical instrument. Many contain identical ratios and demonstrate that the laws of Nature are just as much at work in the heart of a star as within a single cell, a human heart or within heart-felt music. Dr. Stuart Hameroff, physician and professor of consciousness at the University of Arizona, USA, elegantly states something we find relevant. ''Knowing there's this interconnectedness of the universe, that we are all interconnected and that we are connected to the universe at its fundamental level, I think is as good an explanation for spirituality as there is.''


Click on any image in the gallery to enlarge it.

The analysis of other sounds is ongoing and we invite you to revisit this section regularly for updates.



Note1: The graphic images on the right hand side were produced by Robert W. Gray, one of the Mereon team's principle Investigators.


Analytical methods

While not yet a rigorous scientific analysis, in our journey of exploration into the mathematical ratios embedded within CymaGlyphs we are collaborating with two geometers who use different methods.

Intuitive method

US-based musician Clay Taylor, a man passionate about geometry, has conducted the analysis of the images shown in this section. By superimposing accurate geometric forms over a given CymaGlyph, he references the image's primary nodal and / or antinodal points. He then uses an intuitive process to tease out universal ratios, such as those relating to phi and to square roots, both prevalent in Nature, to musical ratios, which are also reflected in the atomic realm. In his own words, Taylor considers his collaboration with CymaScope.com as providing a "holistic analysis of CymaGlyphs, revealing the fundamental rules and behaviours involved in giving shape to these portraits of energy.''

Computer-based analysis in development

Daniel Bell of New Zealand, whose background is computational systems biology, is developing a method that he hopes to use to do a computer analysis of the CymaGlyphs. He states,''I would like to create a real-time version of this computational analysis system, which is 'intelligent' enough to deal with differing CymaGlyphs. I plan on using morphological operators to identify contrasting regions, followed by contour analysis techniques.''

Although Bell's work is at an early stage our hope is that its development can be used in our own small laboratory as well as by scientists who in an intent born of a dream may one day use the CymaScope.

 

 

 

 

 

Click to enlarge

The orbital paths of atomic vibrations can be represented by Euclidian space geometry in which the orbital crossing points (vertices) can be joined by straight lines to reveal the virtual geometry that exists at the atomic scale, and even at the cymascopic scale.

The illustration shows two moments of the Mereon vibration. The white lines represent the mereonic orbit, the yellow-green spheres represent the orbital crossing points (vertices) and the multicoloured geometry within the orbital paths is the resulting virtual Euclidian space geometry created when the vertices are joined by straight lines.
 

 Image credit: Robert W. Gray

 

 

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