Proposal: Symmetry of Crop Circles

Topic:

I wish to explore the symmetry of crop circles by employing the accepted classification scheme for planar symmetry groups. Recognizing that all crop circle designs are planar and ‘revolve’ around a center, point group and, to a lesser extent, wallpaper group symmetry will most likely be involved.

Throughout this study, I wish to delve deeper into rotational and reflectional Euclidean plane isometry theory and explore the ways planar symmetry is classified. In doing so, I hope to gain a better understanding of the ‘language’ of symmetry and perhaps attempt to use this language to decipher some meaning from the crop circle phenomenon.


References:

Web-sites on symmetry classification:

• http://en.wikipedia.org/wiki/Euclidean_plane_isometry
• http://en.wikipedia.org/wiki/Reflection_symmetry
• http://en.wikipedia.org/wiki/Rotational_symmetry
• http://en.wikipedia.org/wiki/Symmetry_group
• http://en.wikipedia.org/wiki/Point_group
• http://en.wikipedia.org/wiki/Cyclic_group
• http://en.wikipedia.org/wiki/Dihedral_group
• http://en.wikipedia.org/wiki/Wallpaper_group
• Derivation and Classification of Groups: http://www.xahlee.org/Wallpaper_dir/c4_Derivation.html

• Tables and illustrations of the 17 wallpaper groups: http://www.xahlee.org/Wallpaper_dir/c5_17WallpaperGroups.html

• http://en.wikipedia.org/wiki/Orbifold_notation
• Field Guide to Orbifolds: http://www.geom.uiuc.edu/docs/doyle/mpls/handouts/node39.html

• http://en.wikipedia.org/wiki/List_of_planar_symmetry_groups
  

Potential books:

• Alexander, S. Crop Circles: Signs, Wonders and Mysteries. Chartwell Books, 2006.
• ISBN: 0785820698
• Burn, R. P. Groups, a path to geometry. New York: Oxford University Press, 1985.
• ISBN: 0521300371
• Location: Daley Library - Math Collection/2d floor south - Books
• Call Number: QA171 .B93 1985
• Butler, Philip H. Point group symmetry applications: methods and tables. New York: Plenum Press, 1981.
• ISBN: 0306405237
• Location: Science Library/3500 SES
• Call Number: QD911 .B89
• Yale, Paul B. Geometry and symmetry. San Francisco: Holden-Day, 1968.
• Location: Daley Library - Math Collection/2d floor south - Books
• Call Number: QA477 .Y3

Crop Circle reconstructions using simple geometry:

• http://www.zefdamen.nl/CropCircles/en/Crop_circles_en.htm

High-quality photos of crop circles:

• http://www.temporarytemples.co.uk/

Critique

Critique of:
Parallel visual processes in symmetry perception: Normality and pathology
By JOHAN WAGEMANS

An overview of the general field of research involving symmetry recognition in humans is presented. As this article is a mini-review, it only gives brief explanations of what seems like a great deal of data. However, the author concludes that more research must be done because thus far results have been inconclusive to explain the physiological mechanisms by which humans recognize symmetry patterns.

What can be concluded from the data is that the human visual system is quite good at perceiving symmetry – so much so that many patterns are recognized preattentively. Vertical symmetry seems to be the most easily perceived, followed by horizontal, and then oblique point symmetry at main diagonals (45 and 135 degrees apart from a vertical or horizontal axis).

What struck me most about the data presented was the apparent adaptivity of humans to perceive symmetrical patterns. The couple cases presented of patients with brain and visual defects proved that even these patients were able to detect symmetry albeit at a preattentive (subconscious) level. This made me think that preattentive recognition of symmetry was an evolutionary phenomenon – an inherent ability of all human beings that somehow contributed to their evolutionary progress.

This makes sense, considering that nature itself appears to operate on symmetrical levels. Symmetry is abundant in plant and animal life, and humans’ ability to recognize patterns in nature helped them classify objects into categories for survival purposes. Classification of the vast amounts of data in the outside world into groups made it easier for humans to operate in this material world and made it possible for them to communicate with each other, thus leading to the development of language and society as we know it today.

Sequence of Numbers

I asked 13 of my friends which sequence of three numbers (3, 6, and 9) they 'favored' and obtained the following results:

369 : 3 (23.1%)
936 : 1 (7.7%)
396 : 2 (15.4%)
693 : 1 (7.7%)
963 : 5 (38.5%)
639 : 1 (7.7%)

Symmetries of Simple Shapes: Revised

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Symmetries of Simple Shapes

Please click on the image to view FULL SIZE.

Symmetry in Crop Circles

In the past decade, crop circles (such as the one to the left, image copyright www.temporarytemples.co.uk) have been increasing in quantity as well as complexity all over the world. A few obvious hoaxes aside, all evidence points to these phenomena being natural. Recently, scientists have started investigating crop circles and their findings seem to confirm the natural authenticity of most crop circles. Scientific papers published in 1999 and 2001 point to the most probable formation of crop circles to be naturally-occurring ‘balls of light’ that emit electromagnetic radiation that then causes nodes on the stems of corn-like plants to lengthen, an observation made at almost all crop circle sites.

Simple summary of findings:
SCIENTIFIC STUDIES "CONFIRM CROP CIRCLES ARE MADE BY BALLS OF LIGHT" by Dr. Eltjo Haselfoff, 31/07/2001; found at:
http://thecropcirclewebsite.50megs.com/page52.htm

Actual 1999 paper, published in PHYSIOLOGIA PLANTARUM, Volume 105: 615624, 1999: “Dispersion Of Energies In Worldwide Crop Formations” by W. C. Levengood and Nancy P. Talbott; found at:
http://www.bltresearch.com/dispersion.html

Actual 2001 paper, published in PHYSIOLOGIA PLANTARUM, Volume 111, Issue 1, Page 123-124, January 2001: “Opinions and comments on Levengood WC, Talbott NP (1999) Dispersion of energies in worldwide crop formations. Physiol Plant 105: 615–624” by Eltjo H. Haselhoff; found at:
http://www.blackwell-synergy.com/doi/abs/10.1034/j.1399-3054.2001.1110116.x


Whatever their origin, crop circles take wonderfully complex shapes that are often symmetrical and easily reconstructed using only the most basic of geometric shapes and techniques. I thought it would be fun and interesting to study the symmetry in various crop circles from around the world.

Internet headquarters for crop circles; features photos, reconstructions, and commentary:
http://www.cropcircleconnector.com/interface2005.htm

High-quality photos of crop circles taken from the air:
http://www.temporarytemples.co.uk/newweb/imglib.php

Vector graphical re-creations of crop circles:
http://www.cropcircle-archive.com/archive/index.php?language=en


Some examples of recent [2007] crop circles (all images copyright www.temporarytemples.co.uk):