Descartes & Geometry
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"Imagine as Descartes did, an interconnected universe. A movement fully complete, a geometry completely full. Where the heavens are liquid and reality is fluid."
- from the film RedFish BlueFish
|Rene Descartes||Descartes: Intellectual Biography||by Stephen Gaukroger|
|A Conservation with Carolyn Merchant||California Monthly, June 2002||by Russell Schoch|
|A History of the Theories of Aether and Electricity||Thomas Nelson & Sons Ltd, 1951||by Sir Edmund Whittaker|
|Golden Proportion||Curious & Interesting Geometry||by David Wells|
|Golden Proportion||Numbers, the Universal Language||by Denis Guedj|
|Equiangluar Spiral||Curious & Interesting Geometry||by David Wells|
|Regular Polyhedra||Curious & Interesting Geometry||by David Wells|
|Dual Polyhedra||Curious & Interesting Geometry||by David Wells|
|Dodecahedron||Curious & Interesting Geometry||by David Wells|
|Octahedron||Curious & Interesting Geometry||by David Wells|
|Cube||Curious & Interesting Geometry||by David Wells|
|Zero||Wolfram MathWorld||by Eric W. Weisstein|
|Integer - a Definition||American Heritage Dictionary||College Edition 1976|
|Difficult Philosophical Questions: Infinity||Aristotle for Everybody, 1978||by Mortimer J. Adler|
|Warren and the Geometrical Approach to i||Wessel Symposium, Copenhagen, 1998||by Caspar Wessel|
|Stanford's Gravity Probe B Confirms Two Einstein Theories||Stanford Report, May 4, 2011||by Staff|
|Einstein was Right About Space-Time||Spokesman Review, October 22, 2004||by Maggie Fox|
|A Brief History of Mind||AdBusters, Nov/Dec 2004||by Nick Wistreich|
|Universe is Finite, "Soccer Ball"-Shaped||National Geographic News, October 8, 2003||by Sean Markey|
|Flight Experiments Study Use of Vortex||Spokesman Review, December 6, 2001||by Andrew Bridges|
|Jet-Propelled Tuna||New Scientist, March 4, 2000||by Bennett Daviss|
It is instructive to practice looking for loops around us. Once we learn to see loops, we begin to find loops everywhere in many shapes and forms.
A symbiotic loop is described by Jimmy Fairchild in the film "RedFish BlueFish":"The earth is bathed in light from the sun. Plants fold the light into plant matter, exhaling oxygen. Animals breathe oxygen and exhale carbon dioxide which the plants breathe. This is an example of a symbiotic loop. With the continuing flow of sunlight, the loop grows. More plants means more animals. More animals means more plants. A causal loop that resonates."The hyperlinks of the above web pages quoted directly from David Wells' "Curious and Interesting Geometry" provide an illustrative example of loops. From within the Dodecahedron web page one might follow the hyperlink to Cube, from Cube to Octahedron, from Octahedron to Golden Proportion, from Golden Proportion back to Dodecahedron.
Language loops are frequent when consulting a dictionary for definitions of words. In the Webster's New Collegiate Dictionary the word "being" is defined as:The word "exist" in the same dictionary is defined as:
- the quality or state of having existence
- something conceivable as existing
- something that actually exists
- the totality of existing things
- conscious existence: LIFE
- the qualities that constitute and existent thing: ESSENCE; esp: PERSONALITY
- a living thing; esp: PERSONFor that matter, every word in a complete dictionary is defined by other words in the same dictionary. A complex structure of loops somehow brings meaning to our language. Perhaps this is how "loopholes" are found in our written laws in which the intended meaning of the law is evaded.
- to have real being whether material or spiritual (do unicorns ~)
- to have being in space and time (the greatest poet who ever ~ed)
- to have being in a specified place or with respect to understood limitations or conditions (strange ideas ~s in his mind)
- to continue to be (racism still ~s to varying degrees)
- to have life or the functions of vitality (man cannot ~ without oxygen)
- to live at an inferior level or under adverse circumstances (starving people ~ing from one day to the next)
- in existentialism: to have contingent but free responsible being
Look for loops and you will begin to see more loops around you.
Descartes & Geometry