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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:

1. 1. the quality or state of having existence
   2. 1. something conceivable as existing
      2. something that actually exists
      3. the totality of existing things
   3. conscious existence: LIFE
2. the qualities that constitute and existent thing: ESSENCE; esp: PERSONALITY
3. a living thing; esp: PERSON

The word "exist" in the same dictionary is defined as:

1. 1. to have real being whether material or spiritual (do unicorns ~)
   2. to have being in space and time (the greatest poet who ever ~ed)
   3. to have being in a specified place or with respect to understood limitations or conditions (strange ideas ~s in his mind)
2. to continue to be (racism still ~s to varying degrees)
3. 1. to have life or the functions of vitality (man cannot ~ without oxygen)
   2. to live at an inferior level or under adverse circumstances (starving people ~ing from one day to the next)
4. in existentialism: to have contingent but free responsible being

For 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.

Look for loops and you will begin to see more loops around you.

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Descartes & Geometry