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Happily, the same is true in three dimensions: the increasing volumes of subdivided tetrahedra (if this is an unfamiliar shape, wait until the next chapter!) supply the third-power values just as accurately as do subdivided cubes: 2 ³ = 8, 3 ³ = 27, 4 ³ = 64, etc. (3) Tetrahedra of course take up less room than cubes, and to Bucky, the choice is clear. We do not, at this point in the text, have the necessary experience to fully understand the third-power model shown in Figure 2-2, but the relevant principles will eventually be discussed. The point to be made now is that squares and cubes cannot boast a special inherent significance for multiplicative accounting. Triangles and tetrahedra are equally reliable (and in some ways more reliable, as we shall see). Fuller argues that our arbitrary habitual references to squares and cubes keep us locked into a right-angled viewpoint, which obscures our vision of the truth. From now on, says Bucky, we have to say "triangling" not "squaring" if we want to play the game the way nature plays it.
Fuller's concern with fine-tuning communication, developing and using words that are consistent with scientific reality, is one facet of the role of language with respect to synergetics. Another deals with the difficulty of describing visual and structural patterns. Anyone who has tried to describe an object over the telephone is well aware of the problems involved; there seems to be a shortage of functional words. The temptation to use your hands is irresistible, despite the futility. This scarcity of linguistic aids is especially severe for non-cubical structureswhich characterize most of nature. That a language of pattern and structure is not widely accessible indicates that humanity's understanding of such phenomena is similarly underdeveloped. We thus join forces with Fuller in an investigation of this neglected field, and in so doing we become more and more aware of the rich complexity of the order inherent in space. Along the way, we are introduced to some new terminology that includes the lesser-known language of geometry as well as some words invented by Fuller. More informationuseful only, it is clear, if the terminology is both precise and consistentleads to better comprehension, which in turn leads to the ability to experiment knowledgeably. Experiment fosters both greater understanding and inventionin short, progress.
In conclusion, Fuller's insistence on employing accurate vocabulary is part of an important aspect of human communication. We join him as pioneers in the science of spatial complexity, the terminology of which is for the most part unfamiliar. The systematic study of structural phenomena is an important and badly neglected aspect of human experience.
There is a strong temptation to ignore synergetics on the grounds that we feel perfectly able to handle mathematical concepts that cannot be seen. Academic "sophistication" leaves us with a certain intellectual pride that makes Fuller's observations with their child-like (but-the-emperor-isn't-wearing-any-clothes) ring to them seem unimportant. Every child is boggled by infinity and surfaces of no thickness, but these are necessary concepts, natural extensions of philosophical "what-ifs." The human mind is not bounded by the constraints of demonstrability.
True enough. However, it is also possible to define a system of thought and exploration that is confined to the "facts of experience," and moreover such a system is able to reveal additional insights about physical and metaphysical phenomena that would not necessarily be discovered following the traditional route. Such is the case with Fuller's synergetics; as we shall see, his hands-on approach led to a number of impressive geometrical discoveries. Synergetics is a different kind of mathematical pursuit, not a replacement for calculus but rather a complementary body of thought. Reading further will not face you with an ultimate demand for a decision of fundamental allegiance: synergetics or the mathematics you learned in school. Rather, you have the option of being additionally enriched by a fascinating exploration of structure and pattern that cannot help but change the way you see the visual environment. When Bucky reminisces, "There is nothing in my life that equals the sense of ecstasy I have felt in discovering nature's beautiful agreement," he offers us an enticing invitation. He has taken an alternate route and it has not disappointed him.
Operational mathematics cannot claim exclusive rights to the name of mathematics, any more than other branches of mathematics can; it is simply a new approach, stemming from the characteristically human drive to experiment. Its claim instead is that exposure to these concepts fosters an understanding of nature's structuring and therefore provides an advantageous base of experience. In short, synergetics is an internally consistent system which has produced significant models with respect to certain physical phenomena and led directly to practical inventions (with "life-support advantage," to use Fuller's terminology). It is likely that thus far we have only skimmed the surface of the applications of synergetics; very few people have been exposed to its principles, and so their full significance is as yet untested.
Finally, Bucky's approach is compellingly playful, and we should read his material with the inclination to enjoy the adventure. "Sense of ecstasy"? Why not? Fuller's unorthodox way of looking at mathematicsand indeed Universecan provide a way to circumvent some of our more rigidly held assumptions. Here is an invitation to start over; with a temporary suspension of disbelief, we can embrace a new understanding of the exquisitely designed "scenario Universe." One of the challenges of synergetics lies in opening rusty mental gates that block discovery, for we are asked to be explorers and "comprehensive thinkers"job titles not usually assigned in our specialized world. The essence of synergetics is "modelability"; anyone can play with these models, and likewise, claims Fuller, anyone can understand science once they get their hands on nature's coordinate system. Its accessibility and emphasis on experimental involvement makes Fuller's thinking extremely important. He offers us an approach to learning and thinkingan open-minded, experimental curiositywhich itself is applicable to every discipline and aspect of life. No question is too simple or too complex to be asked. Fuller's first words in Synergetics are "Dare to be naïve," reminding us that we have the option to see the world through new eyes.
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