Inovation Engineering Episode 14 docx

Shapes, Knowledge and Innovation 357 Figure 20.1. Vortexes above a Delta Wing whose leading edges are at a chosen angle Figure 20.1 shows how, above a Delta Wing placed in a relative wind to which it is highly inclined (the inclination would be seen in profile and it is evidently meant to ensure an upward force called aerodynamic lift), vortexes called lift flaps are developed. Around these, the flow swirl while increasing its speed and decreasing the pressure exerted above the wing. If smoke is emitted in the immediate neighborhood of the front point of the wing, from where the vortexes are created, it splits and follows one or another of the vortexes (here rectilinear, as are the leading edges (front end) of this wing) because the length of the axis of each vortex, the rotation of fluid is nil, while it is intense around them. The smoke therefore shows up a couple of vortexes, thus revealing also that wings whose leading edges form a chosen angle θ11 = 45º creates vortexes placed at θ33 = 30º with respect to each other (Figure 20.1). A wing opened to θ22 = 35.3º, creates, for its part, vortexes angularly distanced by θ55 = 24.1º, just as a wing with an angle of opening called “apex angle” θ33 = 30º produces an inter-vortex angle of θ77 = 20.7º and that, finally, we witness “filiation” θ44 = 26.6º å θ99 = 18.4º. Two other filiations are equally essential: θ42 = 63.4º å θ11 = 45°, and θ32 = 54.7º å θ22 = 35.3º. Thus were established [LER 85] the “laws of filiation” that will play, as will be shown later, an important role in the objects and the text-image matching. 358 Innovation Engineering: The Power of Intangible Networks Figure 20.2. Concorde and its angular coupling Figure 20.2 shows the leading edges of the Concorde with their 30° angle between the anterior portions on each wing, those of 24.1º between each anterior rectilinear portion and the following inflected portion on each wing, and finally that of 54.7° between the inflected portion of each leading edge and the rear edge called “lateral upper band”. These angles have largely contributed to the stability and to the feeble flow noise around the aircraft (distinct noise made by the reactors) during the 34 years of flight of the most beautiful bird created by man to date. Figures 20.3 and 20.4 illustrate the presence of chosen angles in natural structures subject to constant wind action, or which create in front of them, as efficiently as possible, relative wind (case of a bird’s wing in flight): – Very fine sand dunes in the Sahara (Figure 20.3), where the sand grains are so fine that the crests of dunes place their successive inflexions described by Roger Frison-Roche as “pure and quasi-abstract threads that link their ondulations between themselves” in a way that “the moving hills are so completely in proportion that one would not be able to give them dimensions and one would think that, in creating them, nature has divinely respected the Golden Number” [FRI 54]. Shapes, Knowledge and Innovation 359 Figure 20.3. Fine sand dunes in the Sahara, near Douiret (Southern Tunisia) – Successive elements of the leading edges of a bird’s wing (Figure 20.4): the Golden Angle θ42 = 63.4° gives an impressive majesty to the flight of a silver seagull, evoking the following affirmation by Gaston Bachelard: “the movement of flight gives, immediately, in remarkable abstraction, a dynamic, perfect, complete and total image” [BAC 43]. 360 Innovation Engineering: The Power of Intangible Networks Figure 20.4. Silver seagull in flight 20.2.3. Golden angles and other geometric forms These golden angles, along with other geometric forms (golden rectangles, root rectangles) seem to constitute a framework that is especially conducive to evocation of feelings of calm and stability. Numerous works of art from Antiquity show the use of these geometric forms to give rise to these sensations. Figure 20.5. Creation of dynamic rectangles from square and the relation between two consecutive dynamic rectangles and the one preceding this difference Since the early post-Pythagoras era, these rectangles and these numbers have been considered standards of beauty and harmony. Indeed, the chosen angles of the first family are also the angles between the longer side and diagonals of root rectangles, so named because the ratios of their sides are equal to the square roots of Shapes, Knowledge and Innovation 361 successive integers (√1 = 1; √2 = 1.414; √3 = 1,732; √4 = 2; √5 = 2.236; etc.) and described by Plato as “dynamic rectangles”. These rectangles are each obtained from the preceding one by dropping one its diagonals onto its longer side by extending it. The order of a dynamic rectangle is its number in the series which is just defined, the dynamic rectangle of the first order being the square. For example, the square of the first order, having characteristic angle of 45°, the dynamic rectangle of order 3 corresponds to an angle of 30°, and one of order 6 corresponds to 22.2°, in all cases between the longer side (or the short edge for the square) and diagonal (Figure 20.5). Moreover, it is very easy to establish mathematically (as, for example, is shown visually in Figure 20.1 in the case of the angle θ55 = 24.1°) that the difference (case of Figure 20.5) where the sum of two consecutive dynamic rectangles has the same angle between its diagonals as the angle between the diagonal and the longer side of the smaller one of the two dynamic rectangles. As to the chosen angles of the second family, they are, for the 35.3°, common with the first family, for the 54.7° and 63.4° complements of the 35.3° and 26.6° of the first family, the 63.4° being, also, the angle between the diagonals of the famous Golden Rectangle (Figure 20.6) whose ratio between sides is φ = (1+√5)/2 = 1.618 which is the famous Golden Number. Figure 20.6. Square, Golden Rectangle and Golden Number Let us remind ourselves that the Golden Rectangle is a rectangle such that if we remove from it a square constructed on three of its sides the remaining rectangle, which is also a Golden Rectangle, resembles the initial rectangle, thus fulfilling a “thirst for invariance of the Central Nervous System” [PAI 74]. 20.2.4. Contributions of neurophysiology As early as 1980, Le Ray spoke of the link between the existence of chosen angles as criteria of impact, memorization of images and the existence of cerebral mechanisms and structures that would explain the “thirst for invariance of the 362 Innovation Engineering: The Power of Intangible Networks Central Nervous System”. The presence of “genetically pre-cabled detectors of form” was already linked to the functional specialization of the neurons of the occipital cortex (areas 17 and 18) studied since the 1960s by D. Hubel and T. Wiesel. These two neuro-physiologists of the Harvard Medical School in Boston, authors of about 20 publications since 1962, were awarded the Nobel Prize for Medicine and Physiology in 1981. 20.2.4.1. Informative zones One of their most important discoveries concerns the existence of preferred orientations by neurons of the visual cortex or, more exactly, an orientation preferred by each of these neurons. Experiments were conducted in which a micro- electrode was introduced into the visual cortex of cats or monkeys obliquely to the external surface of the brain. The eyes, immobilized in advance, of these animals were subjected to stimuli consisting of black lines on white backgrounds or white lines on black backgrounds, or of black and white zones intersecting. In these three cases, the “informative zones” described by psycho-physiologists were involved. D Hubel and T Wiesel [HUB 77, 79] published some 15 articles giving figures which showed the directions preferred by neurons of one area of the visual cortex, this preference was signaled by obtaining maximum electric potential in this region when the stimulus passed through a “preferred orientation”. 20.2.4.2. The neuronal structures of the visual cortex and the chosen angles Martinache, Le Ray and Levin [MAR 83] proceeded to enlarge these diagrams and studied the angles formed between the preferred orientations of adjacent or neighboring neuronal columns. The results of these studies show that: “every preferred orientation makes chosen angles with at least one other orientation (but usually with two or more others)”. If these results are taken into consideration, it is likely that there exist within the visual cortex neuronal structures that facilitate the perception of chosen angles. 20.2.4.3. Angularly noticeable dipolar nature A dipole, generally, is a combination of a “source” and a “well” (source and attractor of a hydrodynamic and aerodynamic flow, positive and negative charge in electrostatic) placed very near one another and which define the axis of the dipole thus formed by the help of the segment which joins them. This structure in “source and well” is identical in its effects, that is, by the field of speed, to that of the very concentrated rotational loop of a fluid on itself, called a ring vortex, that makes the liquid pass into the interior of the ring and bringing it out along the lines of closed currents. Yet, the common form of the lines of fluid current created by a hydro or aerodynamic dipole and the electric or magnetic field lines created by an electrostatic or electric dipole (made of a small loop of electric current) shows properties remarkably like those of the angle characterizing the position of one point with respect Shapes, Knowledge and Innovation 363 to the dipole and its axis, and the angle characterizing the position of the speed of this point with respect to the line joining the dipole to the considered point, this line being the second side of the preceding angle. These observations make sense if we connect them to the work of neuro-physicists on the measurement external to the cranial box, in width, direction of magnetic fields coming from diverse cortex of the human brain, the measurement which enabled the reconstitution of a map of magnetic fields within the cortex, and of the electric currents responsible for their formation. The loops of electric current, thus revealed create a distribution of magnetic fields whose field lines are very similar to those created by an ideal dipole made of a loop of circular current. Both the dipolar point of view and the general vortex point of view explain the omnipresence of chosen angles. 20.2.5. Contribution of cognitive psychology Although not explicitly stated, the chosen angles and the remarkable angular combinations appear indirectly in theories of cognitive psychology, especially in the recognition of forms and implementation of the attentional process where memory plays an important role. In the beginning, studies on recognition of forms were confused with more general perception processes, such as Associationism and Gestalt [GUI 37] but soon, two theories supported by two different conceptions of identification emerged: – The first concept highlights pairing between two prototypes: being from the Gestalt thesis [WER 23], it opines that identification is based upon global perception. Secondly, Rosch [ROS 73, 76], introduced the idea that comparison between the example and the prototype could result in a judgment of closeness. Certain examples would be closer, more typical of, the prototype than others. – The second, coming from “associationism” is based upon the description of images in lines, with the identification models [NEI 64] or componential [SMI 74]. Diverse contributions from quantum physics, neuro-physiology and cognitive psychology have rarely been used in fields so closely connected to marketing and design wherein forms, images constitute the apex of success of products sold to different consumers. 20.3. The spatial quantification of an object In this section we shall present some analyses on two objects: the new Perrier bottle and a bottle of Coca-Cola. Previously, we referred the reader to some publications by the authors, or by one of them, and especially to the first of the works cited, which is the most thorough, with 16 graduated figures in domains from 364 Innovation Engineering: The Power of Intangible Networks Hydrodynamics to Pictorial Art, via natural forms [LER 80], as also to the most recent work, which is also quite comprehensive [MAT 04]. Every object, before any stylistic study [CHR 96], whether new or innovated, presented to a prospective consumer, must have an attractive shape, and as we have demonstrated [MAT 01, 02], in the case of wine bottles, this characteristic is linked to the presence of chosen angles and remarkable proportions, and to resonant combinations thereof, in different parts of the bottle and between themselves. In this perspective, and to complete the works cited above on bottles, we have chosen the new Perrier bottle that is identical in shape to the type “FLUO”, and its equivalent in the market, the new bottle of Coca-Cola, that are current references in the soft drinks market. As we shall show in the following analysis, these two bottles possess fundamental directions that are dynamic and/or structuring. In the Perrier bottle, the left-right and right-left crossings of the sides that do not correspond to angles of divergence greater than or less than 35.3° and 54.7° determine the angles 45° = (35.3°+54.7°)/2 and 45° = (54.7°+35.3°)/2 (Figure 20.7) which contributes to the unity of the form, Figure 20.7. 50cl “FLUO” type Perrier bottle Shapes, Knowledge and Innovation 365 Moreover, the angle of divergence, this time towards the top of 24.1° (Figure 20.8) transforms the single filiation 54.7° å 35.3° into a double 54.7° å35.3° å24.1°. Figure 20.8. 50cl “FLUO” type Perrier bottle On its part, the Coca-Cola bottle, a priori more classical and more austere, perhaps less spontaneous dynamically, shows, in contrast, a resonant structuring that is more elaborate, wherefrom, literally, emerges an impression of authority. Figure 20.9 (with the angles 45°, 54.7° and 35.3°) is particularly subtle, complete and stable. 366 Innovation Engineering: The Power of Intangible Networks Figure 20.9. 50cl Coca-Cola bottle Figure 20.10 shows the initial divergence-convergence at 45° (compared to “Bourgogne Tradition” bottles) that was seen from the outset. This divergence- convergence must obviously be taken up again in Figure 20.11, already referred to for explaining the effects of perpendicularity and resonance with elements of the main body of the bottle. [...]... 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Concorde and its angular coupling. remarkable abstraction, a dynamic, perfect, complete and total image” [BAC 43]. 360 Innovation Engineering: The Power of Intangible Networks Figure 20.4. Silver seagull in flight 20.2.3 the square roots of Shapes, Knowledge and Innovation 361 successive integers (√1 = 1; √2 = 1. 414; √3 = 1,732; √4 = 2; √5 = 2.236; etc.) and described by Plato as “dynamic rectangles”. These