Inovation Engineering Episode 14 docx

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

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

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]

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]

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

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

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

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

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

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

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 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

divergence-Figure 20.10 50cl Coca-Cola bottle

Figure 20.11 with the angles of 63.4° and 26.6° and the effects of perpendicularity associated with it shows the phenomena linked to two “Golden wing-backs” (with diagonals at 63.4° between them), both of vertical axis, one sideways, the other flat These different angular sets of diagonals indicate a pertinence of the placing of the “waist” (the narrowest part) of the bottle, in the framework of the general architecture of the bottle, defined in Figure 20.11 The

appearance of 63.4° and 26.6° completes almost totally (with the exception of the 30°) the use of significant chosen angles in the geometry of the bottle

Figure 20.11 50cl Coca-Cola bottle

The shape of the main body of the bottle, from the top bulge to the bottom of the divergent portion, up to the widest part of the lower portion (section characterized by

an identifiable seam in the photograph, but clearly visible on the object) appears as a Rectangle whose diagonals are at an angle of θ32 = 54.7° between them This corresponds to a longer side to shorter side ratio, which in this case is, height upon width (diameter of the cylinder enveloping the bottle) equal to x = ( √3+1)/√2 =

√2/(√3-1) = 1,932 This ratio can be split up as x = √2+(√3-1)/√2, or x = √2+1/x (A), a ratio that is very similar to: φ = 1+1/φ (B), defining the Golden Number and the accompanying Golden Rectangles, whose difference is a square, and whose inter- diagonal angles are equal to θ42 = 63.4° Here, the role played in (B) by the unit is played in (A) by √2 = 1.414 The relation (A) shows clearly that the large rectangle that is lying vertically, and whose inter-diagonal angle is 54.7° is the succession: – of a rectangle of relative height √2 which is clearly a dynamic rectangle of the second order, characterized by its angle between longer side and diagonal

θ22 = 35.3° and its angle, complementary to the first one, between smaller side and diagonal equal to θ32 = 54.7°;

– and of a rectangle of relative height 1/x = (√3-1)/√2=√2/(√3+1) = 0.518, similar, of course, to the large rectangle of proportion x, but “flat” (that is, with large horizontal sides), however, the first one is “on its side” (that is, with longer sides vertical) This new rectangle, similar to the entire rectangle, has, also, diagonals at 54.7° between themselves, each of these diagonals being perpendicular to a diagonal

of the similar, vertical large rectangle (as seen in Figure 20.11), making an angle θ22 = 35.3° (not labeled in the figure, but easily identifiable in the rectangle triangles containing the angle θ32 = 54.7° = 90° – 35.3°) with the other diagonal of the large vertical rectangle

Finally, in its turn, the dynamic rectangle of proportion √2 (with its angles θ22 = 35.3° and θ32 = 54.7° between diagonals, and respectively, its longer and shorter sides) can be reduced to a square (with, obviously, its 45° angles between sides and diagonals) and a rectangle constituted by the difference between the initial rectangle and the square, hence by the difference between the consecutive dynamic rectangles of proportion √2 and √1 = 1 Indeed, we know, from the general theorems about the sum and the difference of two consecutive dynamic rectangles that the angle between the diagonals of the difference rectangle is, here too, equal to θ11 = 45° The angular analysis of the bottle (Figure 20.11) makes clear all these successive elements from the various elements that have just been described in detail The sides and diagonals of each element of the general combination are, for the most part, remarkably associated with morphological or graphic elements of the bottle and its label

The lower square extends from the maximal lower section cited at the beginning

of this analysis up to a first increase in the bottle’s contour just below the label Above it is the rectangle whose diagonals are at a 45° angle Its lower edge is obviously the upper side of the previous square, that is, the bulge or excrescence that

has just been mentioned

The upper edge of this rectangle, which is, evidently, the lower side of the next rectangle of the decomposition, is mixed with the lower level of the Coca-Cola logo

on the label, spectacularly highlighting this label and the famous logo

This highlighting is even more striking because the diagonals at 45° between themselves are each, on the one hand perpendicular to the side of the angle, which itself is 45°, and which frames the upper divergence of the bottle, and on the other,

at 45° with the other side of the angle of this divergence Thus, we are faced with a fundamental whole of stable and resonant elements, with an aerial and dynamic character that we may compare, as we have done earlier in the case of certain wine