INTRODUCTION
“The theory of the form "taught at the School of the BAUHAUS had followers until Latin America.
Our professor of architecture, Henri CIRIANI, left his country, Peru, at the end of the Sixties, and in a didactic way this discipline restored us which thus never
completely disappeared.
Formed to follow the evolution of the forms and spaces in architecture, it is at the end of the Eighties, that I wondered for the first time about the possible applications
of this discipline in cosmology.
Walking me close to the station St Lazare, I initially considered a limit which moved, then I took a reversed image of cosmos, (to privilege the vacuum) bubbles in a soft
body bordered by a crust, with the following idea: If the limit between the empty bubbles and the full soft body is frank, the universe is bordered by a crust.
However the edge of the universe isn’t a crust it seems? and nobody could affirm me that there was an indivisible particle, infinitesimal part of the matter.
(Science and Future Nov./DEC 97, J.Mr. ALIMI, Astrophysicien at the Observatory of Meudon proposes an image which takes into account the scale of the galaxies as a whole
allowing a continuity of full and vacuums overlapping which satisfies better the remarks developed in this text).
Little time afterwards, I read the book of S. Hawkins with a persistent idea. Why did a universe “limited without end” evoke it and described it origin like a closed system?
Why the universe it would not be limited without end of any share?
Ghost with my preceding investigations, I realized later that it was necessary to reverse the proposal until the end.
That gave planets in a space rather close to the vacuum bordered by a vacuum emptier than the precedent probably compensated by intense fluctuations. The crust also had its
negative.
There did not need more frank limit between full and vacuum, it could exist an edge of the universe avoiding the question of beyond that. The universe generates its own
context.
For me, that did not plead in favour of an infinitesimal indivisible particle of the matter, even if the matter and the vacuum are of different nature.
(The principle of exclusion prohibited to 2 material particles to be in the same place whereas 2 interactive particles (particle of the vacuum) can it. This concept
immediately allured me because it placed the vacuum in the centre of the system).
Several years after, at the time of a wedding service in Laguiole, after having read an article employing the “elastic” word, I thought for the first time of putting in
parallel the property of expansion of the universe and character fluctuating the possible of the edge of the universe with his possible share of autonomy.
Previously I established a correspondence in a chronology ternary of different states, full, empty, edge putting the vacuum at the centre of all things. There it was a
question of generalizing the idea that all in the universe is extensible, included the matter.
Thus the infinite one became a local property and everywhere at the same time, very distant from the hereafter, and which one could plan to describe the mechanism.
“The infinite one is on the shoulder of my neighbour, was my first intuition ".
I would conclude my introduction by evoking the property from “not recursivity” evoked by the mathematician Penrose.
Intuitively, I think that this property qualifies rather well what divides the 2 complementary worlds mentioned above.
That consisted of bubbles in a soft body bordered of a crust and universe.
This “division” or this “passage” is the topic of this text and my work of architect.
Walking in front of the Cook villa, to Boulogne 12 years after having left the school I realize of the difficulty which we had to analyze architecture. This normal period of
training did not enable us to apprehend globality. The obsession of our teacher to refuse any formalism and all recipes, required us of perseverance.
The principal error of judgment relating to modernity is undoubtedly systematically to associate it the concept “speed and of expressivity” and to consider dissymmetry like
a new dogma. For as much we were conscious that there was an order in this new manner of conceiving space.
“To build the vacuum “is a beautiful formula, but that is not natural, a long training is necessary so that our way of structuring the vacuum definitively carries it on a
purely sculptural design of architecture.
My file joint with this text, written after my studies is the assessment of this training of the design of space.
In the prolongation of this file, there are 4 fields who interest me, the impact of vibratory movements, the description of the scaling in space
(threshold of inversion of scale), concept of polarization who integrates the preceding one and the process of evolution by taking architecture
like model.
These 4 topics are integrated, in my opinion, in an overall process.
1 EVOLUTION
The world seems to roll in the same circle but this circle is a spiral which always rises. (History of the Romans - Victor DURUY)
It is by systematically photocopying the majority of the reviews and books of Architecture that I became aware of this permanence of the movement of
pendulum who characterizes the evolution in this field. That the humanistic ones reassure that does not destroy the role of the individual. The evolution nead
the means of the individuals. The individual nourished collective knowledge, the mechanism of exchange is permanent and the exceptions in cycle evolution confirm
the rule. (Persistence of bunches “traditional“ during one time with dominant ”baroque“ with all the tendencies possible intermediaries).
The term of pendulum can actually lend to confusion because the arrow of time is not reversed, I would say
that there is 2 cyclic dimensions and 1 dimension in evolution.
(Conflict in space between symmetry point and axiality of the space subjected to vibrations, prohibited the reversibility of time, see conclusion of the
text).
It seems that the tendencies alternated with bursting or with integration forms and their spaces are done increasingly extreme and more and more rapids.
Actually I think this mechanism of alternation is constant in the duration but it breaks up in under increasingly brought closer sets. With a certain scale the evolution
can seem being linear.
(For certain person, the recent resurgence of conflicts and epidemics discredits the idea of a “end of the history”. For me, it is this permanence of these mechanisms which
could have killed the history).
In the same order of idea, if you analyze the progression which characterizes the “sonata with the moonlight“ you realize that the topic is not simply
repetitive. All the parts are overlapping. A singular note of the beginning announces the medium of the piece and the fall.
(The movement is internal, the curve braces the construction, the system is recurring).
Architecture can be sometimes revealed of a blow as with the Pantheon in Rome. The music, even coherent as a whole is a succession of measurements made up of notes or
agreements. The superposition of several notes gives an agreement, the superposition of silences does not exist, only their duration can be prolonged.
This overlap of the notes and silences characterizes the evolution of a piece.
Moroever it context, never identical, influences the evolution of architecture. The context influences the actors, those influence more and more the
context, the 2 form the same entity. I do not oppose nature to the man and its capacity of abstraction, the 2 form our world. conscience of the cyclic process evolution does not
allow one unlimited acceleration progress. On the other hand it supports significant jumps of this evolution.
Gravity of the history, gravity of the knowledge, recurrence phenomena supports of the evolution.
Example of rational inscription in the chronology of the history of architecture
BALDEWEG, (Spanish architect, see file) by reinstating in its manner the cupolas flattened of the architect
19th SLOANE, proposes an identifiable space in a fluid unit.
To fix space thus reinstates a typical approach of past architecture which requires an effort curiously.
That does not have anything naturalness at first sight. This step is in fact the base of all “revolution” in architecture. Bruneleschi, Palladio, Le Corbusier are turned
over to the sources.
Modernity – abstraction : There are no pure systems a priori - any system can find its balance.
The bursting of the forms is with the measurement of the quantity of material implemented .
The simple forms can be poor or integrate an internal sophistication.
There is an architecture “baroque“ pure as it can exist a “traditional“ architecture exempt of contents. Paradoxically at “the pre modern
ones” or “decadents” the bursting is apparent and peripheral (Theo Van Doesburg, precursor of architecture cubist, primarily destroyed the external volume of its constructions). Those which one
describes as revolutionists like Corbusier, disturb the heart of their compositions and recreate a coherent unit (registered in a simple figure or not in reaction and/or symbiosis with the
context).
Architecture purist and minimalist of Le Corbusier do not represent degree 0 of architecture. He purified the external and apparent forms of its buildings while
integrating the beginning of an intern volumetric sophistication unequalled before. By comparison, the provocation of the white sheet of certain painters appears futile, it acted exactly of the
trap of modernity.
EXTRAPOLATIONS
It is into 1978 that I tried to apply this design of the evolution to other fields. Whereas I was in the vicinity of Orly I wondered whether the future engines of plane
would use again propellers. My father who worked in aeronautics assure me that there were studies in this direction in the USA. The motivations were economic, and perhaps it is
the fall in the price of the oil which returned this research without object.
It is interesting to note that the shape of these propellers was completely different from their ancestors, they became “baroques”, heavy etc… It was not a
regression, but a new synthesis.
In another way, I was interested in Spanish architecture, then completely ignored, by finding reviews of this country at the University of Berkley in 1980. However I think
that each point of the sphere has a singular “colouring” and that evolution nourished these particularisms.
It seems to me in addition that North-South contrast is stronger than East-West contrast. Thus,
in 1987, I indicated, following successive deductions, that the countries of north were going to play an important part. I was thus not astonished when a few times later the
bookshop of the Monitor devoted its front to works concerning Swedish architecture.
At the same time, I indicated the northern border of Finland and I employed the expression “finlandisation of the USSR". I was unaware of the existence of
the Baltic States.
Deviated southern northern evolution. Principle of exclusion - the evolution can be done with difficulty in all the directions at the same
time - cold materials or heats - cold colors or heats - certain criteria can be superimposed in a way complementary to others cannot it, at least on a certain level of synthesis.
(The earth being spherical, one can say that there are all possible colourings. With a certain scale one can consider that the points in the medium of the ocean are
reconstituted on average insofar as the continents are sufficiently dispersed to be representative of the various climates. If the ground were larger each point would become a circle. There is no
limit with the evolution. Each point becomes a cone.
DETERMINISM
Following a readingrelating to the equations of Lorentz, I drew a figure which resembled a wheelbarrow.
The wheel was the source, the vat resembled a volume expanding regular and the curved handles represented lines which stretch space.
Thus, by comparison, if the trajectories of the particles are probabilists, I associate a volume expanding regular it. I tend to consider that the regularity in 3D confers
one coherence with the unit, even if the particles can borrow ways which all are not inevitably finalized and relevant. They traverse “the Universe of
Possible”.
In an imbricated system, the architect can control the whole until the coherence of the details by some
specific controls. Either we draw until finding a solution which appears coherent to us, or we
let us imagine a space which we then represent with a minimum of useless layouts. In all the case we
let us be brought to to make corrections. The first method is sometimes striking, the second can be more virtuoso since imagination is not attached by the means of
representation.
The fact to not finding immediately a solution coherent does not mean that our preliminary layouts are the fruit of chance, I think that they are conditioned by our
environment.
The passage of the 2D with the 3D appears essential to me. One can summarize by proposing an unspecified whole in a determined one etc... Actually I think that our
vocabulary is unsuited.
A probabilistic whole in a determined unit produced it a vaster unit, determined?
The scientifics like the philosophers admitted that the earth was not the center of the universe, for as much any opposite excess privileging the thesis of the absolute
chance, making disorder a new dogma is in my opinion an error which constitutes a form of vanity again.
“The order” and symmetry also exist at the modern time, it is to us to approach these concepts in a way more abstracted and disconnected from any mystical value (mysticism
which can exist besides without the centrality).
The architects know that anything of destroyed symmetry better than 2 shifted symmetries.
Finally it seems to me that duration only cannot explain our universe. The probability so that a monkey does not press its elbow on the keyboard of a
typewriter with brought closer intervals is null even for an infinite time. Time has a form associated with dilation with the universe.
If a mathematical model is always needed, as Thom requires it, I think that it must integrate a level of
fluctuations for which the framework of the current probabilities is unsuited.
COMPLEMENTARITY
Rome, for example would be a geographical and climatic singularity compared to the time of its apogee. Opposite sum, to some extent, of the “cruel” people which surround it.
Rome would have been used as catalyst of the Area, being located at the centre and everywhere. This complementarity is also exerted in time.
Moreover there is undoubtedly a sparing relationship between dimension and life. The man is perhaps the smallest as possible. Is clay, for example a resistant material if
one manufactures it in a proportion easy to realize and to implement at the hand (is this coincidence?). The use of brick in the modern architects answers
with a step where intervenes of the psychological criteria possibly stripped of any traditional connotation and very required constructive.
Cosmological constancy makes me think of ice floe going up on the surface of water while being diluted but the universe its own context generates
context + species = context general (integration by compression)
The rolling up of protein it is coming from interior or in osmosis with the context?
The chameleon does not change a color solely by will, need, practice or adaptation but by complementarity in the chains.
One puts sometimes this insoluble question which hen or egg initiates the species?
This problem of anteriority is not it not a problem of space (time), which included the other?
Can be exists it male elements and elements females like it exist the particles + and -, it would be the absence of this duality or complementarity which would be
insupportable to consider. The genesis is exerted can be initially by simple contact + and -, inclusion, the third dimension becomes a need at one time of the process towards the life. There
would be thus a process towards the life. A world monolith is unimaginable, it is a world still-born.
This process of the genesis of the species presents, to a certain extent, of the similarities with that of the creation of new materials by various accumulations and
overlaps.
Does the centripetal shape of the receptacle of egg generates it centripetal forces supporting the centrifugal forces of the development? Even if I regard the
complementarity centripetal forces/centrifugal forces as very creative, my answer is rather reserved before finding a new synthesis. Imagine the Eiffel Tower like orbiting station, perhaps it
would forms a crescent? Which is the role exact of the context? I would say that it is the place of exchange.
One could speak in this case about symbiosis (complementarity without force). (as water is diluted in water; Borges). The influence of FLOWS, forces
resulting is undoubtedly preponderant.
The modern ones exaggerated this concept of force, which ended up becoming a recipe in the painters for example; force = gesture = expressivity. I prefer the emotion caused
by calculation in Piero Della Francesca (control of space). The forces compensated by flows fall under a complex space system.
2 POLARIZATION
Opposite characters - a seemingly calm person can be a highly-strung person contained opposed to an irritated person. There is dominant characters, but an
individual consists of a multitude of sometimes contradictory features of characters seemingly. 2 opposite individuals can have points which bring them closer.
For as much these opposite characters answer my opinion with description that I consider for the polarized systems.
There is continuity within a multidimensional framework. But on a certain scale there are 2 classes of individuals who in a certain manner seem to belong to 2 different
worlds.
(Diagram following page)
For two individuals with opposite characters corresponds 2 lines of distinct characters AB and CD
which way traversed in space by the “ticket” so that in a plan, 2 of the poles of these lines are opposed and the 2 others meet.
When one spread the ticket so that the 2 lines AB and CD are found in 2 perpendicular plans,
- One notices a new intermediate line EFF. EFF is the line of character of a new individual produces of the 2 precedents.
- It is noticed on the one hand that the 2 spaces induced between AB/EFF and CD/EFF have opposite orientations. Thus one can say overall (3D) that 2 individuals are opposed,
then that in detail (2D) they are opposed on certain points and approach on others. (Without it being about similarity, it can be a question of intelligence at one and intuition at the other for
example).
- It is noticed then that F belongs to the line CD and that E is apart from any pre-existent line.
That lets suppose that there exists at a new individual of the stable elements of natures taken at one of the parents and others which are create. Thus certain features of
characters persists, they seem to remain intact with the wire of the generations (Creation without dilution).
(In reality it seems that progress of hygiene and medicine causes to attenuate the morphological singularities).
To compare with the equation of Lorentz: Stable elements - elements in evolution = evolution
EFF slightly deviated compared to symmetry = non reversible.
3 SPACES FORCES FORMS FLOWS - THRESHOLD OF INVERSION OF SCALE
The observation of the axonometric sights of the Villa “La Roche” (current foundation Corbusier) has me used as principal support for the whole of this text.
The plan of this villa translated the concerns of this time, never the concept of space time was not so systematic application of manner in architecture.
I try to show in these lines that in my opinion the organization of the villa “La Roche” anticipates largely compared to the current concepts, in particular those of “chaos”
(description of the singular mechanisms of changes of states in a continuous system).
Chaos: confusion of the Elements before the creation of the world. . Confusion, disorder.
The base of the theory of chaos does not reside perhaps in common interpretation of this word synonymous with
disorder. This definition corroborates my assumption according to which chaos describes as much the phenomena of degeneration, which those of genesis. Descriptions which the
specialists make of chaos associate in my opinion that with the concept of “passage”, appreciated by contemporary painters.
“Passage“ for painters, is used like a letter that one insert by compression, in a word on a screen. It is about a geometrical means of to
give depth, by prohibiting any form of expressivity. (“folds” of the Feigenbaum mathematician). Paradoxically chaos would not be synonymous with rupture, but contrary to
continuity.
The villa the Rock (presented following pages) seems to be the place of integration of 4 complementary concepts: MAGNETICS SPACES/TENSIONS/FORMS/FLOWS = SPACES/FORCES
/FORMS/FLOWS
This house of a pictures collector is organized according to a plan at right angles.
We can describe the principal space of entry as being centrifugal in centripetal cube with the angles open and the opaque sides in a cube to the closed angles and the open
sides (or the reverse indifferently).
One should not imagine the interior cube surrounded by a peripheral volume. The 2 are overlapping.
The originator dilates and compresses the 2 cubes at the same time until finding the balance of each space and of the unit.
The picture gallery develops on the other part of the square. It is composed of a curved wall bordering a slope, the other side is right. The slope is obviously the place of
FLOWS.
The link with the space of entry makes the square, space is narrowed at this place. The staircase seems to be the prolongation of the slope in the space of entry. Thus
circulations slope/staircase creates the bond between the 2 parts.
To simplify, I would say that the villa associates a dilated cube (sphere) a deformed cone laid out on both sides of a square whose junction, spaces compressed time is the
origin of the orthogonal system.
Thus the cone (here curves + straight), is a “turned up” space located on the other side of the origin but which acts on the space of the sphere.
The contour of this figure points out to me the figures of Klein as well as the figures generally associated chaos.
It seems to me that one finds such configurations in various organizations. The contour of a foetus for example :
A mathematician of Mulhouse carried out objects articulated out of metal which showed how a space could be turned up by keeping the continuity of contour and spaces. It thus
described the chaotic character of the development of the stomach in the embryo.
It seems to me that one finds of such figure in the organization of the universe.
The expanding universe would integrate forces of concentration permanently even if we observe the total expansion of the system. (centripetal/centrifugal).
The cone (shift curves/straight) would be the hidden part of the universe, the beam and can be the spark of the system. (This hidden part can be superimposed on the
observable universe and to be of the same order as the black holes.) The origin, very compressed with the intersection is never summarized in a point.
In this system, I associate MAGNETIC SPACE and SPACE, FORCE and ENERGY, (tension in architecture),
FORM and MATERIAL, FLOW and TIME. (It remains to find the place of the GRAVITATION).
FLOWS play a determining part. Dependent on shifts in space, they prohibit the total closing of space by maintaining a minimum space which explains why the origin cannot be
limited in a point.
These flows are the complements of intrinsic energies. This system appears me to be in agreement with the principle of exclusion.
THE BRAIN
This combination Spaces/forces/forms/flows as well as the concept of scale appear determining to me to describe the difference between the human brain and the animal
brain.
The criterion would not be simply the mass of the brain but the distribution of the vacuums supporting about, flows, the intensity (forces) and finally the form.
Thus the size of the brain would not be the only parameter to be able to reason, it would be the adequacy of the various preceding parameters which would be in
question.
I would take again then centripetal expression “centripetal, centrifuges deviated” (which is not completely superposable or symmetrical), with the subjacent idea which there
is an internal mass and an external mass of the brain.
Concept of inversion of scale being able to explain that there is a certain apparent similarity between the human and animal brain and a radical difference when with the
performances (difference in nature beyond a certain threshold in the distribution empties/intensity/form/flow).
The idea of the “not recursivity” evoked by the Penrose mathematician appears adapted to the difference which characterizes the distribution of the vacuums and the masses,
as well as energies inside the human and animal brain. This would translate a difference even more radical.
(Foot-note : Science and life 2005 N°1058 “We have a second brain” This article confirms my intuition. Andrea Volterra highlights the astrocytes place of
chemical reactions (and nonneuronal) which interact with the neurons via the synapses).
THRESHOLD OF INVERSION OF SCALE
At this level of this text, I suggest taking again my file concerning architecture.
This phenomenon of threshold of inversion of scale was described at the end of the Seventies by the architect V. Gregotti (Directing of the Casabella review) in its book
“the territory of architecture” (see at the end of my file).
In Architecture, the same figure (made subsets overlapping) simply dilated or narrowed will produce at a time given one threshold of inversion of scale
“without there being intervention of the scalpel of the surgeon” to paraphrase the Penrose mathematician. These phenomena apparently in rupture are continuous.
(inversion of total orientation, or knowing passage of the scale more specific of a house to an urban scale than a place is not a simple dilation of a stay, this dilation
produces at one time of the radical structural changes. for example on an urban scale the horizon tends to move away modifying the impact radically from our interventions).
In Athens, the columns of the Erechthéion temple are sculptures of women.
The compression of a spiral does not produce the same effect in the centre and the periphery
The effect believes in an exponential way when one approaches the centre - saturation - need for the 3D.
Some figures with “male” or “female” tendency imbricating males or females subsets.
To note how by digging a space one can reverse the tendency without using expressive means.
How the pointillist resolution of a line can reverse the general orientation of overlapping spaces.
The concept threshold of inversion of scale within the framework of a unit made up of “SPACES, FORCES, FORMS and FLOWS appears me to be a determining data.
_________________________________________FORCES FORM
(tension) (matter) curve/straight
FLUX tightening of space time
SPACE centripète/centrifuge – expansion/concentration (same side from origine)
Open/shuted angles – open/shuted side
4 VIBRATIONS - RESONANCE
Object: sand grains
When P.G. de Gennes presented at B.Pivot the experiment of the sand grains ( the sand grains concentrate in the center under the effect of a vibrating plate), I tried
to apply the criteria to it used in our discipline, (influence of the context, spaces, form, material, continuity, tension, scale, threshold of inversion of scale, etc).I wondered at the time if
under certain conditions, the grains of sand were not going to flee the centre.
An article of J.P. Troadec, Professor at the University of Rennes and E. Directing Guyon of the School of Normal Sup, Sciences and Future, December 94/Jan 95 NR°99,
confirmed my intuition.
If the sand grains gather in the centre by effect of mass or group, it seems to me that the concept of edge is not indifferent, some would be surrounded by their
similar, others would be in peripheral situation. However I note that while shaking my limps of sawdust of pencil scattered, the convergence of movement whatever the position of the sawdust is
immediate. It seems to me that the grains which move all worms the same central point all are opposed and translate actually the same vertical orientation, with the image of movement of the
bacteria on the surface of the ground. It is the agreement of the movement which characterizes the vibratory effect.
For me the sand grains should jump on the spot. But as the columns of the Parthenon are bent at the ends to correct the effect of the prospect, I think that one would need
very complex experimental conditions to produce such an apparently neutral situation.
In this almost perfect experiment the centre represents for me “no choice”, I call it the 5th edge by defect and I thus associate the idea of vacuum. In architecture, in the
case of hierarchical continuous spaces 2 by 2, a centred figure is not inevitably closed. It is about a particular case of superposition of spaces in opposition to an overlap of those along a
line.
Take a 8, to even fold up it on him, you obtain a polarized figure whose poles meet, the centrality exists only from one certain point of view. The junction is only apparent
- no contact - particular case of open spaces.
The situation in the event of acceleration of the vibration is with the first experiment what the Baroque is with the Traditional one, (alternation “bursting -
integration”).
In this experiment there is opposition between a concentrated figure and a figure pointillist with a uniform distribution of the sand heaps which correspond to a reduction
of the centres, knowing that in the beginning I consider that the position of the grains can be indifferent and that the nature of the vibratory movement is determining. Any centre
(cosmology).
With the scale of the sand grains we pass easily slow speeds at fast speeds however the idea of a perceptible threshold appears probable to me. Although it is not essential
on a sand grain scale the existence of such a even embryonic intermediate movement would have the appearance of a model to describe the threshold which shares integration and the bursting.
According to the conditions of the experiment, other variations can possibly appear, such as chaotic movements of the sand grains or such as their propulsion in
space.
With other scales, the apparent order or the centrality would actually correspond to very unstable singular situations in systems where the vibrations and the masses
would have effects of reciprocity.
COINCIDENCE
At the time of a lunch a friend asked me
the following question:
To find the ray of a circle C2 whose centre is with the periphery of a circle C1 so that the surface included at the same time in the 2 circles is = to the 1/2 surface of
the circle C1.
My first intuition was to draw an absurd solution, a circle C1’ of ray = R1 = to the ray of the circle C1, the surface of inclusion of the 2 circles being included in the
half-surface of the circle C1 is thus smaller.
Then I drew a circle approaching the solution apparently
I noted following coincidence then: draw the cord with the intersection of the circle C1 and C1' having for radius = half R1 it cord is the height of an equilateral triangle
of with dimensions = R1. Prolong with dimensions equilateral triangle = R1 with dimension R proposed as probable solution, you will find then a point located on the tangent of the circle C1
drawing a new equilateral triangle homothetic of the first with height = R1.I initially noted that the 2 1/2 cords, heights of these 2 triangles were very brought closer.
This singular solution induced a ray R required: R = R1/cos 30 = R1/0,866 =
1,154 R1
By the continuation I drew another solution as absurd as first, R passing by the diameter of C1 with a half surfaces of C1 included in the surface of inclusion of the 2
circles obligatorily larger.
I then drew a circle whose radius was the average of the 2 absurd solutions, this solution seems again bad. I then drew the average between the preceding average and the
first absurd solution (R = R1) this solution seems still bad.
(the solution right amounts finding a S1 surface = S2 (see diagrams), it seems that when one moves away slightly from the solution right surfaces S1 and S2 are very
disproportionate).
By against the average of the 2 average preceding ones seems to be the solution right.
The average between 2 absurd solutions is a absurd solution the average between the preceding average and an initial solution absurdity R = R1 is a absurd solution.
The average of the averages, the average of the averages of 1st and 2nd generation is a solution right.
Conclusion
The evolution of very disproportionate surfaces S1 S2 when one moves away from the solution of balance could describe, in my opinion, the situation of the poles and the
nodes (passage, origin, etc..) that mean singular situations.
This exercise shows whereas the origin as well as the poles fit in chains which thus precedes them and follows them. The origin and the poles exist well in as long as
entities, as soon as one moves away from the origin or about the pole it is not any more an origin or a pole. (On the other hand the origin as the poles have without doubt a thickness, spaces
vacuum, one would say today that they are fractals).
However in this exercise the intersection of S1 and S2 is a point, but my diagrams are limited to a perception in plan. It is then necessary to imagine the circles on stages
different like the stages from pedals. That brings me closer to perception that I have polarization which I describe as “polarization on floor”
The second remark relates to the proximity of the cords such as I described them above. For me which practises the guitar, that or not recalls me the expression being in
phase. Thus in the solution right I would say that the cords are in resonances, which would suppose that we are in a system which points out that of the vibratory movements. The 2
relatively brought closer cords coincide with equal surfaces S1 S2 the exercise puts in parallel a sinusoidal figure and a linear figure.
I point out that the initial objective of the exercise is to compare a surface bordered by 2 arcs of circles with a surface bordered by an arc of circle and a line. That
amounts comparing the passage of a line with a curve.
(A the Villa the Rock space beyond the node, is bordered by a curve and a line shifted, as if the tension of the 2 produced at a given time this tightening which constitutes
the original node, leading to centripetal space, centrifuges on the other side of the square. To notice that this exercise in 2D shows how one passes from a state to another without using the
scalpel of the surgeon ". Surface of 2 circles, passage of a surface limited by a curve on a surface limited by a line.