The Theory TK of Visual Proportions

The theory TK of visual proportions establishes the relations between the Observer of the space and the limits of its zone of good vision (the part of the space that he sees without excessive deformations). Kim Lloveras i Montserrat wrote the first version in 1982.
== The theory TK located in the history " The introduction of the Person in the Architecture " ==
Exhibition based in the Article " Kim Lloveras, el espacio a medida del hombre " in the Section " Our Brains " in "Science" of La Vanguardia (1988), in the theses “end of study” of Quentin Goulard (Institut Supérieur D'Architecture de Mons, Belgium, 2002). and Etienne Grosclaude (École nationale supérieure d'architecture de Montpellier, France, 2006) and in the works on Vitruvio and The Modulor of Le Corbusier by Juan Manuel Franco Taboada, Dr. Architect and Professor of the University of La Coruña
Marco Vitruvio Polión's human fractional body (1st century B.C.)
* Vitruvius is the author of De architectura developed in 10 Books, about the year 25 adC. (He was 55 years old)
* Vitruvius comments that he analyzed the works of “the former architects “Greco-Romans.
* Vitruvius exposes " The origin of the measures of the temple " in the Chapter I of the Third Book. In the first paragraph he comments: “It is impossible that a temple possesses a correct disposition if he lacks symmetry and proportion, since it happens with the members or parts of the body of a man well form "; later he does a detailed fractional description of the parts of the body between themselves. Also he exposes that "The navel is the natural central point of the human body" to that it is possible to circumscribe a circumference and a square. Also he comments the use for " the former ones " of units referred to the measures of the body: " Equally from other members of the body, they concluded the calculation of the different measures that are precise in any construction, since they are the finger, the span, the foot and the elbow ".
The measures of the Man of Leonardo da Vinci (1452-1519).
* Leonardo da Vinci draws the proportions of the figure of the Man, following the indications of Vitruvius, framed by a square and a circumference. (He was 33 years old) . The graphical scale of the low side of the square allows to climb the parts of the body. The height of the vision is not an information. " To see the representation of the Human Figure in: "
The abstraction of Andrea Palladio (1508-1580)
* Andrea Palladio wrote I quattro libri dell'architettura(The Four books of the architecture). (He was 62 years old)
* Continuing to Vitruvius, analyzes the buildings of the Greco-Roman antiquity, but he comments that " The measures and proportions … do not agree very with Vitruvius, but with the observations that I have done in several ancient buildings ".
*In the First Book he analyzes the five Orders “used by the former ones “(Toscano, Doric, Ionic, Corinthian and Compound). Palladio uses the "Module" to provide the architectural elements of the different styles. The "Module", or unit of reference of Palladio, is related (in the same way that Vitruvius) with the measure of the column (its measure or his half). The "Module" is not any concrete measure and does not have any relation with those of the Man. Palladio, as Vitruvius, tries to propose Models of perfect, finished, closed composition, for the buildings.
* In the other three Books he refer to the measures of the Villas and to urban elements of major scale. The reference of measure of them is the peeped of Vicenza that he takes as unit of reference.
* The human figure does not appear in any of his Four Books.
Le Corbusier (1887-1965) and the measures of the Man
* Le Corbusier wrote the Modulor (at the age of 63).
** His Modulor is a firm offer to use the series of measures that he was finding in the human body as measures of the architecture. The measures of the Modulor are provided by the golden relation.
*The offer of Le Corbusier is not only a fruit of the study of the ancient architecture, as Vitruvio and Palladio, but also of the vernacular one who has found in his trips.
* Corbusier breaks with the Renaissance abstraction of measures of Palladio and with the fractional use of the measures so much in Vitruvius as in Palladio.
** The fact of using the series of measures instead of fractional (Vitruvius, Palladio) supposes a radical change with the previous expositions. Also it is the fact of eliminating the Model idea of the buildings and his ornaments (Vitruvius, Palladio) and to choose for a free composition
** The architecture already is not done by the proportions of Vitruvio's human body, but they are the measures of the Man of the Le Corbusier those who are used. The abstract modules of Palladio's measure give up.
* Now then, his offers (red series and blue) of the Modulor refers to the measures of the Man, but never at a height of his vision, height from which he sees the world around itself: The Man of Le Corbusier was "blind". View Modulor representation in writing Taboada Juan Manuel Franco "El Modulor of Le Corbusier 1943-1954
The theory TK of visual proportions
* Unlike all the previous ones, the point of item already is neither the study of the proportions of the human body nor the Man, not so at least the proportions of the classic or ancient architecture, but the search of a scheme of vision provided with the Person; (geometric-mathematical) scheme that takes the vision of the Person as a point of item. The Man of whom his measures are analyzed is replaced by the Person who observes the space perceived by his good vision. The proportions of the Person form a part of the space provided by his own vision. The composition even is freer of the offer for Le Corbusier.
* The Theory TK of 1982 begins with the following phrase: " The point of item is the man who looks, that observes other men and to everything what him makes a detour, but who simultaneously is observed and looked surrounded with the same things. It is not a question of the physical man, of harmonic proportions, that it creates objects based on his good configuration, but of the Person who lives wrapped in his own world of objects and who tries to provide them with made measures of agreement with his own visual scale. In sum, it is a question of a theory which aim is not other one that of helping to satisfy the need of harmony that the man feels when it opens the eyes and observes the world that him makes a detour ".
* As Lluís Reales comments in an article appeared in 1988 in the section of Science of La Vanguardia, " The work came to the hands of Jerzy Soltan, disciple of Le Corbusier and teacher of the Graduate School of Design of Harvard. From these moments several architects and mathematicians, between them William Mitchell, person in charge of the department of Harvard's computers, have been interested in Kim Lloveras's postulates, to whom it has proposed to go to the American university in order that it develops his revolutionary theory ". Unfortunately it could not be; due to it Jerzy Soltan exposed the topic to Roger Aujame, in those days Secretary of the Foundation Le Corbusier.
The theory TK and the Le Corbusier Foundation
The best synthesis of The Theory TK of Visual Proportions, of which the author is Kim Lloveras i Montserrat, Professor of the Polytechnic University of Catalonia, we can find her in the writing of recognition done for Roger Aujame , former disciple of Le Corbusier, 13 September 1989, on the occasion of receiving, as Secretary of " The Fondation Le Corbusier, a copy of the Theory.
Textually, he says: "It is true that she opens the way towards the system investigation of proportionate measures. The reference to the Modulor of Le Corbusier is pertinent since his beginning also is based on the human moderation and golden ratio. But the Theory goes beyond with the three-dimensional concept of a series of measures based on the own vision of the person. I am sure that Le Corbusier would not have been insensitive to a study as this one".
The drawing for Jerzy Soltan
The best graphical explanatory synthesis can be in the drawing that Kim Lloveras i Montserrat sent (1988) to Jerzy Soltan, copies of which also it submitted to The Fondation Le Corbusier.
Jerzy Soltan was a collaborator of Le Corbusier and companion with Roger Aujame in the workshop of "35 rue of Sèvres". Both were involved in the conception of the Modulor, the system of series of measures created by Le Corbusier.
The Cone of Good Vision of the Theory TK , that zone of light of the space that we perceive with a minor deformation, delimited on the outside of our Blind Spots (see Blind spot vision) , remains defined by only three-dimensional relation, TK. When the Person is in A, she feels yourself inside, into the dark of the room. When the Person is in B, she feels yourself to be out, into the exterior light.
The existing relation, in the plane of our vision, between the ends of the Blind Points and us, the Observers of the space, is the golden ratio.
The medieval emptiness and the theory TK
" Exhibition based on the these end of study of Etienne Grosclaude (École nationale supérieure d'architecture of Montpellier, France, 2006), the publication "La cátedra de Antoni Gaudí. Estudio analítico de su obra " and the references to "La Piedra de Mesura de Veruela” Moderation in "Santa María de Veruela" of María Luisa López Sardá .
From Vitruvio up to the Renaissance there is a great theoretical emptiness of offers that relate the measures of the human body with used in the building construction. Torn emptiness, partly, for the drawings of the Notebook of Villard de Honnecourt (S. The XIIIth). Nevertheless, the name of someone of the measures used in the construction (spans, feet, elbows, …) they indicate an evident relation with those of the human body (in a similar way to Vitruvio); whereas other medieval units not (alnas, varas, canas, …)
Kim Lloveras i Montserrat exhibits, in " La Piedra de Mesura de Veruela “and in “La lumière à Sénanque ", which all the medieval Catalan measures can be copnstructed easily with the measures of the “Set square NT ". The measures of the Set square NT are series of the golden proportion. Also in both publications he exhibits, as he had defended in his Doctoral Thesis, which in the medieval used a scheme of Good Vision of the Person related to the proposed one for the Theory TK. The horizontal limits of the Good Vision of both schemes coincides with the horizontal ends of the Blind Spot.The variation takes place in the vertical sense. The Scheme of Good Medieval Vision takes a circle as a straight section, whereas the proposed one as the Theory TK has an ellipse, the ellipse TK.
The relation of the theory TK with other disciplines
The Theory TK, the Good Vision and the mental Images "
" Exhibition based on the these end of study de Etienne Grosclaude (École nationale supérieure d'architecture of Montpellier, France, 2006),) "
* H.M. Traquair and the limits of the “Island of vision "
** H.M. Traquair defined the interior of the zone of Field of vision where we see well as a “island of vision inside a sea of blindness ". The “island of vision“ is delimited by the horizontal ends of the Blind Spot. The angle between the horizontal limit of the Blind Spot " is, according to Traquair, of approximately 34,34 degrees; the same one that includes a small side of the golden rectangle " (to see golden Number, section Euclid's golden rectangle) " from the half of the opposite one to it.
* The bottom of vision of the Theory TK of Visual Proportions
** The bottom of the Good Vision coincides, very approximately, with the proposed one for H.M. Traquair
* The limit of the mental image ‘‘‘
**Ronald Finke He is a pioneer in the study of the existing relation between the mental image and the visual perception; it is to say, his visual limits. It obtained practically identical results between the limit of the mental image done by an Observer of a royal model and of the appraisal of her when this one has been projected on a screen. The mental Image has an elliptical form and spreads beyond the zone of Good Vision of Traquair and of the Theory TK, including part of the zone of deformed vision.
* The Theory TK, the Good Vision and the Mental Images
** If we superpose in the same scheme the straight section of Traquair's Field of vision for the right eye, the scheme of the limits of the mental image of Finke and the bottom of Good Vision of the Theory TK, there is obtained a scheme that makes understand the existing relation between these two disciplines of our perception and the Theory TK of Visual Proportions.
The experiences TK
" Exhibition based on the these end of study of Etienne Grosclaude (École nationale supérieure d'architecture of Montpellier, France, 2006) and the references of the cartels and conferences related to the Experiences published by the institutions where they were done. . "
*In 2002, twenty years after the publication of the Theory, and after of a theoretical emptiness of the continuation of the current offer, emptiness dedicated when the medieval model develops and to consolidate, at the beginning of century it begins the period of public validation of the Theory; principally regarding his initial and principal idea: the Cone of Good Vision of the Person.
* Several have done to themselves Visual Experiences TK in The School of Architecture of Barcelona (2002-2003-2008-2009), in The Technical Top School of Architecture of the Vallés (2008), and in The Institute of Sciences of the Construction Eduardo Torroja (2008), of Madrid, belonging to The Consejo Superior de Investigaciones Científicas(CSIC). In Arquiteturarevista, of the University of Unisinos, is summarized what they are the Experiences TK of the Cone of Good Vision of the Person.
Publications TK
" Exhibition based on the publications of her Technical University of Catalonia, UPC Commons, and in them of her Biblioteca de Catalunya . "
* Publications of the Theory
** Theory TK of Proportions is published, to particular level and in Castilian, in 1982 In 1997 it publishes, in Catalan (based on the original French version), the Teoria TK de Proporcions Visuals 1997 for the Technical University of Catalonia and the Department of Graphical Expression I of the same university. In 2007, on the occasion of 25 anniversary of his first publication, it publishes, in Catalan, Frenchman, Castilian and Englishman, the Theory TK and Laws of Positioning 2007 , In that there is gathered the treatment of the interior of the Cone of Good Vision.
** Principal publications of the medieval Epoch where there are exposed both models of scheme of Good Vision of the Theory TK of Visual Proportions.
***La Piedra de Mesura de Veruela (The Stone of Measure of Veruela) 1990
***La Lumière à Sénanque (The Light in Sénanque) 1992.
Architectures done with the Theory TK
*A sample of application of the Theory TK is the building of the ICMAB, of Consejo Superior de Investigaciones Científicas, in the Universitat Autònoma of Barcelona.

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