Mueller Science - model: draft design hypothesis - archtectural models prototypes paper tools CAD

VI: Draft, design, hypothesis

content

Sketch sheets

Architectural competitive tender

1-1200 To build from models and ideas, but not from drawings?

Use of architectural models

Since 1450: First theories of architectural models

Since 1390: architectural models

The modeling process in mind

Hypotheses and prototypes

Theories and hypotheses

Henri Poincaré (1902-1908)

Learning from models - tinkering

Working models

1845-1873: “Electrical images” - “mechanical representation” - “geometrical model” - “imaginary system” - “working model” „Paper tools“ in chemistry in the 19th century

Computer Aided Design (CAD)

Theories of design

see also in German: Die Modellmethode der Renaissance

Sketch sheets

The high quality of ice-age art - to start with the cave paintings from approx. 20,000 BC – implies a degree of experience, practice and training.

Since a lot of original artwork and so-called "sketch sheets" have been found it is assumed that there were already professional artists and fine art schools. The artwork was probably transmitted also via tribal magicians. At this time even engraved pebbles, panels and bones have been found on which we can see corrections of the lines. Multiple overlapping indicate that again and again new drafts were scratched; finally only the lines of the interesting animal were rubbed with color.

Architectural competitive tender

It is not the same if we use an architectural model for the purpose of sketching a building to be erected or as a representation of an already existing building. In Old Greece the use of the former is first documented by Herodotus (450 BC). Julius von Schlosser (1891, 36 ff., 62 ff.), Otto Benndorf (1902) and Ludwig Heinrich Heydenreich (1937) describe accurately how whole or partial models (paradeigma; exemplar, typos) of public buildings were produced before building commenced. There were also competitive tender for architects; they had not to remain anonymous. The artists had to defend their calculations and models and then the council of the community choose the one who proposed the cheapest, best and most rapid solution (Hans Straub, 1964, 57). Partial models – rosettes and leaf ornaments formed in wax – are preserved for the ceiling of the Erechtheion on the Akropolis in Athens (Otto Benndorf, 1902).

1-1200 To build from models and ideas, but not from drawings?

We do not have much information on the efforts of architects, builders and artists since Vitruvius until 1200 AD (Martin Warnke 1976; Günter Binding 1993). There are only some reports on the use of little wax models for buildings and churches.

Bishop Gregor of Nyssa (380 AD) reports in an Easter homily of littel wax models („holigo cero“) for whole buildings with adumbrations of forms of sculptures. For the erection of the church of the abbey of Saint-Germain in Auxerre (9th century) the artist who were entrusted with the operation first produced a model in wax („concepti operis exemplar conficitur ... caeris brevibus“). Around 830 master builder Einhard sent to his son a directory of obscure technicals terms by Vitruvius. The son should have let explain these terms with the help of al little box „with ivory columns in the manner of the works of the Old“, whose preparation has been ordered by abbot Eigil.

Architecture drawings have been preserved only for the Gothic – since 1230 concerning Reims and Siena, others drawn by Villard de Honnecourt. In general the architect relied on heavenly inspiration – by vision or dream – or archetypical ideas. “In mente conceptum” was a standard formula. Martin Warnke (1976, 138) gives a sociological explanation: „To have the plan ‚in mind’ means to have the power of control over the whole building enterprise.“

Use of architectural models

see in German: Die Modellmethode der Renaissance

A sketch of an early architectural model theory can be found in a letter by Robert Grosseteste to Magister Adam Rufus just before 1228 („imaginare in mente artificis ... utpote in mente architecti“ – see Günter Binding, 1993, 20-21, 181-182 – for theories of imagination see below and Fig. 49).

The first models with respect to the construction of the Dome of Florence are mentioned under Francesco Talenti: in 1353 two wooden models for the Campanile, two years later for the choir chapels and a part of the nave (Rolf Bernzen, 1986; Roland Müller, 1997). In 1366 the building authority ordered designs for the completion of the cathedral. After short time two drawings and a model from brickwork were available. The three-dimensional structure was named "Chiesa piccola" and had to meet a double similarity (similitudo): On the one hand it had to be similar to the drawing, on the other hand the church to be built had to be similar to that model.

For technical reasons the project was held up for fifty years. In the meantime (in 1390) Hugh Herland, master carpenter to King Richard II, used 3D-models in designing the timber roof structure of Westminster Hall (Eugene S. Ferguson, 1992, 102-105, 66, 153). In 1392 masters Heinrich von Gmünd and Simone da Cavagnera prepared 3D-models for parts of the Dome of Milan (Andres Lepik, 1994, 46-48)

In 1417 Filippo Brunelleschi became an advisor to the Dome-of-Florence-project, and soon a great number of carpenters were busy producing models for the construction of the dome (Howard Saalman, 1980; Eugene S. Ferguson, 1992, 66; Ross King, 2000). These were now called for the first time "modello", "modelo", "modeglio" and in Latin "modellus". In the year 1420 one was selected. With the help of further models – also for elevators and cranes - the construction of the dome was advanced step by step; an engineering master-performance.

Since 1450: First theories of architectural models

on theories of model see also: chap. 05: Reflection on the use of models

Soon afterwards – around 1450/60 - the polymath Leon Battista Alberti (Fig. 36, 37 and 38) and the artist and engineer Antonio Averlino, detto Filarete, and twenty years later Francesco di Giorgio Martini (Fig. 39) developed the first theories on architecture and particularly on the use of models and plans (Fig. 50).

Since 1420: architectural models

Inspired by the Florentine artists around 1390 also the building masters of San Petronio in Bologna and of the cathedral of Milano - where there were heavy discussions – began to prepare partially enormous models for their buildings.

Besides the three partial models of a total model of the Dome of Florence of 1420 (Andres Lepik, 1994, 66-71, 197-198, Abb. 21ff.) only since 1490 small-scale architectural models are preserved, for example from the Palazzo Strozzi in Florence and from the cathedral of Pavia (Ludwig Heinrich Heydenreich, 1937). The papier-mâché model of St. Maclou in Rouen (around 1500) was only executed after the completion of the church.

Instructions by Serlio (1537-51), Doni (1549), Lanteri (1557) and Vignolo (1562)

Of great importance were the six illustrated handbooks on architecture of the Mannerist architect Sebastiano Serlio (1537-51).

Later advises are from the writer Antonio Francesco Doni. In 1549 he gave under the title “Disegno” an answer to Paolo Pino’s "Dialogo della pittura" (1548) and at the same time an instruction for painting and sculpturing, among them also for models.

In two dialogues the engineer Giacomo Lanteri (1557) – who served the King of Spain in Naples and North Africa – gave instructions for the construction of military fortresses – according to Euclides – and for preparing models for them (Gloria Vivenza 1975).

„Rules of the five orders of architecture“ were published 1562 by the architect Giacomo Barozzi da Vignola.

Most popularity gained the „Quattro libri dell’architettura“ by Andrea Palladio (1570) as well as the buildings he erected 1540-80.

The modeling process in mind

see: Fig. 49: Theories of imagination

bibliography: Imagination, imagery, mental imagery

The Ancient Greeks called the modelling process in mind „ phantasia”. Influential was the description of Aristotle in „De anima III, 3“. Romans used „imago" (almost never: imaginatio, repraesentatio, perceptio).

Already Augustinus (400 AD) differenciated between three kinds of phantasia:

· productive,

· reproductive and

· synthetic.

In medieval philosophy the word „imaginatio" was common, e. g. with Abelard, Hugo of St. Viktor and Thomas Aquinas.

Since 1500 imagination and fantasy are frequently described and discussed. In German we have also the words “Einbildungskraft”, “Vorstellung” and “Anschauung”. In English is used: „idea”, in French: „idée".

Hypotheses and prototypes

Hypotheses and prototypes have the feature in common to be amended. Therefore Copernicus was cautious. In the title of his main work (1543) he wrote: „et novis insuper ac admirabilibus hypothesibus ornatos“. In 1571 Caspar Peucer characterized the Copernican discoveries as: „Hypotheses astronomicae, seu theoriae planetarum”. In 1570 Johannes Bruno published likewise: „Theses Physicae de mutationibus et motu“, and in 1598 Lambertus Croppet: „Theses astronomicae“.

In 1585 when Pope Sixtus V decided to move the Vatican obelisk, he appointed a commission to review the several hundred proposals put forward by contenders for the job. The successful contender, the Ticinese master-builder Domenico Fontana - who later finished the cupola of St. Peter - used an elaborate model to demonstrate how he intended to lift and move the unwieldy monolith (Hans Straub, 1964, 132) - for a picture see C. Graf von Klinckowstroem (1959, 36; viz. 127) and Eugene S. Ferguson (1992, 153).

This heuristic use of models systematized Simon Sturtevant in the equally modern as well as detailed and vivid chapter „Heuretica“ of his patent application "Metallica" of 1612 (John Desmond Bernal, 1970, 390f.; see Fig. 51).

Three years later Galilei was to appear in court. High inquisitor cardinal Bellarmin advised him to declare the Copernican system “ex suppositione”, i. e. as hypothesis. But Galilei insisted it were the truth and he could prove that. In this respect he was mistaken, as Eduard Jan Dijksterhuis (1956) annotates.

Much later, Isaac Newton is cited for his statement: “hypotheses non fingo” (1726). Dijksterhuis rectifies that he liked nothing more than to conceive hypotheses (1956, 541, 543).

Since then, hypothesis and theory, system and law, model and principle are often confused.

Theories and hypotheses

see e. g.: Economic publications through the ages (2400 BC – 1900)

Menschenbilder und entsprechende Staatstheorien (340 BC – 1908)

294 Theorien zu ... paradoxem Entscheidungsverhalten (1670-2003)

bibliography: Psychology of Personality (1841-2005)

Führungstheorien (1880-2002)

bibliography: Models in Psychology and Psychiatry (1891-2005)

Discussion of the use and utility of hypotheses started in the times of Immanuel Kant and flourished a first time around 1830/45 (Auguste Comte, 1830-42; John Stuart Mill and Rudolf Hermann Lotze, 1843).

Adherents of a science without hypotheses were some positivists as Comte, Ernst Mach and Wilhelm Ostwald. Other scholars distinguish between:

· good and bad hypotheses; or

· arbitrary and well founded hypotheses.

Hans Vaihinger in his "Philosophy of 'as if'" (written in the 1870s; published 1911) has pointed out that most hypotheses are „fictions“.

Henri Poincaré (1902-1908)

Henry Poincaré (1902-1908) differenciated deeply theory and hypothesis. Theories are based on three kinds of hypotheses:

· natural hypotheses (e. g. „that the effect is a continuous function of its cause“)

· indifferent hypotheses (e. g. metaphors) as well as the

· „real generalizations“.

Hypotheses are mostly provisional assumptions. Some models are that. In contrast theories pretend to explain phenomena or claim to express truth, validity or usefulness with respect to reality – and turn out as false again and again. If there is a contradiction between two theories then the cause lies in the images we relied on instead of the real objects.

Poincaré urged scientists to test their hypotheses (1902). He saw the progress of science in falsification not verification of hypotheses. A rejected hypothesis is the best chance to make new discoveries because she is the reason for new experiments. Ifo ne had made the discovery only by chance, one could not have drawn conclusions of it.

Learning from tinkering with models

Leonardo da Vinci and Michelangelo often used the word „modello“ (Herbert von Einem, 1959, 1973; Michael Hirst, Claire Bambach Cappel, 1992 - see Fig. 35). And they used, among others, a variety of models. They constructed and used models not only for buildings and devices of all kinds, but also for drawings and pictures, sculptures and giant plastics.

Of Leonardo, Vasari writes:

„And all days he constructed models and draw devices to ablate mountains or to bore through them to reach one side from the other; likewise he shows how to lift big loads by means of levers, hoists and screws and to move them; further he invented procedures to deepen harbors and pumps to drain of low-situated regions. This strange brain never stopped fantasizing“ (Giorgio Nicodemi, 1939, VIII).

Around 1575, young Galileo Galilei tinkered with machines and mechanical toys (Leonardo Olschki, 1927, III, 143). The first biographers report it. „Whilst Gherardini repeadedly refers to Galilei’s technical activity in connection with the theory of mathematics, Viviani tells with a wealth of details that Galilei diverted himself in the first years of his childhood producing instruments and machines, which he invented himself or which he copied after the commonly used“ (Olschki 1927, III, 143).

Later he confessed that it was just the experience of the builders of machines and apparatus „opened the causal relation of marvelous phenomena, which before were considered inexplicable and unbelievable“.

In 1656, at the age of 14, young Isaac Newton intended to become a farmer. However, as he spent a lot of time solving problems and constructing mechanical models his mother – jwidow in her young years - thought him to be born for a higher profession. His uncle advised her to send Isaac to Trinity College in Cambridge, where he had been himself. Isaac entered in 1661 and kept his fellings and experiences in a diary.

Nearly a hundred years later (around 1745) young James Watt tinkered in the workshop of his father and tried to repair many devices to make them operate „as a clock“. Later he learned the craft of instrument maker.

Another hundred years later (around 1842) young James Clerk Maxwell at the Edinburgh Academy tinkered with models.

Working models

In 1669 the mathematician and philosopher Gottfried Wilhelm Leibniz praised the construction of small scale “Modulis” in order to design fortresses in his sketch of the “Ars inveniendi”:

„De figuris item Modulis, ita is qui volet exstruere fortificationem utiliter conficiet Modulum omnes loci elevationes et incommoda repraesentantem, idem hoc modo facilè poterit variis modis eum redigere in perspectivam“ (1903, 163)

Seven years later Leibniz praises in detail the construction of small models ("exiguis modulis ligneis (aut cereis)") to foster imagination (1903, 596).

Using models was also central in developing the steam engine. Since end of the 17th century mechanics and inventors were busy to construct a "working model" of the atmospheric or steam engine. Before 1700 Thomas Savery exhibited "a model of his engine before King William at Hampton Court" (Robert Stuart 1824, 35). John Theophilus Desaguliers announced in 1716: "we resolved to have a working model" (75).

In 1760 James Watt in Glasgow was entrusted with the care of the ,university's collection of mechanical and philosophical (i. e. scientific) models" (95).He was not particularly interested in these apparatus, but when a model of Newcomen did not function any longer, he began to repair it around 1763/64 (see also Simon Schaffer 2004, 72). Then, ambitioned, he developed the numerous improvements which led in 1769 to the first patent and to the centrifugal governor.

This is a classical example of the fascination by models and learning by model with patience and toilsome trying resulting in the improvement of the model.

The use of images in the 19th century physics

19th century science is characterized by two contradictory movements:

the replacement of thinking in substance by thinking in structures and functions. Experimental and mathematical methods of dynamics expanded on non-mechanical areas of physics. That means physics to become more and more abstract. It starts after Euler, D’Alembert, Lagrange and Laplace around 1800 with the mathematicians Jean Baptiste Joseph Fourier and Siméon Denis Poisson.
the attempt of physicists to make vivid invisible phenomena, visualize their ideas, and to illustrate their findings. Visualizing of ideas starts after Ernst Chladni and Thomas Young around 1820 with the famous experimenter Michael Faraday aiming to realize the postulation of Immanuel Kant to turn notions into sensuality (KrV, A51).

t is important to admit that there is not at all the same to visualize (1) natural phenomena, (2) ideas, mental concepts or hypotheses and (3) theories.

In every case the use of images has been a versatile tool of serious scientific research. This tool can be seen from three angles:

(1) as representation (see chap. XIV: Representation, description, image)
(2) as draft, design or hypothesis (see below),
(3) as visualization (see chap XII: Visualization, illustration).

The bases are always analogies (see chap. IX: Analogy).

The theory itself is mostly not vivid. It consists of predicates, abstract terms, formulae and laws (see chap. VIII: Theory).

The functions of the diverse images can also be communication and teaching (Gerald L’Estrange Turner, 1996; Ursula Klein, 1999 and 2003; Christoph Meinel, 2004).

A fictious distribution of magnetic fluid

A milestone of „graphic representation“ („graphischen Darstellung") along the lines of sensualizing has been the „Atlas des Erdmagnetismus" by Wilhelm Weber (1840). It relied on the general theory of geomagnetism by Carl Friedrich Gauss where he states:

"The pattern of the real distribution of the magnetic fluids in the earth remains necessarily vaguely … The one and same effect in the whole exterior area is to be derived from infinitely many different distributions of the magnetic fluids inside. But we can show the fictious distribution on the surface of the earth which is exactly equivalent (“vollkommen äquivalirt”) to the real distribution inside with respect to the outward emerging forces from it" (1839, 46f; also 1840, 30f; 1867, 165).

A constructible imagination of the propagation of electrical particles

In 1845 Gauss wrote in a letter to his friend Wilhelm Weber (1867, 629-631) that he had treated in vain Ampères fundamental law ten years ago. Nevertheless he had hoped to succeed perhaps later „with the subjective conviction that one would first need to give a constructible imagination („construirbare Vorstellung“) of how the propagation [of electrical particles] happens”.

In his „Treatise on Electricity and Magnetism" (1873, § 861 ff., II, 435 f.) James Clerk Maxwell reports that 20 years later Carl Neumann proved Gauss’ analogy with the propagation of light as false. But he himself had not been able „to construct a consistent mental representation of Neumann's Theory". This is a remarkable confession at the end of a 850page publication based o the conviction that there is a „medium in which the propagation takes place", namely the ether, and that concludes with the sentence:

,If we admit this medium as an hypothesis, I think ... we ought to endeavour to construct a mental representation of all the details of its action, and this has been my constant aim in this treatise" (1873, II, 438).

1845-1873: “Electrical images” - “mechanical representation” - “geometrical model” - “imaginary system” - “working model”

In 1845 the Scottish physicist William Thomson proposed, in a letter in French, the „principe des images pour la solution de quelques problèmes relatifs à la distribution de l’électrictité“ (1872, § 208, 144), i. e. the „principle of electrical images“ for the distribution of electricity on globular conductors. In 1847 he introduced in a paper „On a mechanical representation of electrical, magnetic and galvanic forces“ this visualization into electro- and thermodynamics (see also in the „Baltimore Lectures“, 1904, 45).

In 1849 he explained the reason for using the term “electrical images” for thought: electrical points or groups of points in perfect analogy to optical images:

„The term Electrical Images, which will be applied to the imaginary electrical points or groups of electrical points, is suggested by the received language of Optics; and the close analogy of optical images will, it is hoped, be considered as a sufficient justification for the introduction of an new and extremely convenient mode of expression into the Theory of Electricity“ (1872, § 127, 85).

In chapters III and V of his „Mathematical Theory of Magnetism“ (1849-50; 1872, §§ 430-554, 340-425) Thomson introduced „an imaginary magnetic matter“ (1872, § 463, 352; §§ 477ff., 360ff.).

All this inspired the young James Clerk Maxwell to the lectures: „On Faraday’s Lines of Force“ (1855-56). Here Maxwell not only introduced the term „physical analogy“. In the specific case of lines of forces of an electrified body he tries to give „a geometrical model“ of the physical forces and, “by referring everything to the purely geometrical idea of the motion of an imaginary fluid“, to obtain “a geometrical construction which completely defines the motion of the fluid“.

“My aim has been to present the mathematical ideas to the mind in an embodied form, as systems of lines or surfaces, and not as mere symbols, which neither convey the same ideas, nor readily adapt themselves to the phenomena to be explained.”

Maxwell emphasises again and again that this does not imply any assumptions or hypotheses on the „physical nature“ of electricity. And: “This representation involves no physical theory, it is only a kind of artificial notation.”

In his article “On Physical Lines of Force” (1861-62) Maxwell described his “theory of molecular vortices” and concludes:

”We have now shewn in what way electro-magnetic phenomena may be imitated by an imaginary system of molecular vortices. Those who have been already inclined to adopt an hypothesis of this kind, will find here the conditions which must be fulfilled in order to give it mathematical coherence, and a comparison, so far satisfactory, between its necessary results and known facts …”

We note that Maxwell denotes his ideas in the same article as theory as well as hypothesis.

A dozen years later Maxwell wrote in his „Treatise on Electricity and Magnetism" (1873, § 831, 416f.) on his theory of vortices, i. e. the rotation of very small portions of matter: