The Concept of Model and its Triple History
Opening lecture
of the 13th International Conference on History and Philosophy of Science (organized by the IUHPS/DHS-DLMPS Joint Commission), University of Zurich, 19-22 October 2000; topic: “Scientific Models: Their Historical and Philosophical Relevance”
IUHPS = International Union for the History and Philosophy of Science
DHS = Division of History of Science
DLMPS = Division of Logic, Methodology and Philosophy of Science
(If you wonder at some wording, please consult the tentative translation key)
German translation see: Modellgeschichte ist Kulturgeschichte (Kurzfassung)
red = corrections and additions
Model history is culture history
To trace the history of the concept of model is one of the most fascinating ways to pursue culture history. The creation and use of models belong to the elementary occupations of humans.
Even contemporary physics is culture historical. Take for instance the concept and idea oft the atom, which is about 2500 years old. Or take the concept "quark" (in the so called "standard model"), which is taken from the novel "Finnegan’s Wake" by James Joyce.
The history of the concept of model is likewise 2500 years long.
Arguments around models become rapidly very emotional, no matter whether it concerns model in general or specific contents. The reasons for that become clear by the following explanations.
The history of a concept is not equal to the history of the named things
We must start out of the following facts:
1. The history of a concept and the history of the named things are two different kinds (fig. 0). Already the early people and the cavemen built, produced and used models, but we do not know, how they called them.
2. The history of the things is not at all easy to determine. It depends on the one hand on the richness and quality of the archaeological or documentary material, on the other hand on the interpretation of the same. And this interpretation constantly changes.
3. We have to take seriously whether the author itself speaks of a model or not. Retrospectively we can call "model" all understandings, „philosophies", "systems" or "theories". But neither Ptolemy nor Copernicus, neither Galilee nor Newton, neither Darwin nor Marx, etc. have named their interpretations or sketches "model".
4. There are many other concepts, which describe the same meaning or parts of this meaning as the concept of "model", e. g. representation, abstraction or concretion, idea or idealization, illustration, sensualization or view, pattern or scheme, shape and configuration, picture, symbol, sign and icon, metaphor and allegory, analogy and example, fiction and vision, draft and plan etc.
Very popular are also prototype and archetype, paradigm and exemplar.
In scientific language we have since 1600: system and hypothesis, theory, philosophy, treatise and principles, doctrine and teachings, law, rule, formula, etc.
In the German Zedler’s „Universallexicon“ (1739) we find as synonyms:
„Modell, Modele, Modello, Modulus, Typus, Exemplar, ein Modell, Vorbild, Abdruck, Form, Muster, Leisten, Richtschnur, oder Vorschrifft, darnach man etwas machet ...“
Funk & Wagnalls’ „New International Dictionary of the English Language” (1987) lists the following declared synonyms for the noun “model”:
archetype, copy, design, ectype, example, facsimile, image, imitation, mold, original, pattern, prototype, replica, representation, type; and further: idea, ideal.
"Colliers English Dictionary and Thesaurus" (1993) has many more synonyms, namely:
1. copy, dummy, facsimile, image, imitation, miniature, mock-up, replica, representation
2. archetype, design, epitome, example, exemplar, gauge, ideal, lodestar, mould, norm, original, par, paradigm, paragon, pattern, prototype, standard, type
3. poser, sitter, subject
4. mannequin
5. configuration, design, form, kind, mark, mode, stamp, style, type, variety, version
Synonyms for "mould" are here:
1. cast, die, form, matrix, pattern, shape, stamp
2. brand, build, configuration, construction, cut, design, fashion, form, format, frame, kind, line, make, pattern, shape, stamp, structure, style
3. calibre, character, ilk, kidney, kind, nature, quality, sort, stamp, type.
5. Language lives in its use. Therefore it would be desirably to study how researchers coin and use certain words in their laboratories and in daily life. The first empirical studies start 1975 and come from Harry M. Collins, well known for his „Golem“-Books (1991, 1993) and Bruno Latour, known for his „Pandora“-Essays (1999). A concise overview is from Karin Knorr-Cetina (1999).
6. Some theorists use the model term thoughtless, e. g.:
· Antje Korsten: Modelling the modelling language. Manchester: University of Manchester 1995.
· Margaret C. Morrison: Modelling Nature. Between Physics and the Physical World. Philosophia naturalis 38, 1998, 65-85.
7. To define a concept we usually use numerous other „heavy" concepts, which need a definition themselves, e. g.: “Model, in logic a system of areas and concepts, in so far as it fulfils the axioms of a fitting formulated theory.”
8. All this becomes even more difficult, if you combine two heavy words. Then you have "model ideas" and "idea models" or "system models" and "model systems".
9. The same object or phenomenon is differently named in each language, e. g. gr. phantasia; lat. imago; scholast. imaginatio; English: idea; French: idée; German: Einbildung, Vorstellung, and in addition: Phantasie, Imagination.
10. So far there is neither a comprehensive theory of knowledge nor a differentiated ontology of models. Most scholars in the 20th century had in view only the relation "image". One of the first who worked out the triple relation “subject-model-original” was Klaus-Dieter Wüstneck (1963). Georg Klaus followed him 1967 in his „Wörterbuch der Kybernetik“.
Reflections on the use of models
see at length: Reflections on the use of models
Since when is there a reflection on the fact that we use models and think in models?
Beginnings are already with Xenophanes (540 BC) and Platon.
Just before 1228 Robert Grosseteste outlined a model theory in a letter with respect to architecture.
Briefly after 1300 Duns Scotus developed a conception theory and his pupil William of Ockham the conceptualism. Around 1450 the religious philosopher Cusanus submitted a picture theory and the art theorist Leon Battista Alberti a model theory. Shortly after followed Antonio Averlino, detto Filarete.
Pronounced we find a reflection since the beginning of modern science, for example with Francis Bacon in his doctrine of idols (1620). He distinguishes four kinds of false ideas humans like to form: collective and individual aberrations, public opinion and tradition.
The next wave of consciousness starts with the Cambridge philosopher William Whewell (1840) and the American Scientist Charles Sanders Peirce (1868-1903). They were followed since 1875 by the German philosopher Hans Vaihinger, the two Austrian physicists Ernst Mach and Ludwig Boltzmann, the German physicist Heinrich Hertz, the French physicist Henri Poincaré and the Russian physicist Nikolai Alekseevich Umov.
Present reflection on model thinking and the use of models begins in the year 1942. Since 1945 this model-movement was so vehement that in 1951 the Viennese physicist Erwin Schrödinger portrayed in his booklet "Science and Humanism" on five pages the "nature of our ‘model'".
Since 1957 model thinking and the concept of model are discussed at numerous international symposia. In January 1960 and in August 1994 the IUHPS (International Union for the History and Philosophy of Science) dedicated congresses to the topic “Model” in Utrecht (Leo Apostel et al./ Hans Freudenthal 1961) and Warsaw (William E. Herfel 1995).
Word history of „modell“, „model“, „modèle“, „modul(e)“, „moule“, „mould“ (fig. 1)
see: Nachschlagewerke für Begriffsgeschichte
In German as in all other European languages the words modell, model, modèle, modul(e), moule and mould have to be taken together for linguistic and historical reasons (Randle Cotgrave 1611; Jacob und Wilhelm Grimm 1885; Godefroy 1888, 1902; Walther von Wartburg 1966; Roland Müller 1980, 1983, 1997).
The variety of the ways of writing shows up very beautiful in English. In the "Oxford English Dictionary" we read the following forms for model:
"modill, moddell, moddel, modell, modle, modull, modil, modelle, model".
It is important to see that particularly in English for two hundred years (until 1750) the way of writing „modell” (with two l) was used. In the German language the contrary took place: until 1800 "Model" (with one l) was still in use e. g. for painter model and architectural model.
In all these concepts five fields of meaning interweave.
Five fields of meaning in Greek and Latin
The first meaning field goes back on the Greek word "metron" (yardstick, measure, boundary) and Latin "modus" (respectively in the reduction form: "modulus"). The primary meaning is measure in a double meaning, as unit (content) and as measuring instrument (yardstick).
The second meaning field goes back to the Greek word "typos" (form, sculpture, mould, figuration), Latin "forma" (figure, mould, casting) but not: type.
The third meaning field goes back to the Greek word "paradeigma", Latin "exemplar". It was used for small-scale representations of buildings, ships and machines, and in addition, for the (usually male) painter model. The use of architectural models is known since Herodotus (450 BC).
The word was also used in the abstract. Aristotle criticizes in his "Metaphysics" (991a21) Plato's theory of ideas: "If you say, the ideas are models/or patterns (paradeigmata) and the other participates in them, then these are empty words and poetic metaphors" (viz. also 101a27).
The theoritician of science Thomas S. Kuhn (1962) has forth-fished the word paradigm in the 50's, but in a very special meaning, approximately in the sense of "current opinion"; the culture-anthropologists speak of "belief system".
The fourth meaning field is the most diverse. It goes back to the philosophically weighty Greek words "idea" and "eidos" (shape, form, idea, Urbild, picture), "eidolon" (image, deceit picture) and "eikon" (picture). In Latin we have for it "imago" and "effigies" (picture, ideal, image, conception - viz. Lexicon of the Art 1987-94). Also we have the wide variety of meanings for “species” (appearance, picture, idea, classic example, species) and “simulacrum” (image, pattern, doll, silhouette, dream vision, fake, characterization).
The fifth meaning field concerns plastic representations in wax. In Plato’s dialogue "Timaios" we find that God creates the human body like a modeller in wax ("keroplastes"). The verbs "keroplasteo" and "proplasso" were used very rarely for the process of forming. Gr. "proplasma" occurs only in the Roman time. For all types of "wax pictures" the Romans frequently used "cera".
The multiple history of “modulus”
40 BC to 1750: "modulus" (lat.): measure, figure, architectural model, small scale representation
The Latin word “modulus” is the reduction form of "modus", with the same primary meaning: measure, yardstick. It was not used very much in ancient Rome. It occurs shortly after 40 BC with Horaz and Varro; then it was used by the well-known architect Vitruvius in his "Book on Architecture" (approx. 23 BC) various times, mostly as architectural standard, namely the half column diameter.
The verb „modulor“ for regulating sounds in music and rhetoric was already used by Cicero (55 BC) and Vergilius. Vitruvius used it likewise, as well as „modulus“, also in the realm of music and introduced „modulatio“ for inflection of tone.
In his „Two Books on the Water Supply of the City of Rome“ (100 AD) the politician and writer Sextus Julius Frontinus used the word „modulus“ ca. 30 times for standardized pipes used in 25 sizes. Pliny the Elder and Gellius expanded the meaning of „modulus“ to the blood pulse. Then it was the church father Tertullian (approx. 200 AD; he also coined the concept “innovatio”), who expanded the meaning on the small figures of the sculptors, after which a marble sculpture was made for instance.
For patterns and paragons, examples and exemplars of all kinds as well as for small-scale devices Old Romans as well as the Middle Ages scholars used always „exemplum“ or „exemplar“.
In the national languages we find derivations from “modulus” since the year 1000.
We have to note that the Latin "modulus" (like "exemplar") was used until 1750 in the scholarly world, since 1450 (Alberti) particularly for the architectural model, and in addition, for other small-scale representations of real objects.
A prominent exponent is Leibniz. Following the description oft the benefits of making “Modulis” for the construction of fortresses he mentions in the year 1669 in his sketch of the “Ars inveniendi” the collections of models, which were very popular in his time: „de Theatro Naturae et Artis seu de Modulis rerum ipsarum conservatoriis" (G. W. Leibniz 1903, 163).
Shortly after he proposed in his “Atlas universalis” a department of objects, which “oculis subjici possunt”: „Mechanica, ubi omnis generis Machinae et moduli" (223). And at the same time he praises in detail the making of “modulis ligneis (aut cereis)” to be good for imagination (596f).
In English „modulus“ has been introduced in 1722 by Roger Cotes and is used until today in physics and mathematics.
First development: „modulus“ becomes German „Model“/“Modul“, French “modle”/”mole”/”moule”, English „mould„, Italian „mòdano„
We hear (not testified) that in German the early loan word "Model" was already used in the times of Charlemagne by the religious master builders as architectural measure.
From 1000 it is – accompanied by “Modul” - in freer use, on the one hand in the abstract sense as rule, pattern, form, example, on the other hand as industrial moulds for things like dragnets and bricks, later documents (e. g. contracts), fabrics and embroideries. Also the forms for printing on textiles and all kinds of hollow forms for casting goods and pastries were called “Model”.
Quite similarly we have in French: "modle", "mole" and "moule" (otherwise: patron) and in English: "mould" (otherwise: pattern).
It is nice to see that in English first came the abstract meaning of “mould”, namely “distinctive nature as indicative of origin” (1225), and that it took a hundred years until the meaning became concrete, in the sense of hollow form or “pattern” (1320).
In the 13th century we find in Italian "mòdano" as instrument for the asterisk measurement; only in 16th century it is used as measure, model and mould (otherwise: stampo). Since 1563 also „modanatura“ is used for "profilatura" or „elemento decorativo architettonico“.
The respective words are in German „modeln“ (since Minnesang), in English „mold“ or „mould“ and in French „mouler“.
„Moulding“ we find in English since 1327, for „ a raised or incised ornamental contour or outline“ in architecture since 1448, and as ornament on wood or metal since 1679.
„Mollage“ we find in French since 1415 (droit des mouleurs du bois), „moulage“ since 1680 (terme de potier). In English „moulage“ apperas first in 1886, in German perhaps around 1850.
Second development: „modulus“ becomes Italian „mòdulo“, French and English „module“
In Italian "mòdulo" appears in the 13th century in the sense of the Vitruvius' column measure. "Module" appears 1547 in French and in 1586 in English. We note that in English “module” is not only used for measure or unit or standard, but also for design, architectural model, image, example.
In the strict sense as measure “module” held itself through the times, similarly in physics as proportionality factor with distortion characteristics (elasticity: Hooke, Young), in techniques (with gear wheels) and in mathematics (logarithms, congruencies, Abel groups, etc.). For the English Language it was Roger Cotes who introduced 1722 the concept of “modulus”.
In the years 1942-48 the famous Swiss architect Le Corbusier developed the "Modulor", an architectural standard, based on a man of 6 feet.
The use of "module" for a standardized construction unit emerges in 1946 in English an expanded rapidly into the other languages.
Third development: „modulatio“ becomes Italian „modulazione“, French and English „modulation“
It was also Vitruvius who used the variation of “modulus”: “modulatio” not only for the regular meeasure of columns, but also for inflection of tone, modulation.
In Italian „modulazione“ appears before 1342 in the sense of „parlare, cantare, suonare armoniosamente; variazione regolata“. The verb is „modulare“ (since before 1492).
„Modulation“ we have in French since 1365 and in English since 1398, both in the meaning of „changement d’intensité dans l’émission de la voix“ and „chant d’allégresse, harmonie“ resp. „the action of singing or making music“. Later the meaning was expanded to forming something according to due mesure and proportion.
The respective verbs are „moduler“ (1458) and „moduliser“(1508) in French, „modulate“ (1557 or 1567) as well as „modulize“ (1605 or 1656) in English.
In German „Modulation“ appears 1571 for „Akkordfolge, Übergang einer Tonart in eine andere“. The verb „modulieren“ appears at the same time.
The use of the English words modulate and modulation in telecommunication starts 1908. The other languages followed soon.
Fourth development: 1366-1417: The complicated birth of the Italian word "modello”
The often spread statement, that the vulgarly Latin word "modellus" is precursor for “modello” is not plausible. This word was used in the whole Middle Ages only around 1330 twice as wall crusher, twice as vessel in the household.
The Italian word "modello" appears in respect to the construction of the Dome of Florence.
Neither Arnolfo di Cambio the first master builder of the new construction, planned since 1294, nor the artist Giotto submitted a three-dimensional model for the Campanile (around 1334 - viz. Howard Saalman, 1964; Rolf Bernzen 1986; Roland Müller 1988). Only under Francesco Talenti two wooden models are mentioned: 1353 for the Campanile, two years later for the choir chapels and a part of the nave.
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. One of the drawings ran under "desingnum seu modellum". 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. (Presumably the well-known Fresco in the Spanish chapel of S. Maria Novella in Florence shows this model.)
For the time being the construction was not to realize for technical reasons. Fifty years later (1417) Brunelleschi became an advisor, and soon a lot of carpenters were busy producing models for the execution of the dome (Howard Saalman 1980; Rolf Bernzen, 1986, 122-137). These were called now for the first time in Italian "modello", "modelo", "modeglio", in Latin "modello" or "modellum". In the year 1420 one was selected. With the help of further models - also for elevators and lifting devices - the construction of the dome was advanced step by step. An engineering master performance.
Models etc. in the Middle Ages and Renaissance
Imagination, analogy, metaphor and representation
Important concepts in the Middle Ages were imagination, analogy, metaphor and representation.
Phantasia, imaginatio
The Ancient Greeks called the modelling process in mind „ phantasia”. Romans used „imago "(almost never: imaginatio, repraesentatio, perceptio). Only Boethius (ca. 500 AD) explained in its „ Consolatio "(V. book): „Imaginatio vero solam sine materia iudicat figuram "(engl.: Imaginative power judges the shape without matter). In medieval philosophy the word „imaginatio " was common, e. g. with Abelard, Hugo of St. Viktor and Thomas Aquinas.
A good overview is given by Murray Wright Bundy (1927) and John Martin Cocking (1991).
Since 1500 imagination and fantasy are frequently described and discussed. In German we have also the words “Einbildungskraft”, “Vorstellung” und “Anschauung”. In English one used „idea”, in French „idée".
Analogy
Of course the Ancient Greeks already knew analogies. The concept of analogy got attention since the Franciscan and mystic Bonaventura (ca. 1250) and the Dominican Thomas Aquinas (ca. 1270) and is richly discussed up to today particularly in catholic theology.
Artists and scholars in Renaissance used analogies virtuous and often. Since that time the use of analogies is common in science and everyday life. With Kant and Goethe (ca. 1800) the concept of analogy became again interesting.
Metaphor
Ancient Greeks used also metaphors, i. e. pictures to illustrate an ordinary expression. Scholars in the Middle Ages concentrated on the interpretation of metaphors and the like in the Scripture. Research on metaphors begins only 1878.
Anthologies of beautiful essays on metaphors in history were arranged 1978 by Hayden V. White and 1994 by Frank Rudolf Ankersmit.
Repraesentatio
New interest in “repraesentatio” showed the specialists for the Middle Ages around 1970. Poor historical knowledge in this respect is found in the publications of Max Wartofsky (1979), Jerry Alan Fodor (1979), Ian Hacking (1983), Allan Paivio (1986), Hilary Putnam (1988), Patrick Suppes (1988), Robert A. Cummins (1989; 1996), R. I. G. Hughes (1997) and Michael A. Forrester (2000).
Cerae and Effigies
Since the first pilgrimage to Santiago de Compostela (950) the catholic church makes a cult out of votives made in wax (cerae).
The cult of “effigies” with respect to funerals and magic rape or execution is well documented from 1300-1800.
Since early 12th century: artistic and anatomical wax models
We can assume continuity from Antique to Renaissance workshops using objects of imitation made in clay or from wax, especially to train artistic expression.
A byzantine miniature of the 12th century (“St. Luc. Atelier d’artiste”) shows very well the use of antique masques, a statue and a column as models.
Likewise we assume that the first anatomical models have been shaped in the early 14th century in the course of investigating the vascular system. Molten wax was injected into the vessels, forming a cast that was carefully dissected out from the surrounding tissue. Another of the earliest models was created by none other than Leonardo da Vinci, who injected wax into the ventricular septum of the brain to bring out the detailed structures, and carefully recorded his method in his notebooks.
And more: Leonardo and Michelangelo used not only extensively the word “modello” but have already made, constructed and used a wide variety of models, not only for buildings of all kinds and for devices but also for artistic purposes, i. e. for drawings and paintings, sculptures and giant sculptures.
Since 400: Toys
Most toys create model worlds. Toys are well-known since earliest time of antiquity.
Because the medieval education system was rough and undemanding, toys were the same way.
Christmas cribs are mentioned in sermons around 400, rag dolls (simulacra de pannis) in the 8th century, mechanically moved dolls and birds around the year 1000. In the “Hortus Deliciarum" (1175-95) we see two children playing a tournament with knight figures, moving them like jumping Jacks.
Since these times toys were offered on fairs by flying dealers (Antonia Fraser 1966). Toys have survived since 1250: female figures and fable animals from tone, the tin figure of a knight in armament on his horse, a water jug in the shape of a horse.
From 1283 dates a accurate description of chess, games of dice and board games.
Since 1300 we have drawings of hobbyhorse, wind wheel, hand doll play (1338), kite (1405) and paper toys.
The first professional peg-doll carver (Dockenmacher) is mentioned in Nuremberg 1413. The invention of the peep box is attributed to Leon Battista Alberti (1437). First reports of a baby-house (doll’s house) date from 1558, of silver household appliances for children from 1571. A mechanical Christmas crib with music was created 1589 by the Nuremberg constructor of automats Hans Schlottheim.
Since 600: Beauty of bronze casting
From antiquity nearly no bronze statues have survived because they could be easily melted.
Artistic casting experienced a high level already in the dark Middle Ages. It begins in the 7th century with plaques of the Vikings and Langobards, continues with art work of the time of Charlemagne and in the dome of Hildesheim (1015/20), as well as with elaborate fonts out of brass (1118) and bronze (1225) and the lion of Braunschweig (1166) and ends with the first free standing human sculpture, „David" of Donatello (1440), and later “Perseus” of Cellini (1550).
The only preserved book describing the technique of casting is from Theophilus Presbyter (around 1123).
0-1500: Printing forms
In Japan a kind oft printed textiles were known in the first century AD. Real prints on bright, uncoloured linen are known since the 4th century from Egypt and since the 7th century from Europe and the Coptic areas of North Africa; likewise Chinese colour prints on silk.
The Gothic picture prints were devotion pictures in woodcut technology. Some prints served also as patterns for embroideries, i. e. they were over-stitched by hand. Beautiful examples have survived since the 13th century.
First documentary records of form cutters, i. e. carvers of the wooden printing models, originate from the year 1397 from Nuremberg and 1398 from Ulm. The models were used both for textile printing as well as for printing block books (popular books with woodcuts and short texts). The ornament stitch developed around 1450.
Printing with mobile type characters is said to be practiced around 1000 in China. In Europe Johannes Gutenberg introduced it around 1440.
13th-15th century: Baking tins
The oldest preserved baking tins (except from antiquity) date from the second half of the 13th century and are from limestone. From the 15th century about 150 models survived in middle Europe, particularly from tone, and also from slate and other stones. Representative, large models up to 40 centimetres in diameter start from 1500. They were usually carved in wood and used for marzipan, gingerbread and honey cake (Swiss: Tirggel).
Since 900: Model books and pattern books
Because the designations model book and pattern book are usually confounded, we have to differentiate between
· patterns for craftsmen and women (for book illustrations, ornamentations and architectural parts, later embroideries and laces, furniture and other articles)
· and samples, in the sense of specimen (first of textiles and silks, later of furniture and ceramics) for trade and sales.
Robert W. Scheller (1995) has collected and described with utmost care 28 model books with patterns for illustrations and architecture from 900-1470. The well-known collection by Arthur Lotz (1933) of Renaissance patterns for embroideries and laces follows.
Beautiful examples are from the 11th century the codex of the learned monk Adémar of Chabannes (1025) and from the first half oft the 13th century the album, sketch book or lodge-book by Villard de Honnecourt and the pattern books of Rein and Wolfenbuettel.
Around 1300 the Florentine textile industry had worldwide reputation. It is plausible that the practice of showing and dispatching samples (Italian „mostra”) started here. Since 1400 the word for it is in German „Muster” and in French „échantillon".
Soon these samples were put on cardboard according to quality, colour and material (wool, flax, cotton, silk).
Since 1300: fashion dolls
Already in the 2nd millennium BC there were jointed dolls in Babylon. In the grave of the Egyptian king Tutenchamon a wooden torso was found, presumable used as a tailor’s dummy. In Old Greece they made jointed dolls of clay.
At the courts in the Middle Ages there were tailor’s dummies in the precise sizes of the noblemen and noblewomen so that the tailor could adapt his cloths without bothering them.
Since about 1300 lay figures were used by artists in their studios. Also since then fashion dolls of all sizes are used as carriers and ambassadors of the newest fashion.
0-1200 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; Günther Binding 1993).
Architectural 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.
A culture historical curiosity are the “models of donors” (Stiftermodelle). We find a least 100 exemplars form the times of the Roman Empire to 1500.
Since the 6th century: Pleasure gardens
For primeval times gardens are models: images or drafts of “paradise "or images or drafts of the “world”. Derek Clifford (1962, 16) states: „It is a world made to our own measure."
Starting from the 7th century we know of generously equipped pond gardens in Japan, sketched after Chinese model and serving as pleasure gardens for wealthy and mostly noble owners. Often they were miniature reproductions of the world at that time.
The Sassanide King Chosru I. (or Chosros I.; ca. 570) is said to have had marvelous gardens around his pleasure castles in Persia (Hans Sarkowicz 1998).
In the Arab culture (also in Spain under the Moors) we find at the same time the shaping of gardens with flowers, trees and bushes as well as with colored tiles, ponds and fountains. Today still impressing is the garden „Generalife" in Granada, probably put on before 1250 (Germain Bazin 1988).
In his “Roman de la Rose”, written around 1230, Guillaume de Lorris describes a dream garden, „the garden of pleasure". His work was finished 40 years later by Jean de Meun. In the 15th century it was richly illustrated several times.
Since that time gardens were described again and again by:
· Jean de Garlande (around 1230)
· Albertus Magnus (“de Vegetabilibus” 1257)
· Pietro de Crescenzi (“Ruralia commoda", 1306)
· Giovanni Bocciaccio in the Third day of the “Decameron" (1348)
· “Le Ménagier de Paris” (1393)
· Leon Battista Alberti (“De re aedificatoria”, 1450/60)
· Francesco Colonna (“Hypnerotomachia Poliphili", 1499).
The first German book concerning „Pleasure gardens and planting "appeared 1530 with Egenolff in Strasbourg and with Steiner in Augsburg. Of large impact was the book „Tutti l'opera architecttura” of Sebastiano Serlio (1537-1547).
Since 1494 beautifully arranged gardens according certain patterns were called “knot gardens”, since 1579 in French “parterres”.
500-1500: Models for thinking and for behavior (fig. 1b)
Some important world models, ideas, ideals and behavior models of the Middle Ages – in Europe and the Middle East - were:
· Economics: Feudalism (beginning of 6th cent.), crop rotation (6th cent.), fiefdom (Merovingian donation of land; Karl Martell 725), cities (1000), slave trade (Pope Urban II 1095; Henry the Navigator 1441), fairs (12th cent.), private banks (1163), Franz of Assisi (poverty 1208), household (Walter de Henley 1250; Leon Battista Alberti 1444; also ecology), Thomas von Aquin (ban on interest, theory of work, property theory 1270), money economics replaces pay in kind; public banks (1401), stock exchange (1460/85 Antwerp)
· Ideal life: Epic („Digenis Akritas” 11th cent.; „Ruodlieb "1050; „Roland" 1090; „El Cid "1140; „Nibelungen” 1200), „Christian knight" (Bonizo 1090), minne, courtly life (Troubadours since 1100), service (Franz of Assisi 1210), humanism (since 1300: Dante, Petrarca, Boccaccio), „Della vita civile "(Matteo Palmieri 1438), discovery of the individual (Pico della Mirandola 1492)
· Political procedures: Sovereignty (Manegold 1085), „Domesday Book "(1086 in England: land register and tax book), parliament (1265 in England); „voluntary subjecting contract" (William of Ockham 1330)
· Instructions for behavior: Benedikt of Nursia (529), Konstantin VII (De „ceremoniis "950), Avicebron (1050), „Regimen sanitatis" (1050), Petrus Alfonsi (1120), Petrus Abaelard (“Ethica" 1136), Johannes of Salisbury (1159), fashion (12th cent.)
· World models: apocalypse (999), Bernhard Silvestris (1148), Hildegard of Bingen (1180), Joachim de Fiore (1190), Sacrobosco (1220/30), Robert Grosseteste (metaphysics of light 1250), Konrad of Megenberg (1350), Cusanus („coincidentia oppositorum“ 1438)
· Science: „House of wisdom" (Bagdad 813), Gerbert (990), nominalism (Roscelin 1092; William of Ockham 1330; Nicolaus d'Autercourt 1347), separation of faith and knowledge (Adelard of Bath and William of Conches, before 1150; Alfredus Anglicus 1217; Siger of Brabant 1270; Johannes Duns Sotus 1300), universities (from 1155: Bologna, Paris, Oxford), experience (Roger Bacon 1268; Petrus Peregrinus 1269), Platonic academy (1459)
· Thought Models: Chess (500), dialectics (Berengar of Tours 1050), „Sic et non" (Petrus Abaelard 1140), combinatorics (Raymundus Lullus 1303).
Since 1542: The model concept in French, German and English
Since 1542: "modello" arrives in French, German and English
Around 1550 the Italian word „modello „came
into French as "modelle" or "modèle",
into German as „Modell" and
into English as "model" or "modell".
Whereby the variety of meaning expanded rapidly into the present-day abundance.
The continuous change in the usage shows up very beautiful in English, where since middle oft the 16th century not only the word “model” was used for models of buildings, machines and landscapes, but also “modell”, "moddel" and “module". On the other side the “modulus” of Vitruvius was translated with „module ", "modulus" and "model".
Shakespeare used several times "modell" (with two l) in the sense of an architect’s set of designs, a person that is the likeness or „image” of another, and mould.
“Mould” was also written as French “moule” and also as “mowle”.
In German both "Model" and "Modell" were used for architectural models. The meaning rapidly expanded on patterns and examples. The uncertainty of writing, once with one l, once with two l, continued for a long time.
In fashion (French: "à la mode" or "modo") we find already in 1640 in German "models of clothes and shoes". In the other languages this seems to be the case 200 years later.
The respective verbs are „modeler“ (French, since 1585: „rendre semblable“) and „modellare“ (Italian, 1598), in English „modelize“ (1605) and „model“ (1625), in German „modellieren“ (see 1739 in Zedlers Lexicon).
Starting from 1555: Mental designs or forms as models
It is remarkable that at that time already mental designs were marked as models, such as the reformation (“il modello di Martino Lutero” by the monk Giacomo Moronessa 1555), the “new Theorick” of Copernicus (by Thomas Digges 1576), Bacon’s "New Atlantis" (1627), Descartes’ "Discourse" (by himself and Huygens) as well as "The German Principality” of the Cameralist von Seckendorff (1656).
The philosopher Pascal defined model in this sense as: "ouvrage d'esprit ou action morale, dont on peut s'inspirer".
Partial rivals of the concept of model
After his birth the concept of the model term immediately got in rivalry to numerous other concepts.
Copernicus used neither in his “Commentariolus” (approx. 1515) nor in “De revolutionibus orbium coelestium” (1543) the concepts “system” and “model”. But in the title of his main work we find the word „hypothesis". As early as 1540 Joachim Rheticus spoke of the „systema” of Copernicus. In 1576 Thomas Digges wrote of the models of Ptolome and Copernicus.
Since then further persistent partial rivals of the concept of model are „theory" (lat.: theorica), „philosophy" (philosophia), „treatise" (tractatus) and „principles" (principia).
Humans as "models"
Drawing from a human model was begun again in the Renaissance. In 1270 Cimabue painted the "countess X". Still over 100 years passed until artists dared to paint (1380/1400) from the naked body.
Another three hundred years later the word for it was "modello" (Italian 1672; later also: modella), "modelle" (French 1676), "model" (English 1691) and "Modell" (German 1717).
In the years 1953-54 Picasso painted 70 pictures to the topic "the painter and his model".
A woman displaying clothes is called "mannequin" since 1850 (in French) and “model” in English since 1904 ( “mannequin” since 1919) .
One of the many examples of the so called "Americanisation" of the German language after the World War II is the substitution of the words “Probierfräulein”, “Fotomodell”, “Vorführmodell”" and "Mannequin" by "Model" since 1968, whereby in the 80's still both forms were used.
Model as euphemism for prostitute is used in England since 1963 and soon spread on the continent.
Starting from 1600: The use of models in science and education
Model experiments
Since the beginning of modern science, which is at about 1600, not only the concept of model is used more frequently, but one begins also with model experiments.
The clergyman Simon Sturtevant described in 1612 in his patent application "Metallica" the heuristic use of models. The first model experiments in the sciences made the two Dutchmen Simon Stevin and Cornelius Drebbel, the Englishman William Gilbert (1600 with his terrella, a small iron ball as earth), the Italian Galileo Galilei (1638 in the "Discorsi": experiments on the bend of beam) as well as the German Otto von Guericke (1663 attempts with the Magdeburger hemispheres).
Since 1600 there were constructed ship models for hydraulic experimenting, first in England, then in Holland, France and Russia.
Visual instruction
Most important with the model are visuality, manipulating and improvability. No one has this expressed more beautifully than the famous "uomo universale" of the Renaissance, Leon Battista Alberti.
But only in the baroque his ideas were picked up. Campanella placed a reform program for education in his "City of the Sun” (1602 respectively 1623), which is based decisively on the use of models. Bacons "New Atlantis" (written 1624) brings something similar.
The famous pedagogue Jan Comenius emphasized in his "Bohemian Didactics” as well as in his "Great Didactics" (1633-38; published 1657) the character of models as always capable of improvement, and he publicised the visual instruction.
At that time there were presumably models with cords and wires, from cardboard or gypsum for geometrical bodies for instruction. They are mentioned in Christian Wolff’s "Mathematical Lexicon„ (1734 - viz. Gerd Fischer 1986). In instructing mathematics it was learned to modelling on the basis of the five Platonic bodies.
The use of hydrodynamic analogies
The ancient Greeks and the artists and scholars of the Renaissance had already used analogies virtuous. In the course of the "mechanization of the world view" hydrodynamic analogies arose. William Harvey’s discovery of the blood circulation (1616) was inspired by hydrodynamic analogies. Also Descartes was stimulated from the hydraulic engineering arts of his time. Giovanni Borelli (since 1666) used likewise analogies from the hydrostatics; he invented the Iatromathematics or Iatrophysics, a preliminary stage of biophysics.
Whether François Quesnay could be inspired for his model of the economic circulation (1758) of the blood circulation or of hydrodynamics, is disputed. In the physics of electromagnetism since 1820 (Faraday, Gauss, Maxwell) there were used a lot of hydrodynamic analogies.
Holistic thinking: The organism as analogy
There are also analogies in the other direction. Very popular was the (in fact: idealized) organism as a model for social or economic things, sometimes as well as for the universe.
The English statesman and philosopher Thomas Hobbes compared the State (1651) to a “artificial man”.
Economists and philosophers of the Romantic as Adam Müller (1809) and Franz von Baader (1832) have been inspired by the natural philosophic concept of the organism. The most prominent representative of this kind of thinking was Albert Schäffle. He has tempered the extreme - and therefore wide spread - formulations of his main publication, “Structure and life of the social body” (1875-78) in its second edition (1896). He can be regarded as one of the pioneers of systems sthinking.
19. century: Reality, visualization and theory in mathematics and science
Animals as substitutes for humans
Lamettries „L'homme machine "(1748) initiated psychological research on animals, and the animal experiments of the universal scholar Albrecht von Haller (1750) laid the foundation for neurobiology.
Since 1820 François Magendie and others regularly made experiments with animals. Pierre Flourens, professor for comparative anatomy in Paris, removed by exstirpation certain brain parts of pigeons and dogs and observed in consequence a decline in performance (1824).
Already in 1831 the neurologist and physiologist Marshall Hall set up guidelines for experiments with animals. The first investigations into isolated hearts took place 1846. And immediately the first protests against vivisection arouse (Evalyn Westacott 1949).
1998 Kenneth Joel Shapiro came to the conclusion that the investigation into animals does not help understanding of human behavior.
Samples as extracts from society
William Petty was the first to make a sociograph exploration in 1655-56 and soon founded „political arithmetic". First statistic work originates from the same time around 1660.
But only about 1740 - when the first consequences of the industrialization began to show up - social sciences took serious the conditions of the working poor. Already around 1795 the Englishmen David Davies and Sir Frederick Morton Eden used a kind of questionnaire to explore them.
A kind of “social experiments” claiming some representativeness was practiced since 1800 by the so-called utopian socialists Charles Fourier (1804-1836: “Phalanstère”, and thereof inspired 1844-46: Brook Farm Colony in Massachusetts), Robert Owen (1824-27: “New Harmony”) and Louis Blanc (1840: productive cooperatives).
Empirical social research has been pioneered by the members of the “Royal Commissions” of 1825, whose efforts culminated in the law for factory inspection of 1833. Their results of research were used still by Marx and Engels.
Since 1840 in many countries social enquêtes belong to the agenda.
The journalist Henry Mayhew used already 1851 „nondirective interviews". The mining engineer Frédéric Le Play refined 1855 the "observation method".
1895 the Norwegian Anders N. Kiaer presented his idea of a sample based on what he called the "representative method" for the first time to public. Later he used many representative samples as a basis for statistics, especially with regard to income statistics. In England Sir Arthur L Bowley used 1912-14 the procedure of random sampling.
1790-1880: American patent models
The United States Patent Office represented an early form of Federal support for science. This support enabled scientists, inventors, and entrepreneurs to secure property rights for their innovations. While many of the original thirteen American Colonies had some form of patent law, Thomas Jefferson (among others) influenced the development of the first national patent system in 1790. President George Washington signed the Patent Act of 1790.
Until 1880, to obtain a patent, the inventor submitted to the U.S. Patent Office an application, which consisted of a proper specification, carefully measured drawings, and, in most cases, a physical model of the invention. Well-known examples are the washing machine, septic tank and alarm systems (William and Marlys Ray 1974; American Enterprise 1984; Icons of Invention 1990).
Fire in the Patent Office 1836 and 1877 destroyed more than 80 000 models, but 150 000 remained when the obligation to submit a model was dropped. Today the office demands only a model when the applicant has to show that his inventions works in practice.
Nowadays there are various collections, private or public, of these patent models, e. g. with the Smithsonian Institution or the N. E. C. Group, Inc.
Science since 1840
Another differentiation of the model concept started approximately 1840. On the one hand, it was used for industrial products manufactured in great quantities (David S. Landes 1968); on the other hand it played a new role in physics.
We were told tat the modern model discussion begins 1840 with the investigation of the Cambridge professor William Whewell „The Philosophy of the Inductive Sciences", which was influenced by Kant. At the same time a second wave of visualization began in science. First such concepts were used as picture, illustration, idea, analogy, etc. In 1855 the Scotsman James Clerk Maxwell tried to give a "geometrical model" oft the physical forces. (In German the concept of model in physics appears more than twenty years later, 1879, with the translations of Maxwell's writings.)
Real visualizations of the theory by apparatuses were built since the 1870’s in particular by the Englishman Oliver Lodge (who later devoted himself to the examination of psychic phenomena) and the Irishman George Francis Fitzgerald. In the autumn 1892 the German Union of Mathematicians organized an exhibition in Munich of such apparatuses. The extensive "Catalogue of mathematical and mathematical-physical models, apparatuses and instruments" (ed. Walther Dyck 1892) appeared with a preface of Ludwig Boltzmann.
Already in 1893 the French physicist Pierre Duhem made fun of the efforts of his English colleagues, in particular William Thomson. More than a dozen years later he brought an extended version (70 pages) of his essay as Chapter Four in his legendary work "La théorie physique - son objet et sa structure” (1906; German: 1908; Engl. 1914).
It was Heinrich Hertz who introduced 1894 the concept of model explicitly in German science with his theory of "dynamic models".
Another Scotsman, Archibald Couper, introduced 1858 to chemistry the graphic visualization by the structural formula with valence lines. The German chemist August Kekulé relied on it and built atomic models and models of molecules from balls and wires "because of an irresistible need of visualization". Likewise many mathematicians, e.g. Julius Plücker and Ernst Eduard Kummer, started the plastic modelling of complicated mathematical and geometrical curves and bodies. Gerd Fischer (1986) published two rich and beautiful illustrated volumes.
The case of William Thomson, 1894 vs. 1904
How intensive was his search for models?
Generations of historians and theorists of science have quoted the following sentences of Sir William Thomson (1892: Baron Kelvin):
„I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I can understand it. As long as I cannot make a mechanical model all the way through I cannot understand; and that is why I cannot get the electro-magnetic theory… But I want to understand light as well as I can, without introducing things that we understand even less of. That is why I take plain dynamics. I can get a model in plain dynamics, I cannot in electro-magnetics.”
These sentences are from the beginning of the last of 20 lectures held by Thomson in October 1884 at Johns Hopkins University in Baltimore. A. S. Hathaway made a record in shorthand. Of this in December the same year a “papyrograph volume” was edited. The careful revision of these texts took Thomson 20 years.
Only 1904 the hardcover edition of the „Baltimore Lectures on Molecular Dynamics and the Wave Theory of Light“ was edited – without the sentences quoted above! Reason for that? Thomson had supplemented most lectures, and more, in the years 1901-03 he wrote Nr. 16-20 totally new.
Therefore we can ask if it is fair to quote again and again the shorthand notes and to ignore the final edition of 1904. (The 20 lectures “in their original form” have been edited by Robert Kargon and Peter Achinstein as late as 1987. Here we find the quoted sentences on page 206.)
bibliography see: model: special topics – William Thomson (1892: Baron Kelvin)
"Levels" of models in mathematics and science (fig. 2)
If we summarize the efforts of mathematicians and scientists in the 19th century we can differentiate six "levels" of their access to the things:
1. As starting point or "objects" we have on the one hand, mathematical ideas or ideals, on the other hand „reality", that means physical and chemical objects and processes
2. The area of the equations and formulas, laws and axioms, which are set up concerning the appearances and structures of the first level
3. The level of the "thought pictures" or hypothetical constructions
4. These "pictures" can be brought to paper as graphic representations
5. The level of the three-dimensional, material visualization of these "pictures".
6. The level of the theories.
Unfortunately many renowned physicists give rise to considerable confusion, because the use the word model for things of the level 2 (e.g. axioms or analogies) as well as for things of the levels 3 and 6. One of the fir