XII: Visualization, illustration
content
Symbols and Metaphors
Descriptive world models
Illustrated books for instruction
Drawings of descriptions and drawings of explanations
Graphic visualization
The Golden age of visual instruction: Baroque
Since 1650: improvement of common education
Visualizing a physical theory or law in the 19th century
19th century: Visualization also in mathematics …
… in chemistry …
… in medicine …
… and in psychology
Visualization in economy in the 20th century
21th century: still models as visualizations
For art see:
chap. XVIII: worlds of art, amusement & entertainment
For an overview of different kinds of pictures and shapes see: Fig. 55.
see also bibliographies:
The “pictorial turn”/ “iconic turn” - Bildwissenschaft
Symbols and Metaphors
Symbols and metaphors are different means to visualize abstract ideas or complicated phenomena. Whilst signs, in the narrow sense of the word, need some transcription code, metaphors and symbols speak for themselves – admittedly interpretations may differ, but not greatly.
Symbols can be traced back to cave paintings, astral religions and handicrafts of early times.
Metaphors can be found since the early high cultures, e. g. in sayings or proverbs of Old Sumer and Egypt (see Fig. 58, dealing also with research on metaphors since 1844).
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Descriptive world models
The world view of the Old Egyptians is characterized by the fact that contradictions between different views and systems were accepted as natural. Therefore, the old Egyptians were not shocked one of their world models looking as follows: The earth is - according to the four cardinal points - a quadrangle with a round baldachin of the sky above.
The Old Greeks dissolved this geometrical contradiction. "Hesiodos imagined the construction of the world as follows:
The round disc of the stable earth with mountains, rivers and seas is surrounded from the Okeanos which is also the connection to the likewise stable sky. The iron sky is a hemispherical bowl whose diameter corresponds to that of the earth, so that skies and earth form a hermetically closed unity. Underground there is a hemispherical bowl equal in size of the sky forming the Tartaros, the underworld." Outside of this sphere there is the "chaos" or "chasma" which existed before the other gods or hypostases of natural forces originated (Friedrich Krafft, 1971, 92).
Anaximander refined this view (Krafft, 1971, 114f.). Philolas put a central fire in the middle of the universe, not earth (Krafft, 1971, 224-227). Plato suggested a heliocentric world order. He and Aristotle stylized the movements of the celestial bodies in circles (Krafft, 1971, 336 and 351-353).
That was so convincing that already Copernicus (1507, published 1543) and Galilei adhered to it. Copernicus regarded in old tradition the sun as “soul, lantern of the universe”. Only Kepler discovered that the movements of the planets were elliptical. But Kepler was not always unemotional. He hoped to find as measure for the proportions of the universe the Platonic bodies one into each other (viz. Friedrich Wagner 1970, S. 58f.). The picture of 1596 is one of the first visualizations of a theory (John Desmond Bemal, 1970, 397).
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model: special topics - Wissenschaft im Altertum/ Wissenschaft
Illustrated books for instruction
There are a lot of illustrated books on „images of science“, e. g. Brian J. Ford (1992), Harry Robin (1992), Brian Scott Baigrie (1996), Jennifer B. Lee and Miriam Mandelbaum (1999).
Pictures in books with the aim of instruction can been seen in the works of Kurt Weitzmann (1959), (Alfred Stückelberger 1994) and Clemens Schwender et al. (2005) – see Fig. 59.
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model: special topics - Abbildungen - Illustrationen
Drawings of descriptions and drawings of explanations
Drawings to illustrate knowledge and drawings to explain processes and phenomena cannot be rigorously distinguished (see Fig. 60). Additionally we find many articles and books on illustrations as well as on explanation under “representation” (see chap. XIV: Representation, description, image).
Brian J. Ford (1992, 146-147; 136-137) also shows some explanatory drawings. We find further drawings of explanations in the illustrated volume of Harry Robin (1992).
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model: special topics - Abbildungen - Illustrationen
Graphic visualization
We are indebted to Nicole d’Oresme, the first natural philosopher writing in French (died 1382) for the graphic visualization of „functions“ by geometrical figures (forma).
It was René Descartes who developed a system for the graphic representation of quantities. The „curve“ on Cartesian coordinates is the tracking of a mathematical relationship between the properties of a body, a device, or a system (Eugene S. Ferguson, 1992, 148). The Cartesian Coordinate system may also include a third axis. The system led to analytical geometry and this in turn led to geometric calculus, which represents differentials as instantaneous slopes of curves and integrals as areas under curves.
In the 1860s Carl Culmann of the Swiss Federal Institute of Technology (ETH) developed a coherent system of graphic statics that was adopted by many engineers throughout the world. Some years later the French researcher Maurice d’Ocagne of the Ecole des Ponts et Chaussées, brought together a number of specialized graphical methods to solve particular mathematical equations and called his theory „nomography“ (1891).
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model: special topics - Design/ technisches Zeichnen/ Gebrauchsgegenstände
The Golden age of visual instruction: Baroque
Plato in „Timaios“ (40D), whilst explaining the complicated movements of stars and planets, recognized:
„To describe all this without an inspection of models (i. e. such instruments as a celestial globe or planetarium – i. e. ancillas of view) of these movements would be labor in vain.“
However, scholarship in Renaissance relied mainly on books, words and art.
Only during the Baroque period learning happened in the native tongue and with visual teaching:
· learning by imitation and exercise with models;
· use of originals, samples and pictorial representations with explanations (especially Jan Amos Comenius);
· gradual buildup of cohesive courses and methodology;
· promotion of understanding by insight instead of rote learning.
Tommaso Campanella placed a reform program for education in his "City of the Sun” (first draft 1602; publication 1623), which is based decisively on the use of models. Francis Bacon’s "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) visual instruction and instruction by models. In the central 20th chapter of this important oeuvre on “the method for the sciences” he postulated the didactic rule that men must learn everything by seeing and sensual demonstration (per autopsiam et sensualem demonstrationem doceamus omnia).
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 (see also J. H. Zedler, 1739, Sp. 714f, quoting broadly Wolff; later Ernst Prieger 1978).
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Nachschlagewerke für Begriffsgeschichte
Since 1650: improvement of common education
Since 1650 an improvement of common education took place (Albrecht Timm 1964, 27 u. 31 ff.) thanks to such mercantilists and cameralists as Veit Ludwig von Seckendorff and Wilhelm von Schröder. Since 1860 Johann Joachim Becher has aimed to spread technical knowledge by means of “Werkhäusern” (handicraft houses) and schools of arts. The idea of August Hermann Francke to connect religiousness with usefulness in handicraft teaching (since 1670) and in the so-called “Realschule” (since 1700) spread through whole Europa (Hertmut Sellin, 1972), especially as vivid, “practical education” relying on a broad collection of teaching aids, among them also instruments, machines and models (see e. g. J. G. Krünitz 1803, S. 549ff.).
A very famous collection (“laboratorium mechanicum”) was established by Christopher Polhem in Stockholm around 1700 (Sigvard Strandh 1980, 56-60; Albrecht Timm 1964, 27).
Eugene S. Ferguson (1992, pp. 105-147) gives some nice examples of the „didactic role“ of 3D-models from 1610-1875.
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Invention/ Erfindung – and some history of technics and technology
Visualizing a physical theory or law in the 19th century
One of the most interesting but also most ridiculed movement of the 19th century physics was the tendency to illustrate scientific findings in physics using mechanical apparatus. This movement lasted from 1820 to 1905.
for more details see in German:
Zur Geschichte des Modelldenkens und des Modellbegriffs – chap.
2.7. Innere Anschauung und Versinnlichung;
2.8. Dynamische Veranschaulichung mechanischer Konstruktion (ideal und real);
2.10. Äquivalente Abbildung von Zuständen beliebiger Systeme
as well as table:
Mathematische und naturwissenschaftliche Modelle des 19. Jahrhunderts
see also in English:
The Concept of Model and ist Triple History
chap.: 19. century: Reality, visualization and theory in mathematics and science
3D-models of physical theories
One of the first to construct 3D-models of physical theories has been the British physicist and inventor Charles Wheatstone. Around 1820 he started building and improving various kinds of musical instruments and experimented on sound and its transmission. In 1842 or in the late 1840s he built his legendary „wave machine“. Two visitors to his laboratory saw it: the German Julius Plücker in 1848 and the Italian Padre Angelo Secchi in 1849. At home Plücker charged the teacher and mechanic Friedrich Fessel to construct one whilst Secchi built one himself. All in all around 30 wave machines were built.
Perhaps already in the 1820s George Biddell Airy of Cambridge and in the 1830s Baden Powell of Oxford constructed similar apparatus (Christopher Haley, 1996, 162-164). In the 1840s followed Ebenezer Strong Snell of Amherst College.
Baden Powell designed a machine to illustrate the propagation of light waves in the ether and praised the advantage of such a device:
“A glance at an illustration of this kind enables the mind to grasp the idea at once, even when unaccustomed to the mathematical analysis of it” (1841, lvi).
Famous model makers since 1850 have been e. g. in Boston Eduard Samuel Ritchie and in Paris Rudolph Koenig, later Ferdinand Ernecke in Berlin and Max Kohl in Chemnitz.
bibliography:
Physical apparatus in the 19th century
From mechanical models in mind to curious apparatus
For the past history of the use of images in the 19th century physics see:
chap. IV: Draft, design, hypothesis
In 1861-62 Maxwell developed his ingenious „theory of molecular vortices“. Though he made in the publication a graphic illustration of the particles between the vortices the idea was only in the physicists imagination. But the desire to represent this and alike ideas in three-dimensional devices grew. Maxwell himself is said to have constructed a first device in the 1870s in his Cavendish Laboratory.
In short time a real mania arose to construct such mechanical apparatus with wheels, gears and elastic bands, etc. to illustrate the physicist's ideas. Pioneers were Oliver Lodge (see his „Modern Views of Electricity“, 1889) - an enthusiastic pupil of Maxwell – and George Francis Fitzgerald, but also William Thomson (see: The Concept of Model and its Triple History – paragraph: The case of William Thomson 1884 vs. 1904) and Ludwig Boltzmann as well as Hermann Ebert.
In the autumn 1892 the German Union of Mathematicians organized an exhibition in Munich of such apparatus. The extensive "Catalogue of mathematical and mathematical-physical models, apparatus and instruments" (ed. Walther Dyck, 1892) appeared with a preface of the physicist Ludwig Boltzmann. In it he differentiated 1892 (90f, 97) three types of models (translated):
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Models for instruction in mathematics and physics like geometrical "forms in gypsum, models with fixed and mobile cords, bars and links of all kinds ... mechanical models, visual wave planes, thermodynamic planes in gypsum, wave machines of all kinds, apparatus to make visible the laws of the refraction of light and other laws of nature";
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calculating machines, which "take over from humans the real operations of calculating, beginning with the for basic operations and ending wit integrating";
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the models of theoretical physics: "For the time being all these mechanical models existed only in mind. They were dynamical illustrations in fantasy and could not be practically realised. Because of their great relevance they provoked realisation at least of their basic types."
Most scientists laughed about
Already in 1893 the French physicist Pierre Duhem made fun of the efforts by his English colleagues, in particular William Thomson (Fig. 61). More than a dozen years later he published a much-cited extended version (70 pages) of his essay, which appears as Chapter Four in his work "La théorie physique - son objet et sa structure” (1906; engl. 1908).
Much more understanding showed Henri Poincaré to Maxwell in 1905 (Fig. 62) and Paul Ehrenfest in his necrology for his teacher Ludwig Boltzmann in 1906 (with a picture of the bicycle model).
Despite the tendency of many scientists to laugh at these curious devices the efforts to visualize theories or laws continued to 1905.
Arthur Rosenblueth and Norbert Wiener (1945, 318) judged them as „sterile and actually misleading".
bibliography:
Zur Geschichte des Modelldenkens und des Modellbegriffs
model: special topics – James Clerk Maxwell/ William Thomson
The effort to visualize knowledge is also found in other sciences..
19th century: Visualization also in mathematics …
For more details see in German:
Zur Geschichte des Modelldenkens und des Modellbegriffs – chap.
2.9: Anschauliche Modelle in Mathematik und Chemie
Mathematische 3D-Modelle im 19. Jahrhundert
Inspired by the French physicist Gaspard Monge, who had introduced in 1766 the descriptive geometry, some scientists and engineers began to visualize geometrical figures and surfaces by 3D-models in gypsum or with threads. Alexander Brill (1889) mentions such models, produced by the French Théodore Olivier (dynamic string models around 1830) and Fabre de Lagrange (1822 – rather 1872). Many of these models are preserved till today and located in the "South Kensington Museum” in London, at Union College in Schenectady, the United States Military Academy at West Point and Harvard University.
It is said that these models inspired artists such as Man Ray and Max Ernst (1934-36) as well as Henry Moore..
Also in Germany some mathematicians, e.g. Julius Plücker and Ernst Eduard Kummer, started, in around 1860, the plastic modelling of complicated mathematical and geometrical curves and bodies (Karl Fink, 1890).
Herbert Mehrtens (2004, 291-292) mentions that Plücker had the idea of working with models from the French physicist Faraday and that the physicist Heinrich Gustav Magnus in Berlin had already prepared a model of a wave surface as early as 1840 (sources: Alexander Brill, 1889; Karl Fink, 1890, Engl. 1910, 277).
In 1868/70 a former assistant of Plücker, Felix Klein, and his colleague Eugenio Beltrami were successful in preparing a visual euclidean model of non-euclidean geometry. Klein tried 1882 to visualize complex transformations by flow pictures – inspired by Kirchhoff and Maxwell (Rudolf Seeliger, 1948, 135, 126).
Since 1875 Felix Klein and Alexander Brill established at the Technische Hochschule München a scientific collection of mathematical models. Till 1884 more than 100 models from wood or gypsum were constructed. Around 1900 these models changed in the hands of Martin Schilling. His „Catalog mathematischer Modelle“ of 1903 registered already 300 objects.
Nice examples are also shown in the “Encyclopedia Britannica” from 1929 till 1973 (George W. Cussons, 1929-1973). Gerd Fischer (1986) published two beautifully illustrated volumes. Herbert Mehrtens (2004) gives a fine sketch of the aims of these mathematical models.
But not only Walther Dyck (1892), Martin Schilling (1903), George W. Cussons (1929) or Gerd Fischer (1986) and Herbert Mehrtens (2004) produced catalogues or descriptions of mathematical models.
Other researchers have been: Benjamin Pike (1848), Ferdinand Engel (1854), James W. Queen, S. L. Fox (1859), William Ladd (1868), Fabre de Lagrange (1872), H. Smith (1876), Alexander Brill (1889), E. M. Horsburgh (1914), Arnold Emch (1921, 1927), David Hilbert, Stephan Cohn-Vossen (1932), Hugo Steinhaus (1938), Henry Martyn Cundy, Arthur Percy Rollett (1951) and P. A. Kidwell (1996).
Not all two-dimensional surfaces can be built in three-dimensional space. They only can be described algebraically. Wilfrid Hodges, author of the “Theory of Models” (1993), calls them “monsters”.
The first example to be discovered in the 19th century was the non-euclidean hyperbolic plane. Later Henri Poincaré pointed out the real projective plane and the “Klein bottle” (1882). The geometers solved this “modeling problem” by introducing two devices: “pseudomodels” and “abstract models”. While the first can at least be drawn on the page, the latter is a abstract mathematical structure, at first denoted as “interpretation”.
For these interpretations see the next Chap: XIII: Interpretation of a theory
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… in chemistry …
The visualization of molecular constitution in chemistry that is found since 1810 resp. 1857 could likewise be seen as the visualization of theories, but the historian of chemistry Christoph Meinel (2004, 243, 265, 270) interprets the 3D-models merely as a „new way of communicating“ - see Fig. 52: „Paper tools“ and 3D-models in chemistry in the 19th century, and chap VI: Draft, design, hypothesis.
If we disregard the English teacher John Dalton who made around 1810 atomic models using wooden balls of various sizes (Christoph Meinel, 2004, 270, footnote 1), visualization of chemical theories starts in 1857 with the German chemist August Kekulé (Christoph Meinel, 2004, 259) building models of molecules with wooden balls and wires "because of an irresistible need of visualization" (Leopold Horner, 1965, 240). Shortly after followed with other constructions the German chemist August Wilhelm von Hofmann in London and the Scotch James Dewar in Edinburgh. In 1885 resp. 1890 Adolf von Baeyer and Hermann Sachse were able to gain new insight by means of tetrahedral constructed wire models resp. folded pieces of paper. In 1934 Herbert Arthur Stuart introduced the calotte model (or: space-filling model).
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model: special topics - Anschaulichkeit in der Chemie
… in medicine …
From an often-reprinted textbook of physiology from 1876 (Michael Foster, J. N. Langley, 1876) we learn that also in this area there were many attempts to make the principles of blood circulation visible through the use of elastic tubes, glass connections, hand pumps and pressure gauges.
In 1891 Henry H. Donaldson gave an overview on 3D-brain-models made of strings or wires, cardboard or gypsum. He describes among others the models prepared by Charles Aeby, Sigmund Exner, Ludwig Fick and Adolph Ziegler.
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Modelle in der Psychologie und Psychiatrie - Models in Psychology and Psychiatry
… and in psychology
Since Wilhelm Wundt – around 1880 – psychology used 2D- and 3D-demonstration-models in the classroom (Hugo Münsterberg, 1893; Edmund C. Sanford, 1893; Edward Bradford Titchener, 1903; Christian A. Ruckmich, 1916).
In 1923 Edwin Garrigues Boring and Titchener described models (using a lot of drawings) made of cardboard and wood to demonstrate as much as 360 facial expressions. Seven years later Joy Paul Guilford built a new model with William E. Walton to show facial expressions frontally.
Another kind of models was used around 1930 in learning psychology. To illustrate the “conditioned reflex” H. D. Baernstein constructed an electro-mechanical model for Clark Leonard Hull in 1929, and in the same year J. M. Stephens presented a „learning machine“ to demostrate the law of effect. In the next year Albert Walton described among other demonstration devices also a „conditioned reflex machine“. A refinement of it has been presented in 1933 by George K. Bennett and Lewis B. Ward. Some more models have been proposed by D. G. Ellson (1935) and H. Bradner (1937).
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Modelle in der Psychologie und Psychiatrie - Models in Psychology and Psychiatry
Visualization in economy in the 20th century
Under the title „economic-mathematical models“ the sowjet economist Wassili Sergejewitsch Nemtschinow (1966, 87-106) gave a very good description of the „tableau économique“ (1758 and 1766) of the French physiocrat François Quesnay (1966, 87-106). This tableau is famos because it contains a great number of formulas and „speaking“ graphics and flow-diagrams, e .g. the so-called „zig-zag“.
Other models are the numerical models of S. G. Strumilin (around 1920/30) and the input-output model (German: Verflechtungsbilanz) of a national economy. The latter is often attributed to the American economist Wassily Leontief (1941), whereas Nemtschinow points out that this method was already used in the URS in 1925/26.
The famous economist Irving Fisher was also a model builder. Mary S. Morgan (1999, 347-388) shows his „accountig-balance model“ of 1911 as well as his „connecting-reservoirs model“ of 1894/ 1911 (see also Marcel Boumans, 2005, 149-174). Together with Marcel Boumans (2004) Morgan shows the head-high 3D-model of Bill Phillips, made in 1949/50. It shows the macroeconomy by flows and stocks of coloured water in a system of perspex tanks and channels (see also Marcel Boumans, 2005, 11-14).
Another, much simpler, mechanical device has been proposed by Erik Christopher Zeeman in 1972. His so-called “Catastrophe Machine” illustrates how a small perturbation can give rise to a discontinuous consequence (Hans Poser, 2008, 181f with an illustration).
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Modelle in der Ökonomie und Ökonometrie - Models in economy and econometry
Hans Poser: Modelle, Simulationen, Weltbilder. Der Aufbruch in die Komplexität. In Ulrich Dirks, Eberhard Knobloch (Hrsg.): Modelle. Frankfurt am Main: Peter Lang 2008, 172-186.
21th century: still models as visualizations
Yet in 2003 Manfred Kelm presented an instructive example how to make phsico-chemical processes visible.
He constructed a plexiglas model of only 28 cm length of a glass melter for the vitrification of radioactive waste. The aim of the modeling was to visualize the glass flow in the melter under different operation conditions, e .g. different electrodes circuitries, different power distributions between the electrode gaps and under the influence of precipitating electrically conductive particles.
Kelm could demonstrate that this method gives qualitative results within a short time span and requires no sophisticated instruments. It gives fast and directly observable response to variations in the operating conditions.
Manfred Kelm: Physical Modeling of a Glass Melter. In Tibor Müller, Harmund Müller (Eds.): Modelling in Natural Science. Design, Validation and Case Studies. Berlin: Springer 2003, 357-377.
Dr. phil. Roland Müller, Switzerland / Copyright © by Mueller Science 2001-2016 / All rights reserved
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