Home IX: Analogy

 

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Analogies in language and literature, mystics and theology, art and technics

Kepler, Newton, Leibniz, Clarke

The use of hydrodynamic analogies

Holistic thinking: The organism as analogy

Mechanical models

Analogy in 19th century physics

Atoms as solar system, electrons as saturn rings

Theoretical approaches

 

 

see also:

Fig. 56: Mary Hesse on analogies (1967)

 

 

Analogies in language and literature, mystics and theology, art and technics

 

Of course already the Old Greeks knew and used analogies (Franz Brentano 1862; Paul Grenet 1948; André Rivier 1952; Erhard-Wolfram Platzeck 1954; Karl Bärthlein 1957; Johannes Hirschberger 1960; Eberhard Jüngel 1964; Geoffrey Ernest Richard Lloyd 1966; Wilfried Fiedler 1978; Mario Puelma 1986; Ralf M. W. Stammberger 1995).

 

The term „analogy“ has been used and disputed since the Franciscan and mystic Bonaventura (around 1250 - Karl Werner 1876; L. Berg 1955) and the black friar Thomas Aquinas (around 1270 – Ludwig Schütz 1881; Gerald Bernard Phelan 1941; George Peter Klubertanz 1960; Ralph M. McInerny 1961, 1996; Barbara Delp Alpern 1980; Norbert W. Mtega 1981) till today mainly in the catholic theology (Battista Mondin 1963; Richard Swinburne 1992).

Legendary were the many editions of bishop Josef Butler’s „The analogy of religion“ (1736).

 

Because analogy allows the combination of phantasy, eruditeness and life, artists and scholars in the Renaissance period have used frequently and virtuoso analogy (Leonardo Olschki 1918-27; Ernst Cassirer, 1927). Michael Randall (1996) analyzed the „analogical imagery“ of the French Renaissance.

 

The first masterpiece of the modern era for a mathematical work animated by examples, anecdotes, proverbs, citations and sayings is the already mentioned "Summa" of Luca Pacioli (Olschki I, 164ff.). Here science and pedagogy merge with meticulousness and vividness. Pacioli borrowed from Boethius the comparison of perfect and imperfect numbers with an able-bodied man and a cripple. In a series of analogies and allegories he further developed it (I, 169).

 

We find perfection of visual thinking with Leonardo da Vinci. He was convinced of the equality of art and science as instruments of cognition. Leonardo Olschki (I, pp. 365-413) shows a plentitude of analogies used by da Vinci in order to describe and explain natural objects and phenomena.

 

 

Kepler, Newton, Leibniz, Clarke

 

At least as important was the disengagement of the mythological and religious world, i. e from philosophy and theology. Astronomer Johannes Kepler is a typical example. At first he looked at nature as a "heavenly souled being“, and after 1623 as "clockwork" (Dijksterhuis, 1956, pp. 345ff.). In the same year he substituted the idea of „moving souls“ in the planet with ordinary forces.

 

Giedeon Freudenthal dedicated an interesting study to "atom and individual in the age of Newton" (1982). Starting point is the discussion between Isaac Newton and Gottfried Wilhelm Leibniz on the absolute space. "Newton proceeds from an assumption on the quality structure of the elements and infers on the result for the world system. Leibniz proceeds from an assumption on the system and infers on the quality structures of the elements (Giedeon Freudenthal 1982, 79).

Newton considered an interference of God in the world system as necessary. He formulated, the space is the "sensorium of God". In contrast Leibniz held the world as a perfectly designed clock by God, which continues to function without his co-operation.

 

Freudenthal has worked out carefully that around 1715 two different kinds of clocks could be used as models: the coarse craftsman's clock (clock) and the pendulum clock or scientist's clock à la Galilei and Huygens (watch). The first one often needs the intervention of a supervisor. Hence, Samuel Clarke, a Newtonian, characterizes the world, the work of God as a "clock", and attributes God „inspection and government“. In contrast the scientist's watch runs by itself; therefore for Leibniz God is a perfect mechanic: scientist and learned watchmaker in one (Gideon Freudenthal 1982, 108). The Leibniz-Clarke correspondence has been edited in 1956 by Manchester University Press in English, in 1957 by Presses Universitaires de France in French and in 1990 by publisher Meiner in Hamburg in German.

 

Although in general rather Newton than Leibniz prevailed in the natural sciences, one can say with Dijksterhuis (1956, 549): „The mechanization of the world view leads with irresistible consequence to the view of God as a retired engineer, and from here to his complete elimination it was only a step.“ Laplace did it 100 years later.

 

 

The use of hydrodynamic analogies

 

During the course of the "mechanization of the world view" hydrodynamic analogies arose. William Harvey’s discovery of the blood circulation was inspired by hydrodynamic analogies (Franz Vonessen, 1989). In his first handwritten notes of the year 1616 he says, having demonstrated with the nature of the heart, "that the blood flows in continuous stream of the lungs into the aorta as by two valves of a water pump used to lift water" Van Leeuwen et al. 1946, 75). In another note Harvey compares the heart as the “fountainhead of life” with the sun as “heart of the world“ (J. D. Bemal 1970, 411). This picture reminds us of Copernicus who saw the sun according to old traditions as the soul or the „lantern of the universe“.

 

The first material model of the blood circulation was produced by the German Salomon Reisel in 1674.

 

Also Descartes was stimulated from the hydraulic engineering arts of his time. We find many references in „Les passions de l'âme“ and in the “Traité de l’Homme” (postum 1664). The souled body consists of blood vessels caring like a system of tubes for the transport of so-called "life spirits" (already described by Telesio). In the head, more exactly in the area of the pineal gland under the brain, the soul "governs" as a kind of tube master, who determines, which and how many life spirits for what time flow through the vein (Rainer Specht 1966; Richard Burnett Carter 1983).

 

Giovanni Borelli (since 1666) used likewise analogies from the hydrostatics; he invented the iatromathematics or iatrophysics, a preliminary stage of biophysics.

 

Whether François Quesnay – himself as Harvey a physician - could be inspired for his model of the economic circulation (1758) of the blood circulation or of hydrodynamics, is disputed. Heinz Rieter (1983, 65) verified that he did not rely on the blood flow but on the mechanistic natural philosophy of his time. “It is an analogy of movement and mechanism which transfers the cognitions of the Cartesian physics to the level of political economics in order to derive ‘natural’ social laws.” This mechanistic approach was further developed by classical economists such as Adam Smith (1776), Jean-Baptiste Say (1803), David Ricardo (1817) and Johann Heinrich von Thünen (1826).

 

In the physics of electromagnetism since 1820 - Faraday, Gauss, Maxwell - many hydrodynamic analogies were used.

Inspired by these attempts the economist Dalgairns Arundel Barker constructed in 1906 a „hydraulic model“ for the currency system between national economies. Likewise Irving Fisher constructed a „connecting-reservoirs model“ in 1894/1911 (Mary S. Morgan 1999, 369-388; Marcel Boumans, 2005, 149-174). Well known ist he model which has been built after World War II by the New Zealand economist Alban William Phillips at the London School of Economics (Mary S. Morgan, Marcel Boumans, 2004, 369-401; Marcel Boumans, 2005, 11-14).

 

In 1895 Sigmund Freud, in his sketch of a psychology (published 1950), used a hydraulic model for his first demonstration of the drive dynamics of the „psychic apparatus“. Physiologist Archibald Vivian Hill (1936) used also a hydraulic model to illustrate „excitation“ and „accommodation“ in nerve.

 

 Similarly Konrad Lorenz founded his theory of instinct since 1935 on a hydraulic model (see already Robert Aubrey Hinde, 1956), which in the 1970s served as the only example of a model in a „Primer in Psychology“.

Psychologist Raymond Bernard Cattell (1957) used also a hydrodynamic model for „personality and motivation“.

 

 

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 structures, sometimes as well as for the universe.

The English statesman and philosopher Thomas Hobbes compared the State (1651) to a “artificial man”. Whe around 1670/80 egg cell and sperm cell were discovered, researchers thought to find already the completed man in small-scale („homunculus“) in it.

 

Economists and philosophers of the Romantic such as Adam Müller (1809) and Franz von Baader (1837) 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).

 

D. J. Haraway (1976) reports on organismic metaphors in 20th century’s developmental biology.

 

 

Mechanical models

 

In the 18th century state and economy were often regarded as machines. The Cameralist Johann Heinrich Gottlob von Justi wrote in 1764:

”A perfect established state has to be totally similar to a machine in which all wheels and transmissions fit into each other with utmost precision.”

And the Cameralist August Ludwig von Schlözer proposed in 1793:

“The most instructive kind of teaching politics is to regard the state as an artificial, extremely complex machine serving a certain purpose.”

For Europe this has been explored by Ahlrich Meyer (1969), for America in 1997 in the Harvard Law Review.

 

In the realm of social philosophy Saint-Simon devised a Newton religion with Newton temples, etc. shortly after 1800. The basis was the following assertion: „The only cause of physical as well of moral phenomena is the universal gravity.“ Also Saint-Simon’s pupil Auguste Comte tried to impute social phenomena to natural laws. If society is mechanistic, then she can be controlled scientifically, i. e. she can be governed by a council of social physicists (see Floyd W. Matson 1969).

 

In 1816 psychologist Johann Friedrich Herbart formulated: „The regularity in the human mind resembles exactly the one in the starry heavens.“ No wonder he tried to establish an „exact“ psychology, mainly a mathematically founded psychology of imagery („Vorstellungsmechanik“).

 

In 1930 the psychologist and behaviorist Karl S. Lashley tried to develop a theory of the functions of the brain in analogy to the Telefone system:

„The model for the theory is a telephone system. Just as two instruments can be connected only by certain wires, so the sense organs and muscles concerned in any act are connected by nerve fibers specialized for that act.“

 

For the analogy of man or mind with a machine see:

Petra Gehring, Geert Keil and Klaus Sachs-Hombach in Jörg F. Maas (1993).

 

Since World War II new attempts were made to find „mechanical models“ for economic, biological and psychological phenomena (Morehouse et al., 1950; Smith, Erdley, 1952; Tustin, 1953; Broadbent, 1957). Rolf Günther was very critical of such attempts in his thesis: „The problem of analogy between economic and electrotechnical processes” (1957).

 

Also in the 1950s the analogy of brain and computer was widley discussed. It is said that in 1955 Herbert Alexander Simon told his students in a seminary: „Around Christmas Allan Newell and I have invented a thinking machine.“

In 1958 John von Neumann published his widely read study on „the Computer and the Brain“, three years later Frank Honeywill George: „The Brain as a Computer“. Therefore Dean Everett Wooldridge could speak of „the Machinery of the Brain“ (1963). The German logician Gotthard Günther philosophized since 1953 on the „consciousness of machines“ (as a book, 1957) and published a „Cybernetic Ontology“ (1962). Critical to these analogies were among others John E. Searle (1980) and E. A. Spiegel (1983).

 

In an interview in 1959 the French anthropologist Claude Lévy-Strauss used the analogies of clocks and steam engines: Societies studied by the ethnologist resemble clocks and can be regarded as „cold societies“ whilst our „great“ modern societies resemble steam engines and therefore are „hot societies“ (Georges Charbonnier: Entretiens avec Claude Lévy-Strauss, 1960, 38; English: Conversations with Claude Lévy-Strauss, 1969).

 

 

Analogies in 19th century physics

 

Analogy was a key concept in 19th century physics. In 1842 the 18 year old Scottish physicist William Thomson postulated an analogy between the formulas for heat and attraction:

„The general conclusions established in it show that the laws of distribution of electric or magnetic force in any case whatever must be identical with the laws of distribution of the lines of motion of heat in certain perfectly defined circumstances“ (1872, 1, footnote of 1854).

Three years later he emphasised, in a „note on induced magnetism in a plate“, the analogy between a result on induction and a result on optics:

„It is hardly necessary to point out the analogy between this [i. e. a result for induction] and the corresponding result in optics“ (1872, § 157, 105).

But it was only in 1855-56, in his lectures “On Faraday’s Lines of Forces”, that 24 year old James Clerk Maxwell introduced the concept of analogy in physics:

“In order to obtain physical ideas without adopting a physical theory we must make ourselves familiar with the existence of physical analogies. By a physical analogy I mean that partial similarity between the laws of one science and those of another which makes each of them illustrate the other.
Thus all the mathematical sciences are founded on relations between physical laws and laws of numbers, so that the aim of exact science is to reduce the problems of nature to the determination of quantities by operations with numbers.”

Since the realm of mechanics, including gravity and hydrodynamics, is very pictoral, its laws can be used to illustrate phenomena in other realms without making any assumptions on the physical nature of electricity (James Clerk Maxwell, 1895, 4 and 9; Edmund Taylor Whittaker, 1910; Joseph Turner, 1955-56; Alan Chalmers, 1973; 1986; Nancy J. Nersessian, 1984; Walter Kaiser, 1989 - see also Fig. 62: Henri Poincaré on Maxwell, analogy and images).

 

For the use of analogies, images, models, etc. in 19th century physics, see:

Chap. VI: Draft, design hypothesis

For visualization and illustration in 19th century physics see Fig. 61.

 

 

Atoms as solar system, electrons as saturn rings

 

In 1913 Niels Bohr proposed his legendary atom model (Paul Kirchberger 1922; John L. Heilbron, Thomas S. Kuhn 1969; Ulrich Hoyer 1974; Arthur I. Miller 1984). He called it  de facto „atom-model“ -  whereas Ernest Rutherford (1911; see Lawrence Badash 1987) two years ago had spoken of an „atomic system“. However both reseachers spoke also of the „theory of the structure of atoms“: Rutherford of the one of Sir J. J. Thomson, Bohr of the one of Prof. Rutherford.

 

It may be of interest that the analogy with the solar system has been used already in 1904 by J. J. Thomson verwendet wurde. Niels Bohr (1913, 2) relied on it. Less known ist he fact that already in 1904 the Japanese Hantaro Nagaoka had postulated a „Saturnian“ model for the atom: a central attactive mass is circled by rings of electrons.

Bohrs philosophy is thoroghly commented by Henry J. Folse (1985), Dugald Murdoch (1987), Jan Faye (1991), David Favrholdt (1992) and Sandro Petruccioli (1993).

 

 

Theoretical approaches

 

Despite analogies are widely used there are not many attempts to deal theoretically with them.

However, around 1840, at the same time when the use of analogy started in physics and biology theoretical considerations arouse (see Fig. 57).

 

 

bibliography

Analogie – analogy (1733-2001)

 




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