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2018 | OriginalPaper | Chapter

3. Vilfredo’s School and University Education

Author : Fiorenzo Mornati

Published in: Vilfredo Pareto: An Intellectual Biography Volume I

Publisher: Springer International Publishing

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Abstract

This chapter consists of an original and documented study of Pareto’s scholastic and university education. Drawing on what little direct documentation we possess, as well as on the copious legislation of the time, the first two sections will be devoted to a detailed reconstruction of the curriculum he followed at the Technical Institute in Casale Monferrato and thereafter in Turin at the faculty of mathematics and at the school of specialisation for engineers. In order to contribute further to the elucidation of this hitherto fairly obscure period in Pareto’s intellectual biography, which (with the exception of the now-complete list of his exam results) certainly warrants further investigation, brief biographies are provided of many of his university and also his school teachers. In Sect. 3.3, a broad description is given, based on unpublished documentation, of two of the courses he followed: calculus and theoretical mechanics. As a result, we finally gain a clearer picture regarding the two logical tools most used by Pareto in his later scientific career, that is, calculus and the concept of equilibrium. Section 3.4 consists of a description of Pareto’s scientific and mathematical patrimony at the conclusion of the decade dedicated to studies under the guidance of his father. This aspect of Pareto’s intellectual biography has hitherto been largely neglected but is clearly indispensable to achieving a better understanding of his later scientific work, with its overarching reference to the concept of equilibrium, characterised by an extensive but not fanatical application of mathematical analysis. Further examination on the part of historians of mathematics in relation to Pareto’s exposure to these two disciplines could lead to a welcome addition to our understanding of this interesting youthful span of his intellectual biography.

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previous chapter An Outline of the Life of Raffaele Pareto
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Footnotes
1
On the history of the beginnings of technical education in unified Italy, see Limiti (1959).
 
2
The so-called Casati law, from the name of the minister Gabrio Casati who proposed it.
 
3
The physics curriculum covered “heat”, light, magnetism, electricity, electro-magnetism, meteorology, Royal decree n° 4464 of 24th November 1860.
 
4
The mathematics curriculum for the first year covered geometry of solids, algebra and logarithms, rectilinear trigonometry, ibid.
 
5
The mathematics curriculum for the second year covered practical and descriptive geometry, ibid.
 
6
Pareto, a mother-tongue speaker of French, was able to read English but not German and did not use either of these languages in writing or in speaking, Pareto to Maffeo Pantaleoni, 17th March 1897 and 20th October 1898, see Pareto (1984, pp. 53, 235), Pareto to Irving Fisher, 7th January 1922, see Pareto (1975, p. 1076).
 
7
The curriculum for mechanics covered the composition and resolution of movements and forces, the centre of gravity, the movement of a physical point and elements of hydraulics, Royal Decree n° 4464 of 24th November 1860.
 
8
The curriculum for technical drawing consisted in the graphical representation of “notions concerning the mutual intersection of two solids”, ibid. It also included the basics of axonometric projection and its use in the drawing of machinery. This course, which Pareto followed in 1863–1864, almost certainly inspired the first of his publications of which we have knowledge; see Pareto (1866, p. 1). This publication contained a lengthy overview of the applications of this type of projection, whose object is “to render clearly at first glance a given mechanism or the shape of a given body”.
 
9
Access to the technical school was via an entrance examination consisting of written tasks, including grammatical analysis, essay-writing and answering a “question in mathematics concerning basic operations on whole numbers and on ordinary fractions” (provisions for implementation of 19th September 1860, articles 90 and 119).
 
10
Vilfredo to Domenico Pareto, 19th December 1860, see Pareto (1981, p. 21). In this letter Vilfredo describes how his summer study programme in preparation for the supplementary examination was undertaken under Raffaele’s guidance, with particular regard to arithmetic and plane geometry.
 
11
On the history of the Institute (known as the Germano Sommeiller Institute after 1883) in the early 1860s, see Montaldo (2003, pp. 143–155).
 
12
List of teaching staff in public education in the city of Turin in the 1862–1863 academic year.
 
13
On Giuseppe Bruno, who was also a member of staff in the faculty of physical, mathematical and natural sciences at the Turin institute, see Roero (1999a).
 
14
Whom Pareto was to encounter again as a teacher at the school of specialisation.
 
15
Royal Technical Institute of Turin, academic curriculum approved by the Ministry of Agriculture, Industry and Commerce for the academic year 1863–1864.
 
16
Raffaele to Domenico Pareto, 15th August 1864, see Giacalone-Monaco (1966, p. 17).
 
17
City Hall, Turin, List of students meriting prizes or honours for the school year 1863–1864 in the Turin Technical Institute, the High Schools, the Junior High Schools and the Technical Schools, VI June MDCCCLXV. The only schoolteachers mentioned by Pareto (see Pareto (1869, p. 71); Vilfredo to Domenico Pareto, 19th December 1860, see Pareto (1981, p. 21); Pareto to Teodoro Moneta, 8th October 1893, see Pareto (2001, p. 70)) are Ferdinando Pio Rosellini (1814–1872), school-manager and teacher in the mathematics at the Leardi, see Benvenuti (1967), and Giangiacomo Arnaudon (1829–1893), teacher of chemistry and commodity economics at the Sommeiller, see Gliozzi (1962). Arnaudon, see Arnaudon (1892, pp. 50–51), cites his student Pareto as one of the most active members of Italian Commodity Economics Society founded by Arnaudon.
 
18
Law of 23rd November 1859, article 47.
 
19
See Matteucci (1862, p. XII).
 
20
Ibid.
 
21
Ibid., p. XIX.
 
22
Provisions for implementation of 14th September 1862, Faculty of physical, mathematical and natural sciences, articles 2–4.
 
23
Vilfredo to Domenico Pareto, 26th November 1864, see Pareto (1981, p. 22).
 
24
Provisions for implementation of 14th September 1862, Faculty of physical, mathematical and natural sciences, article 1.
 
25
Historical archive of the University of Turin, register of enrolments in the first year and in the courses of the Faculty of Theology, Philosophy and Letters, Physical, Mathematical and Natural Sciences, IX. A 81, roll number 102.
 
26
Ibid., Faculty of Physical, mathematical and natural sciences, Minutes of the special examinations for inorganic chemistry, X D 86, first part, p. 67.
 
27
On Angelo Genocchi (1817–1889), see Giacardi (1999a) and Conte and Giacardi (1991).
 
28
On Michele Peyrone (1813–1883), see Cerruti (1999).
 
29
On Angelo Marchini (1804–1870), see Navale (1999).
 
30
On Francesco Faà di Bruno (1825–1888), see Giacardi (2004).
 
31
On Gilberto Govi (1826–1889), see Ferraresi (2002). For many interesting aspects of Govi’s conception of science see Govi (1862), which is the introduction to the course for the academic year 1862–1863, pp. 5–26. Scientific progress consists in “(continually) making deductions about the scientific nature of real-world phenomena on the basis of the examination and the comparison of sensations and facts”, thus leading to the refinement of knowledge by dividing the various phenomena into their component elements, ibid., pp. 10–12. Further, while considering mathematics to be “the most valid tool for scientific enquiry”, Govi, ibid. p. 20 considers that it is “of no profit” to transform “the exposition of scientific research into complex and laborious mathematical formulations”. Having said that, according to Govi, ibid. p. 21, the rigorous procedures of physics, that is, “reducing all natural phenomena to a handful of axioms” requires “a more detailed study than has so far been performed on the links between different classes of phenomena”.
 
32
On Bartolomeo Erba (1819–1895), see Giacardi (1999b).
 
33
On Camillo Ferrati (1822–1888), see Roero (1999b).
 
34
In the Turin University Historical Archive, Registry book of Diplomas from 2nd January 1863 to 31st December 1869, the award of the graduation diploma to Pareto is recorded with the number 1721 (undated).
 
35
Provisions for implementation of 14th September 1862, Faculty of physical, mathematical and natural sciences, article 17.
 
36
Ibid. article 18.
 
37
Historical archive of the Polytechnic of Turin.
 
38
On the early years of the Turin institute (after 1906 Polytechnic), see Richelmy (1872).
 
39
Regulations of the Turin engineering school of specialisation, article 1, 11th October 1863.
 
40
Ibid., article 7 and the Historical Archive of the Polytechnic of Turin (for the marks).
 
41
On Prospero Richelmy (1813–1883), see Curioni (1884, pp. 46–47). Richelmy, see Richelmy (1872, pp. 19–20) declares himself in favour of the study of “those elements of mathematics …. having the most frequent applications” both because the latter are “the ultimate objective of engineers” and because it is “pointless to seek [in] calculus that rigorous exactitude which then could not be satisfied in reality”. The course in applied mechanics relates to the theory of machines together with “motors where no use is made of elastic fluid, measurement or water input”, Regulations of the Turin School of Specialisation for Engineers (11th October 1863), article 9.
 
42
On Agostino Cavallero (1833–1885), see Curioni (1885). The course in steam engines and railways concerns the theory of machines where “an elastic fluid is used” and where locomotion is “especially by steam”. There are also exercises relating particularly to “[the] practical study of steam engines [and the] development of a design for such machines”, regulations of the Turin School of Specialisation for Engineers, article 10 (11th October 1863).
 
43
On Giovanni Curioni (1831–1887), see Signorelli (1985). The course in construction dealt with “the resistance of materials, urban buildings, plumbing and roads”, regulations of the Turin School of Specialisation for Engineers, article 11 (11th October 1863).
 
44
On Carlo Promis (1808–1888), see Fasoli and Vitulo (1994). The course in architecture dealt with “the aesthetics of the art and the composition and disposition of buildings”, regulations of the Turin School of Specialisation for Engineers, article 12 (11th October 1863).
 
45
On Bartolomeo Gastaldi (1818–1879), see Morello (1999). The course in mineralogy dealt with “minerals and rocks of use to engineers, where they lie and methods for their extraction and exploitation”, regulations of the Turin School of Specialisation for Engineers, article 13 (11th October 1863).
 
46
On Ascanio Sobrero (1812–1888), the well-known inventor of nitroglycerine, see Di Modica (1988, pp. 5–13). The course in practical (i.e. industrial) chemistry dealt with “the rules relating to sampling [i.e. chemical analysis] and to the principal chemical industries of importance to engineers”, regulations of the Turin School of Specialisation for Engineers, article 14 (11th October 1863).
 
47
On Giuseppe Borio (1812.1887), see Michel (1930).
 
48
On Giovanni Pezzia, see Curioni (1884, p. 49). The course in legal issues dealt with “[the] laws applying to building work, waters, domestic staff, [the] administrative regulations relevant for civil engineers and [the] principles of political economy”, regulations of the Turin School of Specialisation for Engineers, article 16 (11th October 1863).
 
49
On Pietro Mya, see Curioni (1884, p. 45). The course in practical geometry dealt with “surveying, levelling, factory measurements …. to be performed on site and drawn up at the school”, regulations of the Turin School of Specialisation for Engineers, article 17 (11th October 1863).
 
50
Turin Polytechnic Historical Archive.
 
51
On the critical importance of the theory of elasticity in contemporary studies of the resistance of materials and, in general, in the science of construction, see Capecchi and Ruta (2011).
 
52
Regulations of the Turin School of Specialisation for Engineers (11th October 1863) article 30.
 
53
Works which have not come down to us on: applied mechanics and hydraulics (On steering-wheels. Geometric shapes most commonly used for these and the technical reasons for such geometric shapes. Calculations for a steering-wheel); civil and hydraulic construction (On foundations in general and those of bridges in particular. Foundations with closed or open tanks and caissons); steam engines and railways (Second fundamental principle of thermodynamics; its demonstration on the basis of Clausius’ theories of equivalence and of the W. Thomson method. Correspondence denied by Clausius but admitted by Saint-Robert regarding the quantity (1/A) Z with dv); practical geometry (Trigonometrical levelling); architecture (On solid iron roofs and their use in civil construction); agricultural economics and land valuation (On drains (and drainage)); chemistry (Analysis of a tin, lead, copper, nickel, cobalt and iron alloy); mineralogy and geology (On the ice age in Europe), see Pareto (1869, p. 50).
 
54
Ibid., p. 27.
 
55
Ibid.
 
56
Ibid., p. 28.
 
57
Ibid., p. 29.
 
58
Ibid., p. 28.
 
59
Ibid., pp. 30–32.
 
60
Ibid., p. 28.
 
61
Ibid., p. 38.
 
62
Ibid., p. 43.
 
63
Genocchi and Curioni are the only university teachers mentioned, with gratitude, by Pareto, ibid., pp. 27, 71. Immediately after his graduation, Pareto writes to Genocchi, January and 9th February 1870, see Pareto (2001, pp. 1–2), to recall “the beautiful lessons in calculus” to which he owes “everything that he knows [concerning] mathematics”.
 
64
See Viola (1991, p. 17).
 
65
This position, which was much discussed elsewhere, constituted a particularly urgent question in Italy, where by this time “the fashion for discrediting theoretical studies had spread”, see Genocchi (1871, p. 364).
 
66
Including the definitions and the notations used, see Genocchi (1883, p. 195). Genocchi gives a number of examples of definitions reformulated in what in his view is a rigorous manner: the most interesting is that the definition which “fully conforms to the evidence and to geometric exactitude” of the limit identifies it as that value to which a variable “approaches” leaving a difference which is “never inexistent” but is “less than any other given fraction”, ibid. p. 198.
 
67
See Bottazzini (1990, p. 67).
 
68
See Bottazzini (1981, pp. 214–241).
 
69
Ibid., p. 202.
 
70
A. Genocchi, Differential calculus, sheet 1, p. 1. Genocchi’s manuscript relating to the course held in the 1865–1866 academic year is held in the Genocchi Collection within the Old Documents Collection of the Municipal Library of Piacenza.
 
71
Ibid., sheets 2–4.
 
72
Ibid., sheets 11–12.
 
73
Ibid., sheet 17.
 
74
Ibid., sheets 21–22.
 
75
[Anonymous], Genocchi, Differential calculus academic year 1871–1872, p. 273, for the consultation of this document my gratitude is due to friendly courtesy of Professor Livia Giacardi of the Department of Mathematics of the University of Turin. Many years later Pareto, having underlined that at that time in pure mathematics “all kinds of subtleties were pursued in the name of or under the pretext of rigour”, affirms that “for the applications, old-fashioned science is only ever what is required”, as represented by Jules Hoüel, see Hoüel (1878–1881), Pareto to Guido Sensini, 18th January 1905, see Pareto (1975, p. 533).
 
76
Ibid. pp. 273–281.
 
77
See Volterra (1897, p. 148).
 
78
B. Erba, Summary of the lessons in rational mechanics for the academic year 1866–1867, Turin University Historical Archive, Erba Collection.
 
79
Ibid. lessons for 9th and 11th February 1867.
 
80
Ibid. lessons for 11th, 12th, 14th June 1867 specifies that in a system consisting of three points M’, M”, M”’, each is subjected not only to the directly corresponding force (F′, F″, F″’ respectively) but also to those directly corresponding to the other points. Thus if the point M’ had the original position M’ 0 and was subjected only to its own force F′, it would follow the curve M’ 0A: but since the action of the other points modifies the effects of the force F′, M’ will follow the different curve M’ 0B.
 
81
Ibid., lessons for 29th and 30th March 1st and 2nd April 1867.
 
82
Ibid., lessons for 11th, 12th and 14th June 1867.
 
83
Ibid., lessons for 14th and 15th June 1867.
 
84
On Jacob Moleschott (1822–1893), A. Gissi, Jacob Moleschott, in Italian Dictionary of Biography, vol. 75, Istituto dell’Enciclopedia Italiana, Rome, 2011, pp. 335–338.
 
85
See Pareto (1869, p. 27).
 
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Metadata
Title
Vilfredo’s School and University Education
Author
Fiorenzo Mornati
Copyright Year
2018
Book
Vilfredo Pareto: An Intellectual Biography Volume I

Print ISBN: 978-3-319-92548-6

Electronic ISBN: 978-3-319-92549-3

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-92549-3_3