Mathematically-based studies of complex systems in physics, mathematics, chemistry, biology, economy and politics in Nové Hrady in the first half of 19th century and at the beginning of 21st century


D. Štys 2


2Institute of Physical Biology, University of South Bohemia and Institute of Systems Biology and Ecology CAS, Zámek 136, 373 33 Nové Hrady, Czech Republic and institute of Microbiology CAS, 379 81 Tøeboò.

author feels requisitiness to honour the co –authorship of G.F.A. de Lonqueval von Buquoy, lord de Vaux1,

 1Herrschaft Gratzen – panství Nové Hrady, Böhmen – Èechy


Keywords: dynamic systems, heat transfer, glass technology, national economy, mathematical biology



Georg Franz August de Lonqueval, count of Buquoy, lord de Vaux, in his approximately 200 texts, which include at least 24 separately printed books, paved the way to mathematically based study of complex systems. Count of Buquoy was, at the same time, able to test many of his conclusions experimentally at multiple scales and in multitude of areas; from production and examination of physical properties of new sorts of glass, through everyday use of new types of steam machines in mining operation up to testifying of his economical and nature-conservation theories in everyday routine of his possession. This article has two purposes: (i) to classify the work of Count of Buquoy and to indicate main fields of his interest, (ii) to announce the Buquoy symposium planned for summer 2011, the 200th anniversary of Buquoy’s first books.


Georg Franz August de Lonqueval, count of Buquoy, lord de Vaux, was born in Brussels in 1781 (GFAvB later in the text). He studied in Vienna and Prague. Since 1803 he governed the possession of Buquoy family in southern and western Bohemia (Nové Hrady and Èervený Hrádek) until his death in 1851 in Prague. His certitude on the existence of mathematically based rules describing observable events in nature on one hand and his certitude of natural unity lead him to constant passion for search of the rules that govern the nature. At the same time, he was drawn to everyday economy of his possession for which he held responsibility in time of swift technological and economical paradigm change which had little parallel in the history of mankind.

Reviewed works of Georg Franz August de Lonqueval, count of Buquoy, lord de Vaux

As is known to us now, the study of complex systems was to a large extent enabled only by the existence of computers.  Many stories flitter around the word and found their way into non-fiction storybooks describing encounter between mathematicians and researchers in complex systems theory on validity of proof of their theories.

Modern, computer assisted, analysis of just one of the examples given in first works of GFAvB [1-3], the movement of a body with changing mass, lead to conclusions such as “Except for very special initial conditions it is difficult to obtain analytic solution to the equation of motion.” [4]. Despite to the fact that only Newton mechanics rules were used, the system leads to oscillatory solution and the precise behavior of the system is highly sensitive to initial conditions, both properties typical to what has been named complex systems in modern terminology. The analytical mechanics is the subject of more than 20 further works of GFAvB, books as well as journal articles which have been comprehensively analysed in 1970´s and 1980´s in Russia [5-8].

It should be said that except the works in analytical mechanics, the only traceable reviewed work of GFAvB is that of mathematical economy. To list the most important contributions, we must consider his three consecutive books on the theory of national economy [9-11]. GFAvB´s conclusions in those books lead 140 years later to reflections like: “This analysis is so strikingly modern that it deserves a detailed report” [12]. The last reflection to GFAvB is that of the founding president of the Econometric society Joseph Schumpeter who comments GFAvB´s work by words “man and writings are forgotten unjustly, so I think” [13].

Other topics published in the work Georg Franz August de Lonqueval, count of Buquoy, lord de Vaux

The topics which may be traced in the work of GFAvB include: (1) the construction and theory of steam machine and theory of heat propagation, (2) theoretical mechanics, (3) mathematically-based theory of national economy, (4) analysis of common features of events in Nature, (5) theory of infinitesimal calculus and introduction of new methods for solution of oscillatory functions, integration and interpolation , (6) mathematically and physiologically – based theory of philosophy, government and discussion (debatieren), (7) glass technology and technological experiments, (8) theoretical and experimental optics, (9) theory of crystallisation and capillary events, (10) theory of  stoichiometry and chemical reactivity, (11) theory of healing, (12) development of language and its forms, etc. GFAvB published most of his works as separate books, in Annalen der Physik and in the interdisciplinary journal Isis edited by Lorenz Oken. Other separately published works are reported but are not accessible to us. Numerous works, and perhaps the most exciting, exist only in the form of manuscripts deposited in the Tøeboò state archive.

Symposium on the occasion of 200th anniversary of publication of first work of Georg Franz August de Lonqueval, count of Buquoy, lord de Vaux in 2011

We announce hereby our intention to organise the GFAvB interdisciplinary symposium to be held in Nové Hrady in September 2011. Besides historical introduction, we wish (preliminarily) to follow the themes: (1) complex systems, (2) aspects in physical chemistry, (3) mathematical economy, (4) mathematical biology and medicine and (5) philosophy of nature.  We plan for the meeting relatively early since we also want to reserve time for critical reading of at least some of the Buquoy’s work and examination of the conclusions therein by modern methods. Please read the web-page www. for further information.



1.       G.J.F. von Buquoy , Analytische bestimmung des Gesetzes der virtuellen Geschwindigkeiten in mechanischer und statischer Hinsicht . Leipzig: Breitkopf und Härtel, 1812

2.       G.J.F. von Buquoy , Weitere Entwickelung und Anwendung des Gesetzes der virtuellen Geschwindigkeiten in mechanischer und statischer Hinsicht . Leipzig: Breitkopf und Härtel, 1814,

3.       G.J.F. von Buquoy , Exposition d´un noveau principe général de dynamique, dont le principe des vitesses virtuelles n´est qu´un cas particulier . Paris: V. Courcier, 1815

4.       V. Šíma & J. Podolský,  Eur. J. Phys., 26, (2005), 1037.

5.       Mikhailov G K Prepr. Instituta Probl. Mechaniki AN SSSR 49, (1975) 106

6.       Mikhailov G K Mechanika Tverdogo Tela Izv. AN SSSR 5, (1975), 41

7.        Mikhailov G K Georg Bukua i nachala dinamiki sistem s peremennymi massamy, Issledovanija po Istorii Fiziki i Mechaniki, Moscow: Nauka, 1986. pp 191–238

8.       Panovko J G  Mechanika deformirujemogo tverdogo tela: sovremennyje koncepcii, oshibki i paradoksy Moscow: Nauka, 1985, pp 173–8

9.       G.J.F. von Buquoy , Die Theorie der Nationalwirtschaft nach einem neuen Plane und nach mehreren eigenen Ansichten dargestellt . Leipzig: Breitkopf und Härtel, 1815

10.    G.J.F. von Buquoy , Das nationalwitschaftliche prinzip oder was zuletzt alle nationalwitschaflichen Anstalten bezwecken müssen.. Leipzig: Breitkopf und Härtel, 1816

11.    G.J.F. von Buquoy , Erläuterung einiger eigenen Ansichten aus der Theorie der Nationalwirtschaft nebst tabellarischer Uebersicht des Zusammenhanges der wesentlichster Gewerbeunter einander und mehreren Beyträgen zum technischen Theile der Nationalwirtschaft. Zweiter Nachtrag zur Theorie der Nationalwirtschaft . Leipzig: Breitkopf und Härtel, 1817

12.    R. Robertsson Mathematical economics before Cournot, Journal of Political Economy LVII (1949), 527.

13.    J. Schumpeter: History of Economic Analysis (ed. by Elizabeth Boody-Schumpeter), NewYork: Oxford University Press, 1954