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

D. Štys^{ 2}

^{2}Institute
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 Vaux ^{1}**,

^{ 1}Herrschaft
Gratzen – panství Nové Hrady, Böhmen – Èechy

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

**Abstract: **

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 200^{th}
anniversary of Buquoy’s first books.

Introduction

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 200^{th} 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. expertomica.cz/Buquoy* for
further information.

**References: **

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