Introduction. History and Mathematics |
Leonid Grinin. Periodization of History: A theoretic-mathematical analysis |
Andrey Korotayev. The World System History Periodization and Mathematical Models of Socio-Historical Processes |
Arno Tausch. Global Terrorism and World Political Cycles |
Akop P. Nazaretyan. Violence and Non-Violence at Different. Stages of World History: A view from the hypothesis of techno-humanitarian balance |
Michael L. Burton, A. Kimball Romney, Carmella C. Moore. The Use of Cross-Cultural Research Methodology in the Study of Deep History |
Natalia L. Komarova. Language and Mathematics: An evolutionary model of grammatical communication |
List of Contributors
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For centuries there have been disputes over whether mathematics
could and should be applied to the humanities. On the one hand,
most scientists believe that an academic discipline only
acquires the status of a "normal science" when it systematically
applies mathematical and other formal methods. From this
scientific perspective many fields of historical research look
"underdeveloped". On the other hand, in recent decades,
postmodernism and other fashionable intellectual currents have
questioned the status of history as a science, even though
positivism had seemed to provide historians with a sound
scientific basis for developing rigorous methods for searching
for, analyzing and validating historical data. Debates over the
interpretation of narratives and discourses have tended to
delineate and thus limit historical research to the role of
a type of artistic fiction. We believe that the development and
application of mathematical methods for the purpose of analyzing
and modeling historical dynamics could effectively counteract
attempts to eliminate the scientific and objective character of
historical research.
Of course, the famous typology proposed by Wilhelm Windelband
(1848--1915) and Heinrich Rickert (1863--1936) retains its
value. These two scholars proposed to divide the academic
research into nomothetic and idiographic branches.
According to them, sciences that seek to discover general laws
for indefinitely repeatable events and processes are nomothetic; in contrast, disciplines which are idiographic describe what is particular and non-recurrent.
Rickert considered history an idiographic science, as, according
to him, its aim was not to generalize but to analyze specific
historical processes and events; historical studies should deal
with the particular, so selection of facts is inevitable and
such selection cannot but rest on value-assumptions (see, e.g., Rickert 1986). However, it is hardly useful to divide the
sciences so dichotomously and declare that a field of science
only belongs to one or the other camp. Nothing is gained by
building a "Berlin Wall" between the sciences and humanities.
One of the main aims of our almanac is to counteract the
absolutist approach to separating the humanities and sciences.
Its goal is not to unite artificially all the sciences and
humanities, it is rather to contribute to the building of
bridges between them. It does not make sense to deny the
differences in the subject and methods between natural sciences
and the humanities. But this does not mean that cooperation
between these disciplines is not possible.
When we named this almanac History and Mathematics, we
meant both history and mathematics in the wide sense of these
words; its main subject is the study of socio-historical
processes by using a wide range of mathematical methods.
The first attempts to apply mathematics to the analysis of
phenomena that seemed to be rather far from the "World of
Numbers" were undertaken long ago. Developments in both
mathematics and various scientific disciplines led to the
application of mathematical methods to the study of more and
more fields. But the effect was not just in one direction -- from mathematics to other sciences; developments in the other
sciences also spurred the branches of mathematics to develop new
mathematical methods for dealing with new types of research data
and questions. One may suppose that new branches of mathematics
might develop in the future in order to solve various new
problems in mathematical history. For example, Georgy Malinetsky
(Малинецкий 1996: 102) suggests that the development of
mathematical history might result in the development of an
original new mathematical apparatus, as this has already
happened with respect to mathematical economics and psychology.
Rapid computerization both poses additional problems and creates
new opportunities for the application of mathematical methods to
the various fields of the humanities. Presently, we have
a considerable number of publications on the development of
electronic historical databases; there also exist various
computerized information systems aimed at the storage, ordering,
processing, and analysis of historical data (see, e.g.,
Boonstra, Breure, and Doorn 2004; Borodkin, Thaller, and Turner
1995; Denley 1994; McCrank 2002; Speck 1994; Thaller 1989, 1992;
Woollard 1999). One can observe a wide application of
mathematical statistics, methods of multidimensional clustering
and classification, including those based on the fuzzy sets'
theory, to historical research. Computer technologies are widely
used in archaeology, e.g. to visualize three-dimensional
models of excavations, or to analyze stratigraphic data; they
are applied to the study of historical sources (e.g., for
text identification, or information processing); they are also
widely used in the classroom on the basis of network and
multimedia software systems, and so on. A very promising
direction is the application of geo-information technologies in
historical research; for example, these technologies have made
it possible to visualize spatial models through the integration
of various datasets. On the other hand, the development of the
general systems theory, cybernetics, and complexity studies has
made it possible to identify a number of new aspects of
socio-historical phenomena that can be formalized and studied
with the application of mathematical methods.
It appears necessary to emphasize that the role of mathematics
in the study of human history should not be restricted to pure
"cliometrics", that is to the development of computer databases,
systematization and quantification of historical data, as well
as to the mathematical analysis of these databases. Mathematics
can also be used for the development of theoretical
interpretations of human history, for historical modeling and
forecasting. For example, in Russia this process started in the
1980s with the development of mathematical models of concrete
historical processes (see, e.g., Иванилов, Огарышев,
Павловский 1993). In recent years we observe the development of
a number of more general mathematical models that describe
non-linear dynamics of agrarian and industrial societies,
processes of social self-organization (Turchin 2003, 2005a,
2005b; Turchin and Korotayev 2006; Nefedov 2004; Podlazov 2004;
Tsirel 2004; Korotayev, Malkov, and Khaltourina 2006a, 2006b;
Korotayev and Khaltourina 2006).
Of course, the development of the mathematical models of
historical processes confronts a number of problems that are
connected with the following points:
The dynamic instability of social processes produced
by the changes in the moods and motifs of human behavior,
interpersonal conflicts, and the very limited predictability of
the "human factor".
The multiplicity of the parameters of social models;
and the consequent difficulties in the identification of factors
that produce the strongest influence on historical dynamic
processes.
The multiplicity of levels and scales of complex
social systems.
The necessity to take into account socio-psychological
factors that are extremely difficult to formalize, such as:
correlation of personal and group interests, development of
collective effects in social behavior, peculiarities of
individual psychology, ethnic modal personality types, etc.
However, notwithstanding all the above mentioned difficulties,
interest in the mathematical modeling of historical processes is
constantly growing.
This first issue of the History & Mathematics almanac in
English^ is
devoted to the application of mathematical methods to the
analysis and modeling of the global historical processes.
Within this almanac two groups of articles can be singled out.
The first deals with the periodization and modeling of global
development (articles by Leonid Grinin, Andrey
Korotayev, Akop P.Nazaretyan, and Arno Tausch).
The second applies mathematical methods to reconstructing the
deep history of global development (articles by Michael L.Burton, A.Kimball Romney, Carmella C.Moore, and
Natalia L.Komarova).
Within the first group, two articles (by Leonid Grinin and
Andrey Korotayev) apply mathematical methods to problems
concerning the macro-periodization of the history of the World
System (Korotayev's article) and the world historical process as
a whole (Grinin's article). Akop P.Nazaretyan studies the
long-term evolution of social violence and the social means used
to limit it, while also touching upon problems of periodization.
The authors of this almanac study the problems associated with
periodization from different perspectives (i.e.,
technological and economic in Grinin's article; demographic and
macrosocial in Korotayev's; cultural-psychological and
technological in Nazaretyan's). However, all agree that the
mathematical modeling of historical macroprocesses suggests
a fresh approach to the periodization issue.
Tausch presents new quantitative insights on the dynamics of the
contemporary development and, with a complete database for 140
nations, proceeds to an analysis of the determinants of economic
growth and ecological and social development in these nations,
which allows him to make a number of interesing forecasts.
Articles by Grinin, Korotayev, and Nazaretyan also contain
a number of important forecasts.
Ken Boulding (1970) was not only joking when he maintained that
the interpretation of history is a dangerous business. There are
grounds to hope that the application of mathematical methods may
diminish this "danger". In any case, the application of these
methods allows researchers to perform deep historical
reconstruction more effectively than when purely qualitative
methods are used. We believe that this conclusion is confirmed
by the two articles previously identified as belonging to the
second group.
Both of these articles deal with the evolution of human
languages, but from very different perspectives. In the first of
these articles, Komarova proposes a mathematical model of the
formation and development of human language. In the second
article, Burton, Romney, and Moore apply statistical analysis to
both linguistic and cross-cultural anthropological data in order
to reconstruct some important features of the long-term
evolution of human social organization.
Finally, we would like to state that there is one additional
positive point in the application of mathematical methods by the
specialists in the humanities. The point is that they contribute
to their scientific self-discipline, by providing means for
rigorous verification/falsification of their hypotheses. The
introduction of these methods could diminish the current extreme
polysemanticism of the terminology used in the humanities.
Rudolf Carnap (1966) noted long ago that even in physics the use
of words from natural languages (like law) leads to
problems for accurate monosemantic expression of one's ideas.
However, physicists have come to develop and use effective
conventions for the meaning of basic terms. In the humanities
the basic terms still have numerous contradictory definitions.
We believe that the introduction of mathematical methods to the
field can somehow alleviate this problem due to the univocacy of
mathematical language.
The articles published in this almanac have been prepared on the
basis of papers submitted for the presentation at the
1st International Conference "History and Mathematics"
(Russian State University for the Humanities, Moscow, December
20--22, 2006).
Michael L.Burton is Professor of Anthropology at the
University of California, Irvine. Current research interests
include the origin of human systems of gender and family
relationships; the histories of language families; the origins
and development of food production systems, current
transformations in systems of food production, consumption, and
exchange; and the use of quantitative methods in the field of
anthropology. Publications include "Sexual Division of Labor in
Agriculture" (American Anthropologist 1984, with Douglas
R.White), "Regions Based on Social Structure" (Current
Anthropology 1996, with John Whiting, Carmella Moore, and A.K.Romney), and "Language and Region Codes for the Standard
Cross-Cultural Sample" (Cross-Cultural Research 1999).
Email: MLBurton@UCI.edu.
Leonid Grinin is a senior research fellow of the Volgograd
Center for Social Research, a vice-editor of the journals History and Modernity and Philosophy and Society, and
a co-editor of the Social Evolution & History. Current
research interests include the long-term trends in the evolution
of technologies and their influences on sociocultural evolution,
periodization of history, and long-term development of the
political systems. He is author of over 100 scholarly
publications, including such books as "Philosophy, Sociology,
and Theory of History", "Productive Forces and Historical
Process", Formations and Civilizations", "State and
Historical Process". Among his more important journal articles
are "The Early State and Its Analogues" (Social Evolution
& History 1: 131--176), "Democracy and Early State" (Social Evolution & History 3[2]: 93--149), "Early State and
Democracy" (in The Early State, Its Alternatives and
Analogues, pp.419--463. Volgograd: Uchitel), and "The Early
State and Its Analogues: A Comparative Analysis" (in The
Early State, Its Alternatives and Analogues, pp.88--136.
Volgograd: Uchitel). Email: LGrinin@mail.ru.
Natalia Komarova is an Associate Professor of Mathematics,
University of California, Irvine, USA. Her research interests
lie at the interface between the mathematical and life sciences.
The two main topics are mathematical biology (modeling of
initiation and development of cancer, biophysics and virus
dynamics) and mathematical models of language evolution (with
elements of learning theory and historical dynamics). Natalia
Komarova received the 2002 Prize for Promise and a 2005 Sloan
Fellowship. She co-authored the book Computational Biology
of Cancer: Lecture notes and mathematical modeling (with
D.Wodarz; Singapore: World Scientific Publishing, 2005) and
published over 50 scientific articles, including "Oscillations
in population sizes -- from ecology to history" (Structure and Dynamics, 1, 2006), "The Evolution of Altruism:
from Game Theory to Human Language" (Spiritual Information:
100 perspectives, West Conshohocken, PA: Templeton Foundation
Press, 2005, co-authored), "Replicator-Mutator Equation,
Universality Property and Population Dynamics of Learning" (Journal of Theoretical Biology, 230, 2004), "Language Dynamics
in Finite Populations" (Journal of Theoretical Biology,
221, 2003, co-authored), "Language, Learning and Evolution"
(Language Evolution: The States of the Art, Oxford: Oxford
University Press, 2003, co-authored), "Evolution of Universal
Grammar" (Science, 291, 2001, co-authored). Email:
Komarova@UCI.edu.
Andrey Korotayev is Director and Professor of the
"Anthropology of the East" Center, Russian State University for
the Humanities, Moscow, as well as Senior Research Fellow of the
Institute for Oriental Studies and the Institute for African
Studies of the Russian Academy of Sciences. He is a laureate of
the Russian Science Support Foundation Award in "The Best
Economists of the Russian Academy of Sciences" nomination
(2006). He is author of over 250 scholarly publications,
including Ancient Yemen (Oxford University Press, 1995),
Pre-Islamic Yemen (Harrassowitz Verlag, 1996), Social
Evolution (Nauka, 2003), World Religions and Social
Evolution of the Old World Oikumene Civilizations:
a Cross-Cultural Perspective (Mellen, 2004), Origins of
Islam (OGI, 2006, with Vladimir Klimenko and Dmitri
Proussakov). Introduction to Social Macrodynamics: Compact
Macromodels of the World System Growth (URSS, 2006, with Artemy
Malkov and Daria Khaltourina), Introduction to Social
Macrodynamics: Secular Cycles and Millennial Trends (URSS,
2006, with Artemy Malkov and Daria Khaltourina), and Introduction to Social Macrodynamics: Secular Cycles and
Millennial Trends and Africa (URSS, 2006, with Daria
Khaltourina). Email: AKorotayev@mail.ru.
Carmella C.Moore is Associate Research Anthropologist at
the University of California, Irvine. Her research has been in
the fields of medical anthropology, psychological anthropology,
and cross-cultural research methods. Her publications include
The Psychology of Cultural Experience (2001 with Holly F.Matthews), "Material Culture, Geographic Propinquity, and
Linguistic Affiliation on the North Coast of New Guinea" (1994
with A.K.Romney) "Regions Based on Social Structure" (Current Anthropology 1996, with Michael L.Burton, John
Whiting, and A.K.Romney), "The Contribution of Medical
Anthropology to the Comparative Study of Culture" (Medical
Anthropology Quarterly 2001, with Arthur J.Rubel), "The
Universality of the Semantic Structure of Emotion Terms" (American Anthropologist 1999, with A.K.Romney, Ti-Lien Hsia,
and Craig D.Rusch), and "Methods for the Study of Inter-and
intra-cultural variability" (American Anthropologist
1999, with A.K.Romney). Email: CCMoore@Uci.edu.
Akop P.Nazartyan is Senior Research Fellow of the
Oriental Institute, Russian Academy of Sciences and Professor of
the Moscow State University. He is author of over 250 scholarly
publications, including Aggression, Morals and the Crises
in World Cultural development. (Synergetics of historical
progress) (Moscow: Nasledie, 1996, in Russian), Aggressive
Crowds, Mass Panic, and Rumors. Lectures in Social and Political
Psychology (St.Petersburg: Piter, 2003, in Russian), Civilization Crises within the Context of Universal History.
Self-Organization, Psychology, and Forecasts (Moscow: Mir,
2004, in Russian), "Fear of the dead as a factor in social
self-organization" (Journal for the Theory of Social
Behaviour 35 [2005]: 155--169), and "Western and Russian
traditions of Big History" (Journal for General Philosophy
of Science 36[2005]: 63--80). Email: ANazaret@yandex.ru.
A.Kimball Romney is Research Professor of Anthropology at
the University of California, Irvine and a member of the
National Academy of Sciences of the United States. He has made
important research contributions to the cross-cultural study of
socialization, to cognitive anthropology, to the use application
of multidimensional scaling models to anthropology, to the study
of social networks, and to the field of cross-cultural research.
His books include The Mixtecans of Juxtlahuaca, Mexico
(1965), Systematic Data Collection (1988 with Susan
Weller), and Metric Scaling (1990, with Susan Weller).
Important articles include "Cognitive Aspects of English kin
Terms (American Anthropologist 1964, with Roy G.D'
Andrade), "Sibling Terminology and Cross-sex Behavior" (American Anthropologist 1967 with Sara B.Nerlove), "Culture
as Consensus" (American Anthropologist 1986 with Susan
Weller and William Batchelder), "Material Culture, Geographic
Propinquity, and Linguistic Affiliation on the North Coast of
New Guinea" (Current Anthropology 1994 with Carmella
Moore), "Regions Based on Social Structure" (Current
Anthropology 1996, with Michael L.Burton, John Whiting, and
Carmella Moore), and "Methods for the Study of Inter-and
intra-cultural variability" (American Anthropologist 1999
with Carmella C.Moore). His current research is primarily
focused on the study of color perception. Email:
AKRomney@UCI.edu.
Arno Tausch is in his academic function Adjunct Professor
(Universitaetsdozent) of Political Science at Innsbruck
University, Department of Political Science. In his academic
career, he was also Associate Visiting Professor, Department of
Political Science, University of Hawaii at Manoa, and Guest
Researcher, International Institute for Comparative Social
Research, Science Center, West Berlin, upon invitation by the
late Karl Wolfgang Deutsch, Stanfield Professor of International
Peace at Harvard University. He served as an Austrian diplomat
abroad and was Counselor for Labor and Migration at the Austrian
Embassy in Warsaw and he is now Ministerial Counselor in the
Department of European and International Affairs at the Ministry
for Social Security, Generations and Consumer Protection in
Vienna. His research program is focused on world systems
studies, development and dependency studies, European studies,
and quantitative peace research. He authored or co-authored 10
books in English, 5 books in German, and over 110 printed or
electronic scholarly and current affairs publications in 6
languages (English, Finnish, French, German, Russian and
Spanish) for over 40 journals and/or publishing institutions.
Email: Arno.Tausch@bmsg.gv.at.