Mathematics and Archaeology

524 Pages·2015·18.71 MB·English

by  Juan A. Barcelo

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Mathematics and Archaeology
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Mathematics and Archaeology
Editors
Juan A. Barcelo and Igor Bogdanovic
Quantitative Archaeology Lab
Department de Prehistory, Facultat de Lletres
Universitat Autonoma Barcelona
Barcelona, Spain
p,
A SCIENCE PUBLISHERS BOOK
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Foreword
It is sometimes said that “archaeology is too important to be left to archaeologists”.
Of course, this quip means different things to different people. To me it means that
archaeology is not just about treasure-hunting or fi nding attractive ruins to lure
tourists or excavations to entertain mass TV audiences. It is not just about collecting
and analysing excavation and other evidence and reconstructing interesting past life-
ways. It is not even just about the recovery of the past trajectories of particular human
societies as a step towards long-term human social system theory. Ultimately it is about
using such access as we have to our own past to guide our choices for our future as a
species. It is about using archaeological evidence and interpretation to help understand
the long-term dynamics of human society, both in development and in decline, and
hence to make benefi cial strategic decisions for the whole of humanity: promoting
social justice, achieving different kinds of sustainability, and minimising the risk of
catastrophes: meteorite strikes, pandemics, nuclear wars, uncontrolled technological
growth. Prehistory and history must work together on this fundamental task of global
understanding and strategy to ensure the future of our complex and fragile global system
that seems all too vulnerable to both endogenous and exogenous stressors. Concern
for our future is currently centre stage. See, for example, the website of the recently
established University of Cambridge Centre for Existential Risk (CSER).
To achieve this overarching goal, mathematical and algorithmic precision is needed
at all interpretive levels as we climb the ladder to reliable theories and models of human
society and its possible events and trajectories. Furthermore, experience suggests that
these global models will have to be individual (or “agent”) based—unless we are very
lucky and fi nd simple model compressions that can support precise and effective social
modelling.
Global agent-based modelling (ABM) to guide collective strategic action may
at fi rst seem wildly over-ambitious. Yet national scale agent-based modelling is
already being taken seriously by governments, and global work using more traditional
mathematical models dates back at least to 1972 when the Club of Rome published
“Limits to Growth”. Such studies are ongoing now in the contexts of, for example,
climate change impact and war gaming.
We can foresee controversies, challenging predictions and daunting conceptual
and technical diffi culties ahead. Mathematical and computational models challenge
unreliable, ambiguous, often merely fashionable, verbal theorising that is elegant but
has little precision and little practical value. Not all scholars understand or welcome this
challenge or can accept that at our disposal is important “white magic”: “mechanical”
structures and processes running within a digital computer such that their properties
vi Mathematics and Archaeology
(mathematically provable or experimentally demonstrable) can reliably inform our
real world choices.
There are great and well-known diffi culties in carrying through any such research
program. All formal modelling faces problems with the choice and handling of models
involving unavoidable issues of abstraction, calibration, and validation. Additional
identifi able problem areas for agent-based global modelling are (1) the sheer size and
diversity of the system to be modelled, (2) linking archaeological evidence to formal
model-based social theory, (3) capturing human general cognition within a model—
unavoidable if we are to seriously address the dynamics of human society, and (4) the
subtle diffi culty that our collective action choices are sometimes already determined by
a social and physical context potentially itself represented within our models.
The results of model-based studies can themselves trigger disharmony. Consider
the potential impact of global warming and the fractious international response to it.
What if reliable global models told us, for example, that massive self-imposed social
structure backtracks are the best long-term strategy for humankind? What chance of
collective implementation would such a strategy have?
But how is the archaeological facet of this great endeavour actually working out?
How goes the effort to deploy mathematical and computer-based methods usefully in
archaeology? There has been half a century of work dating back, in the UK, to 1962.
Early pioneers included Albert Spaulding, David L. Clarke, David Kendall, F. Roy
Hodson, Jean-Claude Gardin, Carl-Axel Moberg, William S. Robinson, and Jacob
Sher. This list is far from complete. Both David L. Clarke’s “Analytical Archaeology”
published in 1968 and the collection of articles he edited under the title “Models in
Archaeology” (1972) were infl uential. The text I published with Roy Hodson in 1975
had some impact; its fi nal section entitled “The Archaeologist and Mathematics in the
Future” (13.5) makes interesting reading forty years on!
Of course, it was the development of the automatic computer that was the
driver. Once digital computers became generally available, a diversity of methods
and algorithms that had previously been conceivable, but computationally far too
burdensome to use on the available hand calculators, became possible to trial, use,
exploit and develop. Thus many new research threads were discovered and followed
and new more scientifi c attitudes to archaeological evidence developed.
So how ARE things going? Unfortunately there has been ebb and fl ow of fashion
and it seems to me that even now the techniques deployed in archaeological work often
still feel experimental, unproven, a ragbag rather than a structured toolkit. Of the early
ideas and techniques, usually imported into archaeology from other disciplines but
sometimes home-grown, some seem to have had little impact, e.g., the “Horse-Shoe”
method as a seriation tool, the specifi cs of catastrophe theory, and heuristic computer
programs for hypothesis generation (this last one of my own imports). Other techniques
have indeed proved useful and survived, e.g., numerical taxonomy (automatic typology),
archaeological databases, shape description methods, direct methods of seriation,
and multidimensional scaling (metric and non-metric). Currently prominent in the
archaeological research literature (and the social sciences generally) is agent-based
modelling (ABM) fi rst trialled by archaeologists in the early 70s. For recent ABM
studies see, for example, Kohler and van der Leeuw’s “Model-Based Archaeology of
Socionatural Systems”. As I have emphasised, the foregoing ABM fi ts well with a drive
to large-scale social modelling for long-term human strategy choices.
Foreword vii
Why have we not made more solid progress over the past fi fty years and more? Is it
because social systems are so much more complex than cognitive or physical systems?
To expect systems of minds to be no more complex than individual minds is surely
optimistic! Or might it be that disciplinary barriers and distrust too often impede the
necessary cooperation and training? Computer scientists and sociologists have often
been mutually dismissive!
What is certain is that the social sciences and experimental and theoretical
archaeological do need mathematical and computational precision. Natural language
and the level of thinking that goes with it are pervasively ambiguous and too often
engender inferences that are more stylish than sound.
Everything points to the importance of this volume. Professors Barceló and
Bogdanovic have gathered together for us an impressive set of international contributors
who address a diverse range of applications of formal methods in archaeological work.
Formal tools deployed range from mathematical logic, through shape analysis, artefact
databases, cluster analysis, artifi cial neural networks, lattice theory, Bayesian networks
to settlement pattern analysis and the uses of mathematics in heritage studies. Several
chapters report studies using agent-based modelling which, as I have stressed, agrees
well with our current pressing need to understand much more about long-term human
social dynamics past and future and the collective survival strategies open to us. The
editors are fully aware of these needs. I am confi dent that the volume they have put
together for us containing exciting new ideas, results and trends will be a milestone on
our long and dangerous road to self-understanding.
Emeritus Professor James E. Doran
March 2014 University of Essex, UK
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Preface
In May 2013 I received an email from a representative of Science Publishers, addressed
to Juan Antonio Barceló. The email was an invitation to edit a book on some aspect
of Mathematics. Well, I have been working for the last 25 years on “mathematical”
subjects, but this work has always been applied to a discipline that is apparently very
far away of Mathematics. I am an Archaeologist, considered by many as a “crazy”
archaeologist working on esoteric methods like statistics, simulation, machine learning
and data mining. That the publisher of a series of books on Mathematics would invite
me to edit a book on a subject so specifi c was something that I did not understand at
fi rst. The answer actually is pretty simple. I am not the only Juan Antonio Barceló in
the world. There is a famous mathematician in Madrid, and the email was addressed
to him, but it arrived to me. I quickly responded to the publisher indicating that they
should contact the right “Barceló” at the “Universidad Autónoma de Madrid”—and not
me at the “Universitat Autònoma de Barcelona”, my University. At the same time I took
the initiative of suggesting that I could contribute with a different book, a volume on
Mathematics and Archaeology. They asked me for a proposal, and I sent an invitation
to many archaeologists, mathematicians and computer scientists that I knew had been
developing new methods for archaeological research. I received many positive answers,
and with this material Igor and I organized a series of subjects that could be of interest.
The proposal was accepted by the Publisher, contributing authors sent their chapters,
and the result is the book you have before your eyes.
One year after receiving that fi rst misaddressed invitation, the fi nal draft was sent
to the publisher. Igor and I have interacted a lot with the contributing authors, insisting
that all of us should read most of the chapters, so the Project becomes more cohesive.
Therefore, I acknowledge fi rst of all authors and co-authors, the people that interacted
with us, and the people who contributed writing the chapters or with the research
presented in them. This is their book, and should be read as a collective effort.
Since the inception of the Project I wished that two outstanding scholars addressed
some general conclusions from the perspective of a Mathematician and from the point
of view of an Archaeologist. Michael Greenacre accepted at the very beginning, and
Keith Kintigh joined the project at a later moment. Many thanks also to Jim Doran,
one of the pioneers in quantitative archaeology, who has contributed with the foreword
to the book.
Some colleagues have worked as anonymous reviewers, and their comments have
contributed to the present version. I also acknowledge the comments by Mike Baxter,
Ben Ducke, Michael Greenacre, Irmelda Herzog, Keith Kintigh and Dwight Read.