by Ubiratan D'Ambrosio
Abstract: Although the pre-Columbian civilization in the Americas
had mathematical knowledge (now identified as Ethnomathematics),
there was an effort to transfer Mathematics from the European
traditions to the colonies. This condition of consumers of knowledge
produced in Europe continued until the transition from the 19th
through the 20th century, when local production of Mathematics
start to be delineated. This paper will focus on the social,
political and cultural factors in the dynamics of the transfer of
mathematical knowledge to the colonies and of the production of
Mathematics in Latin America.
I. AN OVERALL VIEW.
Introductory remarks.
The great navigations since the 16th century mutually exposed forms
of scientific knowledge from different cultural environments. The
several ethnosciences involved in the encounters, which obviously
include European Science, have been subjected to great changes as
a result. In this paper I will examine some of the consequences of
this mutual exposure of cultures.
By ethnosciences I mean the corpora of knowledge established as
systems of explanations and ways of doing accumulated through
generations in distinct cultural environments.
Particularly important for us is ethnomathematics as the corpora of
knowledge derived from quantitative and qualitative practices, such
as counting, weighing and measuring, sorting and classifying. As with
academic Western Science and Mathematics, the two have a symbiotic
relation.
Both are not new disciplines. Rather they are part of a research
program on history and epistemology. The pedagogical implications
are obvious. Both research and educational programs take into account
all the forces that shape a mode of thought, in the sense of looking
into the generation, organization (both intellectual and social) and
diffusion of knowledge.
The research program, typically interdisciplinarian, brings together
and interrelates, results from the cognitive sciences, epistemology,
history, sociology and education. An essential component is the
recognition that mathematics and science are intellectual constructs
of mankind in response to needs of survival and transcendence.
The need for an intellectual framework to organize the corresponding
systems of codes, norms and practices gave rise to many aspects of
science and mathematics.
In the research program particular attention is given to those
dimensions of knowledge which bear some relation to what became known
as the several discipline of science and mathematics in European
civilization after the 15th century.
Ethnoscience, both as corpora of knowledge and as pedagogical
practices, is supported by the history of science and reflect the
dynamics of cultural acquisition. Some examples illustrate this.
All over the World, much of the weather explanations and predictions,
agriculture practices, processes of cure, dressing and institutional
codes, culinary, and commerce, came from the European tradition
developed in the Middle Ages and the Renaissance. But we see, all
over the World, practices performed in a very distinctive. These
practices, which have their origins in native communities, are
significantly modified as a result of mutual exposition of cultural
forms since colonial times. For example, it is common to see
indigenous peoples in the Americas using Indo-Arabic numerals, but
performing the operations from bottom to top, explaining that this
is the way trees grow. But it is also common to identify, in the
more advanced notions, the influence of this mutual exposition in
everyday life and practices.
Practices of daily life which are scientifically based are easily
recognized. This is evident by looking into professions that require
some scientific knowledge and mathematical abilities.
Practices and perceptions of learners are the substratum upon which
new knowledge is built. Thus new knowledge has to be based on the
individual and cultural history of the learner and it has to be
recognized the diversity of extant cultures, present in specific
communities, all over the world. This is the essence of a new
educational posture called Multicultural Education.
A new educational posture depends on a new historical attitude which
recognizes the contribution of past cultures in building up the
modern world and modern thought, and which avoids omissions and
errors of the past treatment of cultural differences.
We easily identify two categories of scientific knowledge: Scholarly
(or "formal" or "academic") science, supported by a convenient
epistemology, and whose practice is restricted to professionals
with specialties; Cultural (or "practical" or "popular" or "street")
science. These categories are closely related and their main
distinction refers to criteria of rigor, to the nature, domain and
breadth of its pursuits, that is to what and how much one can do
with them.
For example, pre-Columbian cultures had different styles of doing
their measurements and computations and these practices are still
prevalent in some native communities. Most Amazonian tribes have
counting systems that goes as "one, two, three, four, many". And
that is all, since with these numbers they can satisfy all their
needs. We also see important ways of dealing with pottery,
tapestry and everyday knowledge with strong mathematics
characteristics in several cultures. The same with African
cultures. The people from these cultures have no problems at all
in assimilating the current European number system and deal
perfectly well with counting, measurement and money when trading
with individuals of European culture. Land measurement, as
practiced by peasants in Latin America, comes from ancient
geometry transmitted to medieval surveyors since land property
and measurement (geo-metry) is strange to Pre-Columbian cultures.
Another example comes from Africa, where the people deal with
numbers and counting according to their specific cultural
background.
The high prestige of science comes mainly from its recognition as
the basic intellectual instrument of progress. It is recognized
that modern technology depends on science and that the instruments
of validation in social, economic and political affairs, mainly
through storing and handling data, are based on science and
mathematics. Particularly important in this respect is statistics.
This evidently brings to science an aura of essentiality in modern
society. There is a general feeling that there are practically no
limits to what can be explained by science. Many of the applications
which give science such a prestigious position are part of various
forms of cultural conflict.
Studies of ethnoscience and ethnomathematics are motivated by the
demands of the natural and cultural environment and are present
everywhere. It is a fact that, even without recognizing it, just
about everybody deals with mathematical practices, incorporated
in daily routines. When walking or driving, people memorize routes,
in most cases optimizing trajectories, which is a practice of a
mathematical nature. Also when dealing with money, with measurements
and quantifications in general, we recognize an intrinsic mathematical
component. The same with the capability of classifying, ordering,
selecting and memorizing routines.
These practices are generated, organized and transmitted informally,
the same as language, to satisfy immediate needs of a population. They
are incorporated in the pool of common knowledge which keeps a group
of individuals, a community, a society together and operational, and
this is what is called culture. Culture thus manifests itself in
different, obviously interrelated, forms and domains. Cultural forms,
such as language, mathematical practices, religious feelings, family
structure, dressing and behavior patterns, are thus diversified. They
are of course associated with the history of the groups of individuals,
communities and societies where they are developed. A larger community
is partitioned into several distinct cultural variants, each owing to
its own history and responsive to differentiated cultural forms.
Some remarks on Historiography.
History, as a major academic discipline, carries with it an
intrinsic bias which makes it difficult to explain the ever present
process of cultural dynamics which permeates the evolution of mankind.
This paves the way for paternalism and arrogance, for intolerance and
intransigence. And clearly interferes with the understanding, for
different cultural groups, of each other processes of building up
their cultural realities when trying to satisfy their needs of
survival and transcendence.
These biases have been methodological as well as ideological,
particularly in the History of Science. Helge Kragh says that
"History of Science has its own 'imperialism' that partly
reflects the fact that viewed historically and socially science
is almost purely a western phenomenon, concentrated on a few,
rich countries. While science may be international, history of
science is not."
This seems to be almost unavoidable in the framework of
historiographies which rely on reductionist approaches, such as
it is the case of the various supposedly autonomous histories,
in particular in the History of Sciences. The mere fact that to
pursue historical analyses one talks about the Sciences, such as
Physics, Chemistry, Mathematics, as distinct from Religion, from
Art, from Politics, obviously impedes the understanding of the
processes of evolution of ideas and methods, of reflection and
action, which underlies man's struggle to find explanations, to
understand and cope with its environment, and of conviviality
with nature.
The reductionism which characterizes several of the so-called
autonomous histories and also histories based on facts and names,
on places and dates, naturally derive from the prevailing ideology
and justify current actions. Even when we move a step further than
narrative history and go to historiography, the facts get immersed
in the processes and we may be led to be satisfied with the false
impression of having approached the past because we have data
verified and facts described and explained. I agree with Armando
Saitta in saying that historiography should be focused on a
problem, never losing the view of all the forces which play in the
historical reality, and avoiding the unilateral approach of the
specialist and the reduction of the historical flow to a few
elements. Saitta asks for the historian to look into "What today
isn't but tomorrow will be" . He clearly proposes a global history.
When he refuses the history of the "if", he opens the way to an
evaluation of all the alternatives which were present in the process
and he claims that the one alternative which have succeeded should
not imply the rejection of he others. E. H. Carr has the same
opinion when he says that the historical moment in which several
alternatives were open does not imply abandoning those which did
not succeed, but rather looking into the reason for which some did
not succeed and what was the cost of these decision.
Paraphrasing Miguel Leo/n-Portilla, it is a matter of listening
also to the looser. History has been mostly the history of the
winners. This is particularly true in the History of Science.
For obvious reasons, the vision of the looser has been marginalized,
and this is more noticeable in the chapters which deal with the
origins of Modern Science. We use the term Modern Science as the
set of ideas which have supported in paradigms established in the
XVII and XVIII centuries, mainly through the works of R. Descartes,
I. Newton, G. W. Leibniz and followers.
The dawn of Modern Science is identified with the modern geography
of the world, and the appearance of privileges for those capable
of mastering Modern Science and Technology. How did this privileged
role came into being? Why conquered and colonized still have problems
in mastering Science and Technology? Why have Science and Technology
progressed so rapidly and in this progress has left aside, indeed
eliminated, social and above all ethical concerns, thus paving the
way for enormous social, political and environmental distortions?
These questions are germane to the concept of knowledge itself.
Building-up scientific knowledge.
We see knowledge as emanating from the people, essentially a products
of man's drive towards explaining, understanding and coping with his
immediate environment and with reality in general, reality understood
in its broadest sense and in permanent change as a result of man's
own action. This drive, obviously holistic, is dynamically subjected
to a process of exposure to other members of society -- people -- and
thanks to communication, both immediate and remote in time and space,
goes through a process of codification, intertwined by an associated
underlying logic, inherent to the people as a form of knowledge – some
call wisdom. The modes of communication and the underlying logic are
recognized as the result of the prevailing cognitive processes.
Cognitive evolution, related to environmental specificity, gives rise
to different modes of thought and different underlying logic,
communication and codification. Hence knowledge is structured and
formalized subjected to specificity of a cultural nature. Power
structure, which itself rises from society as a form of political
knowledge, appropriates, indeed expropriates, structured knowledge
and organize them in institutions. In this form and under the control
of the establishment and the power structure, which mutually support
each other, knowledge is given back to the people, who in the first
instance generated it, through systems and filters which are designed
to keep the established power structure.
The generation, transmission, institutionalization and diffusion of
knowledge is clearly an holistic approach to knowledge and to the
dynamics of change. This is the essence of the research program on
the History of Science which I call "Ethnomathematics".
The disciplinary approach to knowledge focus on cognition,
epistemology, history and sociology. This clearly makes it difficult
to understand the dynamics of change. Mutual exposure of distinct
approaches to knowledge, resulting from distinct environmental
realities, is global, embracing the entire cycle from the generation
through the diffusion of knowledge.
The process of cultural dynamics which takes place in the exposure is
based on mechanisms which balance the process of change, which I call
acquiescence -- that is, the capability of consciously accepting
change (modernity) -- and the cultural ethos -- which acts as a sort
of protective mechanism against change that produces new cultural forms.
This behavior can be traced back throughout the entire history of
mankind. These conceptual tools are close to the ethos and
schismogenesis introduced by Gregory Bateson in dealing with cultural
contact and enculturation.
In the encounter of the two worlds (Europe and America) this was
violated in many instances. The origin of these violations may be
related to distinct views of nature. A scientific conceptualization,
which resulted from an intertwining of medieval Judeo, Christian and
Greco-Arabic thought, and developed in Europe, lead man to look at
nature and at the universe as an inexhaustible source of richness
and to exploit these resources with a mandatory drive towards power
and possession.
This behavior towards nature and life has lead man to favor a single
model of development, hence to ignore the cultural, economical,
spiritual and social diversities which constitute the essence of
our species.
These reflections question the set of current concepts and models,
and calls for the acceptance of the idea that survival depends of a
global and holistic view of reality. This demands a radical change
which applies to all levels of knowing and doing. Thus we are lead
to look for radical changes in our models of development, of education
and of civilization, based in the recognition of a plurality of
models, of cultures, of spirituality and of social and economical
diversity, with full respect for each one of the distinct options.
Visions of the World.
The European navigators of the end of the 15th and early 16th centuries
reached all of America, Africa, India and China. In the case of Africa
and in Asia, previous contacts with civilizations which had shared,
before, many encounters among themselves and with Europeans. Thus the
encounters of the 15th and early 16th centuries were, indeed, an
amplifications and deeper contacts. But meeting the "new", the unknown,
the unexpected, was experienced by Columbus and the Spaniards, in 1492
and the subsequent voyages.
Although earlier contacts with the Americas are known. But the
motivations and behavior of earlier navigators was completely different
from the Spanish and Portuguese, and afterwards the English, French and
Dutch.
The influence of the navigators and chroniclers, particularly
Portuguese, in building up the mode of thought which underlies modern
European science is noticeable. In the words of Joaquim Barradas de
Carvalho "the authors of the Portuguese literature of the navigation
made it possible the Galileos and the Descartes" essentially through
the development of "objective and serene curiosity, rigorous
observations and creative experimentation".
The low recognition of Portuguese science in the 15th and 16th
centuries illustrates the observations above about biased
historiography. Indeed, the important Tractatus de sphera (early
thirteenth century) written by Johannes de Sacrobosco, was recognized
as "the clearest, most elementary, and most used textbook in astronomy
and cosmography from the thirteenth to the seventeenth century",
received two important translations with commentaries in Portugal.
By Pedro Nunes, in 1537 and by Joa~o de Castro, possibly in 1546. The
translation with comments by Pedro Nunes, an important mathematicians
of the 16th century, incorporates much of the observational and
experimental science which had been pursued by Portuguese navigators
since early fifteenth century and registered in their writings.
Curiously enough, neither are recognized in the most important
study of Sacrobosco, written by L. Thorndike.
Particularly important as chronicles are the Cro/nica dos feitos de
Guine/ of Gomes Eanes de Zurara (1453) and the Esmeraldo de situ orbis,
by Duarte Pacheco Pereira, written between 1505 and 1508, probably
the first major scientific work reporting on what was observed and
experimented in the newly "discovered" environments. In fact, we
have to understand the sense of the word "discovery" among the
Portuguese authors of that period to better realize the role of
the navigations in paving the way for modern science. In his important
historiographical contribution, Joaquim Barradas deCarvalho (see Note
15) gives both an exhaustive study of the Esmeraldo de situ orbis and
the discussion of the meaning of the word "discovery".
The voyages themselves allowed a broader view of the world. Mainly
venturing to the Southern Hemisphere demanded two major enterprises,
the construction of the caravel, an extremely versatile ship built by
the Portuguese in the fifteenth century as the result of a remarkable
engineering project, and novel navigation techniques, relying on
tables constructed from systematic recorded observation carried on
by the commanders of those ships. Themselves with commanding function
they were also responsible for recording the "different skies" which
they were the first Europeans to look at. The contributions of Gil
Eanes crossing the Bojador Cape in 1434, Nuno Trista~o reaching in
1443 the coast of Mauritania, and the major achievement of Diogo
Ca~o crossing the Equator line in 1483, all paved the way for
Bartolomeo Dias to cross the Cape of Hope in 1488 and for Vasco
da Gama to reach Calicut in India, in 1498. Together with Columbus
reaching the Western lands in 1492, the vision of the World changed.
All lands and peoples were within the reach of the navigators. It is
the beginning of a new phase in the History of Mankind.
The "new Sciences" seen in the encounter.
As said above, America and to some extent Africa, were more
surprising to Europeans than what was seen in lands which had
been reached before by land routes. Particularly, America showed
peoples with new forms of explanation, of rituals and of societal
arrangement. Reflections on the so-called Natural Philosophy or
the Physical Sciences, particularly Astronomy, were part of the
overall cosmovision of the pre-columbian civilizations. In other
words, the scientific establishment and scientists, surely present
in the society of the conquered cultures, have not been recognized
as such by the conquerors. One of the earliest registers of these
cultures, Fray Bernardino de Sahagu/n writes, in the 16th century,
that "The reader will rightfully be bored in reading this Book
Seven [Which treats Astrology and Natural Philosophy which the
naturals of this New Spain have reached], ... trying only to know
and to write what they understood in the matter of astrology and
natural philosophy, what is very little and very low". The important
report of Sahagu/n explains much of the flora and fauna, as well
as of medicinal properties of herbs of Nueva Espan~a. But he does
not give any credit to indigenous formal structured knowledge.
This is typical of what might be called an epistemological obstacle
of the encounter.
Another important book is the Sumario compendioso ... con algunas
reglas tocantes al Aritme/tica by Juan Diaz Freyle, printed in Mexico
in 1556, the first arithmetic book printed in the New World. It has
a description of the number system of the Aztecs. But this book
soon disappeared of circulation and the Aztec arithmetic was replaced
by the Spanish system.
Much research is needed on the Science of the encounter. But this
needs a new historiography, since names and facts, on which current
history of science heavily rely, have not been a concern in the
registry of these cultures. A history "from below", which might
throw some lights in the modes of explanation and of understanding
reality in these cultures, have not been common in the History of
Science.
There is some more availability of sources for the history of the
natural and health sciences.
The Basin Metaphor and a Sociology of Mathematics
There is no way to deny that [Western] Mathematics is essential in
the modern world. Public opinion is ready to support investment in
mathematical research in spite of being absolutalety unable to
guess what kind of research is being supported, professionally
successful parents invest in the mathematical education of their
children and even accept that a child does an entire year again if
he/she fails in the final exam - in spite of him/her, successful
parent, declaring that while they were in school and up to nowadays
never understood mathematics. "Miraculously" they graduated in spite
of successive failures in Mathematics and "miraculously" they became
very successful. Their children have to proceed - suffering and
struggling - so they will not depend of miracles! Less successful
parents, which did not have an opportunity of schooling and nave
not the slightly idea of Mathematics punish their children if
they don't show good marks in Mathematics! And peers and society
in general regard those that get good grades in Mathematics as
potential geniuses, while those that do not do well in Mathematics
are regarded as stupid. Socially, this has been instrumental in the
selection of elites, as it has been well studied by Pierre Samuel
in his classic paper on this theme. On the other hand, the evidence
from research showing that both individual and social creativity
is enhanced by self-esteem is not taken into account for those that
do beautifully in the Arts or in Sports but fail in Mathematics.
Let us introduce at this moment some concepts and reflexions that
result from what is now called Social Studies of Science or Science
Policy. This is basically the study of the politics of scientific
development, the backbone of funding agencies. It is very interesting
to analyse the substitution of the colonial discourse by the discourse
of aid - both multilateral, like UNESCO, and bilateral, like ORSTOM,
the British Council and similar. The nature of the deprived
populations did not change in the span of less than ten years. The
strategies to keep them as faithful consumers had to change. But
let us not deviate from the main objective of this paper, which is
the production of scientific, in particular mathematical, knowledge.
When deciding on investments in Science and Technology, it is natural
to expect social benefits. These investments have been substantial,
both through funding agencies, either governmental or through aiding
agencies, either bi- or multilateral. The outcomes in the so-called
Third World have not been encouraging, as recently mentioned by the
Director-General of UNESCO. The gap between central nations and
peripherical nations in the production of scientific knowledge is
enlarging. Over 80% of the benefits of scientific and technological
research benefits the First World. "The gap between rich and poor
countries is a gap of knowledge" as says Federico Mayor. It is clear
that scientific productivity is related to the cultural atmosphere
and self-esteem. Self-esteem can hardly prevail among a population
deprived of its history.
Referring to what was discussed above, the main instrument in the
colonial period was to deprive the conquered peoples of their history
or to produce a history "favorable" to the conqueror. There is no
need to elaborate on the vision of slavery passed on by official
history nor to question why Zumbi (1655-1695) is practically unheard
of by Brazilian students while Cardinal Richelieu, and of course
D'Artagnan, are so familiar.
We may consider, as it is frequent in discussions of policy and
specially in the United Nations and other national and international
agencies, the production of scientific and technological, particularly
mathematical, knowledge as measurable. Scientometrics relies on several
indicators and the studies of quantitative history allows us to speak
of central nations, those who produce new knowledge, and peripherical
nations, those who absorb new knowledge. Production and absorption of
knowledge are clearly distinguishable. The sad situation is that the
peripherical nations have been slow in absorbing new knowledge. The
lack of infrastructure acts as a barrier for this process. The basin
metaphor helps to understand the process. The picture speaks for itself.
The main producers of knowledge (central nations) are represented by
the main stream. The water fertilizes their margins. They will produce
their effect in the margins of the affluents (peripherical nations)
much later, when the waters have already flown along the stream (thus
producing the gap or obsolescence of knowledge). The water (knowledge)
do not flow up stream of the affluents. The water of the affluents
surely fertilize their margins and will add and contribute to the volume
of water of the main stream.
Figure (The basin metaphor)
This corresponds in this metaphor to the brain drain and the results
drain. This is manifest in the classical emigration of academics and,
worst, on the orientation of laboratories and research institutions
as subsidiary of their major homologous in the central nations. This
is clear in the efforts to entice research institutions in the
peripherical nations to join major biotechnology research plans. The
enticement is normally done by the attractive of sending experts, in
many cases scientists with a high reputation, to the periphery for
short visits, in offering fellowships, in many cases giving stipends
higher than the current national salaries, in sending equipment, in
many cases obsolete or already heavily used equipment, and offering
international travel to seminars and congresses. This is true in
academics and, in the more developed peripherical nations, in industry.
Particularly in mathematics, we have numerous examples of such practices
in the post-war period. The presence of monies of the USA Army, Navy
and Air Force research agencies, as well as of the NSF, of the CNRS,
of the British Council, of the DAAD and other agencies, following the
pattern mentioned above, is noticeable.
These cases have not been studied in detail as yet. Both have the
common feature of producing human resources and results without any
analysis of the capability of the peripherical countries to absorb
and to make these resources and results useful for their priority
needs. Normally this is the result of a lack of qualitative directives
in Science Policy of the peripherical nations. Practically every
scientific development plan in the periphery is a program entirely
based in quantitative goals.
Perversely, World Bank, UNDP and other financing agencies rely on,
indeed stimulate, plans based on quantitative goals. Clearly, they
are easier to check. But the benefits for the poor populations of
the peripherical nations is practically nil.
In the basin metaphor, the sources of the rivers, both the main
stream and the affluents, correspond to ethnomathematical knowledge.
Ethnomathematical knowledge, like the waters, flow fertilizing the
margins of the affluent in their way and eventually mixing in a major
stream, contributing to this flow. Waters of the main stream do not
go up-stream through the affluents.
The notion of progress carried on by the main stream will benefit
the margins of the affluent after a long way through difficult land
paths - which correspond to the acquisition of knowledge from other
socio-cultural and environmental sources. The need of the margins -
peripherical cultures - are met by the water of the affluents and
only later receive the benefits coming from the main stream. These
are useful only in fertile grounds.
An alternative to main stream and affluents would be a large lake,
were all the sources contribute equally to the main body of water.
Each source producing according to its environmental history and all
the waters of the lake fertilizing all the margins.
Erosion of the basin in favor of the creation of a great lake - the
deterioration of the current world order - hopefully will lead to a
new planetary order.
Final remarks.
The conquest and colonization had as a consequence an enormous
influence in the course of development of the civilization. The
chroniclers of the conquest tell of absolutely different ways of
explaining the cosmos and the creation and of dealing with the
surrounding environment. Religious systems, political structures,
architecture and urban arrangements, sciences and values were, in
a few decades, suppressed and replaced by those of the conqueror.
A few remnants of the original behavior of these cultures were and
still are outlawed or treated as folklore. But they surely integrate
the cultural memory of the peoples descending from the conquered.
Much of these behaviors are easily recognized in everyday life.
Mathematics, as an human endeavour, is not different. This is one
focal point of the research program known as Ethnomathematics, which
deals with the generation, the intellectual and social organization
and the diffusion of different ways, styles, modes (tics) of
explanation, understanding, learning, coping with and probing beyond
(mathema) the immediate natural and socio-cultural environment (ethno).
This clearly results from the mutual exposition of different cultures
and the dynamics of this process is a major problem we face in doing
the history of ideas in every region of this world.
The conquest paved the way to colonization. In the Americas, the early
colonizers, the Spanish and the Portuguese, paved the way for the
French, the English and the Dutch colonizer and later on for Africans,
Europeans and Asiatic immigrants. With them came new forms of coping
with the environment, of dealing with daily life, and new ways of
explanations and learnings. The result was the emergence of a synthesis
of different forms of knowing and explaining which were generated by
and available to the different communities, to workers and to the
people. We recognize the emergence very soon of new religions and new
languages -- the creoles -- in the Americas, of new cuisines, new music
and new arts. All of these absolutely interrelated as a synthesis of
the cultural forms of the ancestors.
Mathematics, as a cultural form, is not different. The emergence of
new cultural behavior, particularly of Mathematical behavior, is
another focal point of the research program known as Ethnomathematics.
Particularly in the Americas, the variety and peculiarities of the
expositions of cultures and the specificities of the populational
migrations reveal an effort of the colonizer to transfer, with minor
adaptions, the forms of social, economical and political organization
and administration prevailing in the metropolises, including schooling
and scholarship (academies, universities, monateries). The new
institutions in the Americas were based on the styles prevailing in
the metropolises, mostly under influence, and even control, of
religious orders.
All this, which took place during most of the 16th, 17th and 18th
centuries, occurred while new philosophical ideas, new sciences, new
ways of production and new political arrangements were flourishing in
Europe. The cultural facts produced in Europe were assimilated in the
Americas under specific, mostly precarious, conditions. Indeed the
Americas were the consumer of some of these new cultural facts. There
is a clear co-existence of cultural goods, particularly knowledge,
produced in the Americas and produced abroad. The former consumed
mostly by the lower strata of society, the people and workers, and
the later by the domineering classes. These boundaries are not clearly
defined and the mutual influence of the resulting intellectual
productions are evident.
This poses the following
BASIC QUESTION: What are the relations between the producers and
consumers of cultural goods?
This guides my proposal for a historiography of Mathematics and what
I have called "the basin metaphor". Although this is a question
affecting the relations between academia and society in general,
hence between the ruling elites and the population as a whole, it is
particularly important for understanding the role of intellectuality
in the colonial era. Thus Ethnomathematics comes as a fundamental
instrument of historical analysis. These views own much to the
Annales proposal.
Curiously enough, the factors influencing the consumption of what
we might call Academic Mathematics produced in an alien cultural
environment, and what "outsiders" of the profession -- that is,
nonmathematicians -- have to say about Mathematics, have not been
given attention in the prevailing historiographies. My proposal
incorporates to the History of Mathematics, in an essential way,
the views of aliens, in both senses, about Mathematics. This broader
look, suggested by new historical scholarship, comes under severe
attack, in what became to be known as the Science Wars.