Review: Saxe, Cultural development of mathematical ideas

Saxe, Geoffrey B. 2012. Cultural development of mathematical ideas.  Cambridge: Cambridge University Press. 393 pp.

Reviewed by Summar Saad (Wayne State University)

In Cultural Development of Mathematical Ideas, Geoffrey B. Saxe takes an ambitious approach in exploring the cultural and cognitive origins of mathematical thought. Using an extensive number of experiments oriented towards the particular practices of the Oksapmin of Papua New Guinea, Saxe demonstrates that individual action in relation to collective activities such as economic exchange and schooling is the “locus of both the reproduction and the alteration of cultural phenomena, whether collective practices of daily life or cultural forms of representation” (p.191). His conceptual framework, which follows Sperber and Hirschfeld’s critique of the conceptualization of culture as fixed and bounded entities rather than a “property that representations, practices, and artifacts possess to the extent that they are caused by population-wide distribution processes (p.17),” seeks to illustrate the heterogeneity and permeability of cultural and cognitive processes through activity using synchronic and diachronic perspectives.

In Part I, Saxe begins by framing the scope of his study using relevant scholarly work on the area of cognition and mathematical thought, and details his time in the field in 1978, 1980, and 2001. His approach interrogates three genetic processes: 1) microgenesis, the transformation of the body-part form into a vehicle to represent values numerically, 2) sociogenesis, which involves the microgenetic activities of multiple individuals at multiple sites that, collectively, constitute a process in which representational forms and functions are reproduced and altered in a community over time, and 3) ontogenesis, which involves the shifts in form-function relations in activity over the course of an individual’s development (p.29). Using a number of helpful figures, Saxe also unravels the specifics of the Oksapmin body-counting system where one begins counting with the thumb on one hand of the body and continues across to the opposite side ending at the little finger. Familiarity with this system is important for his investigation into how this system changes through time. By this point, the readers are ready to enter the field, where Saxe attempts to tease out the historical and social processes at play in the way the Oksapmin respond to mathematical challenges in collective activities under shifting conditions.

In Part II, Saxe traces the history of Papua New Guinea from a pre-contact period where people traded commodities including a shell currency (bonang) and through the sustained contact of the Oksapmin communities with Western societies, which led to the proliferation of trade stores that supported cash as the universal medium for exchange. Focusing on the activity of economic exchange, Saxe asserts that “with increasing participation in the money economy associated with Oksapmin cohorts, we find a shift from external correspondences that serve numerical functions to internal correspondences that serve arithmetical functions” (p.95). Saxe then shifts his focus from knowledge of Oksapmin body-part counting and Tok Pisin representational forms to look at the semiotic forms people use to represent the objects of economic exchange. What he discovers is that over time, as people began using the body system to quantify currency, reciprocally the currency system became incorporated into the structure of the body-counting system. Ultimately Saxe demonstrates that cognitive processes exhibit uniformity and variation in a single period as well as unity and discontinuity over historical time.

In Part III, Saxe reviews the transformation of schooling in Oksapmin beginning in the early 1960s and following the introduction of “Western schooling,” Bible school, and community schooling. Rather than conceptualizing schooling as a direct cause of cognitive development, Saxe focuses on the dynamics of the reproduction and alteration of the forms of numerical representation and the functions they serve as students and teachers participate in collective practices of classroom life (p. 194). He establishes the ways in which Oksapmin children reproduce the body form as they solve arithmetical problems in the same way that they produce variants in the body form, “inadvertently altering the use of the system to serve new functions (p.236).” With recent educational reforms, he notes a shift in the teaching of mathematics using only English to using Tok Pisin and Oksapmin as well. Saxe observes that with this shift came others including the use of stones in classroom computations as well as a developing facility with Hindu-Arabic-based algorithms.

In Part IV, Saxe brings the discussion full circle and returns to the implications of his findings with regards to his conceptual framework. In his analysis, he points to three key properties that emerge in form-function relations: conventionality, hybridity, and instrumentality. Using parallels from evolutionary biology, he also takes up the question of how form-function relations develop and why. Though not an anthropologist, Saxe deserves great credit for his ethnographic treatment of this serious cognitive question. Saxe successfully presents an alternative methodological approach to our understandings of culture and cognition that does not treat them as independent but rather as an interplay of the two. His work offers great insight into cognition and culture as processes rooted in a multiplicity of contexts and activities. Although this book covers a lot of ground, and is sometimes very abstract, the organization and flow of the content is seamless and easy to follow. Saxe also takes great care to account for any threats to validity, and while each of the eighteen individual studies he conducts are not without their flaws; the overall picture shines clearly at the end: culture and cognition are processes interwoven and linked through activity.

Review: Ingold, Lines: a brief history

Ingold, Tim. 2007. Lines: A Brief History. Cambridge, MA and London: Harvard University Press. 186pp.

Reviewed by Molly Hilton (Wayne State University)

Get out your walking stick and your comfortable shoes as you accompany Tim Ingold on this intellectual wayfarers’ journey exploring the “comparative anthropology of the line” (p1). In his path-breaking book, Lines: A Brief History, Ingold guides readers through a unique theoretical model that explores the interconnected and enmeshed lines of people and things. Ingold argues things and people are the sum of interconnected lines; to study “things and people is to study the lines they are made of” (p5). Lines and their relationships to surfaces offer a provocative frame from which to consider questions central to anthropology.

Anthropologists will find themselves familiar with “lines”: lines of descent, lines of story, lines of travel, lines of movement, lines of music, and so on. Lines: A Brief History challenges established conventions, such as kinship charts that use line to connect the dots, to advocate a theoretical approach that accounts for movement, growth and interrelationship. This challenge is animated by a key theme used throughout the book – the distinction between wayfaring and transport. Wayfaring describes a way of being in that the “traveler and his line are one and the same” (p 76). The path of the wayfarer is where life is lived. Drawing on Gibson, Ingold states that the wayfarer’s path is where knowledge is forged along the way. Transport lines are destination-oriented. They are connectors. The traveler becomes a passenger fighting against time to reach a destination. Transport lines are teleological. Ingold enjoins the reader to become wayfarer, engaging in the journey through chapters building up knowledge as one “goes along” forsaking the impulse for a “built up” conclusion.

In Lines, Ingold commences with the question how did speech become separated from song? He explores the historical relationship between speech, song, writing and musical notation. Before the printing press, both written text and song were performative as were the processes of inscription. Written notation functioned as mnemonic artifact rather than a script or score that ensured a faithful record or copy. Using comparative examples from medieval history, present day Shipibo-Conibo people in Peru, and Japanese noh theater, Ingold argues that the words “speak” to readers not as a representation of sound but in the manner of synesthesia actual sound. Writing could not be accurately conceptualized as a “visual representation of verbal sound” (p27).

Both musical notation and writing involve lines and surfaces. “To read a manuscript… is to follow the trails laid down by a hand that joins the voice in pronouncing the words of a text” (p28). The advent of printing disconnected manual gesture from the graphic output and thereby disconnected the voice (embodiment) from the page of print. Printed works became static documents. What heralded this transformation was a “fundamental change” in the conception of line and its relationship to the surface. The inscribed printed lines (words) changed the manuscript surface from a landscape to be explored into a surface that is fixed and bounded.

Ingold proposes a taxonomy of lines. The two primary types are threads and traces. Threads have a surface and can be made by human hands, or not (i.e. roots, spider webs, yarn, fishing-net, violin strings). Traces are any enduring mark left in a solid surface. Traces can be additive or reductive, or neither (i.e. worn path, chalk on blackboard, stick in sand, snail trail). Ghostly lines have no physical manifestation (i.e. constellations, survey lines, time-zones, borders). Ingold notes that the distinction between ghostly lies and real lines is “decidedly problematic” (p50). The differentiation may privilege a Western perspective. The meridian lines of Chinese medicine may be real according to a Chinese practitioner but considered ghostly (imagined) to a Western observer. Ingold does not offer any guidance on how to resolve this conundrum. He concedes that the entire line taxonomy is imperfect and potentially confusing.

Surfaces are not simply a “taken-for-granted backdrop” (p39). Whether regarded as a landscape, a space to be colonized, the skin of the body or a mirror of the mind, the conception of the surface deeply affects its relationship to line. Threads transforming into traces create surfaces (p61). For instance, knitting constitutes a surface as the knotted threads form a single surface leaving traces of the composition still visible. Traces transforming into threads dissolve surfaces. To explicate, Ingold engages with Alfred Gell’s argument that apotropaic patterns are perceived to lure demonic forces to a particular surface by their fascination with an intricate pattern. Gell’s aerial-view perspective was mistaken. Ingold convincingly argues, the trap is not one of fascination, but rather, the lines drawn cease to be a surface and become threads that trap the demon. This example demonstrates the potential explanatory power of “a comparative anthropology of the line.”

Can lines help us understand the ruptures of modernity? In the final chapter, Ingold explores the implications of “straight” lines. Straight lines are associated with moral uprightness, quantitative explanations, reason and dignity. Somewhat parallel to the metaphor of wayfinding/transport, the “workmanship of risk” has been displaced in modern society by the “workmanship of certainty.” An implement of certainty, modern CAD design embodies no movement or gesture. The straight line, the line of certainty, has become an icon of modernity (p167). This is where ruptures occur. We are reminded that fragmentation can create passages.

Sections of this book are somewhat opaque and/or vague. Given the authors concluding statements we must accept that at some of these “loose ends” are intentional (p170). I’ve already mentioned that the taxonomy of line and surface have much room for elaboration. I’ll mention just one other example here. In the Introduction (p3), Ingold argues that if we envision evolution as a tangle of enmeshed intra-human and inter-species relationships “then our entire understanding of evolution would be irrevocably altered.” It is not clear if Ingold is referring to our proclivity to fix the human lives into “temporal moments.” Alternatively this passage could refer to the enmeshment of multiple species “continually [forging] their own and each other’s lives.” How either alternative would change our conception of evolution is not clear.

Lines: A Brief History invites the reader on a wayfarer’s journey. It’s not entirely clear where one is going or where one has been, but it is clear that one has grown along the way.

Review: Lloyd, Cognitive variations

Lloyd, G.E.R. 2007. Cognitive variations: reflections on the universality and diversity of the human mind. Oxford; New York: Clarendon Press; Oxford University Press. 201 pp.

Reviewed by Grace Pappalardo (Wayne State University)

G.E.R. Lloyd’s Cognitive Variations is loyal to its name, exploring a wide variety of cognitive differences as well as similarities cross-culturally and historically. Lloyd vehemently supports a cross-disciplinary approach to understanding cognitive variations and proves this time and again throughout the text, exploring and analyzing arguments in favor of both nature and culture as well as from universalists and particularists. He also makes the important distinction that he seeks not to prove the validity or falsity of past claims on the topics he explores, but rather to determine to what extent these claims are applicable to the greater argument. Cognitive Variations serves not as a cognitive encyclopedia, but rather as a critical overview of the research that has been done thus far in some areas of cognition. Lloyd does not seek to answer any unresolved matters, but rather to analyze the value of the available data and offer a new platform for further discussion.

Cognitive Variations addresses the commonalities and differences in human cognition using a multidisciplinary approach. In each section, he focuses on a different area of cognition currently under investigation and assesses the research and findings on each thus far. He systematically tackles topics of debate, such as color perception and natural kinds, and forms each chapter in a way that synthesizes the multidisciplinary information provided, alongside his own extensive knowledge of classical Greek and Chinese thought. In doing so, he emphasizes the multidimensionality of phenomena, explaining that across cultures, each group of people will choose to assign importance to one or some of a variety of aspects. Additionally, he grapples with the reality that even people within a common culture can differ from each other considerably, making the discovery of commonalities a challenge. However, these differences are also not solid evidence for particularism, which, as Lloyd establishes throughout, is why an interdisciplinary approach to cognition is truly best. Lastly, throughout the text, he touches on themes of methodological error and erroneous conclusion based thereupon, explaining that presupposing a result can in fact skew that result. He argues that a myopic approach utilizing a single viewpoint or discipline can lead to false conclusions masquerading as accurate findings.

Lloyd very cogently argues this last point throughout his book and is careful to point out errors in methodology that may have led researchers to misleading conclusions about their subjects. This puts much of the evidence he provides into valuable perspective and reminds the reader to take caution in assuming the validity of research results. He address Berlin and Kay’s study on color perception in this way, explaining that, whether or not they intended to, their research question and materials were inherently skewed toward the results they hoped to find. He explains that Berlin and Kay essentially got the results they hoped for by failing to recognize the connotations of the differences they perceived. He claims that in their methodology, they favored hue over luminosity, which does not really allow for an appropriate answer if the informants categorized color in other terms. Lloyd here employs his knowledge of ancient Greek color classification to further explain his opposition to Berlin and Kay’s supposedly conclusive results on color universals. He presents the terms leukon and melan, which he explains are descriptors not of hue, but rather of luminosity. Additionally, Lloyd adds that similar to perceiving luminosity or saturation instead of hue, Berlin and Kay may have overlooked the fact that a color term may not have been the target identifier for a particular object. As Conklin’s findings explain, although an identifier may appear to be addressing color, it may very well be instead addressing a different primary connotation, such as wetness or dryness.

Despite the extreme variability of claims Lloyd addresses in Cognitive Variations, he manages to maintain an unbiased stance on each topic. While he imbues the text with his own judgements, his attempts at a true dissection of past arguments for the betterment of the cognitive discourse are successful. While Lloyd’s book is an impressive piece of scholarship, weaving together arguments made by those with opposing viewpoints, it is certainly an overview of these arguments. This is not to discount his achievements in bringing together such a diverse set of accounts, but rather to note that each chapter does not go into immense detail on each cognitive variation discussed. If more information was desired on certain arguments, further outside reading would be required. However, painstaking detail is not Lloyd’s objective here, but rather to bring together various and often opposing viewpoints and piece them together to make more sense of human cognition.

In total, Lloyd accomplishes exactly what he sets out to do. In sharing such a wide variety of findings from research in biology, psychology, anthropology, history, and more, he rightly concludes that the most effective way to approach issues of human cognition is through an interdisciplinary approach. As he shows throughout the text, failing to look at research findings through multiple lenses can lead to error and misleading conclusions. Taking advantage of the strengths of each discipline can make for more conclusive and accurate discoveries.

Review: Tomasello, A natural history of human thinking

Tomasello, Michael. 2014. A natural history of human thinking.  Cambridge, MA: Harvard University Press. 194 pp.

Reviewed by Heather Buza (Wayne State University)

Is there a cognitive evolutionary relationship between great apes and humans? In his valuable book, A Natural History of Human Thinking, Michael Tomasello discuses current research on great ape as well human adult, toddler, and infant cognition. He provides evidence that great apes and humans share many cognitive features due to descent from a recent common ancestor, then discusses exactly what differentiates human cognition from great ape cognition. He neatly disposes with the idea that language is thought, and attempts to explain why humans think in a more cooperative and coordinated fashion. When did human cognition become substantially different from great ape cognition? What might have caused this shift in cognition? Tomasello theorizes about these questions and offers a plausible two-step shift in human cognition that he terms the shared intentionality hypothesis. From his hypothesis, Tomasello discusses how human cognition, communication and culture emerged.

Tomasello’s book covers a lot of evolutionary ground, tracing human evolution from the emergence of the genus Homo around 2 million years ago when Tomasello believes shared intentionality first emerged. Tomasello uses the term objective-reflective-normative thinking to describe the components of the shared intentionality hypothesis, which consists of three key components: our ability to represent things cognitively, to infer possible outcomes, and to monitor our own behavior in relation to the larger group norms. Thus, human cognition is unique because we are capable of evaluating situations with multiple variables, including various social perspectives, while also accounting for our own behavior and considering how it will fit into the larger behavioral norms of a group.

The first part of the two-step shift in human cognition involves the emergence of socially shared joint goals or joint intentionality. Tomasello offers the example of hunter-gatherers who begin to cooperate in order to acquire enough food for survival. Following joint intentionality, Tomasello describes collective intentionality. This second step occurs later, after the hunter-gatherers have had time to develop some cultural conventions and norms. Ultimately, this second cognitive shift resulted in modern humans’ existence in a matrix of culture and language.

Tomasello acknowledges some gaps in his theory and welcomes input. He is clear, though, that humans are not hardwired to think in a culturally cooperative, group-oriented perspective. Rather, humans are capable, and modern humans may certainly be more prone to thinking in this way, as they are constantly bombarded by culture and language. However, Tomasello reminds the reader that evolution cannot see cognition; rather, it can only see behaviors that affect survival. Cognition and decision-making abilities do not preserve well. Tomasello concludes with two questions, which require further thought. What does the individual bring to the table? While individuals participate in joint attention and joint goals, investigating what the individuals brings to the ‘joint’ portion of the communicative act is an important aspect. Also, humans’ overwhelming tendency to objectify entities should be further investigated.

Tomasello brings important new information together in his book. He highlights important contributions to the field and rightfully acknowledges the limitations of our knowledge. While on the whole approachable, could be improved with less complicated jargon at a few junctures. But importantly, Tomasello does not oversell his theory or make claims that reasonable people cannot accept. A Natural History of Human Thinking is an excellent contribution to the field of cognitive science.

Review: Cerulo, Never saw it coming

Cerulo, Karen. 2006. Never saw it coming: cultural challenges to envisioning the worst. Chicago: University of Chicago Press. 336 pp.

Reviewed by Michael Thomas (Wayne State University)

Evelyn Waugh, a notoriously prickly Catholic satirist, was once asked by his friend Nancy Mitford how he could be so cruel and still call himself Christian, to which he replied, “You have no idea how much nastier I would be if I was not a Catholic. Without supernatural aid I would hardly be a human being.” This pithy anecdote is useful to keep in mind when reading Karen Cerulo’s Never Saw it Coming, for it colorfully illustrates a challenge at the heart of any project seeking to evaluate the relative influence of inferred cognitive or ideological inputs on behavioral outputs.

Cerulo’s is an interesting book for a number of reasons; the curious reader is sure to find it valuable wherever they may stand in relation to its sometimes nebulous premises and impressionistic exposition. That is to say, the book primarily articulates its thesis through offering a fair amount of statistical information and some well formulated examples, though at the expense of some specificity with regard to the concepts and mechanisms underlying the phenomenon itself. Cerulo’s bold attempt at synthesizing cognitive and social theory to explain an interactive social phenomenon she calls “positive asymmetry” is less of an analytical argument than an expansive theoretical hypothesis, and so for this reason the lack of specificity may be forgivable given the scope and complexity of the central claim.

According to Cerulo, positive asymmetry functions as a bias toward privileging positive outcomes in decision-making, which can have an ultimately negative effect in that this phenomenon can occlude imagining “worst case” scenarios. The positive asymmetry is, Cerulo insists, pervasive in American, but not only American, culture and can partially explain the inability of institutions or individuals to foresee “worst case” scenarios, or, more accurately, “especially bad” scenarios. As pervasive as this phenomenon is, however, it is not universal and Cerulo is commendably sensitive to identifying where, and under what conditions, it does not apply. Aside from exceptional circumstances, this widespread failure of imagination leaves organizations and individuals vulnerable to any number of potential failure modes.

Essentially, Cerulo’s thesis is that the structure of human cognition relative to classification and inference is such that in the event of uncertainty, such as in future planning or decision making, the mind will categorize according to “best fit”. Relying on the inductive model of the mind, the “best fit” refers to a classification scheme wherein the most salient instance of a category is considered the most representative and so inferences regarding candidate members of some category are made in relation to that exemplar. Her thesis is built upon the model Eleanor Rosch advances, sometimes called prototype theory or exemplar theory, and is typically formulated in contrast to deductive theory theories such as those of Bob Reider and Doug Medin. What this means in practice is that insofar as negative circumstances, and the effects of negative circumstances, are rendered variously insignificant, they cannot participate in constituting classification criteria. For example, where deviant persons relative to the norms of some cultural milieu are ostracized, shunned, or banished, they are no longer salient. This lack of salience prohibits their inclusion in the category “person” so that the “best fit” for “person” is invariably skewed toward positive representation. Subsequent evaluations under conditions of uncertainty thus skew inferences away from “worst cases”.

This model of cognition allows Cerulo the necessary structure to integrate cultural practice, habitus, relationships of power, and social norms into the process of drawing inferences. Cerulo’s description of positive asymmetries at work in scientific measurement serves as a concise starting point for STS scholars interested in exploring the relationship of cognition and laboratory practice. She addresses the structure by which quality standards embody the positive asymmetry in all variety of forms familiar to social scientists such as power or ideology, but throughout the book she provides a deluge of examples, and it is here that the reader sees most starkly the compromise in specificity for the effect of breadth. Cerulo’s examples are numerous and presented in dizzying modalities. Statistical samples, historical narratives, pedagogical anecdotes, mythology, and case studies are but a few of the means by which positive asymmetry is presented. The technique is effective and nearly makes the reader forget exactly what the ontological status of a positive asymmetry actually is. It is of course a social phenomenon, but of what sort? And what does that mean? It is no doubt an interactive feedback effect of particular social forms and cognitive architecture, but the dynamics are fuzzy and one gets confused trying to track the deliberate modulations between “best” or “worst” being used as (1) normative evaluations relative to human welfare and (2) descriptive accounts of classification membership. Consider an admittedly glib counter example to Cerulo’s example taken from competitive diving. Cerulo discusses quality metrics with regard to competitive diving, but what is a “worst case dive” given (1) the diver performs the dive exceptionally well but suffers a heart attack upon such exertion or (2) a diver decides to withdraw from the competition because he feels he needs rest. Cerulo’s account cannot distinguish because the unit of analysis is never clearly defined.

So one question inevitably emerges, how do you know when you are observing an asymmetry? Thinking back to the Evelyn Waugh quote above, there is no clear objective synchronic measure by which one might determine the relative position of some response. Worst cases can always be worse, and best cases better.

The four case studies Cerulo provides don’t seem to help. For example, in chapter six Cerulo discusses Exceptions to the Rule, one such being the Phoenix document that warned of the 9/11 attack. Cerulo attributes the failure of adequate response to the institutionally structural positive asymmetry, though she notes that the administration was distracted by establishing strategic National Missile Defense (NMD), an action undertaken, if mistakenly, to prevent a clearly worse scenario. The problem, then, was not one of asymmetry, but of improper risk assessment. Unfortunately, an asymmetry analyses can only be performed ex post facto, which invites the question, “How is this theory falsifiable?” An example of a failure mode despite negative asymmetry would go a long way to outlining the extent to which her argument operates, lest it be regarded as an inverse tautology where positive outcomes must equal negative asymmetry.

The book closes with both an account of the structural attributes inhibiting or cultivating negative asymmetry and a tentative plan for achieving balanced perspectives in organizations. If one accepts the premises that (1) positive and negative asymmetry describe actual phenomena and (2) these phenomena are causally decisive, then one will find her propositions interesting to ponder, though interest alone may not suffice to traverse the inferential distance between her data and her proposals. In all, this book tackles an important topic of interest to those in the cognitive, political, and social sciences though ultimately readers may find themselves less than satisfied. A less ambitious project, or more narrowly constrained subject matter, may have permitted a more precise understanding of the relationship between cognition and culture relative to quality evaluation.

Review: Bloch, Anthropology and the cognitive challenge

Bloch, Maurice. 2012. Anthropology and the Cognitive Challenge.  Cambridge: Cambridge University Press.  234 pp.

Reviewed by Sarah Carson (Wayne State University)

Maurice Bloch’s ambitious work, Anthropology and the Cognitive Challenge, suggests nothing less than a complete overhaul of the discipline. Bloch first discusses the rift between social and natural science and how it would benefit both groups to reconcile and understand each other. This opposition is framed in terms of the omnipresent nature versus culture debates (although Bloch avoids the word “culture,” finding the concept problematic and imprecise, preferring “history”). Bloch explains the dichotomy’s falsity as humans being “psychologically and physically one at all levels,” and therefore that cognitive and social scientists are talking about the same thing, the human animal, and should pay more attention to each other to understand a more complete picture of human life within a naturalist framework. Interdisciplinary research and the benefits of cognitive scientists and anthropologists working together form the basis of the book, and Bloch returns to these points throughout.

Bloch insists that the concerns of anthropologists and natural scientists about each other can be worked past. For instance, the innate capacity for genetically transmitted knowledge makes many anthropologists uneasy, because arguments about people’s behavior resulting from biological inheritance can devolve into racist or sexist ideas—beliefs that one racial group is naturally more intelligent, for instance. These are bad arguments for multiple reasons, including “race” being a social rather than biological concept without clear genetic categories, characteristics not being clearly determined by single genes, and the immense genetic differences that exist within populations, which may outnumber the differences between them.  But beyond all of these arguments, Bloch insists, lies the fact that there is no legitimate reason to treat people differently just because genetic differences exist. Thus, recognizing innate psychological differences does not justify discrimination, and social scientists should not shy away from these facts out of a fear of racism or sexism. Anthropologists’ beliefs that humans are different from all other animals because of our complex capacity for history, communication of knowledge and culture should also not be used to avoid considering innate knowledge, something all animals possess. Humans are unique, but we are not absolutely different from all other living species.

This point that anthropologists should not forget that humans are animals returns us to Bloch’s fight against the nature-culture dichotomy. When studying people, innate predispositions (babies’ understanding of basic physics and that people have their own minds, for example) are inseparable from our culturally and historically shaped aspects. The nature versus culture reasoning is inadequate: it is fundamentally static, while people are complex and dynamic. Furthermore, the natural and social scientists are closer than they believe, since scientists and “natives” live in the same world and are the same species, making an internal “native” point of view necessarily external (or all human internal), and the external scientist’s view necessarily dependent on internal factors of history of the person they study. Natural and social scientists are looking at different levels of the self and arguing about who does it better because they think they are looking at the same thing. The human animal must be looked at as a complete being with all characteristics taken into account. So, Bloch’s idea of “the blob” comes into play to explain these levels, which are really points in a continuum.

Bloch’s “blob” consists first of the core, with general characteristics involving “a sense of ownership and location of one’s body” and a sense that one is controlling one’s actions. The next layer of the blob is the minimal self, involving a sense of one’s continuity in time, necessary for long-term memory and recognizing oneself, as well as the ability to “time travel” (Bloch discusses this concept at length, and it refers to remembering information from the past to inform present behavior or planning future behavior, which necessitates having an imagination that allows one to “be” in the past or future). The third level is the narrative self, linked with autobiographical memory, and the ability to tell stories about oneself, the implications of which for consciousness and language remain debatable. Those who create meta-representations, or who tell others about their inner states, have an additional blob element, which Bloch hesitates to call another level since it is not fundamental. The differences between those who create many meta-representations or not are akin to the differences between individualist and collectivist cultures anthropologists study. But all blobs are fundamentally the same, and are also organically united with each other and constantly transforming by connecting with each other both physically (birth and sex) and mentally (social exchange).

Finally, Bloch illustrates his points about how social and natural scientists think they are looking at the same thing when in fact they are not to the topic of memory, which seems straightforward but can mean anything from the mental processes that cognitive scientists study to anthropological ideas of collective memory or public commemorations. He focuses on the neurological theory of connectionism, which suggests that knowledge is organized in webs of interconnected networks. Bloch concludes the book by discussing how, as illustrated by topics like memory, anthropologists often generate conclusions without thoroughly examining the complexity of issues. Ethnography only provides surface glimpses of second-order meta-representations like language, and not scientific analyses of thought processes. Yet anthropological contributions can be important if done in cooperation with other scientific disciplines, in the attempt to look at the total of human physiological, psychological, and historical processes. Thus, Bloch believes that anthropology as a discipline should return in part to its scientific roots.

While Bloch’s observations are undeniably important and deserve consideration, the book is not without fault. Bloch reiterates his thoughts at the beginning of every chapter, which, while helpful if one was reading each specific chapter separately, makes for very repetitive reading. The vocabulary used is sometimes esoteric and cumbersome to the point of making the book a difficult read, yet the subject’s importance indicates it should be accessible to as large an audience as possible. This density also makes the leap when Bloch uses the colloquial term “blob” to explain the self somewhat startling, although welcome.

Bloch’s insistence that anthropologists and cognitive scientists move forward by understanding each other is admirable. However, his challenge to ethnography to look more broadly and examine the particular situation in terms of general questions about humankind could be seen as devaluing ethnography to the point of it being useless if one does not make big-picture, general, or evolutionary statements. Yet Bloch insists that the anthropologist is not equipped to make such claims and should really be collaborating with natural scientists to do so. Bloch’s determination to understand all facets of the human blob and his emphasis on interdisciplinary work is admirable. Hopefully his seemingly radical ideas can become accepted by mainstream natural and social scientists and lead to a greater understanding of cognition within culture.

Review: von Mengden, Cardinal Numerals

This review appeared originally in the LINGUIST List at http://linguistlist.org/issues/21/21-5213.html

AUTHOR: von Mengden, Ferdinand
TITLE: Cardinal Numerals
SUBTITLE: Old English from a Cross-Linguistic Perspective
SERIES: Topics in English Linguistics [TiEL] 67
PUBLISHER: De Gruyter Mouton
YEAR: 2010

Stephen Chrisomalis, Department of Anthropology, Wayne State University

SUMMARY

This monograph is a systematic analysis of Old English numerals that goes far
beyond descriptive or historical aims to present a theory of the morphosyntax of
numerals, including both synchronic and diachronic perspectives, and to
contribute to the growing linguistic literature on number concepts and numerical
cognition.

The volume is organized into five chapters and numbered subsections throughout
and for the most part is organized in an exemplary fashion. Chapters II and
III, where the evidence for the structure of the Old English numerals is
presented, will be of greatest interest to specialists in numerals. Chapter IV
will be of greatest interest to specialists in Old English syntax. Chapter V is
a broader contribution to the theory of word classes and should be of interest
to all linguists.

The author begins with an extensive theoretical discussion of number concepts
and numerals, working along the lines suggested by Wiese (2003). Chapter I
distinguishes numerals (i.e., numerically specific quantifiers) from other
quantifiers, and distinguishes systemic cardinal numerals from non-systemic
expressions like ‘four score and seven’. As the book’s title suggests, cardinal
numerals are given theoretical priority over ordinal numerals, and nominal forms
like ‘Track 29′ or ‘867-5309′ are largely ignored. Cardinal numerals exist in
an ordered sequence of well-distinguished elements of expandable but
non-infinite scope. Here the author builds upon the important work of Greenberg
(1978) and Hurford (1975, 1987), without presenting much information about Old
English numerals themselves.

Chapter II introduces the reader to the Old English numerals as a system of
simple forms joined through a set of morphosyntactic principles. It is
abundantly data-rich and relies on the full corpus of Old English to show how
apparent allomorphs (like HUND and HUNDTEONTIG for ‘100’) in fact are almost
completely in complementary distribution, with the former almost always being
used for multiplicands, the latter almost never. This analysis allows the
author to maintain the principle that each numeral has only one systemic
representation, but at the cost of making a sometimes arbitrary distinction
between systemic and non-systemic expressions. This links to a fascinating but
all-too-brief comparative section on the higher numerals in the ancient Germanic
languages, which demonstrates the typological variability demonstrated even
within a closely related subfamily of numeral systems.

Chapter III deals with complex numerals, a sort of hybrid category encompassing
various kinds of complexities. The first sort of complexity, common in Old
English, involves the use of multiple noun phrases to quantify expressions that
use multiple bases (e.g. ‘nine hundred years and ten years’ for ‘910 years’).
The second complexity is the typological complexity of Old English itself; the
author cuts through more than a century of confusion from Grimm onward in
demonstrating conclusively that there is no ‘duodecimal’ (base 12) element to
Old English (or present-day English) — that oddities like ‘twelve’ and
‘hundendleftig’ (= 11×10) can only be understood in relation to the decimal
base. The third is the set of idiosyncratic expressions ranging from the
not-uncommon use of subtractive numerals, to the overrunning of hundreds (as in
modern English ‘nineteen hundred’), to the multiplicative phrases used
sporadically to express numbers higher than one million. Where a traditional
grammar might simply list the common forms of the various numeral words, here we
are presented with numerals in context and in all their variety.

Chapter IV presents a typology of syntactic constructions in which Old English
numerals are found: Attributive, Predicative, Partitive, Measure, and Mass
Quantification. In setting out the range of morphosyntactic features
demonstrated within the Old English corpus, the aim is not simply descriptive,
but rather, assuming that numerals are a word class, to analyze that class in
terms of the variability that any word class exhibits, without making
unwarranted comparisons with other classes.

In Chapter V the author argues against the prevalent view that numerals are
hybrid combinations of nouns and adjectives. While there are similarities,
these ought not to be considered as definitional of the category, but as results
of the particular ways that cardinal numerals are used. Because it is
cross-linguistically true that higher numerals behave more like nouns than lower
ones, this patterned variability justifies our understanding the cardinal
numerals as a single, independent word class. It is regarded as the result of
higher numerals being later additions to the number sequence — rather than
being ‘more nounish’, they are still in the process of becoming full numerals.
They are transformed from other sorts of quantificational nouns (like
‘multitude’) into systemic numerals with specific values, but retain vestiges of
their non-numeral past.

EVALUATION

This is an extremely important volume, one that deserves a readership far beyond
historical linguists interested in Germanic languages. It is not the last word
on the category status of cardinal numerals, cross-linguistic generalizations
about number words, or the linguistic aspects of numerical cognition, but it
represents an exceedingly detailed and well-conceived contribution to all these
areas. While virtually any grammar can be relied upon to present a list of
numerals, virtually none deals with the morphosyntactic complexities and
historical dimensions of this particular domain that exist for almost any
language. Minimal knowledge of Old English is required to understand and
benefit from the volume.

The specialist in numerals will be struck by the richness and depth of the
author’s specific insights regarding numerical systems in general, using the Old
English evidence to great effect. Because it is one of very few monographs to
be devoted specifically to a single numeral system, and by far the lengthiest
and theoretically the most sophisticated (cf. Zide 1978, Olsson 1997, Leko
2009), there is time and space to deal with small complexities whose broader
relevance is enormous. The volume thus strikes that fine balance between
empiricism and theoretical breadth required of this sort of cross-linguistic
study rooted in a single language.

With regard to the prehistory of numerals, we are very much working from a
speculative framework, and where the author treads into this territory, of
necessity the argument is more tenuous. It may be true that for most languages,
the hands and fingers are the physical basis for the counting words, but
Hurford’s ritual hypothesis (1987), of which von Mengden does not think highly,
is at the very least plausible for some languages if not for all. These issues
are not key to the argument, which is all the more striking given that they are
presented conclusively in Chapter I.

A potential limitation of the volume is that, by restricting his definition of
numerals to cardinals (by far the most common form in the Old English corpus),
the author is forced into an exceedingly narrow position, so that, ultimately,
ordinals, nominals, frequentatives, and other forms are derived from numerals
but are not numerals as a word class, but something else. But the morphosyntax
of each of these forms has its own complexities — think of the nominal ‘007’ or
the decimal ‘6.042’ – that deserve attention from specialists on numerals.
Numerals may well be neither adjectives nor nouns, but omitting the clearly
numerical is not a useful way to show it. Similarly, the insistence that each
language possesses one and only one systemic set of cardinal numerals is
problematic in light of evidence such as that presented by Bender and Beller
(2006).

When comparing with other sorts of numerical expressions, e.g. numerical
notations, the author is on shakier grounds. It is certainly not the case, as
the author claims that the Inka khipus had a zero symbol, and it is equally the
case that the Babylonian sexagesimal notation and the Chinese rod-numerals did
(Chrisomalis 2010). Similarly, the author seems to suggest that in present-day
English, any number from ‘ten’ to ‘ninety-nine’ can be combined multiplicatively
with ‘hundred’, whereas in fact *ten hundred, *twenty hundred, … *ninety hundred
are well-formed in Old English but not in later varieties.

It is curious that von Mengden does not link the concept of numerical ‘base’ to
that of ‘power’, but rather to the patterned recurrence of sequences of
numerals. Rather than seeing ’10’, ‘100’ and ‘1000’ as powers of the same base
(10), they are conceptualized as representing a series of bases that combine
with the recurring sequence 1-9. But a system that is purely decimal, except
that numbers ending with 5 through 9 are constructed as ‘five’, ‘five plus one’
… ‘five plus four’, would by this definition have a base of 5 even though powers
of 5 have no special structural role and even though 5 never serves as a
multiplicand. This definition is theoretically useful in demonstrating that Old
English does not have a duodecimal (base-12) component, but as a
cross-linguistic definition will likely prove unsatisfactory.

Because the Old English numerals are all Germanic in origin, with no obvious
loanwords, it is perhaps unsurprising that language contact and numerical
borrowing play no major role in this account. Yet on theoretical grounds the
borrowing of numerals, including the wholesale replacement of structures and
atoms for higher powers, is of considerable importance cross-linguistically.
Comparative analysis will need to demonstrate whether morphosyntactically,
numerical loanwords are similar to or different from non-loanwords.

The author has incorporated the work of virtually every major recent theorist on
numerals, and the volume is meticulously referenced. There are a few irrelevant
typos, and a few somewhat more serious errors in tables and text that create
ambiguity or confusion, but no more than might be expected in any volume of this
size.

This monograph is a major contribution to the literature on numerals and
numerical cognition. Its value will be in its rekindling of debates long left
dormant, and its integration of Germanic historical linguistics, syntax,
semantics, and cognitive linguistics within a fascinating study of this
neglected lexical domain.

REFERENCES:

Bender, A., and S. Beller. 2006. Numeral classifiers and counting systems in
Polynesian and Micronesian languages: Common roots and cultural adaptations.
Oceanic Linguistics 45, no. 2: 380-403.

Chrisomalis, Stephen. 2010. Numerical Notation: A Comparative History. New York:
Cambridge University Press.

Greenberg, Joseph H. 1978. Generalizations about numeral systems. In Universals
of Human Language, edited by J. H. Greenberg. Stanford: Stanford University Press.

Hurford, James R. 1975. The Linguistic Theory of Numerals. Cambridge: Cambridge
University Press.

Hurford, James R. 1987. Language and Number. Oxford: Basil Blackwell.

Leko, Nedžad. 2009. The syntax of numerals in Bosnian. Lincom Europa.

Olsson, Magnus. 1997. Swedish numerals: in an international perspective. Lund
University Press.

Wiese, Heike. 2003. Numbers, Language, and the Human Mind. Cambridge: Cambridge
University Press.

Zide, Norman H. 1978. Studies in the Munda numerals. Central Institute of Indian
Languages.