Shady Characters

In all the hurly-burly of the past couple of months, I completely neglected the birth of a fascinating set of essays in progress at Shady Characters, a new blog by Keith Houston about the history and social context of punctuation. This is a subject on which I have blogged occasionally (e.g. A biography of the ampersand or A typology of quotation marks) but so far, Mr. Houston puts my efforts to shame. Of particular note is his three-part essay on the pilcrow (paragraph mark):

Part 1
Part 2
Part 3

Check it out!

Link roundup

Do you speak Scots? If you’re not sure, the text and audio samples at Aye Can will help you decide if you do. This is of particular relevance this year due to the 2011 Scottish Census.

Errol Morris, whose news essays have featured elsewhere on this blog (see here), has a compelling five-part essay ‘The Ashtray’ about his relationship with the philosopher of science Thomas Kuhn at the Institute for Advanced Study, and whose title derives from an object hurled at Morris by Kuhn (no, really!).

Popular Linguistics magazine is an important addition to the wealth of online resources relating to language and linguistics, with a particular focus on materials for nonspecialist readers. It promises to present material written by linguists (not just language mavens like Safire) in an accessible manner.

I had no idea that there were four distinct ways of saying ’10:15′ in German, or that they divided so neatly along well-defined isoglosses (lines marking distinctions in language). In North American English there would be similar, geographically-delimited variability but not for 10:15, but rather 10:45. Do you say ‘quarter to eleven’ or ‘quarter of eleven’?

Finally, as someone who has sent out two articles in the last ten days and desperately hopes not to get rejected, here is the Journal of Universal Rejection, the world’s most selective (and thus best) journal, with a 100% rejection rate. At least they promise to be prompt!

Numeration and Numeracy in Cognition, Language, and Culture

Last month, at the Society for Anthropological Sciences annual meeting in Charleston, SC, I organized a panel of some really interesting material on the broad topic of numeration. I want to take this opportunity (again) to thank all the presenters for their attendance and hard work. The abstracts (as also published in the conference program) were as follows:

Toward a cognitive, historical, linguistic anthropology of numerals
Stephen Chrisomalis (Wayne State University)

For over a century, the study of numeration, number systems and allied topics has been a key part of the comparative study of thought, language, and culture. The anthropology of numbers and mathematics has traditionally been a locus for unilinear evolutionary thought linked to notions of primitivity. The papers in this panel constitute a call for a culturally-grounded cognitive science of numeration within four of the disciplines of cognitive science (anthropology, linguistics, philosophy, and psychology).

Recent research in language evolution, linguistic relativity, and cultural aspects of mathematical cognition draw attention to the need for anthropologists to re-engage with this new agenda. First, the cross-cultural study of numerals allows the investigation and evaluation of universal and particular aspects of numeration and their relationship with social organization. Because numerals have multiple modalities (e.g., verbal, graphic, gestural), examining patterns in number systems beyond linguistics allows us to evaluate to what extent number concepts can be separated from language, including universal grammar. Finally, just as the cognitive anthropology of plant and animal taxonomy contributes to ecological and environmental anthropology, the cognitive anthropology of numerals and mathematics underpins economic anthropology and the anthropology of science.

Spatial-numeric associations in literates and illiterates
Samar Zebian (Lebanese American University, Beirut Lebanon)

Several independent studies have reported a cognitive association between small numbers and the left side of space and larger numbers andthe right side of space among individuals who read and write from left-to-right (SNARC effect). These associations are reversed for individuals who read and write from right-to-left. The SNARC effect has widely been taken as evidence that numbers are conceptualized as points along a mental number line, however there is growing evidence that this systematic spatial performance bias related to writing directionality is an instance of strategic processing rather than a reflection of inherent spatial attributes of numbers. In an attempt to explain the “deeper” origins of these associations researchers are examining the linkages between number and finger counting. The current study examines whether finger counting practices reveal consistent spatial-numeric associations and whether there are any spillover effects to other tasks that involve object sorting and counting and other non-counting but quantitative tasks such as line bisection and speeded parity judgment. If, in fact, finger counting practices and not the directionality of writing set up spatial-numeric associations than we should be able to observe the same type of spatial biases in literates and illiterates. Preliminary evidence suggests that the finger counting practices of literates and illiterates are not same and furthermore that the spatial biases found in finger counting are not observed across tasks.

Zero’s beginnings: the Mayan case
John Justeson (SUNY, Albany)

This paper addresses linguistic and (Mayan) historical evidence concerning the origins of a numerical concept of zero. Comparative linguistic evidence suggests that zero is not part of basic numerical cognition; rather, it develops out of computing practices of mathematical specialists. Specifically, while zero is often assumed to be prerequisite to the invention of positional notation, it seems on the contrary to emerge as a notational device within such systems. This is clearly the case in Mesoamerica. A system of place-value notation arose in Guatemala and Mexico among Mayans and epi-Olmecs by 36 BCE, with no symbol corresponding to a zero coefficient. Although data is limited, circumstantial evidence is consistent with the following scenario for the emergence of a numerical zero: Mayan calendar specialists developed discourse practices, associated with calendrically-timed ritual events, that used the word “lacking”; the associated dates were represented in a new, non-positional system of notation, which replaced positional notation except in calculating tables; the sign for “lacking” was transferred from the new notation into these tabular positional notations; as a side effect of the algorithms that specialists used to add and subtract positional numerals, the “lacking” symbol was reinterpreted numerically.

Methodological reflections on typologies for numeral systems
Theodore R. Widom and Dirk Schlimm (McGill University)

Past and present societies worldwide have employed well over 100 distinct notational systems for representing natural numbers, some of which continue to play a crucial role in intellectual and cultural development today. The diversity of these notations has prompted the need for classificatory schemes, or typologies, to provide a systematic starting point for their discussion and appraisal. In the present paper we provide a general framework
within which the efficacy of these typologies can be assessed relative to certain desiderata. Using this framework, we discuss the two influential typologies of Zhang & Norman and Chrisomalis, and present a new typology which takes as its starting point the principles by which numeral systems represent multipliers (the principles of cumulation and cipherization), and
bases (those of integration, parsing, and positionality). We argue with many different examples that this provides a more refined classification of numeral systems than the ones put forward previously. We also note that the framework can be used to assess typologies not only of numeral systems, but of many domains.

Social relationships as a lexical source for numeral terms in Amazonia
Cynthia Hansen and Patience Epps (The University of Texas at Austin)

Due to the relatively high degree of etymological transparency found in the numeral systems of Amazonia, it is possible to see the range of lexical sources from which the numeral terminology emerges. In this paper, we present the range of strategies used to create numeral terms below 5, based on an extensive survey of the numeral systems of close to 200 Amazonian languages conducted by the authors. More specifically, we discuss a strategy that is well-attested in Amazonia but that is not attested elsewhere in the world: a ‘relational’ strategy where terms for 4 (and sometimes 3-10) are built using a social relationship term, such as ‘sibling’ or ‘companion’. We propose that this strategy mirrors a gestural counting strategy found throughout the region where fingers are grouped in pairs.

Cultural variation in numeration systems and their mapping onto the mental number line
Andrea Bender and Sieghard Beller (University of Freiburg)

The ability to exactly assess large numbers hinges on cultural tools such as counting sequences and thus offers a great opportunity to study how culture interacts with cognition. To obtain a more comprehensive picture of the cultural variance in number representation, we argue for the inclusion of cross-linguistic analyses. In this talk, we will briefly depict the specific counting systems of Polynesian and Micronesian languages that were once derived from an abstract and regular system by extension in three dimensions. The linguistic origins, cognitive properties, and cultural context of these specific counting systems are analyzed, and their implications for the nature of a (putative) mental number line are discussed.

From ancient to digital archives

Belatedly, I note that Numerical Notation features prominently in the annual report of the Persepolis Fortification Archive Project published online last month (the section on my book is near the end). Matt Stolper, the head of the project, graciously gave me permission to reprint the Old Persian cuneiform tablet Fort. 1208-101 in my book, as it features the first evidence of the Old Persian numerals for the higher hundreds (in the numeral phrase ’604′), and is the only known Old Persian document that serves an administrative function. Ultimately, the tablet was chosen by my editors to grace the extremely attractive cover.

Stolper alludes indirectly in the report to the serendipitous inclusion of this tablet in my research. I’ll be more direct: online publication and open access to the research findings of the Archive are the only reason I was able to integrate this important artifact into my research, at what was a fairly advanced stage of publication. If Stolper and his co-author Jan Tavernier had not published their findings directly online (Stolper and Tavernier 2007), enabling me to rapidly track it down once the media began to report on the tablet’s analysis, I could never have discussed it. (I should also give full credit to my wife, who first alerted me to the news articles on Fort. 1208-101). There are other arguments, such as cost, in favour of this model of publication, but access and speed – especially in fields like this, where data can lie unpublished for decades – are absolutely critical.

Romeyka

Happy New Year! I’m not a believer in new year’s resolutions but I do intend to post more frequently here over the next couple of months, at least with news items of interest.

Check out this interesting article in the Independent yesterday presenting Ioanna Sitaridou’s claim that Romeyka, an endangered dialect of Pontic Greek still spoken by around 5000 Muslim Greeks on Turkey’s Black Sea coast, preserves features of archaic Greek not known in any other modern variety. For instance, Romeyka preserves the use of the infinitive in various contexts in which you would never find it in standard Greek, or (apparently?) even in the Pontic Greek spoken in Greece and the diaspora. Sitaridou is completely correct in noting,”What we don’t yet know is whether Romeyka emerged in exactly the same way as other Greek dialects but later developed its own unique characteristics which just happen to resemble archaic Greek.” There doesn’t appear to be a formal publication associated with this article, but I’ll be looking out for one.

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.

Search results

I’ve been playing around with the Google Books Ngram Viewer amidst grading and procrastinating from grading. Here are a few interesting results (along with the corpus and date range for each). Any others you can find?

soda vs. pop, American English, 1900-2008
sneaked vs. snuck, English One Million, 1800-2008
douche, English One Million, 1800-2008
milliard, British English, 1940-2008
encyclopedia vs. encyclopaedia, American English, 1800-2008 vs. encyclopedia vs. encyclopaedia, British English, 1800-2008

Two new tools

Over the past couple of days, two remarkable new tools have become available for social scientists of all stripes who are interested in visualizing data.

The New York Times Mapping America project uses data from the Census Bureau’s American Community Survey of 2005-2009 to give a block-by-block visualization of the ethnic composition of census tracts and individual neighbourhoods down to the block level. As someone who works in Detroit, by most accounts the most segregated city in the country, this is a really neat tool, especially for teaching purposes, to discuss how ethnic separation emerges, and where it doesn’t.

Then Google released its Books Ngram Viewer, which allows you to trace and compare the relative frequency of words or phrases in any of ten subsections of the total Google Books corpus of over five million volumes. If this had existed a couple of months ago I would have had all my students hunting through this like mad for their Lexiculture projects (along with existing corpus data like COCA and COHA, which are, for all their scholarly value, much smaller bodies of text).

Check them out, and let me know what you think.

As I was going through the Times…

Recently, there has been a “Puzzle Moment” in the science section of the New York Times, with an eclectic mix of articles combining scientific pursuits with cognitive and linguistic play of various sorts. One that caught my eye is ‘Math Puzzles’ Oldest Ancestors Took Form on Egyptian Papyrus’ by Pam Belluck [1], which is an account of the well-known Rhind Mathematical Papyrus. The RMP is an Egyptian mathematical text dating to around 1650 BCE, and is one of the most complete and systematic known accounts of ancient Egyptian mathematics. It’s a fascinating text, written in the Egyptian hieratic script rather than the more famous hieroglyphs, and it gives us considerable insight into the economy, social organization, and technical practices of the Second Intermediate Period.

The central conceit of the Times article is that the well-known “As I was going to St. Ives” poem-puzzle has its earliest ancestor in the RMP. This is vaguely true in that the RMP has a section involving repeated multiplication by seven, resulting in an addition problem. But Ahmes the scribe, despite his insistence that his text would reveal “obscurities and all secrets”, was not writing a mystery, but an exercise that formed part of scribal training, in an era where the literacy rate was at most 1-2%. While one can argue fairly that this is not a ‘real’ problem, and that the structure of it is meant to hold the learner’s attention through its repetitions, to call it a puzzle is only true in the broadest possible sense.

I’m a professional numbers guy, not an Egyptologist, but the article we are presented with not only tells us nothing new about the Rhind. I was very pleased, on the one hand, to see Marcel Danesi, whose work may be familiar to many readers of this blog, commenting on the widespread cross-cultural and cross-historical interest in puzzles (not only numerical puzzles, but including them). It’s not often enough that linguistic anthropologists get quoted in the Times. And like Danesi, I have broadly universalist sympathies. But I disagree with Danesi, who has made this claim about the RMP elsewhere, in his The Puzzle Instinct (Indiana, 2004, pp. 6-7) that it was “shrouded in mystery” or that “mystery, wisdom, and puzzle-solving were intrinsically entwined in the ancient world.”

The better example of numerical play in Egyptian scribal traditions mentioned in the Times article is the Horus eye, or wedjat, a combination of six symbols whose constituent parts signify the fractional series {1/2, 1/4, 1/8, 1/16, 1/32, 1/64} which when summed totals 63/64, or nearly one (see below). As the Egyptologist Sir Alan Gardiner reckoned it, the remaining 1/64 would be provided by Thoth who would heal the Eye and thus produce unity. It’s a nice story, and at least at some periods or for some writers, this narrative may have been relevant.

Source: wikimedia.org

But the Horus-eye illustrates one of the central problems in the transliteration of Egyptian texts, namely that while the vast majority of Egyptian mathematically-relevant texts are written in the cursive hieratic script, they are transcribed, and all-too-frequently theorized, as if they were hieroglyphs. This transcriptional practice leads us to think of the Rhind as a hieroglyphic text that just happens to be in hieratic in the original, but in the case of the Horus eye it couldn’t be more misleading. The Horus symbols in the Rhind don’t look like the above image, and more generally, the hieratic numerals look nothing like, and behave nothing like, the hieroglyphic numerals. We now call of these six Horus eye components by the less evocative name of ‘capacity system submultiples’ in recognition of the fact that these components were originally nonpictographic, part of a metrological system of grain measurement, and only at a much later date were they composed into the wedjat-eye. This isn’t to say that the Egyptians weren’t numerically playful, but they weren’t especially playful in the Rhind.

In short, the RMP is not an especially good example of numerical play in Egypt, and certainly not an especially relevant example from a cross-cultural perspective. It illustrates, to be sure, that mathematical texts are not purely functional or economic documents, but include semiotic and linguistic elements far beyond their pragmatic use. But this is not new knowledge about the Rhind or about mathematics. And it runs a grave risk of othering a document whose function was largely pedagogical, and is thus not so different than, for instance, the ‘ready-reckoners’ of early-capitalist sixteenth-century England.

I am thrilled to see numerical texts treated as objects of inquiry beyond the facile ‘Did they get the answer right?’ I am sympathetic to Danesi’s claim that puzzles and riddles have universal salience. Yet I worry that, at least in the case of the Rhind, the link to puzzle-like behavior is so far-fetched that it turns our best glimpse into Egyptian sociomathematical practice into an inappropriately arcane and obscurantist account. This ‘mysteries of lost Egypt’ nonsense should have been set aside decades ago.

If you wanted to pull out some cross-cultural examples of numerical play, you could easily find lots of better examples, from well-covered territory such as Hebrew gematria practices, to the richly evocative varnasankhya systems of number-word associations in premodern South Asian texts, to the complex cluster of quasi-cryptographic numerical systems used by Ottoman administrators and military officers. Or if you were really stuck on Egypt, you could investigate the cryptic numerals used on late Egyptian votive rods and Ptolemaic inscriptions, richly infused with homophony. (For a more extensive discussion of these and others, see my Numerical Notation: A Comparative History (Cambridge, 2010). There is a rich, although disciplinarily diverse, comparative body of material on numerical practices including puzzles, but the Rhind just isn’t part of it.

(Crossposted to the Society for Linguistic Anthropology blog)

Deutscher, Through the Language Glass

Deutscher, Guy. 2010. Through the Language Glass: Why the World Looks Different in Other Languages. New York: Metropolitan Books.

Guy Deutscher’s new book has attracted a great deal of attention among linguistic anthropologists, not least because anthropology is virtually made invisible throughout. It has a few very serious flaws; nonetheless, it is nonetheless the best presentation of a wide range of specialist literature on linguistic relativity for laypeople and introductory students. It should be read widely and critically.

Deutscher begins with four chapters on a particular theme in linguistic relativity, colour terminology, and ends with a fifth chapter on that subject. His approach is historical – many linguists and anthropologists, even ones who know this field well, will find surprising historical tidbits in his narrative. Deutscher takes us from the classical speculations of Gladstone (yes, the same one) through the seminal work of Berlin and Kay, through modern refinements and interpretations. It is not quite an alternate history, but one that notes rightly that interest in the language-cognition interface with respect to colour is a longstanding part of the history of our disciplines, not one emergent from the cognitive sciences in the past half-century. Deutscher’s correct answer is that both perceptual and cognitive constraints are at play – biology does not determine how we categorize the colour spectrum, but neither are we completely free to divide it however we wish. This is not an especially innovative answer, but it is a well-presented one that will appeal to people who are new to this subject.

Chapter 5, ‘Plato and the Macedonian Swineherd’ is both the weakest chapter and the most out-of-place. Deutscher sets up a straw man in claiming that “For decades, linguists have elevated the hollow slogan that ‘all languages are equally complex’ to a fundamental tenet of their discipline, zealously suppressing as heresy any suggestion that the complexity of any areas of grammar could reflect aspects of society” (125). Deutscher tries to resuscitate the idea of different levels of linguistic complexity by rephrasing the question in terms of complexity within specific domains of language. But we’ve known for a very long time that different languages have different numbers of phonemes, or that there are correlations between social complexity and domains like colour terms and number words (a topic sadly neglected in the book), and Deutscher is wrong to imagine an inquisition against the subject. Worse, Deutscher links these ideas to statements such as, “If you are a member of an isolated tribe that numbers a few dozen people, you hardly ever come across any strangers, and if you do you will probably spear them or they will spear you before you get a chance to chat” (115). In so doing he will doubtless reinforce the pervasive myths of primitivity: that small-scale societies are more isolated, more xenophobic, and more violent than larger-scale ones. It is very interesting that smaller-scale societies have smaller colour lexicons than larger ones, but this doesn’t provide an answer. For this reason alone I suspect that I will not give this book to introductory students. Moreover, it is poorly linked to the general theme of the book – it neither advances any particular claim between the relation between language and cognition nor supports the other chapters’ claims. The whole chapter would have been better omitted.

In Part II, ‘The Language Lens’, Deutscher begins by lambasting Benjamin Whorf’s ‘language prison’ model of linguistic relativity in favour of the model proposed by Franz Boas and Roman Jakobson, which emphasized what languages require their speakers to say, rather than the Whorfian question of what they allow or prohibit their speakers from saying. The fact that some languages require one to specify the gender of inanimate objects, or that others require you to note evidentiality when making factual statements (how you know what you know), develops habits of thought that, over time, lead individuals to favour particular modes of cognition over others. He supports this through two newer themes of research – the effects of spatial language on the cognition of the relationships between physical objects, and the role of gender categories in affecting the semantic connotations of inanimate objects. These are well-known fields among specialists, but are presented here in an engaging fashion, allowing novices to experience radically different modes of spatial cognition through the eyes of Guugu Yimithirr speakers of Australia, for instance.

Perhaps the most striking absence for linguistic anthropologists is the complete absence of discussion of a number of central figures in the field, from the early work of Lucien Levy-Bruhl to modern scholars such as John Lucy, Eve Danziger or Anna Wierzbicka, who are neither mentioned nor cited. Through the Language Glass is not, and is apparently not intended as, a full recounting of the history of linguistic relativity concepts, which is fine except insofar as it sometimes claims to be one. Because Deutscher is not, and has no plans to be, a scholar doing original research in this field, he is perceived, rightly or wrongly, as an interloper whose contribution is to summarize the work of others without consulting them. While this is not a mortal sin, one can question his judgement in failing to work with the body of scholars whose work he intends to present to a general audience.

Despite these failings, Through the Language Glass is an engaging presentation of an important theme in linguistics and anthropology. With the exception of one chapter I found it very enjoyable to read and a good presentation of important past and present research, and in particular on the field of colour studies I learned much of the history of the field that I had not previously known. It would be highly suitable for use in undergraduate courses with the caveat that it should be discussed critically.