# Dravidian kinship controversy

(in process) The Generative Logic of Dravidian Language Terminologies - Dwight Read

## Contents

- 1 Wikipedia
- 2 Godelier
- 3 Denial of Dravidian
- 4 Burkhart on Marriage cycles
- 5 Pauline Kolenda statements May 2 2011
- 6 Dravidian Hill Madia helical model
- 7 Vedda matrilineal Dravidian kinship
- 8 Tue, June 15, 2010 1:17 am Subject: Dravidian; From: "Paul Jorion" <paul_jorion@msn.com>
- 9 from Dwight Read - Dwight Read Kariera vs. Dravidian Mon, May 24, 2010 2:49 pm
- 10 References
- 11 Kris Lehman
- 12 Kris Lehman agrees with the viri-sided model for Telegu and Tamil
- 13 Kolenda's data on Tamil ( Nattathi Nadars) agrees
- 14 Dwight Read
- 15 Definitions
- 16 Theorems and proofs
- 17 Diagrams
- 18 Dravidian Kinship
- 19 Off-generation marriage
- 20 Off-generation marriage??
- 21 Kin terms
- 22 References

## Wikipedia

Wikipedia:Kinship_terminology#Discovery_of_Dravidian_kinship_terminology Even/Odd but it could be through males, females, or both (D. R. White)

- Wikipedia:Kinship#Bibliography See Houseman and White 1998a 1998b (White and Johansen not Dravidian)

## Godelier

## Denial of Dravidian

Anthony Good. 1996. On the Non-Existence of Dravidian Kinship.

## Burkhart on Marriage cycles

David, Thanks for this Burkhart reference. I made and attached a pdf and did an analysis. There is one non-uxorisided marriage but the network is perfectly virisided (if marriage partners have a common ancestor, the total number of their female links to that ancestor is an even number). You are the only Dravidian ethnographer of four I have queried who have provided actual data that form marriage cycles (leaving out the Pul Eliya data), which is the only way viri- and uxori-sidedness can be determined. I would note for Ruth that Burkhart only had to find one deep ancestral link from a single wealthy important couple to get closure on generally deeper aspects of the cycles. It is not a complete census that is required to assess the marriage structure. Burkhart finds many cycles, some small, some large: and the most fundamental short-cycle pattern is four-fold, which is what Ruth seems to have. Perhaps Ruth's cycles have no symmetries between pairs in marriage alliances but if so her's is partly a (probably earlier) variant type similar to Burkhart's cycles. Deborah apparently has fuller network data but has analyzed only inter-village marriage frequencies which is uninformative as to Dravidian marriage structure and sidedness. Deb and Ruth: probably you already have this article so this will not be news to you, if so, sorry for the bother. I would be happy to analyze actual data like Burkhart's from any Dravidianist and return a neat diagram that shows cycles and sidedness without having to draw the whole genealogy by hand as did Burkhart.

-- best to all Doug White http://intersci.ss.uci.edu/wiki/pdf/ScanBurkhartLocalCircles1.pdf -- best to all Doug White http://intersci.ss.uci.edu/wiki/pdf/ScanBurkhartLocalCircles1.pdf BurkhartLocalCircles1.pdf

## Pauline Kolenda statements May 2 2011

The reference on mother's sister's marriage is in Goody in the last chapter on India in Ancient Oriental Primitive.

As for mother's brother-sister' daughter (ZD) marriage, as I recall Brenda Beck has an article concerning same, as does Bill McCormack.

- Brenda for the Coimbatore region and
- Bill for some part of Karnataka.
- Tomorrow I'll try to check my files for more specific details. Best, Pauline K>

A couple who confided to me that they were related as mother's brother and sister's daughter were Catholics from Goa. When I asked from what community they had been converted, he said Saraswat Brahmans. Pauline K>

## Dravidian Hill Madia helical model

Grigson (Eg3 Hill Maria Gond 21025 subsistence) "These are not terms that the Madia normally use for themselves. They prefer to call themselves the Gaitha or Koithor." - Ruth Manimekalai Vaz, 2010, p.9. Ruth Manimekalai Vaz (email at kastanet is or was a research student at the Fuller School of Intercultural Studies, Pasadena, California. Fuller Theological Seminary. School of Intercultural Studies ... (626) 584-5200 (800) 235 2222 135 N. Oakland Ave. Pasadena, CA 91182. One of her advisors is Sherwood Lingenfelter. provost@fuller.edu 626-584-5205. PhD, University of Pittsburgh. Probably a student of Murdock.

From: "Woodrow Denham" <wwdenham@gmail.com> Date: Mon, May 16, 2011 3:24 pm To: "Doug White" <drwhite@uci.edu> Options: View Full Header | View Printable Version | Download this as a file | View Message Details

A few days ago, a graduate student sent me a message and a link to her paper that seems to have come from her dissertation.

It is at: http://www.isca.ox.ac.uk/fileadmin/ISCA/JASO/JASO_Jan_2011/Vaz.pdf

I haven't had time to study it yet.

You might want to take a look at it. ... wwd

Ruth Manimekalai Vaz, 2010. The Hill Madia of central India: early human kinship? JASO-online: Journal of the Anthropological Society of Oxford, New Series, Volume II, nos. 1-2: 9–30

Ruth Manimekalai Vaz, 2010. The ‘Big Bang’ of Dravidian kinship, JASO-online: Journal of the Anthropological Society of Oxford, New Series, Volume III, no. 1: 38-66.

## Vedda matrilineal Dravidian kinship

- p60 is Henebedda
- p61 is Sitala Wanniya/Godatalawa

- http://bit.ly/gFjx9z - SCCS 080: Vedda
- http://intersci.ss.uci.edu/wiki/svg/Vedda/P-VeddaUxori-Sides.svg
- http://intersci.ss.uci.edu/wiki/svg/Vedda/P-VeddaViri-Sides.svg
- http://intersci.ss.uci.edu/wiki/svg/Vedda/VeddaMatrilines.svg
- http://intersci.ss.uci.edu/wiki/svg/Vedda/VeddaPatrilines.svg
- http://intersci.ss.uci.edu/wiki/svg/Vedda
- p. 59: "The genealogies ... show the relationship existing between the various individuals of the three Vedda communities, which still retain enough of the old Vedda mode of life to make a study of their organization valuable.... The genealogies show how small are these communities and, since every Vedda should marry a first <cross-> cousin, marriage does little or nothing to enlarge the number of his connections. Further, each of the people with whom he comes in contact is related to in a definite manner and is called and spoken of by a definite kinship term, so that personal names come to play a very small part in the daily life of the Veddas."
- In fact, there are two MBD and one FZD marriages in the genealogy, two of the latter for sisters marrying the same man, and a third of these sisters marrying a brother of this man, technically as FMZSWZ. Of these six marriage, three are with cross-cousins, one with an affinal classificatory cross cousin, and two of sisters with a man who is also an affinal classificatory cross cousin. Technically, although all marriages are with classificatory cross cousins only half (three) are with actual cross cousins.

do not open these:

- http://intersci.ss.uci.edu/wiki/svg/Vedda/P-VeddaUxori-Sides.htm
- http://intersci.ss.uci.edu/wiki/svg/Vedda/P-VeddaViri-Sides.htm
- http://intersci.ss.uci.edu/wiki/svg/Vedda/VeddaMatrilines.htm
- http://intersci.ss.uci.edu/wiki/svg/Vedda/VeddaPatrilines.htm

## Tue, June 15, 2010 1:17 am Subject: Dravidian; From: "Paul Jorion" <paul_jorion@msn.com>

re: 2010 Submitted. Egocentric and Sociocentric Structure in Classificatory Kinship Systems. Mathematical Anthropology and Cultural Theory.

Brilliant paper !

Paul

## from Dwight Read - Dwight Read Kariera vs. Dravidian Mon, May 24, 2010 2:49 pm

Dear Doug,

When a mathematical model captures only some stylized characteristics of some phenomena, such as a “mechanical model” of Dravidian “cross-cousin marriage” preferences, the model does a disservice if it does not also capture the distinctive features of the phenomena modeled. This is where in Dravidian and Australian systems differ. In Australian systems, G+/-2 marriages are a possibility and are actualized, but are not documented as actualized in Dravidian systems; whereas G+/-1 marriages are a possibility and are broadly actualized in Dravidian systems, unlike Australian systems.

You are on the right
track. The mathematical model has to be driven by the ethnographic
facts, not by some idealized or hypothetical system. One of those
facts is the o/y distinction for cross-cousin, which has no explanation
in the logic of the Kariera terminology, hence that fact alone says
there has to be a difference in the generative logic of Kariera versus
Dravidian, and that is precisely what I have demonstrated. Despite
superficial similarity in the two terminologies, they are generated by
different logics.

You write:

The
brilliance
of Dravidian terminology in general is that there is no
kinship term
for wife,
unlike
Australian systems where the kin term used for spouses create a precise
set of
constraints on marriage (see Denham and White 2006). Nänā is not
the term for wife (footnote 8) but may
be used for WZ or BW. [[I couldn't get all of
your text to all appear in blue for some strange reason]]

Very nice -- this is exactly what I have shown. In
Kariera, the generative logic requires a "cross-cousin" marriage term
for a man's wife; in Dravidian, the generative logic implies that
"cross-cousin" marriage is emergent, therefore it is NOT a marriage
rule, but expresses that same generation marriages will, de facto, be
"cross cousin" marriages when marriages are consistent with the logic
of the terminology. Two different generative logics, with very
different implications for cross-cousin marriage, yet both
terminologies appear to be the same -- except that little things like
o/y "cross cousin" and two- terms in +2, -2 generation are not merely
"adjustments" to a Kariera terminology but are indicative of the fact
that we are dealing with a different generative logic that,
nonetheless, leads to terminologies that are very similar.

That Nana is a term that includes WZ, BW (kin type
product) is exactly what the generative logic predicts as can be seen
in my Figure 12(A) (where Sp is actually Wife since the figure is from
the perspective of a male self). The generative logic implies that the
"cross cousin" position labeled Nana will be Daughter of Sister of
Father + Daughter of Brother of Mother + Sister of Husband + Wife of
Brother (using kin term products) or FZD + MBD + HZ + BW (using kin
type products). I didn't fully appreciate the importance of what I
demonstrated through working out the generative logic of the Dravidian
terminology until I read your above comment! (By the way, your figure
1 for nana and massina is from the perspective of a male self; one can
also express nana and massina from the perspective of a female self as
shown in my Figure 12(B), where we would have HZ instead of WZ for
Nana.)

My intuition is that the whole matter of cross versus
parallel can be made far simpler now that we have the generative logic
for the Dravidean terminology; rahter than trying to express X and //
genealogically (which is not incorrect -- it just makes it more
complicated than it need be, I think) we need to see how to express it
from the viewpoint of the generative logic of the terminology. That's
why I keep pushing for trying to get the notion of sidedness clear and
how that relates to X and // and the terminology generative logic.

## References

### A Type case?

- David West Rudner. 1994. Caste and Capitalism in Colonial India: The Nattukottai Chettiars. Berkeley · Los Angeles · Oxford. UNIVERSITY OF CALIFORNIA PRESS. E-Books Collection.

- Nakarattar kin terms 31c. acci makal oZD

"Caste and Capitalism in Colonial India" http://iimk.ac.in/gsdl/cgi-bin/library?e=d-000-00---0sociol--00-0-0--0prompt-10---4------0-1l--1-en-50---20-about---00031-001-1-0utfZz-8-00&cl=CL2&d=HASH322bad8064c4bf17402365.7>=1

Review of "Caste and Capitalism in Colonial India"

### Tamil

Vikash Pandey. 1994. Agrarian Transformation and Co-operatives: Continuity and Change. Economic and Political Weekly. April 9.

## Kris Lehman

Doug, I would like you to explain a bit more clearly to me what is meant by the distinction between uxori~viri- sided. In your very useful Comment thing on the Barbosa paper I still find this pair of terms just a bit unclear. Sidedness, of course,I understand fully --- your reference to my communication on the matter makes that clear. But these two new terms are only explained obscurely in the caption to figure-1. Yes, "uxor' is Lain for wife, and viri is the Lain root form of the word for a man/husband. But I am still a bit uncertain about these two for kinds of sidedness.

Thanks, Kris

F. K. L. Chit Hlaing Emeritus Professor Department of Anthropology University of Illinois at Urbana-Champaign

### Answer and a question from Doug

In a kinship network of the Weil type where nodes are marriages then links between nodes or marriages are either husband (male) to parents or wife to parents (female), i.e., two kinds of links - male or female.

In a viri-sided network you can separate all the male links into two sides, and there will be female links between the sides. When female links can be split into two sides, and there will be male links between the sides.

If cycles exist in the network, viri-sided implies an even number of female links in each cycle; uxori-sided implies an even number of male links. These even number of links keep the two sides distinct.

If two strangers meet it a viri-sided network they can ask each other "do we have any ancestors in common? If yes, are there an even number of female links in the chain from x to ancestor back to y. If so: we're viri-sided. If we count the number of male links and its an even we're uxori-sided.

Typically a South Indian society with Dravidian terminology will ask only one of these two questions (Pul Eliya: virisided only among consanguineals).

ASKING YOU as an ethnographer: which is it for societies you know? It could be both if that is encoded rather strictly somehow in the Dravidian terminology. But even at +2 -2 levels there is no sidedness. Its usually only in the 0,+1,-1 generations. So to find a society like Pul Eliya thee has to be something more at work for consanguineals to be viri-sided.

Viri refers to male links, uxori to female links.

## Kris Lehman agrees with the viri-sided model for Telegu and Tamil

Thank You. Your definition of viri and uxori sidedness is clear now and makes sense to me. Pul Eliya (Sinhalese) is strange. I understand Telegu and Tamil systems better. And there the sidedness is calculated, so to say, from an agnatic standpoint.So it is female links (mothers of male ascendant) that one looks for. -- F. K. Lehman (F. K. L. Chit Hlaing) Professor Emeritus Department of Anthropology University of Illinois at Urbana-Champaign

1993 The Relationship between Genealogical and Terminological Structure in Kinship Terminologies, Journal of Quantitative Anthropology 4: 95-122.

Pauline: for Tamil (nadu means "place")

- With respect to your question. If I understand what you are asking. Yes, the Nattathi Nadars of southernmost Tamilnadu whom I recorded as a caste knew who the appropriate mate was for a marriageable youth. They had terms that translate as 'proper girl' and 'proper bridegroom'. These would be cross-cousins.
- Most marriages in India are arranged by parents or elders, not by a couple themselves. So let's say the two sets of elders know that the two fathers had a common ancestor a few generations back. Among the Nadars, Saiva Pillais and other castes of southern Tamilnadu where I did fieldwork, there were patrilineal names called indi Peers. If the two families had the same inti peeru, then the children should not marry. With cross-cousin marriage, the bride and groom always have different indi peers. So if they had different indi peers, the children could marry. There are many paths back to a common ancestor. The indi peeru path is in a strict male line, only one out of several possible paths back to a common ancestor.
- With respect to the question of whether the common ancestor would be the same number of generations up for both bride and groom, quite often not. Actually, I used to have fun figuring out how a couple were related a number of different ways.
- Did a bride and groom with the same indi peeru ever marry? I think not. Quite frankly I have not been deep into these data for quite a long time. The last couple of years I have been working on north India field data that I had not analysed. But I do recall coming across marriages that were not murai (proper) when I was working on the south India caste/marriage network. Right off hand, I don't remember why they were not murai.
- No, with respect to Trautmann or others. Ever since I completed the project in the mid-1990's I have been at a loss to know how to publish such voluminous data or how to summarize it.

## Kolenda's data on Tamil ( Nattathi Nadars) agrees

Dear Douglas White,

You asked in your first email early in June what terms were used for husband and wife among the Nattathi Nadars. I think most common would be purusha (man) and penjadi (woman, wife). My Christian Nadar research assistant from the nearby town of Nagercoil did refer to her husband as 'attan' which is equivalent to older male cross-cousin, but I don't recall the NNs using cross-cousin terms for spouses. A local NN research assistant used purusha and penjadi.

Over the past few days, stimulated to do so by your queries, I did unpack the boxes of the NN study. As I mentioned to you, I thought I was studying a caste, supposedly an endogamous group. Almost half of the Kanyakumari District caste of NNs I believe were located in one town, the rest in 15 "villages" in the region. I hesitate to say how many - perhaps 3500 living persons as of 1993 and including ancestors and forebears about 1000 families. Of course, the KK NNs had relatives who had gone out. Those I also recorded.

Quite frankly, rifling through the charts, I don't see much cross cousin marriage. Here are some marriages. You asked if there were couples who had ancestors back different numbers of generations. One man married his father's mother's brother's son's daughter's daughter (DRW: FMBSD viri and uxori-sided G0). Some second cousin marriages were a man marrying mofabrosoda, momosisoda (DRW: MFBoSD MMZSD - G0 same generation dual sided).

**DRW: These marriages are all dual sided in G0 but the ZD marriage**
is consistenti with viri-sidedness in G+/-1 marriage. There is no
evidence that contradicts viri-sidedness.** **

There may be some instances of FZ marriage, but this was not preferred. I remember William McCormack found MyB/eZD marriage in Karnataka, and I may be wrong but I thing Scarlett Trent Epstein also found it in Karnataka.

It's probably possible to trace back for relatives in the past, since I seem to have analyzed some 32 genealogies, several going back into the 1800's. The furthest back is 1800, a couple who had over 900 descendants.

I have read you 1999 article, but don't completely grasp it. When you talk about relinking, do you mean a couple have a common ancestral couple? All for now. Best, Pauline K

Right now, I have relatives visiting, but next month I'll try to do some reading as you suggested and also look more at the KK data to see where I think they might fit. With respect to cross-cousin marriage, the NNS themselves, I believe, think of it as marriage between the children of brother and sister. So for esample, if two sisters have children of opposite sex, the sons of sister A are considered to be brothers to the daughters of Sister B. So the Asisoson may marry Bsidada and that would be considered a proper marriage of the children of bro and si.

Interesting idea of marriage between strangers within a long-

time endogamour population such as the NN caste. How distantly related would a couple have to be to be considered strangers?

Thanks very much for contacting me. More later. Best, Pauline K

>> Dear Douglas White,
>> As I emailed you yesterday, I did manage to get your comment on
>> BdeA paper printed out. It makes me aware that there has been a
>> considerable discourse going on with respect to Dravidian kinship.
>> I probably need to be much more versed in the issues being
>> discussed. So thank for the readings you suggest. The problem that
>> I had with the network book of yours and the anthropologist from
>> Cologne was that I could not understand many of the diagrams and
>> references to graph theory. If I don't sound too intelligent about
>> that book, it's because I read a library copy quite some time ago
>> and no longer have it.
>> You encourage me when you say that Leach's and mine are the only
>> field surveys of Dravidian kinship. Mine is quite a bit larger than
>> his. I did not think of myself as doing a survey of Dravidian
>> cross-cousin marriage but rather I was trying to document an entire
>> caste, an endogamous group.
>> All for now. Best, Pauline K
>
> So much the better. My fairly new findings on sidedness, if they apply,
> should make that task easier. There should be locatable subsets in which
> marriages are with consanguineals and the group forms a cohesive set,
> within which there is sociocentric sidedness.
>
> I had no idea of this kind of structure when we met, my first inkling was
> the 1999 paper.

## Dwight Read

### Thu, April 29, 2010 11:56 pm Dwight Read

With regard to BdA, his algebra of kin types generates four categories of kin types in +2, -2 generation of necessity due to it being an algebra and there is no structural equation that simplifies any of the +2 -2 products (other than products such as ffb = ff (kin type products) from the classificatory equations expressed using kin types). So formally he is correct to have four +2, -2 generation terms in his algebra. But that's simply due to a decision in the formalism not to have any structural equation at the +2, -2 generation.

The basic generative logic of Dravidian that I worked out is in partial agreement in the sense that one ends up with four kin term (not kin type) products FF, FM, MF and MM so long as there are no structural equations that reduce any of these products. However, it is equally clear that is a lineality pattern (see center part of Figure 1A and 1B and Figure 12A and 12B) that runs from -1 to +1 generation and if that pattern is extended to +2 and -2 then one will have the equaitons FM = FF and MF = MM (kin term products).

Evidently some Dravidian terminologies have used one idea for +2, -2 generations and so have four +2, -2 terms, and others have used the the second idea and have two +2, -2 generation terms.

I don't think we can say, on formal grounds alone, that one terminology form or the other is the "real" Dravidian terminology. Both are equally "real". Nor is it immediately evident that one or the other terminology form is derived from the other; there is the possibilty that there are two root proto-Dravidian terminologies.

Analytically we can imagine changing one into the other -- if there are two terms, bifurcatge them into four terms and conversely if there are four terms, collapse them into two terms. But this ignores the ramifications that the logic leading to two terms has for the terminology as it plays out against marriages and how that structures the society (here I'm thinking that this may be where your ideas of sidedess come to the fore -- how does sidedness play out with one terminologial form versus the other?), hence from a pragmatic, on the ground perspective, changing from two to four or from four to two may have radical implications for how the whole system actually works out, hence is improbable.

This is speculation on my part, but I think we (generic we, not any particular we) need to get a better handle on how the whole system works and the interconnections between various parts and how these interconnections act as constraints on posssible changes that my not be evident when one focuses on just one part. (This comment reinforces arguments you have made about the fact that some unnamed theorists have treated their kinship diagrams as if they are equivalent to what folks actually do on the ground.) This is where, I think, one runs into problems with assuming "x-cousin" marriage rules translate into isomorphically constructed marriages on the ground," without first working out the logic behind the "x-cousin" marriage rule. Intuitively it seems to me that an emergent marriage rule (emergent from the generative logic of the terminology) acts as less of a constraint than a marriage rule that is intergral to the logic of the terminology. For this reason, the Dravidian "X-cousin" marriage rule may allow for variants such as eZD (kin type products) since it is consistent with the "//" / "x" division of non-marriageable, marriageable and that seems to be the fundamental constraint, not that the marriage has to be with "X-cousin". That is, the rule in Indian Dravidian systems is more of the "marry your 'X-cousin'" with a but: "but marriage with other kin relations is possible if circumstance warrant it, though the marriage must be consistent with the marriageable/non-marriageable dichotomy." A marriage with a non "X-cousin" does not violate the generative logic, per se. It only violates the emergent "X-cousin" marriage rule.

Does this make sense?

### Wed, April 28, 2010 11:51 pm Dwight Read

From: "Dwight Read" <dread@anthro.ucla.edu>

Just to add a bit more to my previous email. If you look at Figure 1 in the Polynesian paper, I'm using the idea of a family space with concepts that are broad and perhaps best described as intuitive (mother, in a broad sense, not mother in the specific sense of genetrix, for example) and how genealogical space and kin term space are derived from this (and hence their interconnection). I include the concept of marriage via spouse; however, if one adds a "marriage space" as conceptually mapping to family space and from marriage space one has its expression in actual marriages, we would now have a link to the network analysis of marriages and could begin to work out more fully how these cultural spaces are conceptually interconnected and how that relates to behavior "on the ground" and conversely.

On 4/28/10 1:50 PM, drwhite@uci.edu wrote: Doug,

> >> Doug, >> I think we're talking past each other. >> > I don't think so but thanks for taking my point about the Telugu. What is > the reference for the Nakaratta? Is the case discussed in Trautmann and if > so, where? I do think you can see the point, even if you are not dealing > with it, that if an actual marriage network is viri- or uxori-sided, and > if actual marriages are viri- or uxori-sided a comparison can be made with > the terminology. There is a book by Rudner reviewed at > http://cis.sagepub.com/cgi/reprint/31/1/147.pdf. I don't see anything > about Nakarattar in the Trautmann index. > > >> First, a correction. I mistakenly said I was working with the Telegu >> terminology -- that's not correct. The terminology is the Nakarattar >> terminology since it has a structure that Trautmann identifies with >> proto-Dravidian. The attached file has the right name for the terminology. >> Second, the paper proceeds from the question of how we can structurally >> account for older/younger distinction in cross-cousin terms, a >> distinction that does not occur in Kariera, the Polynesian terminologies >> etc. So the paper is primarily addressing that question and in so doing, >> identifies a structural basis for the o/y x-cousin distinction that then >> distinguishes it from the Kariera terminology and a different logic by >> which one has a x-cousin marriage rule. >> >> I am not dealing with whether marriages will be viri- or uxori-sided, >> but just with the structure of the terminology. >> Cheers, >> Dwight >> >> On 4/28/10 10:29 AM, drwhite@uci.edu wrote: >> >>> In taking as a type-case for Dravidian a stylized case like the Telugu, >>> you run a great risk of inaccurate ethnography as to the terms and the >>> marriages. The terminology is given as a mere side-note in Tyler's >>> (1966) >>> Koya terminology paper (Trautmann p164). Then, of the Koya, Trautmann >>> p188 >>> of Tyler 1966 and 1968 "which must be taken together" (which indicates >>> that bits and pieces are missing in each case) he says "The paradigms in >>> both have been models for my own in positive and negative ways, FOR BOTH >>> CONTAIN OBVIOUS ERRORS.... My representation of Tyler's data, Fig. 3.31, >>> TAKES THE LIBERTY OF PUTTING THEM INTO THE TRANSCRIPTION SCHEME FAVORED >>> IN >>> THIS BOOK." >>> >>> Thus, I can't have any confidence in anything you say about Telugu as >>> based on real data about a Dravidian case accurately described, so as to >>> be able to distinguish viri-sided terminologies vs. uxori-sided vs. >>> Trautmann-sided. >>> >>> In our analysis of the Pul Eliya case (which is not typical Dravidian >>> according to Trautmann) we reconcile the terminology (which is very >>> simple) and which marriages are consistent with the terminology and with >>> viri-sidedness: 100% for marriages among consanguineals, including >>> marriages that are not same generation but that are viri- and not >>> uxori-sided, with all the exceptions to viri-sidedness for marriages >>> that >>> are not between consanguineals. >>> >>> Note that for each of S. Kanara Jain p165, Telugu p.66, and, Koya p189 a >>> male’s BD is parallel, and where reported a male’s ZD is cross. This is >>> true for viri-sidedness but not for uxori-sidedness. (S. Kanara Jain has >>> no report for a male’s ZD.) Throughout the ethnographic corpus cited by >>> Trautmann BD marriages are not reported but ZD marriages are not >>> infrequent. This speaks ill for Trautmann model of Dravidian. >>> ---------------------------- Original Message >>> ---------------------------- >>> Subject: Generative logic of Dravidian terminologies >>> From: "Dwight Read"<dread@anthro.ucla.edu> >>> Date: Tue, April 27, 2010 11:59 pm >>> To: "Doug White"<drwhite@uci.edu> >>> -------------------------------------------------------------------------- >>> >>> Doug, >>> I'm attaching a paper I just finished (submitted to MACT) that works out >>> the generative logic of Dravidian language kinship terminologies (I use >>> the wording deliberately since one of my findings is that there are >>> significant, deep structure differences between terminologies such as >>> Kariera and the kinship terminologies used by Dravidian speakers in >>> India). It all works out very neatly and gives as a nice way to >>> distinguish between classificatory terminologies that occur in the >>> Polynesian area (including the Trobriand terminology and undoubtedly >>> others), the classificatory terminologies that occur in Australia for >>> which Kariera is a canonical example, and the classificatory >>> terminologies used by the Dravidian speakers in India. Each is >>> generated by a different solution to the same task: connect disjoint >>> structures of male marked terms and female marked terms into a single >>> structure. (This task also arises in the domain of descriptive >>> terminologies with "hyperdescriptive" terminologies such as the Polish >>> terminology, but there it is done though connecting male self and female >>> self as husband and wife.) >>> >>> Separately, to avoid excessive length of attachements, I am sending a >>> paper that I also just finished that will be published as part of a book >>> based on a workshop held last summer on looking at kinship terminologies >>> from a historical perspective. I work out a proto-Polynesian >>> terminology based on changes in the structure of polynesian >>> terminologies. This has the implication that the standard >>> proto-polynesian terminology based on changes in the word-form of kin >>> terms is actually just a proto-terminology for East Polynesia. >>> >>> In this paper I lay out more completely that I have in other papers the >>> conceptual basis I see for kinship systems as a whole from which one >>> derives both the genealogical space and the kin term space, with the >>> latter two coming together through genealogical instantiation of the >>> generating terms for the kin term space. I show that recursion is the >>> basid operation that generates the genealogial space and concept product >>> in the form of kin term products is the basic operation that generates >>> the kin term space and both operations are an interpretation of >>> "intuitive" concepts about mother, father, husband and wife that are >>> intergral to what, culturally is meant by "family" as a distinct social >>> unit. >>> >>> Any comments would be much appreciated. >>> >>> Dwight

## Definitions

- Kinship in André Weil format. Weil undertook "to show how a certain type of marriage laws can be interpreted algebraically, and how algebra and the theory of groups of substitutions can facilitate its study and classification" (Weil 1949, in Levi-Strauss 1949, English translation: p. 221). His elements for these algebraic groups are types of marriages. The operators are links from one marriage type to another following gendered (♂,♀) parental (P) and progeny (p) links. Thus each marriage type x is linked to a different marriage type y by either a directed male ♂ link or a directed female ♀ link. If the set links (♂,♀) between marriage types is a permutation of these types then the marriage network constitutes an algebraic group. If in addition each marriage type has an outgoing (♂,♀) link then the marriage network constitutes an algebraic kinship group. (The same mathematics can be used for marriage networks where the elements are the individual marriages and the links are to parental marriages, even if the resultant structure is not an algebraic group but a special kind of directed asymmetric graph (DAG), called a P-graph, in which individuals have no more than two parents and no marriages are same-gender pairs.)
- P-graph. Here, following Weil (1949), but for concrete marriages rather than marriage-types, "let the number of types of marriages be n", and let each marriage be numbered from 1-n, as distinguished in Fig. 1, where ♂ links (and descent lines) are shown in black and ♀ links in red. (In a P-graph there are only links between parent and a male or female child, and many of the nodes will represent marriages or couples with children. These will have two parental links, one male pointing to the husband's parents, the other female pointing to the wife's parents. Some nodes may represent unmarried children with but a single parental link according their gender.)
- Pajek or P-graph generations. The P-graph is a directed asymmetric graph (DAG) with generations equal to the length of the longest directed path, which insures that every generation will have at least one parent in the preceding generation.
- Sides and sidedness. These are implicit moiety structures in the marriage network. Here, a P-graph can split into two halves, within which nodes are uniquely connected by the links of one gender and between which they are uniquely connected by the links of other gender. (In general, siblings do not all have to marry spouses of the same generation.)
- Viri-sides. Here, a P-graph can be split into two halves, uniquely determined, within which nodes are uniquely connected by parent/son links and between which they are uniquely connected by parent/daughter links.
- Uxori-sides. This is a P-graph that can be split into two halves, uniquely determined, within which nodes are uniquely connected by parent/daughter links and between which they are uniquely connected by parent/son links.
**Canonical marriage generation numbers**. A marriage x has a pair of canonical numbers s and t iff (1) it is on or has paths composed entirely of HZ, HB, WZ or WB links to a marriage at generation s for the longest generations of female lines and t for the longest generations of male lines within the range , i.e., following equivalence of siblings or siblings-in-laws links, (2) all such paths from marriage x has the same canonical numbers s,t for each distinct longest generation of male or female lines, and (3) if the s,t numbers computed for distinct female lines can be aligned for the whole network or a large subnetwork and (4) similarly for s,t numbers across male lines.**This can be done for example, for large subsets Australian section system networks, with a minority of generational assigmments for the sets of siblings differing by two.****Canonical marriage generations**. These exist for a subnetwork if every marriage x has a canonical marriage generation numbers s,t for females and males, respectively.**Alternatively**, if connected subsets of the generations in (1) above have parents in another connected subset of one of these generations, forming in successive generations a large subset of the entire network, these form a subnetwork of canonical marriage generations.- Same-generation marriage rule. A same-generation marriage rule obtains for a marriage P-Graph if it has canonical marriage generations for a large subnetwork.
**Generations for males, generations for females.**Generations for males are counted only for a single apical ancestor and counted in terms of the canonical marriage generation numbers for each marriage in patrilineal succession. Similarly for females. These numbers do not necessarily converge for males and for females, starting from the same ancestor, for a given marriage. E.g., in an Australian section system, starting from a common ancestor, wives of female generation 4 might marry regularly with men of male generation 2, consistent with younger ages of childbirth for females and older average age of fatherhood for males.- Generational moieties can only occur if there are a large subset of marriages that conform to the same-generation marriage rule and all other marriage have a canonical number an even number of generations above or below their canonical number.
- Bicomponent of a marriage network. A bicomponent of a marriage network containing marriages x and y is a maximal subgraph B containing x and y in which for any node z there are two or more disjoint paths between very pair of nodes in B. (All links between the nodes in B that occur in the main graph are by definition also in the subgraph B.)

### Definitions: Marriages and egocentric sidedness

- Consanguineal marriage. A marriage is consanguineal if husband and wife have a common ancestor.
- Consanguineal marriage cycle (CMS). A consanguineal marriage is composed of parental links from husband to a common ancestor and child links to the wife with the a common ancestor.
- A CMC is viri-cross if the F = the number of female links to and from the common ancestor is even, F = even.
- A CMC is uxori-cross if the G = the number of male links to and from the common ancestor is even, G = even.

## Theorems and proofs

### Sidedness Theorems

**Theorem 1**. Every connected consanguineal marriage network with no F = G = odd marriages will be sociocentrically sided.

**Proof of Theorem 1**. I.e., If either F or G = even or both the network will be sociocentrically sided. If F = even then the Hu’s side (parallel kin) will include his patriancestors (PAs) and there are S PA groups including and from the Wi’s PA to new PAs through other maternal links, terminating in Hu and Wi’s common ancestor. Because F = even requires S + S’ = even then if S = even, S’ = even links through daughters and their PAs back to Hu’s PA. If S = odd then S’ = odd. For every j=1,…, S + S’ the j = even PA’s are on the Hu’s side and the j = odd PA’s are on the Wi’s side, so every consanguineal marriage folds into two sides. It follows that because any other consanguineal marriage cycle folds into two sides, any two such marriages having a common member C will fold into two sides, C’s side, and the opposing side. The same proof follows if F = even or F = G = even. That is, egocentric sidedness will produce a consistent sidedness structure between sides. Figure 9-2 in Houseman and White (1998a) for the Makuna is a perfect example for F = G = even consanguineal marriages (100% viri- and uxori-sided), i.e., F = G = even for all these marriages, which also implies they are all same-generation (White n.d.B). For the Makuna F = even with a single (1%) exception among all marriages, including those that are nonconsanguineal. Houseman and White (1998a) found “sided” kinship networks similar to the Dravidianate in Amazonia, and created the percentage measures of the extent to which they were sociocentrically viri-sided, uxori-sided, or both.

**Theorems 2-4**. The presence of both viri-sides (condition V) and uxori-sides (condition V), for a network of consanguineal marriages, logically entails implicit generational moieties (condition M) in a bicomponent of a marriage network. This includes the possibility of an ego at generation marrying someone at where the absolute difference |i - j| ia an even number, e.g., +2 or -2 generations. Further, the presence of a same-generation marriage and either viri-sides and uxori-sides logically entails the complementary type of sidedness.

**Theorem 2**. U and V, and consanguineal marriages => M, including implicit alternate-generational moieties.**Theorem 3**. U and M => V**Theorem 4**. V and M => U

### Proofs

**Proof of 2.**

- Suppose U and V and consanguineal marriages. For a subnetwork in which every marriage is between consanguines (blood marriages), then marriages in which husband and wife have marriage cycles with ancestors that are both U an V, then the cycle will have even number of female links, even number of male links, and an even number of total links. If the ancestral graph is drawn from parent to child in successive generations then either husband and wife are of the same generation or one is an even number of generations above the other. This will apply to all such marriages.
**Q.E.D.**This proof will generalize to Australian section systems.

**Counterexample in the case of nonconsanguineal marriage. **

- Suppose U and V and a network with nonconsanguineal marriages one of which is a man who marries a
**BDHBD or**BDHSD. Then the number of males is even (4) as is the number of females (2), qualifying for U and V but the marriages are not same-generation. (Change in bold)

**Proof of 3.**

- Suppose M. In these cases M may apply so that the generation number of each marriage is one more than the generation number of the parents of the husband and that of the wife. This entails that any marriage cycle will have an even number of links.
- Suppose U and M. U in addition to M requires that any marriage cycles with have an even number of male links, thus an even number of female links in order to add up to an even number of male links. Hence the network is V.
**Q.E.D.**

**Proof of 4.**

- Suppose V and M. Exchanging U and V above: U, V and M entail U.
**Q.E.D.**

Q.E.D.s for theorems and proofs: Doug 18:58, 26 April 2010 (PDT) Validation of date

## Diagrams

- Fig. 1: Viri-sides for a consanguineal group with two sets of non-consanguineals

Douglas R. White. 2010 Letter of comment on Barbosa de Almeida. On the Structure of Dravidian Relationship Systems Submitted to Mathematical Anthropology and Cultural Theory.

## Dravidian Kinship

- Hage, Per 2006. Dravidian Kinship Systems in Africa. L’Homme 117/118: 395-408.

- Abstract. Dravidianate kinship systems based on a rule of bilateral cross-cousin marriage are usually taken as the starting point in universal theories of kinship evolution while Iroquois systems, which lack such a rule, are regarded as devolved versions of Dravidian systems. Dravidian and Iroquois systems, however, have an uneven geographical distribution. The former are well known from South Asia, Australia and America but not from Europe or Africa, while the latter are known from many regions of the world but not from South Asia. The purpose of this paper is to describe a Dravidian kinship system in a Bantu-speaking society and to suggest the presence or former presence of Dravidianate systems elsewhere in Africa.
- (DW: Thus the Dravidianate has more universal distribution regionally, counting African cases.)

## Off-generation marriage

McCormack, William. 1958. Sister’s daughter’s marriage in a Mysore village. Man in India 38(1):34-48.

## Off-generation marriage??

- home: Anthony Good
- Aiyappan, A. 1934. Cross-Cousin and Uncle-Niece Marriages in South India. In Congrès International des Sciences Anthropologiques et Ethnologiques. Pp. 281-282. London.
- Good, Anthony. 1980. Elder sister's daughter marriage in South Asia. Journal of Anthropological Research 36:474-500. http://www.jstor.org/stable/3629617 (Reprinted in S.M. Channa (ed.) 1998. Family and Marriage: a Critical Appraisal. International Encyclopaedia of Anthropology, Vol. 10. Cosmo Publications: Delhi).
- Good, Anthony. 1981. Prescription, preference and practice: marriage patterns among the Kondaiyankottai Marawar of South India. Man (n.s.) 16:108-29. (Reprinted in Robert J. Parkin & Linda Stone (eds.), 2003. Kinship and social organization: a reader. (Blackwell Anthologies in Social and Cultural Anthropology) Oxford: Blackwell: Oxford)
- Good, Anthony. 1985. Markedness and extensions: The Tamil case. Man 20:545-47.
- (With Alan Barnard) Research Practices in the Study of Kinship (ASA Research Methods in Social Anthropology, 2). London & Orlando: Academic Press (1984; paperback 1988).
- Good, Anthony. 1993. On the Non-existence of "Dravidian Kinship." Paper presented for the Maison Suger Conference on Kinship Systems, Paris.
- Tharakan, George C. 2006. Louis Dumont and the Essence of Dravidian Kinship Terminology: The Case of Muduga. Journal of Anthropological Research 62(3): 321-346. http://www.jstor.org/stable/20371028

## Kin terms

## References

Tjon Sie Fat, F. E., and T. R. Trautmann. 1998. On the Formal Analysis of “Dravidian,” “Iroquois,” and “Generational” Varieties as Nearly Associative Combinations. Pp. 59-93, In, Godelier, Trautmann and Tjon Sie Fat (eds.), Transformations of Kinship, Washington and London, Smithsonian Institution Press

Trautmann, T. R. 1981. Dravidian kinship. Cambridge: Cambridge University Press, 1981.