Diagrams bearing gifts

The title of this post arises from remembering about a one-time colleague who used to talk about non-information bearing diagrams. The post itself being a development of references 1 and 2.

The snap above being derived from a figure in the appendix of reference 3, reference 3 being a doctoral thesis which looks again at the myth described by Lévi-Strauss at reference 4. What exactly is the structure that Lévi-Strauss and his followers were so keen on?

The starting point

The starting point is an ideal population, quite unrealistic in various ways, but maybe informative in other ways.

We suppose that we have a closed, finite population containing an equal number of men and women.

Everyone is married monogamously, with all men marrying their mother's brother's daughter; MBD in the jargon of anthropologists, often contrasted with FZD, father's sister's daughter. Cross-cousin marriages.

Every marriage has exactly two children, one girl and one boy. There is no infant or child mortality, and all these children grow to adulthood, to marry and have children of their own.

In this world, everyone has exactly two parents, one sibling of the opposite sex and four cross cousins, two on each side, two of each sex. No parallel cousins at all.

Note that in this diagram, all the marriage links from women to men go from left to right. This is not the case in the FZD version, where they alternate as you go down the page. The two cases are different; there is more going on than a change of labels.

For present purposes, this ideal population has the important property that it can be mapped, through time, in a reasonably simple two-dimensional diagram or array, an example of which is snapped above. Each row represents one generation of the population, with successive generations going down the page. We suppose that people are tidy and that they all have both their children when they are twenty years of age, thus avoiding the generational drift of the real world.

Looking forward, I see no reason why the rectangular sheet above should not be joined back on itself to form a vertical cylinder, thus closing the population without any loose ends. Although the top of the cylinder does bring us up against the creation stories, previously noticed at reference 5.

The next step: clans

We next suppose that our population is divided into exogamous clans, with clan membership being inherited through the mother. So siblings are always in the same clan, husband and wife are always in different clans. Two such clans, the red and the blue, are marked on the snap above.

Slightly different, property such as land (perhaps in the form of hunting rights), is held by men but transmitted in the maternal line, from a man to his sister's son. Making the male blue diagonal a line of inheritance, keeping the property in the clan, if not the family. Plenty of societies have been studied where this particular relationship is important, perhaps as important as that between father and son.

One issue is the number of clans, often a power of two. But is that just human tidiness: what about seven, a number which crops up all over the place, in other contexts?

Another issue is whether it is possible to appropriate to express rules about marriage in terms of clan membership rather than biological descent?

Suppose then that we have seven clans: yellow, lime, apple, sky blue, royal blue, black and purple; in real life likely to have been named for plants or animals. With the rule being that a yellow lady must marry a lime man, a lime lady must marry an apple man and so on. Forgetting all about this kinship business, it being much easier just to track clan membership, which is always that of the mother.

[to be completed]

Tilings

The snaps above were constructed a little laboriously in Powerpoint, although things were made a little easier by using the 'select objects' feature. Furthermore, the lining up started to fray a bit as I went along. I did not turn up a suitable 'snap to grid' feature, such as one would expect in a mainline drawing package such as AUTOCAD or DRAWBASE - this last being the one that I am slightly familiar with.

What I wanted, after the event, was a single tile that I could paste all over the slide. The tile would indeed tile the slide. Such a tile is highlighted in blue in the snap above, a tile which includes the links but not the three people bottom right, two men and one woman.

With this snap illustrating a bit of tiling. If one had a big screen, one might stick four such tiles together to make a super tile.

Problems

In the real world, both men and women may have zero, one or more partners during the course of their life, rather than exactly one. More often in the case of men, more than one at a time. Some anthropologists talk of group marriages. Not to mention extra marital partnerships.

In the same way, a marriage might result in zero, one or more children, which might or might not be split evenly between the sexes.

Including all this on a two dimensional array, never mind one as neat and tidy as those above, is challenging - as can be seen in the second half of reference 2.

Variation in age of marriage and in birth intervals causes more problems in that generations re no longer neatly separated out. Generations works in the immediate vicinity of a nuclear family, as seen from inside that family, but goes downhill rapidly as one moves away from that.

In the case of the cylinders above, one can make an effort by joining up the two ends of the rectangle one gets on paper or on the screen with an offset. But apart from providing mathematical curiosity, I am not sure that it helps much - although there is the paper at reference 6 - which I believe is an attempt to deal with the fact that, certainly at one time, in Aboriginal Australia, men were commonly ten or more years older than their wives.

One might argue, and I believe Lévi-Strauss does argue, that such diagrams represent an ideal, towards which a society might drift. There might be a tendency or desire to do things that way, even if one falls rather short. And it certainly true that in a stable population, neither growing nor shrinking, the average number of surviving children needs to be close to two.

It might even be the case that people like the idea of such neat and tidy arrangements, not so much because they are useful but because they are pretty; attractive and interesting.

Conclusions

Another illustration of both the attraction and the limitations of two dimensional models.

Further material which might be developed to go along with that at reference 1. What does such a model tell us about what goes on on the ground?

From where I associate to an economist of my student days telling us that mathematical models provided a useful peg on which to hang a discussion of the real world: how well they described the real world was another matter.

PS: it so happens that, in parallel with this post, I have been reading a short story - reference 7 - by Galsworthy about the perils of decent people being stuck out in the wilderness, more or less by themselves, for too long. Mining people in this case, rather than anthropologists doing their field work. I dare say plenty of such stories came out of British India where we were very thin on the ground, once you got away from the big cities, but all I can think of at the moment is Galsworthy's contemporary, Conrad, at reference 8. Maybe Somerset Maugham?

Google adds some checkable bibliographical detail. And reminds me that old Jolyon Forsyte from the 'Forsyte Saga' gets a walk-on part.

While Gemini gets into quite a muddle, although he recovers well as I correct him. I thought his near closing sentence was rather good:

'... Galsworthy leaves the reader with the unsettling thought that Pippin’s death was an act of surrender rather than a mistake. He couldn't find the "words" to anchor himself to the world of the living, so the silence simply claimed him...'.

And he drags in the tors of Dartmoor yet again, which I once asked him about - and which he does not seem to be able to let go of. Perhaps this is his idea - not that unreasonable, if a little heavy handed - of making conversation.

Perhaps I will check this one properly and, inter alia, try to work out whether he has access to the text or whether he is relying on secondary sources. He is certainly doing a good deal more than making it all up.

References

Reference 1: https://psmv6.blogspot.com/2026/04/a-thought-experiment-on-forensic.html.

Reference 2: https://psmv6.blogspot.com/2026/04/more-clans-and-marriages.html.

Reference 3: Structuralism and "The Story of Asdiwal": A Re-analysis of a Tsimshian Myth – Darcee L. McLaren – 1990. 

Reference 4: The story of Asdiwal – Lévi-Strauss – 1960. Being the (famous) Lévi-Strauss take on a myth from the far north west of British Columbia.

Reference 5: https://psmv6.blogspot.com/2026/03/clans-and-marriages.html.

Reference 6: Aranda and Alyawarra kinship: A quantitative argument for a double helix model – Denham, W.W., C.K. McDaniel, J.R. Atkins – 1979. Which Denham, leaving aside Denham Grove, was previously noticed at reference 2.

Reference 7: The silence - John Galsworthy - 1901. In 'Caravan', previously noticed. See, for example, reference 9 below. A very good, if chance, buy!

Reference 8: Heart of darkness - Joseph Conrad  - 1899.

Reference 9: https://psmv6.blogspot.com/2026/01/galsworthy.html.

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