In 1857, Maria Mitchell (1818-1889), the first female American astronomer, went on a tour of Europe.

She was already very famous. At 29, she’d discovered a comet (after calculating its expected position), was elected to the American Academy of Arts & Sciences a year later, and was the first female professor of the United States. These bland biographical details obscure a more interesting story. It was an age where women were considered too stupid to be entrusted with the vote. It was an age where a Thomas Huxley could argue that women were not worthy of membership in learned societies because they were, ipso facto, amateurs. It was an age where the American Academy felt it necessary to mention in their 1848 report that they’d decided to grant her membership “in spite of her being a woman” [1]. The next admission of a female to that august assembly would be in 1943!

In Europe, she met everybody who was somebody: Roget, Babbage, Humboldt, Somerville, George Airy, Leverrier, Stokes, Struve, Herschel … the list is a who’s who of 19th century Arts & Science. Her diary reveals a keen mind with a droll sense of humor [13]. For example, she comments that:

Thus far England has impressed me seriously; I cannot imagine how it has ever earned the name of ‘Merrie England.’

She demolishes the ever-reliably pompus William Whewell with:

An Englishmen is proud; a Cambridge man is the proudest of Englishmen; and Dr. Whewell, the proudest of Cambridge men.

She comments about a statue of Dr. Johnson that, “It must be like him, for it is exceedingly ugly.”

Then there’s her entry on November 2, 1858. She commented that:

It was hard for me to become accustomed to English ideas of caste. I heard Professor Sedgwick say that Miss Herschel, the daughter of Sir John and niece to Caroline, married a Gordon. ‘Such a great match for her!’ he added; and when I asked what match could be great for a daughter of the Herschels, I was told that she had married one of the queen’s household, and was asked to sit in the presence of the queen!

“When I hear a missionary tell that the pariah caste sit on the ground, the peasant caste lift themselves by the thickness of a leaf, and the next rank by the thickness of a stalk, it seems to me that the heathen has reached a high state of civilization — precisely that which Victoria has reached when she permits a Herschel to sit in her presence!

This particular entry got me thinking. It’s a natural and intuitive analogy. However, Ms. Mitchell made two errors. First, though the caste system is related to class, race and religion, it’s a very distinct entity. Second, though the caste system establishes a pecking order, it’s not a hierarchy. I will attempt to justify both statements.

Like most Indians, I grew up in a caste system. It’s so all-encompassing that it’s invisible. I was almost 24 years old before I realized that all my friends were from the “upper” castes, that there were skin creams called “Fair & Lovely”, that there were old people who were very fussy about what they touched, and that unless I showed initiative, I would be restricted to finding a mate from a very small pool of candidatesJust consider the odds. A SETI/Francis Drake-type calculation leads to an estimate of just 86 potential mates. Why? 86 = Number of Keralites (31 million) × % of females (0.5) × % of Nairs (0.14) × % of population in the 21-29 age group (0.2) × collision factor (0.001) × compatibility factor (0.2).^†. And ironies abounded. The Civics or History teacher could lecture us quite sincerely, say, on the evils of the caste system. But it was quite besides the point that he/she wore caste marks on their foreheads or had married off their sons/daughters to members of the right caste.

I’ve also come to realize that many educatedKapil Kapoor, the rector of Jawaharlal Nehru University, observed in a talk on decolonizing Indian minds: “I am reminded of Ananda Coomaraswamy who uses the expression ‘educated Indians’ and then gives a footnote — ‘That is how victims of Indian education are described.’^† Hindus prefer to deny the relevance of the caste system. The anthropologist Joan Mencher noted this tendency in 1975.

“One meets today in India, as well as abroad, many Indians who with all sincerity will state that the caste system no longer operates, at least in the cities. (This is much like the white liberal New Yorker’s seeing no discrimination against blacks.) It is significant that none of the persons who have said this to me is a member of the lower castes.” [14]

Her observation is on the money. Of course, the regrettable sideswipe against “liberal New Yorkers” is another instance of the erroneous idea that caste, class and race are more or less the same sort of thing. It’s time we drove a stake through the idea. Fortunately, Oliver C. Cox completed that thankless task more than sixty years ago [3,4,5].

In the 1940s, Llyod Warner, W. Allison Davies, Kingsley Davies, John Dollard, Buell Gallagher and other sociologists were claiming that race relations in the South between whites and blacks constituted a de-facto caste system. The logic was simple: one is born into a race, one can’t change one’s race, there’s a racial hierarchy, races often have characteristic cultural practices, there are restrictions to mixing, and finally, inequities abound when racism is used to organize societies. But Cox was able to show that the analogies were superficial. For example, in the caste system, blood has a very different cultural import. To cite the simplest non-trivial example: there is no such thing as a half-Brahmin or a quarter-Sudra or a one-eighth Untouchable [5]. Cox also argued that endogamyn. Marriage within one’s own tribe or group as required by custom or law.^† and hypergamyn. The practice of marrying into an equal or more prestigious social group or caste.^† have been overstated aspects of the caste system. The mixing of races dilutes racial divisions, whereas the mixing of (sub)castes either leaves the system intact or merely creates a new sub-caste. As Cox observed:

“It should be emphasized that a definition of a ‘caste’ does not define the ‘caste system.’ We have shown elsewhere that upper-caste men have always been able to marry women of lower castes without disturbing the caste system, a procedure which could not be sanctioned in the south. Endogamy may be an isolator of social classes, castes, tribes, sects, or any other social groups which think they have something to protect; hence the final test of caste is not endogamy but the social values which endogamy secures.” [3] (italics mine)

Cox demonstrated that the social values — reflected in what people can do — of a racist society and those of a caste system are very different. The way one does business, makes love, gives to charity, worships god, and handles conflict are all fundamentally different. Inter-caste rivalry and jealousy tend to strengthen the caste system, not  weaken it!

In short, racist societies are inherently fragile, whereas the Hindu caste system is anything but. The three hundred years of US history is marked by several bloody slave rebellions; similarly, the peasant /serf rebellions in feudal Russia led to death tolls in the millions. It’s very hard to think of comparable statistics in the 3000-plus year history of the caste system.

Finally, race is not very good at separating people and/or division of labor. If everyone looks more or less the same, race proves to be too weak a classificatory criterion.  Should one hire a talented octoroon accountant with perhaps a blob of Jewish blood over an incompetent melungeon who may merely look white? The computational costs begin to add up.

In the caste system, however, there are dozens of subtle cultural (not biological) cues. The way a person drinks water, sits, uses words; the food they eat; their names; the people who can vouch for them; the festivals they observe and the gods they worship; and most importantly, the things they find “impure” or “pure.”  Culture is a superb metal detector.

Another misconception about caste is that it is a hierarchy of types. For example, in his definitive work, Homo Hierarchicus, Louis Dumont (1911-1999) argued that the Hindu caste system is based on the hierarchical opposition of the Pure with the Impure. As he put it:

“This opposition underlies hierarchy, which is the superiority of the pure to the impure, underlies separation because the pure and the impure must be kept separate, and underlies the division of labor because pure and impure occupations must likewise be kept separate.” [1. pp. 43]

He is partly right. The pure is made impure via pollution. Pollution is of two kinds: permanent and temporary. A Brahmin who accidentally touches an Untouchable is temporarily impure. A ritualistic bath removes such temporary impurity, because water is held to be a purifying agent. So are things like the tulasi plant, sessamum oil, turmeric, gold and the  panchgavya — the five products of the cow. In fact, pollution is attributed to parts of the body (e.g., above the navel is superior to below),  to material objects (e.g., silk over cotton; gold over other metals), to plant life (e.g., fig-trees, banyans,  and tulasi rank higher than others), to animals (e.g., the cow, cobra and some monkeys versus the pig and fowl), and to all forms of human fluids (e.g., breath, urine, semen, sweat, mucus …). The details are mind-numbing. Thankfully, H. Stevenson has compiled a fairly complete list [17]. But does ordering (pure is better than impure) imply hierarchy? Is the caste system a hierarchy?

At first, second and third sight, the idea of the caste system as a hierarchy makes a lot of sense. A hierarchy is a collection of inclusions. And the Hindu people are divided into two: the twice-born and the once-born. The twice-born are divided into two sub-groups: the Brahmins, Kshatriyas lie in one group and Vaisyas in the other. The once-born group divides into Sudras and the Untouchables. The Brahmins in turn divide…

It gets pretty baroque. In Bengal, the Brahmins are divided into the Radhi, Vaidika, Varendra and Grihavipra groups. The Radhi are divided into the Kulin and Srotria. The Kulin, in turn, are divided into the “real” Kulins and the Bhanga. The Vaidika are divided into the Paschatya and Dakshinatya. The Paschatya are divided into Kotalipara Samaj Brahmins and Bhattapara Samaj Brahmins. The Dakshinatya are divided into the Kulin, Mulik and the Bansaja. So on and so forth. Or, take the case of the Kayasthas (who, by the way, are neither Brahmins nor Kshatriya nor Sudras nor Vaisyas). They are divided into 5 groups in Bengal and 16 groups elsewhere. Naturally, each group has its own hierarchy. Each group tries to outdo the others in terms of ritual purity; over the centuries, this has led to a fantastic set of procedures for auspicious touching, chanting, bathing, hand-washing and genuflectionSinclair Stevenson’s Rites Of The Twice-Born is a veritable catologue of the symptoms of obsessive-compulsive disorder. Not that such rituals are unique to the Hindus. According to Robert Sapolsky, the Orthodox Jew has to observe 613 rules each day. And the Christians are no slouches either. The connection between OCD and religion has been explored in the last essay in Robert Sapolsky’s book, The Trouble with Testosterone and Other Essays.^†.

Physicists have proved that at the very bottom of the chain — the cold, dark, mariner-trench deep, irreducible, absolute bottom — is the quark.

Of which there are 6 types…

The idea that the caste system is a hierarchy is, of course, not particularly novel. André Béteille sniped:

“It appears to me that Dumont’s originality lies less in the substance of his argument than in the uncompromising manner of its presentation. [3, pp. 45]

But what was original was Dumont’s insistence that the caste system should not be studied as the sum of its parts (castes, sub-castes). He claimed that it was the whole that give the parts their meaning. For example, he would say that it wasn’t the separation of groups of people that lead to hierarchical system; it was the hierarchy that led to the separation of people [3, pp. 41].

The analogy of the ant-heap comes to mind. In the holistic view — Dumont’s view — the ant-heap is a super-organism with the ants as its limbs and senses. To ask why a limb does this or that with some another limb is simply silly. In the reductionistic view, the ant-heap is an emergent phenomenon; something that arises out of the structured, atomistic actions of the ants.

I think Dumont was right about the whole determining the parts, and right about the the system being an elaboration of the notions of pure/impure. But I think he was incorrect about the caste system being a hierarchy.

Hierarchies are built up of sets. Any hierarchy may be shown to be a collection of sets such that any two sets are either completely unrelated or one set is completely included in the other. Figure 2 shows the Figure 1’s hierarchy recast in terms of set. As such it does not reveal that Brahmins are ranked higher than Untouchables (say). Hierarchy does not necessarily entail inequality. Conversely, the mere existence of inequalities does not point to a hidden hierarchy.

The King Chicken theorems of H. G. Landau should cure the illusion that systematic pairwise inequalities imply a hierarchy. Chicken flocks have well-defined pecking orders. Landau defined a chicken X to be king if for any other chicken Y in the chicken flock, either X pecked Y OR X pecked a chicken Z which pecked chicken Y. He proved that every chicken flock had (i) a king but (ii) there were also flocks in which every chicken was king. The chicken coop was ordered through and through; everybody got bossed or had some other chicken to boss. But this ordering wasn’t a tree, a hierarchyStephen Maurer’s paper provids a delightful overview [12].^†.

Besides, does the concept of a caste really correspond to that of a set? The most basic aspect of a set is membership. Given a set, it should be possible to say what’s in the set and what’s not. When instances of the set exist in the real world, the set is said to be a natural kind. Conversely, a natural kind can always be modeled as a set.

Biological categories like “cow”, “zebra” and “fish” appear to be natural kinds, but on closer examination, things turn out to be much more complicated. A coelacanth is a fish by phenetic criteria but not a fish by cladistic criteria. Both criteria are equally respectable. So is the coelacanth a fish or not?

As Ernst Mayr pointed out, the moral is that biological categories are not natural kinds. Distinguishing a zebra from a fish is not like distinguishing an electron from a proton. Rather than force organisms to fit into precise taxonomies, biologists use the much more subtle and flexible concept of “species.” Mayr defined a species as,

“…groups of actually or potentially interbreeding populations, which are reproductively isolated from other such groups.” [10, pp. 188]

It is a provisional definition. Species are not natural kindsNot all biologists agree on this point. David Hull gives a brief review of the quarrel [3]. Muhammad Al Khalidi’s paper is a good introduction to what philosophers have to say about natural kinds [8].^†. Mayr’s thesis has been spelled out with characteristic forcefulness by George Lakoff [10, pp. 187-195], where he lists seven critical differences between species and natural kinds. One key difference is the lack of necessary and sufficient conditions for what should belong to a species and what shouldn’t. Thus, it’s generally true that two groups belong to the same species if they interbreed. But if they don’t, then it doesn’t automatically mean that they don’t belong to the same species! It’s upsetting, I know, but that’s the way the word works.

The word “caste” is much closer in meaning to the word “species,” I think, than to “set” or “natural kind.” It explains why the word is so hard to pin down.  Figure 3 shows what happens when the idea of the caste system as a hierarchy is given up. It is no longer possible to ignore those groups who “live” in the intersection regions of the diagram; things are a lot messier now. The species view also enables some interesting predictions. For example, it predicts that some people may belong to more than one caste — there are no necessary and sufficient conditions to determine caste (species) membershipThe Nairs (Nayars) of Kerala, South India, are a good example. They are Sudra-like in that they lack the sacred thread of the twice-born, but they’re also clearly Kshatriya-like in terms of traditional occupations, influence and tacit community consensus.^†. We can predict that the same population may belong to two different castes in two different placesFor example, the Nais of North India (not to be confused with Nairs). Traditionally, the Nais (sub)caste worked as barbers and general factotums. Schwartzberg’s landmark study of 212 villages in the Indo-Gangetic plain showed them to be very widely distributed; they constitute somewhere between 1% to 2% of the population. They were considered “untouchable” in most of northern India, but in Bengal however, the Nais are considered not only “clean” but high-enough in the hierarchy to assist Brahmins at all high-caste marriages [16].^†; species too are geography-dependent. And we can also predict that we’ll find the convergent evolution of castesMost castes in South India have parallels to castes in the North. South India began to get “sanskritized” around 200 B.C.E — 100 C.E. This means that the caste system entered South India relatively late. While there’s evidence of Brahmin migration from the North, the same cannot be said of other caste groups. It was convenient to tacitly assign the locals to various castes, perhaps on the basis of their occupations. Over time, the caste system in the south became even more rigid than the parallel system in the north.^†.

If the structure of the caste system doesn’t really correspond to a hierarchy (tree), then what does it match?  We could say it’s a
“network,” but the trouble is, almost anything is a network. We need something more specific than a network but less  specific than a tree. In fact, because the caste system has tree-like aspects, we need something that’s a generalization of the concept of a tree.

Enter, closure systems. A closure system is a collection of sets such that the intersections between the sets are also part of the collection. So if A is the set: {1,2,3} and B is the set: {2,4, 5}, then the closure system would contain {A, B, {2}} since {2} is the stuff common to both A and B. A hierarchy or tree is a special kind of closure system, namely, one in which any two sets have either nothing in common or one set is a proper subset of the other. Closure systems don’t do away with sets; but they recognize that because sets are imperfect containers, the stuff that could possibly fit into multiple sets also needs to be included. All hierarchies are closure systems but not conversely. The caste system is a closure system rather than a hierarchy.

Closure systems are ubiquitous in mathematics and computer science; for example, it can be shown that designing a good database system is essentially the task of designing a good closure system. Similarly, it can be shown that Herbert Simon’s “nearly-decomposable” systems — which lie in between fully-modular systems and fully- connected systems — are closure systems. It has recently been shown that nearly-decomposable organisms are much more resilient to evolutionary processes than organisms that aren’t [18].

But closure systems pop in many other contexts as well. The architect Christopher Alexander claims that natural cities (that is, cities that’ve evolved “organically” over time)
don’t correspond to neat little hierarchies. Instead, the spaces of a natural city intersect in complex, and not completely predictable, ways. Since these cities have evolved out of actual usage rather than predicted usage, they are usually comfortable, multi-functional places.
Alexander claims that natural cities are closure systems, or as he calls it, semilattices. Such cities are very persistent and resilient. Damascus, Baghdad, Constantinople, Rome, and Delhi are still around. In contrast, it’ll be astonishing if our carefully designed, zoned-out
suburbs last even half a century.

It’s a pity that the caste system is not a tree; if it had been, it would’ve become extinct a long time ago. As was pointed out earlier, it is appallingly robust. However, there is hope. Cox saw it in the fundamentally heretic nature of capitalism (for him, capitalism was Western culture).

“The caste system of our own time is not very much different from what it was some three thousand years ago, being a very powerful form of cultural organization. The early Greek invasion left almost no imprint upon it; and when the modern Europeans came upon it, Mohammedanism seemed just about to be swallowed. Evidently, however, Hinduism, like all other cultures, has met its match in Western culture.The caste system is not yet in its death throes, but it is squirming under the impact of capitalism.” [3]

While we should probably hold off on buying the noisemakers and party hats, an economics approach to the caste system does provide interesting insights.

Let’s consider a specific example. The economist and Nobel laureate, George Akerlof, spent many years in India. Out of that experience came a great paper on the economics of caste [1]. Now, much had been written on the economics of caste; in fact, as early as 1898, one of the founders of Indian economics, Mahadev Govind Ranade, had pointed out almost none of the postulates of western classical political economics applied in the Indian context [2, pp. 143]. Akerlof’s insight was that while economic transactions in a free market system are dyadic (buyer, seller), those in a caste system are triadic. In addition to the buyer and the seller, there is a third element: the community. In Akerlof’s words:

“In previous models current transactions (so long as they are legal) do not result in changed relations with uninvolved parties in subsequent transaction. For example, if farmer X makes a contract for sale of wheat to speculator Y, his subsequent dealings with speculator Z will be unaffected. On the contrary, in a caste society any transaction that breaks the caste taboos changes the subsequent behavior of uninvolved parties towards the caste-breakers. To take an extreme example, consider what would happen if a Brahman should knowingly hire an outcaste cook: the Brahman would be outcasted, and the cook would find subsequent employment almost impossible to obtain.” [1, pp. 609-610]

More generally, a triadic transaction involves the buyer, the seller and a group of other people. Akerlof goes on to demonstrate that economics in a caste system has its equilibiriums, that coalitions can disrupt this equilibrium, and he even derived bounds on the required sizes of such coalitions.  If progress is the art of replacing social problems with economic ones, then Akerlof’s paper represents progress in its best form.

Akerlof’s point may be reframed as the statement that there are contagion effects between transactions. The probability of a transaction between person X and person Y depends on prior transactions; unlike exchanges in most neo-classical economics, exchanges are not independent of each other. It turns out that models developed for ecology, such as the theory of replicator equations, provide an elegant way to study contagious transactions. Biology, in fact, is the science of triadic transactions [11].

Contagion is contagious. Contagion models are used, among other things, to explain fads, the spread of epidemics, rumors, gossip, accident statistics, entrepreneurial failure rates, and traffic jams. Learning is a form of contagion, and to the extent human behavior is mimicry, contagion helps explain how caste norms get established and maintained.

Might as well end with what Ms. Mitchell had to say:

“I have never been in any country where they did not do something better than we do it, think some thoughts better than we think, catch some inspiration from heights above our own–as in the art of Italy, the learning of England, and the philosophy of Germany.” [13]

Contrast this with the Hindu worldview, as reported by Alberuni (al-Biruni) when he visited India in 10 century C.E.

“The Hindus believe that there is no country like theirs, no nation like theirs, no king like theirs, no religion like theirs, no science like theirs …. If they travelled and mixed with other nations they would soon change their mind, for their ancestors were not so narrow-minded as the present generations.” [15, pp. 116-117]

It’s a mistake Indians should not re-make. Especially since there are so many millions of Indians now travelling and mixing with other nations. Many of those millions are here, in Maria Mitchell’s land. What did she think her country believed in, even if it practiced that belief but imperfectly?

“Ours is a democratic country. We recognize no caste; we are born ‘free and equal.’ We honor labor; work is ennobling.” [13]

It’s not a bad lesson to keep in mind.

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