Mythical Chronology - And Anachronisms

Note: This post has benefitted from inputs from Anand of Locana (link on the right panel) and from Gopal.

In its ancient Indian variant, the game of dice had a scoring system based on modular arithmetic - the best throw 'krita', was when the numbers shown by the dice added up to a number perfectly divisible by 4. The other scores, in descending 'desirability' were 'treta' when the sum of the displayed numbers left 3 on dividing by 4, 'dwapara' when the remainder was 2 and finally 'kali' when the remainder was 1.

The 'chronology' of Indian myths and legends is also largely based on cycles of 4 eras or yugas - the first yuga would be the longest and the best era; and then all the good things gradually decline until the fourth and shortest and final yuga - we are there at present - would end in utter chaos and dissolution. And rather appropriately, the 4 yugas have been named (indeed ranked) after the scores in a game of dice. 'krita' being the early halcyon days and the present, 'kali' being by far the worst. The era immediatly preceding 'kali', the 'dwapara' was also none too good a time(*).


Indian mythology has personified 'Dwapara' and especially 'Kali' as two largely malevolent spirits who are out to create trouble for men and even gods - they feature prominently in the story of king Nala for instance. I have not seen any personifications of 'krita' and 'treta' in the mythology. Many (mostly but not only firangees) have confused this Kali with the fierce and hideous but ultimately benevolent goddess whose name is spelled the same way in English (and pronounced rather differently in Sanskrit). One telling instance is the 'Time' magazine cover story on the horrors of Indian Partition of 1947. This article, available online, is also full of lurid orienatlisitic imagery and stereotypes. The cover of that issue of Time can be seen here. A curious thing about that picture is that the outlined maps of India and Pakistan there show Kashmir firmly with India, very unlike American media! And here is yet another cover from the same source; the 'fine printed' caption is particularly interesting. Anyways, let me not digress!

Within the above 4-yuga scheme, the huge corpus of Indian Itihasas (Ramayana and Mahabharata) and Puranas has been accommodated. Most of the 'action' takes place in the middle two eras - Treta and Dwapara (indeed, the 'krita' yuga seems to have been a rather boring, equal music time, just like heaven. There were few troublemakers and consequently few juicy stories (**)). Forming the backbone of the chronology of these two yugas are two vast dynasties ('vamsas') of kings, each with perhaps hundreds of listed names - named after Surya and Chandra (sun and moon). The Suryavamsa flourished in the Tretayuga and Chandravamsa in the Dwaparayuga.

The events of Ramayana (a Suryavamsa story) is believed to have occured in Treta and the Mahabharata in the Dwapara. Indeed, the characters of Mahabharata generally seem aware of Rama and his adventures and those characters who feature in both epics (Hanuman for instance) appear in the Mahabharata as much aged; so the basic idea of Mahabharata post-dating the Ramayana (in a mythical time sense) appears justified. And this chronological sequence is strictly followed in some art forms like the Yakshagana (this dramatic art form from coastal Karnataka acts out episodes from the myths with great emphasis of extempore improvisation of dialog. However, if the story being enacted is a Ramayana based one, no reference to Mahabharata or Krishna will be 'tolerated').

A very curious thing about this mythical chronology (especially, since at least 'Kaliyuga' is part of the common vocabulary of most Indians) is that it is probably not very old. The Vedas and even the Itihasas were ready in their final form long before this modulo-4 framework was worked out - perhaps even before such a scheme was even conceptualized. Classical Master Kalidasa who lived in or before 5th century AD was probably unaware of the grouping of the mythical kings into the above two Vamsas - in his 'Raghuvamsam', king Nahusha(***), of the Chandravamsa and hence the Dwapara yuga is referred to by Rama (of the earlier Treta) - a clear 'anachronism' (Kalidasa also appears to have been unaware of the status of the god Ganesha, who must thus have been a later addition to the pantheon!). The 'Adhyatma Ramayana', a devotional, early medieval(?) retelling of the Ramayana (probably post-dating Kalidasa) also has similar anachronisms - in its Malayalam translation(?) by Ezhuthassan, Rama refers to prince Puru's great sacrifice (the latter was Nahusha's grandson and hence from Chandravamsa).

Nevertheless, those smart guys who worked out this chronological scheme did a god job at least with the main Itihasas, inserting several references to the Ramayana in the Mahabharata and probably excising from the former all references to the latter. Characters featuring in both the epics were a prolem (their life-spans would straddle two eras each lasting hundreds of thousands of years or more) which appears to have been solved by collecting them into a tight list of Chiranjeevis ('immortals').

And here is a very 'contemporary' anachronism: The Malayalam film 'Vaishali' is about the mythological story of Rishyasringa, clearly assigned to the Treta yuga (the hero marries Rama's elder sister). A song in the movie (penned by eminent Malayalam poet ONV Kurup) has romantic allusions to an episode from the Shakuntala story, which would get played out in the 'future' Dwapara yuga, just a few generations before the Mahabharata war!

And let me conclude on a personal note - a very distant memory (from childhood) of a visit to the temple at Rameswaram. The priest-guide who showed us around pointed out two large sculptures which faced each other across a long and somewhat gloomy corridor. One showed the figure of a male warrior sitting on the shoulder of a much larger female figure. The warrior held a sword aloft but he appeared to be smiling. In the other sculpture, the roles where reversed, a midget female sat on the shoulders of a colossal male; I do not remember her expression - that of her huge bearer dominated everything - anger written all over his face, bloodshot eyes,... and he brandished a sword and seemed poised to strike the onlooker. The priest told us these were allegories of the Krita yuga and Kali yuga respectively. He did not explain further -and I was too overawed to ask anything further....

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(*)- I would have imagined the best Yuga to have lasted the least but then that is from a perspective informed by the worst of times! And the present Kali yuga is by no means the end - the 4 yugas repeat indefinitely in a cycle.

(**) - There are of course, many stories assigned to the Krita yuga but these generally concern the conflicts and intrigues between the Gods and the Asuras; Humans hardly feature and presumably had a good time.

(***) - 'Nahusha' strikes me as a rather heavily Persian name.

The Rolling Stone

This is a dialog driven parable - from real life:

Master: "Have you heard the saying 'The rolling stone gathers no moss'. If one wants success, one ought to focus on the important things and not jump around and dabble in a zillion different areas!"

Student: "But Sir, the accumulation of moss is hardly a sign of success; rather it shows disuse, even decay. Moreover, as Pandit Nehru said in 'Letters to my Daughter', a rough stone gets polished into a smooth and shiny pebble by rolling on and on!"

Master:"Smart! but then, you need to know when to stop. Roll *too much* and you will crumble into an insignificant grain of sand. Beware of that!"

Student (several years later): "Guess I now understand, Sir!" (aside) "And yet, perhaps, the grain of sand can wait eternally for someone who will perceive the World in it - or maybe even think the World of it!"

Etymology And Computers

I heard recently from a wellwisher that one reason this blog has very few regular readers is that "not too many really care about etymologies of obscure words and such". Of late, I have cut down on etymological searches and have been spending more time with good old computer science material. But then, sometimes the twain do meet (or old habits die hard :) ).

Note: what follows does have a bit of com-science jargon but that is not consequential.
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The B-tree is a fairly standard data structure which most self-respecting basic CS courses teach. The massive Algorithms text by Cormen et al. says: "B trees were developed by Bayer and McCreight in 1972. They did not explain the origin of the name".

Wikipedia says: "The B-tree's creators, Rudolf Bayer and Ed McCreight, have not explained what, if anything, the B stands for. The most common belief is that B stands for balanced, as all the leaf nodes are at the same level in the tree. B may also stand for Bayer, or for Boeing, because they were working for Boeing Scientific Research Labs at the time."

Let me add one more guess: The data structure was first implemented in the B programming language (This B was a precursor to C language, as most people who studied the latter have heard. B was apparently a scaled down version of something called BCPL => there was no language called A to begin with).

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A somewhat more intricate data structure which I missed out on in my student days and have got to know now is the 'Red Black tree'. Tom Cormen's tome says: "These trees were introduced by Bayer and studied extensively by Sedgewick and Guibas, who introduced the red-black coloring convention." - there is no mention of why these two colors were chosen. Even Wikipedia is silent on this.

So let me float another guess: Either or both of Sedgewick and Guibas were admirers of (19th centure French novelist) Stendhal and his masterpiece "The Red and the Black" hence the choice of colors!

Well, I dont think the guess is that outlandish. Let me quote a bit from the Wikipedia article on this novel:
"The most common and most likely explanation of the title is that red and black are the contrasting colors of the army uniform of the times and of the robes of priests, respectively. The hero Julien Sorel observes early on in the novel that, under the Bourbon restoration it is impossible for a man of his class to distinguish himself in the army (as he might have done under Napoleon); now, only a career in the Church offers social advancement and glory. Alternative explanations are possible, however: for example, red might stand for love and black for death and mourning; or the colours might refer to those of a roulette wheel, and may indicate the unexpected changes in the hero's career."

Perhaps Guibas and Sedgewick's reluctance(?) to explain their choice of colors is a smart tip of the hat to the cloak of mystery in which Stendhal left the novel's title!

The same wellwisher quoted at the beginning of this post also said to me: "your blog is too impersonal. You are not very visible anywhere!". Anyways, let me add a personal note here. I do have a choice from among the alternative explanations Wikipedia offers for the title: "Red and Black" (no I have not read the novel, never got past page 3; this choice is purely (and very) personal) - the roulette wheel one signifying "unexpected changes in the hero's career".