Kurinji? Yes, But...

This is in continuation of the previous post here, reporting on a suspected sighting of the 'Kurinji' in bloom at Kate's Point, Mahabaleshwar.

Here is a slightly edited copy-paste of a mail from Shrikant Ingalhalikar, author of 'Flowers of Sahyadri', clarifying some of the issues therein:
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Dear Nandakumar

The Strobilanthus you found at Kates Pt. is Reticulatus, now named as Nilgirianthus Reticulatus (it was not Strobilanthus Sessilis). The gregarious flowering of all Stobilanthus species occurs usually once in 7 to 12 years - the year CANNOT be accurately predicted but the month of flowering is October. As exception, A FEW plants flower EVERY YEAR. The next (collective) flowering is likely in 2007.

Regards,
Shrikant Ingalhalikar
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The 'Kurinji' Blooms ...

While looking around Kate's Point, Mahabaleshwar (120 km to the south of Pune, Maharashtra, India) day before yesterday, we saw several clumps of a shrubby plant with clusters of deep blue flowers. Leafing thru Shrikant Ingalhalikar's delightful field guide "Flowers of Sahyadri" (which we religiously take along on all such trips), I felt a sharp pulse of electric excitement: "Neelakkurinji!"

Back home, I revisited Theodore Baskaran's collection of Nature Essays, "The Dance of Sarus". It contains a short piece: "When the hills turn blue" about the Kurinji phenomenon.

'Kurinji' (its Tamil name) or 'Neelakkurinji' (Malayalam) blooms in the highest reaches of the Western Ghats, above 1500 meters of altitude - once in 12 years according to tradition - and entire hillsides are said to turn blue with the flowers. Baskaran tells us, even the ancient Sangham texts (almost 2000 years old) talk about Kurinji. Indeed, kurinji is taken as a marker for one of the five ecosystems or regions - 'Tinai's - that Southern India was divided into. Baskaran goes poetic thus: "Murugan, the presiding Lord of the Kurinji Tinai, offered a garland of Kurinji flowers to his bride Valli". However, in these troubled times, the Kurinji habitat is under severe threat. The best place to enjoy the beauty and purity of this realm said to be an 80 km trail from Kodaikanal to Munnar along an east-west ridge in the Ghats.

Baskaran informs us that Kurinji is not a single plant species: there are several dozens of 'Strobilanthus' species (family: 'Acanthaceae') and all of them share the 'blue flowers blooming once in several years' character. Ingalhalikar lists about 6 species and says flowering happens once in 7 years rather than 12. My best guess, based on his filed guide: what we saw at Kate's point (and later at Lodwick point) was Strobilanthus Sessilis (also called Pleocaulus Ritchei). I don't remember reading in any newspaper that the Kurinji is in bloom nowadays so there is some chance that I may be barking up the wrong, well, shrub!

I also (very apologetically) plucked a single Kurinji flower and deposited it before a picture of Murugan at home.

Note 1: The Kurinji is called 'Karvi' in Marathi - not sure if the kind of romance associated with it in the South is shared by Maharashtra. Perhaps it blooms in the foot hills of Himalayas also and (just a guess!) the 'Karbi' people of Assam took their name from this flower.

Note 2: We took an offbeat path out of Pune - down Sinhagad Road past Donje Phata, Khanapur, Paybe Ghat, Welhe and Nasrapur on the Satara Highway to join up with the 'normal route' to Mahabaleshwar. The road condition is not great but bearable. From the crest of the Paybe Ghat, one gets a breathtaking panoramic view of Rajgad and Torna forts - and this stretch abounds in wild flowers!

Note 3: Sorry Sumesh, I still dont have a digi-cam so cannot post proper images. And Ravindra, you ought to have come along!

Of Conversations And ... Conversations!

I wonder if someone has done serious scientific studies on the way conversations evolve; how the subjects change, develop, lead on to further subjects, get sidelined and sometimes revive all over again (an incredibly wild but seldom really discontinuous process) and how a group conversation breaks down into smaller cliques which again realign into larger groups and ...

Aside: Indeed, more intimately, if one were to sit quiet and simply watch one's own thoughts over even a short period...!

Anyways, here is the approximate transcript of a conversation that took place today over coffee at around 11 am in a software office. Let me name the participants A, B, C, D.

(B C and D are seated already with their cups of Espresso. Enter A with a cup)

A: Hey, did you see that Vikram Seth is editing today's Times!
B: yeah, saw that. He is the honorary editor or something for just a day! strange!
A: I think it is not really a new stunt. Times has done it before with others, I guess. Actually, Times is too good at this kind of thing...
C: ..and in little else, 'page 3' excepted of course! In newspapers, I am an out and out 'Hindu fanatic'. Too bad you dont get it out here (in Pune)!
D: Yes, 'Hindu' is anyday the better paper. And, I guess Vikram Seth need not need not have been party to this kind of gimmicks.
B: Well, he is promoting his new book. He too has his own business to mind. Fair enough, isnt it?
D: (thoughtfully) I guess you are right.... But that concept of being in power for a day; that is interesting! Somewhat like 'Nayak' (the movie where the commoner hero is the chief minister of a state for a day and cleans up the place) one can say.
C: But that is not really a new idea either. I vaguely remember something from my history text. Mughal Emperor Humayun had such a deal with a water carrier.. well, the Hindi word for water carrier is 'Bhishti' or something like that. Humayun was, you know, running away from a battle, having got thrashed by the other guy,..
D: Sher Shah?
C: right, Sher Shah! and then he almost drowns in a river and the water carrier saves him. Humayun tells him, 'if I get back my kingdom, you will sit on the throne for a day' and I think, he kept his word!
A: So, is there any record of what he did while in power?
C: No idea, really. If the chap were real smart, he would have kept his mouth shut for that day, had fun at the harem and moved out gracefully!
B: There is yet another episode - from the mythology. Some king gets Indra's(king of Gods) position for a limited period and creates havoc in the heavens and gets kicked out and cursed to become a snake or something!
A: thats right. I have heard this story as well. Actually he physically kicks someone, some sage and gets cursed first - and then kicked out of heaven!
D: and the Greeks seem to have a story where someone gets to drive the Sun God's chariot for a day and it ends in some major disaster!
C: A common thread out there is, when someone is put in a place where one ought not to be, that is big trouble, eh?
B: Yeah, one ought to be where one belongs! You know, there is a Tamil song: "Garuda saukyama?" means "Garuda, how do you do??". You, know, the snake that sits coiled around (Lord) Siva's neck smugly says "Howdy!" to Garuda (the mythical Eagle, his natural nemesis) and Garuda says: "fine! and one stays fine, as long as one stays where one ought to stay!" matlab, the snake had better sit tight where he is (Siva's neck) or he is done for! How is that?
D: Ha, that is interesting!
A: Hey, what is that song, again??
B: "Garuda Saukyama?" (gets up with his empty cup)
C: (getting up as well, sings in an improvised tune) "Garuda Saukyama!"
(A joins C, totally offkey. They all stand up and walk towards the pantry to dump the cups).
D (to B): Btw, is it a Sivaji Ganesan song? I have seen a movie of his. The original of 'Virasat'.
B: It is 'Thevar Magan'. Awesome actor, that guy!
D: you bet!
(Exeunt, talking).

Note 1: The stuff in brackets above is mine. This conversation, I guess is by no means ATYPICAL in its sweep and chaotic evolution - although the level of pedantry on display might be a tad on the higher side!

Note 2 Btw(an aside, which could launch another track for the discourse of this post!), an eminent Indian academician told me many years ago: "These software guys - they are a rather limited crowd. What do they talk about except money, shares and well, other people's wives? Okay, add movies to that list! then what??"

Ed Witten - the Benchmark

Eminent Physicist A. Zee has written a textbook: "Quantum Field Theory in a Nutshell". In the preface of this book, I read this:

"This book began as a course I taught at Princeton as a beginning Asst. Prof. I was greatly fortunate to have had Ed Witten as my Teaching Assistant. Ed produced brilliant and lucidly written solutions for the problems - so much so that next year, I went and complained to the Chairman: 'Something is seriously wrong with the TA I have this year. He is not half as good as the guy I had last year!' "

I am not well-informed enough to guess the identity of the TA who suffers thus in comparison with Witten. But Zee's remark did remind me of something...

Cut to a time much closer to the present than when Witten was just a promising TA - indeed, to a time when he has already been anointed the Number One Mathematical Physicist in the World; to a time when this blogger was a graduate student of Physics.

While at Grad School, I am passionate about Physics - but this is often insufficient to get me past technicalities pertaining to the way it is practised in Indian Academia. During those days of struggle...

A holiday. I begin my solitary breakfast at our canteen. Hardly anybody about. A much senior (to self) colleague (let me refer to him as Camillo (*) ) makes an entry, looks around awkwardly at the empty tables and finally plants himself opposite to self. Some inanities are exchanged (and we reach the coffee stage of the meal) and he makes his first serious move.

Camillo: "So how is WORK?"
Self (a bit rattled on hearing the dreaded 4-lettered word): "Trying..."
Camillo: "Since when? Don't you think you ought to be getting results by now?"
Self: "Well, I dunno; have been trying..."
Camillo: "But, look at your contemporaries. --- and ---; have they not got papers by now?"
Self: "I guess so. Perhaps a couple each."
Camillo: "You *still* feel confident you too can manage? ... Can I give you some free advice?? (there is an ominous pause) You have some basics seriously wrong. You can't be in Physics if you are uncomfortable with Math and don't want to do calculations! Like,.... If I compare you with ---, "
Self (interrupting): "Look! can you please cut out those comparisons? I have no problems with criticism but personal comparisons...."
Camillo (interrupting back): "Oh, yeah, I am very sorry! You feel belittled by being compared with ...locals. Perhaps I should compare you with, well, WITTEN? That might just about satisfy you, eh??"

---
* - I decided to give latin name to this gent, as a tip of the hat to RK Narayan, who chose 'Marco' for the frigid archeologist in 'Guide'. I considered options ranging from 'Quasimodo' to 'Romeo' but finally settled on Camillo - a name with less interpretative possibilities and literary connotations.

Reflections On 'Angel Problem'

These are speculations on possible connections between critical phenomena (from Physics) and John Conway's 'Angel problem' (from game theory). The following two pages introduce the problem:

www.mathworld.wolfram.com/AngelProblem.html
www.msri.org/publications/books/Book29/files/conway.pdf

In brief, the 'Angel' and the 'Devil' play a game on a 2d infinite chessboard; the Angel tries to escape and the Devil tries to trap him in some finite region. On a 1d lattice the devil wins trivially. In 3d, the
Angel has plenty of space to move (it seems). but 2d remains open - nobody knows if the Angel can surely escape or the Devil can definitely trap him. Fuller details are in above sources, especially the latter.

My doubt: Are there connections between some statistical mechanics model (possibly possessing criticality) and the Angel problem?

As far as I know, one strong (if not defining) feature of criticality is the absence of a length scale in the system and it appearing the same at all length scales - in other words it is a fractal. An example would be a water-steam mixture at critical point - every bubble of steam would contain water drops of arbitrary sizes suspended within each of which would contain steam bubbles of arbitrary sizes and so on...

Conway's paper mentioned above (evocatively) describes a path on a 2d board which can give the Angel *some chance* of escape - this path (sections 7 and 9 of the paper) appears to show fractal property. So, one feels the system is critical (a leap there - and a gap in my understanding! the possible trajectory of the Angel is possibly fractal; not necessarily the system) - there presumably is some mapping between some statistical model that exhibits criticality and the game. Moreover, there is a general *promising* strategy for the Angel, attributed to Korner (and mentioned in Conway's paper) which seems to sweep over all length scales of the system - reminiscent of Scaling theory (?).

There is the issue of interpreting the criticality (of course, assuming it exists in 2d Angel problem). The guess is that the scenario is somewhat like this:

- If the game were played on a 1d lattice, whatever the Angel does, the Devil traps him with infinitely many moves to spare.
- In a 3d lattice of cubes , the angel can win and at every stage he has many cubes to move into and his path can fill a 3d subspace of the full space.
- In 2d chessboard , the situation is perhaps *critical* - the angel can avoid getting trapped but gets confined to a fractally subspace of the 2d
space; he needs to stay on and move on a 1-d fractal and any deviation from this path traps him.

I guess phenomena such as 'Percolation' and 'Anderson localization' in statistical mechanics (the essential nature of both phenomena show dependence on the dimension of the system; I guess the former is a classical phenomenon and the latter is quantum - not sure about the essential difference) might have some relvance to the Angel's quest for free movement.

One also wonders whether the fractal path of the Angel in 2d is like a 'strange attractor'. I have also seen (not understood) 'cool' phrases like 'fractal wave packets'. Any possible links with these thoughts ..? Or is it that the above is 'not even wrong' to borrow Pauli's phrase?!