Long ago

Long, long ago I used to spend numerous, uncountable evenings up on top of the leaky water tank on the roof of my hostel all alone watching flocks of green parakeets fly by against the backdrop of the blue waters of the lake and the expanse of trees, with the distant hum of homebound traffic. Hours would go by as the sun gradually set and the darkness crept in. The question remains -- what was running through my head? This was a question people used to ask me all the time -- Was I thinking profound thoughts? Was I was pining for somebody [nudge, nudge, wink, wink]? Was I contemplating the world's problems? Was I worrying about something? etc., etc. But it was never any of this and the answer was always truthfully "nothing".

Reading this little passage (Jon Elster quoting Georges Perec) puts it in perspective: The visions blurred, became jumbles; they could retain only a few vague and muddled bits, tenuous, persistent, brainless, impoverished wisps...They thought it was happiness they were inventing in their dreams. They thought their imagination was unshackled, splendid and, with each successive wave, permeated the whole world. They thought that all they had to do was to walk for their stride to be a felicity. But what they thought they were, when it came down to it, was alone, stationary and a bit hollow: A grey and icy flatland, infertile tundra.

That's it -- the bleak tundra of daydreams lacking any constraint which would descend into a numb blankness where my brain was simply processing stimuli without registering neither emotion nor thought or anything else for that matter including creating memories. This may be a complete and accurate summary of my life -- existence as an excuse to drift into the blankness of dreamy muddleness.



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Of Thumbs

Of Thumbs (Michel de Montaigne, 1533-1592)

Tacitus reports, that among certain barbarian kings their manner was, when they would make a firm obligation, to join their right hands close to one another, and intertwist their thumbs; and when, by force of straining, the blood it appeared in the ends, they lightly pricked them with some sharp instrument, and mutually sucked them.

Physicians say, that the thumbs are the master fingers of the hand, and that their Latin etymology is derived from “pollere.” The Greeks called them Anticheir, as who should say, another hand. And it seems that the Latins also sometimes take it in this sense for the whole hand;

“Sed nec vocibus excitata blandis,
Molli pollice nec rogata, surgit.”
["Neither to be excited by soft words or by the thumb." --Mart., xii. 98, 8.]

It was at Rome a signification of favor to depress and turn in the thumbs:

“Fautor utroque tuum laudabit pollice ludum:”
["Thy patron will applaud thy sport with both thumbs" --Horace]

and of disfavor to elevate and thrust them outward:

“Converso pollice vulgi,
Quemlibet occidunt populariter.”
["The populace, with inverted thumbs, kill all that come before them."--Juvenal, iii. 36]

The Romans exempted from war all such were maimed in the thumbs, as having no more sufficient strength to hold their weapons. Augustus confiscated the strength of a Roman knight, who had maliciously cut off the thumbs of two young children he had, to excuse them from going into the armies: and before him, the senate, in the time of the Italic war, had condemned Caius Vatienus to perpetual imprisonment, and confiscated all his goods, for having purposely cut off the thumb of his left hand, to exempt himself from that expedition. Some one, I have forgotten who, having won a naval battle, cut off the thumbs of all his vanquished enemies, to render them incapable of fighting and of handling the oar. The Athenians also caused the thumbs of the Aeginatans to be cut off, to deprive them of the superiority in the art of navigation.

In Lacedaemon, pedagogues chastised their scholars by biting
their thumb.  

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Lacedaemon = alternate name for Sparta (follow link to see map of ancient Greece)


And for comparison, follow the link below to see a map of modern Greece

The F.L.A.M.E.S. problem -- SOLVED!!

UPDATE: Here is a first draft

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:) I (and a friend of mine P) have come up with a rigorous solution to the FLAMES problem! It turns out to have a really simple (though not quite obvious) and extremely elegant solution. Full writeup of the proof to be posted within the next few hours.

F.L.A.M.E.S. -- is it fair?

This post is "inspired" by the so called FLAMES algorithm.

For the uninitiated, this is a very simple exercise. Take names of two people, usually of opposite genders and cross out all the common alphabets between the two names. Post that, count the number of alphabets that remain and get that number. Now write F L A M E S on a piece of paper and start counting from F to S, then go back to F and again the same process is done, with the number you have. Every time the count ends, cross out that alphabet, and restart counting from the next alphabet. Repeat this till you cross out five of the alphabets and remain with one....

I've never encountered this before even though it seems to be common knowledge, maybe this was for the better. Anyway, this is a curious little calculation game and out of curiosity as to whether this "game" is really fair or whether it has something about it that makes it unpredictable, I did a little empirical investigation.

Terminology
Mismatched letters: If the names are GEORGE W. BUSH and NELSON MANDELA. Then the number of mismatches is the number of letters that do not appear in both names. Here GEORGE W. BUSH and NELSON MANDELA, so the number of mismatches = 7 + 10 = 17. For simplicity, lets call the number of mismatches M. With that background, I generated the outcomes and the sequences by which they arise for every M in the range 1 to a 1000.

Sequence: The sequence in which the letters of FLAMES are struck out, i.e. M then A then L then F then E then S, etc.

Some interesting findings(yes, yes, I dont have a rigorous proof (as yet) but the following seem to hold true for M = [1,1000])

• Observation - 1: There are only 60 unique sequences for any value of M. Why is this interesting? Since there are 6 letters in FLAMES, the number of possible sequences by which each of these letters can be struck out is 6! = 720. But of these only 60 can occur.
  
  
• Observation - 2: All of these unique sequences occur in the range M = 1 to 60. This means that every M in the range 1 - 60 has a unique sequence associated with it. From M = 61 onwards, the sequences begin to repeat. This is probably why the game seems so unpredictable as most reasonable pairs of names would have M in this range and at every step it seems like you cannot predict what outcome will emerge.
  
  
• Observation - 3: For M greater than 60, the sequences begin to cycle with period 60. The sequences for M = 1, 61, 121, .... are identical and so are the sequences for M= 2, 62, 122, 182,.., for M = 3,etc. In fact this is true for all M in the range 1 to 60 where the sequences for any M' = 60*n + M are identical (where n belongs to the Natural numbers).
  [I dont have a proof of this beyond exhaustive checking]
  
  Observation - 4: Each of the six possible outcome is equally likely in the range 1-60. (see Figure 2 below). So, if pairs of names can uniformly lie in the M = 1 to 60 range, then the outcome is "fair". But if we look at specific ranges then it is not so fair (see Figures 3 onward).
  

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Figure 1: Variation in predicted outcome for different numbers of mismatched letters. Looks arbitrary but is it so?

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Figure 2: Percentage of each possible outcome for numbers of mismatched letters over the entire range 1 to 60. Surprise -- every outcome is equally likely in this range!!!

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Figure 3: Percentage of each possible outcome for numbers of mismatched letters varying from 1 to 10. Definitely skewed towards 'E'

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Figure 4: Percentage of each possible outcome for numbers of mismatched letters varying from 11 to 20. Absolutely no 'S'

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Figure 5: Percentage of each possible outcome for numbers of mismatched letters varying from 21 to 30. Absolutely no 'L'

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Figure 6: Percentage of each possible outcome for numbers of mismatched letters varying from 31 to 40. Absolutely no 'E'

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[More updates on this investigation shortly...]
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A thought (not mine)

From: "The Light of Asia: Book the Eighth" by Edwin Arnold

Ho! ye who suffer! know

Ye suffer from yourselves. None else compels,
None other holds you that ye live and die,
And whirl upon the wheel, and hug and kiss
Its spokes of agony,
Its tire of tears, its nave of nothingness.

Is this vacuous profundity or a glimpse of the "truth"? And then we have the koan

Circumstances arose one day which delayed preparation of the dinner of a Soto Zen master, Fugai, and his followers. In haste the cook went to the garden with his curved knife and cut off the tops of green vegetables, chopped them together, and made soup, unaware that in his haste he had included a part of a snake in the vegetables.

The followers of Fugai thought they had never tasted such great soup. But when the master himself found the snake's head in his bowl, he summoned the cook. "What is this?" he demanded, holding up the head of the snake.

"Oh, thank you, master," replied the cook, taking the morsel and eating it quickly.

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Elements

With the incredible amount of secondary content on the World Wide Web, it is always a rare and extremely delightful experience to stumble on a website with not just excellent primary content but a very high "coolness" coefficient. Today is one such day where I came across the website on Elementymology (by Peter van der Krogt). As the name suggests, it has the detailed etymology of the different elements on the periodic table and does a very excellent job of it (from what I can tell).

Absolutely do check it out!

(Also, see Gernot Katzer's brilliant website on the spices of the world)




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