Putting gives

which can happen if either or . Note that the function which is identically zero satisfies the functional equation. If is not this function, i.e., if for at least one value of , then plugging that value of (say ) into the equation gives . Also, for any , the equation forces as well. Further, so for all .

Next, putting gives , and by induction . Putting in place of in this gives which means (note we’re using here). And again, . So , which completely defines the function at rational points.

[As , it can be written as for some constant , which gives for rational .]

To extend this function to irrational numbers, we need some further assumptions on , such as continuity. It turns out that being continuous at any point is enough (and implies the function is everywhere): note that . Even being Lebesgue-integrable/measurable will do.

Else, there are discontinuous functions satisfying the functional equation. (Basically, we can define the value of the function separately on each “independent” part. That is, define the equivalence class where and are related if for rationals and , pick a representative for each class using the axiom of choice (this is something like picking a basis for , which corresponds to the equivalence class defined by the relation ), define the value of the function independently for each representative, and this fixes the value of on . See this article for more details.)

To step back a bit: what the functional equation says is that is a homorphism from , the additive group of real numbers, to , the multiplicative monoid of real numbers. If is not the trivial identically-zero function, then (as we saw above) is in fact a homomorphism from , the additive group of real numbers, to , the multiplicative group of positive real numbers. What we proved is that the exponential functions are precisely all such functions that are nice (nice here meaning either measurable or continuous at least one point). (Note that this set includes the trivial homomorphism corresponding to : the function identically everywhere. If is not this trivial map, then it is in fact an isomorphism.)

Suppose a point moves in the plane such that its acceleration is always perpendicular to its velocity, and of the same magnitude. What is its path like?

To set up notation: let’s say the point’s position at time is , its velocity is , and its acceleration is .

The result of rotating a point by 90° is . (E.g. see figure below)

So the fact that acceleration is at right angles to velocity means that , or, to write everything in terms of the velocity,

where we can get rid of by substituting the second equation (in the form ) into the first:

or in other words

By some theory about ordinary differential equations, which I don’t know (please help!) (but see the very related example you saw in high school, of simple harmonic motion), the solutions to this equation are and and any linear combination of those: the solution in general is

where and is the angle such that and . And the fact that gives . So . Note that is indeed perpendicular to as we wanted.

The actual trajectory can be got by integrating

to get and . This trajectory is a point moving on a circle centered at point and of radius , with speed or unit angular speed. Note that velocity is also perpendicular to the point’s position wrt the centre of the circle, as velocity is tangential to the circle, as it should be.

With a suitable change of coordinates (translate the origin to , then rotate the axes by , then scale everything so that ), this is the familiar paremetrization of the circle.

Note: Just as we derived from assuming that the acceleration is perpendicular to velocity, we can, by assuming that velocity is perpendicular to position, identically derive , i.e. that the point moves on a circle.

Turns out it’s very easy, and we can basically use the same input method (UIM) as in Linux.

1. Get MacUIM from its website
2. Install it.
3. Go to System Preferences -> Language & Text -> Input Sources, and turn on MacUIM. Tick “Show Input menu in menu bar” too.
4. I now have three input methods: US, EasyIAST (see earlier post), and MacUIM (Roman).
5. Go to System Preferences -> MacUIM -> General, and in Input method, choose m17n-kn-itrans
6. Go to System Preferences -> MacUIM -> Helper, tick “Use Helper-Applet”, and in the list at the right, tick m17n-kn-itrans.
   
7. [Just for me] I have some changes to kn-itrans.mim, to make it closer to HK (and remove nonsense like “RRi” or whatnot just to type ಋ): download this file kn-itrans.mim, and remove the pdf extension. It goes into /Library/M17NLib/share/m17n/kn-itrans.mim

So: let

We will take the following two for granted (both can be proved with some effort):

1. Both power series are convergent.
2. The power series can be differentiated term-wise.

As suggested by (2) above, the first thing we observe is that and .

So firstly:

which means that is a constant and does not vary with . Putting shows that and , so for all .

Secondly, define the angle as a function of , by . (To be precise, this defines up to a multiple of , i.e. modulo .)
Differentiating the left-hand side of this definition gives

(where means )
while differentiating the right-hand side gives

The necessary equality of the two tells us that , which along with the initial condition that says , gives (or to be precise, ).

In other words, we have shown that the power series and satisfy and therefore and for some . The observation that (or our earlier observation that for all ) gives , thereby showing that and .

So much for and . Just as an aside, observe that if we take to be a symbol satisfying , then

the right hand side of which looks very much like the result of “substituting” in the known (real) power series

(which itself can be proved using the term-wise differentiation above and the defining property , say).

So this is one heuristic justification for us to define .
Or, if we define as the result of substituting in the real power series for , this proves that .

a ā i ī u ū ṛ ṝ ḷ ḹ e ai o au ṃ ḥ
k kh g gh ṅ
c ch j j ñ
ṭ ṭh ḍ ḍh ṇ
t t d dh n
p ph b bh m
y r l v ś ṣ s h

In other words, the special characters needed are:

• Letters with macron above: ā ī ū ṝ ḹ plus it may be occasionally useful to have ē and ō as well
• Letters with dot below: ṭ ḍ ṇ ṣ (the retroflex consonants), also the vowels ṛ ṝ ḷ ḹ, plus ṃ and ḥ (anusvāra)
• Letters with other marks above: ṅ ñ ś

There is a keyboard layout that does this: It’s called “EasyUnicode”, created by Toshiya Unebe (Nagoya University), and is documented at http://ebmp.org/p_easyunicode.php (“EasyUnicode version 5″ it says) (PDF version), and you can download it from http://www.ebmp.org/p_dwnlds.php (EBMP) (=Early Buddhist Manuscripts Project, University of Washington) or also http://www.palitext.com/subpages/PC_Unicode.htm “Pali Fonts for PC and Unicode”. (Page in Japanese.)

This keyboard layout is just like the usual (US English) layout ordinarily, but when you hold down the Alt (Option) key and press a, you get ā, similarly Option+s gives ś, Option+n gives ñ and Option+g gives ṅ, etc. The full mapping is available along with other documentation in the download above.

This is very convenient. One issue with the layout is that also overrides a lot of keys for no apparent reason (Ctrl-A / Ctrl-E etc. stopped working for me), so I got Ukelele from SIL, and wrote my own keyboard layout. I’ve called it EasyIAST, and it is available here for now. I plan to add a README etc. and distribute it in some proper way later; for now you can use the instructions from EasyUnicode above. If you find it useful and/or make any improvements, please let me know as well.

If some time is available, it would be good to make a Devanagari keyboard layout along the same lines.

He pulled open the next door, both of them hardly daring to look at what came next — but there was nothing very frightening in here, just a table with seven differently shaped bottles standing on it in a line.
“Snape’s,” said Harry. “What do we have to do?”
They stepped over the threshold, and immediately a fire sprang up behind them in the doorway. It wasn’t ordinary fire either; it was purple. At the same instant, black flames shot up in the doorway leading onward. They were trapped.
“Look!” Hermione seized a roll of paper lying next to the bottles. Harry looked over her shoulder to read it:

Danger lies before you, while safety lies behind,
Two of us will help you, whichever you would find,
One among us seven will let you move ahead,
Another will transport the drinker back instead,
Two among our number hold only nettle wine,
Three of us are killers, waiting hidden in line.
Choose, unless you wish to stay here forevermore,
To help you in your choice, we give you these clues four:
First, however slyly the poison tries to hide
You will always find some on nettle wine’s left side;
Second, different are those who stand at either end,
But if you would move onward, neither is your friend;
Third, as you see clearly, all are different size,
Neither dwarf nor giant holds death in their insides;
Fourth, the second left and the second on the right
Are twins once you taste them, though different at first sight.

I became curious about whether this is just a ditty Rowling made up, or the puzzle actually makes sense and is consistent. It turns out she has constructed it well. Let’s take a look. This investigation can be carried out by hand, but we’ll be lazy and use a computer, specifically Python. The code examples below are all to be typed in an interactive Python shell, the one that you get by typing “python” in a terminal.

So what we have are seven bottles, of which one will take you forward (F), one will let you go back (B), two are just nettle wine (N), and three are poison (P).

>>> bottles = ['F', 'B', 'N', 'N', 'P', 'P', 'P']

The actual ordering of these 7 bottles is some ordering (permutation) of them. As 7 is a very small number, we can afford to be inefficient and resort to brute-force enumeration.

>>> import itertools
>>> perms = [''.join(s) for s in set(itertools.permutations(bottles))]
>>> len(perms)
420

The set is needed to remove duplicates, because otherwise itertools.permutations will print 7! “permutations”. So already the number of all possible orderings is rather small (it is ). We can look at a sample to check whether things look fine.

>>> perms[:10]
['PNFNPBP', 'NPPBNFP', 'FNNPBPP', 'PPPFNBN', 'NPPNBFP', 'PFNNBPP', 'NPBPPFN', 'NBNPPFP', 'NPPFBNP', 'BNPFNPP']

Now let us try to solve the puzzle. We can start with the first clue, which says that wherever a nettle-wine bottle occurs, on its left is always a poison bottle (and in particular therefore, a nettle-wine bottle cannot be in the leftmost position). So we must restrict the orderings to just those that satisfy this condition.

>>> def clue1(s): return all(i > 0 and s[i-1] == 'P' for i in range(len(s)) if s[i]=='N')
...
>>> len([s for s in perms if clue1(s)])
60

(In the code, the 7 positions are 0 to 6, as array indices in code generally start at 0.)
Then the second clue says that the bottles at the end are different, and neither contains the potion that lets you go forward.

>>> def clue2(s): return s[0] != s[6] and s[0] != 'F' and s[6] != 'F'
...
>>> len([s for s in perms if clue1(s) and clue2(s)])
30

The third clue says that the smallest and largest bottles don’t contain poison, and this would be of help to Harry and Hermione who can see the sizes of the bottles. But as we readers are not told the sizes of the bottles, this doesn’t seem of any help to us; let us return to this later.

The fourth clue says that the second-left and second-right bottles have the same contents.

>>> def clue4(s): return s[1] == s[5]
...
>>> len([s for s in perms if clue1(s) and clue2(s) and clue4(s)])
8

There are now just 8 possibilities, finally small enough to print them all.

>>> [s for s in perms if clue1(s) and clue2(s) and clue4(s)]
['PPNBFPN', 'BPNPFPN', 'BPFPNPN', 'BPPNFPN', 'PNPFPNB', 'BPNFPPN', 'PPNFBPN', 'PNFPPNB']

Alas, without knowing which the “dwarf” and “giant” bottles are, we cannot use the third clue, and this seems as far as we can go. We seem to have exhausted all the information available…

Almost. It is reasonable to assume that the puzzle is meant to have a solution. So even without knowing where exactly the “dwarf” and “giant” bottles are, we can say that they are in some pair of locations that ensure a unique solution.

>>> def clue3(d, g, s): return s[d]!='P' and s[g]!='P'
...
>>> for d in range(7):
...   for g in range(7):
...     if d == g: continue
...     poss = [s for s in perms if clue1(s) and clue2(s) and clue4(s) and clue3(d,g,s)]
...     if len(poss) == 1:
...       print d, g, poss[0]
... 
1 2 PNFPPNB
1 3 PNPFPNB
2 1 PNFPPNB
2 5 PNFPPNB
3 1 PNPFPNB
3 5 PNPFPNB
5 2 PNFPPNB
5 3 PNPFPNB

Aha! If you look at the possible orderings closely, you will see that we are down to just two possibilities for the ordering of the bottles.
Actually there is some scope for quibbling in what we did above: perhaps we cannot say that there is a unique solution determining the entire configuration; perhaps all we can say is that the puzzle should let us uniquely determine the positions of just the two useful bottles. Fortunately, that gives exactly the same set of possibilities, so this distinction happens to be inconsequential.

>>> for d in range(7):
...   for g in range(7):
...     if d == g: continue
...     poss = [(s.index('F'),s.index('B')) for s in perms if clue1(s) and clue2(s) and clue4(s) and clue3(d,g,s)]
...     if len(set(poss)) == 1:
...       print d, g, [s for s in perms if clue1(s) and clue2(s) and clue4(s) and clue3(d,g,s)][0]
... 
1 2 PNFPPNB
1 3 PNPFPNB
2 1 PNFPPNB
2 5 PNFPPNB
3 1 PNPFPNB
3 5 PNPFPNB
5 2 PNFPPNB
5 3 PNPFPNB

Good. Note that there are only two configurations above. So with only the clues in the poem, and the assumption that the puzzle can be solved, we can narrow down the possibilities to two configurations, and be sure of the contents of all the bottles except the third and fourth. We know that the potion that lets us go forward is in either the third or the fourth bottle.

In particular we see that the last bottle lets us go back, and indeed this is confirmed by the story later:

“Which one will get you back through the purple flames?”
Hermione pointed at a rounded bottle at the right end of the line.
[…]
She took a long drink from the round bottle at the end, and shuddered.

But we don’t know which of the two it is, as we can’t reconstruct all the relevant details of the configuration. Perhaps we can reconstruct something with the remaining piece of information from the story?

“Got it,” she said. “The smallest bottle will get us through the black fire — toward the Stone.”
Harry looked at the tiny bottle.
[…]
Harry took a deep breath and picked up the smallest bottle.

So we know that the bottle that lets one move forward is in fact in the smallest one, the “dwarf”.

>>> for d in range(7):
...   for g in range(7):
...     poss = [s for s in perms if clue1(s) and clue2(s) and clue4(s) and clue3(d,g,s)]
...     if len(poss) == 1 and poss[0][d] == 'F':
...       print d, g, poss[0]
... 
2 1 PNFPPNB
2 5 PNFPPNB
3 1 PNPFPNB
3 5 PNPFPNB

This narrows the possible positions of the smallest and largest bottles (note that it says the largest bottle is one that contains nettle wine), but still leaves the same two possibilities for the complete configuration. So we can stop here.

Conclusion
What we can conclude is the following: apart from the clues mentioned in the poem, the “dwarf” (the smallest bottle) was in either position 2 (third from the left) or 3 (fourth from the left). The biggest bottle was in either position 1 (second from the left) or 5 (sixth from the left). With this information about the location of the smallest bottle (and without necessarily assuming the puzzle has a unique solution!), Hermione could determine the contents of all the bottles. In particular she could determine the location of the two useful bottles: namely that the bottle that lets you go back was the last one, and that the one that lets you go forward was the smallest bottle.

>>> for (d,g) in [(2,1), (2,5), (3,1), (3,5)]:
...   poss = [s for s in perms if clue1(s) and clue2(s) and clue4(s) and clue3(d, g, s)]
...   assert len(poss) == 1
...   s = poss[0]
...   assert s.index('B') == 6
...   assert s.index('F') == d
...   print (d,g), s
... 
(2, 1) PNFPPNB
(2, 5) PNFPPNB
(3, 1) PNPFPNB
(3, 5) PNPFPNB

It is not clear why she went to the effort to create a meaningful puzzle, then withheld details that would let the reader solve it fully. Perhaps some details were removed during editing. As far as making up stuff for the sake of a story goes, though, this is nothing; consider for instance the language created for Avatar which viewers have learned.

Added:
See also http://www.zhasea.com/logic/snape.html which does it by hand, and has a perfectly clear exposition (it doesn’t try the trick of guessing that solution is unique before reaching for the additional information from the story).

The other is that a Kanarese poem defies anything like literal translation into another language. To give any idea of the spirit of the original it would be necessary to paraphrase freely, to expand the terse and frequent metaphors into similes, and to give a double rendering of many stanzas. An example will make this clear. The opening stanza of the Jaimini Bharata is given in Sanderson’s translation as follows:

May the moon-face of Vishnu, of Devapura, always suffused with moonlight smile, full of delightful favour-ambrosial rays—at which the chakora-eye of Lakshmi is enraptured, the lotus-bud heart of the devout expands, and the sea of the world’s pure happiness rises and overflows its bounds—give us joy.

The following is an attempt, by means of a freer rendering, to retain something of the spirit of the original:

When the full moon through heaven rides,
Broad Ocean swells with all its tides ;
The lotus blossom on the stream
Opens to drink the silv’ry beam ;
And far aloft with tranced gaze
The chakor bird feeds on the rays.

So, when great Vishnu’s face is seen,—
Whom men adore at Devapore—
Like to the sea, the devotee
Thrills with a tide of joy ;
Like to the flower, that blissful hour
The heart of the devout expands ;
And Lakshmi Queen, with rapture keen,
Watches with ever-radiant face
For her great Consort’s heavenly grace.
O may that grace be ours !

I’m wondering about this change. Apart from the versification—you know, being an actual poem instead of stilted prose—when it comes to just the idea, is it better? Why? How? Is it more readable? More understandable? Most importantly, does this change better “retain the spirit of the original”?

[Aside: just to be mischievous, we can with the wonders of technology do the following:

to ruin the poem.]

For one thing, he has changed the metaphor (rūpaka) of the original into simile (upamā).
Probably the reason is that the compressed quality of the original, a prominent characteristic of Sanskrit and other classical Indian literature, is unsuitable for English, whose readers are typically unprepared for it. Is there more to it? Is this a general difference between the two literary cultures?

I’m wondering all this because Daniel Ingalls says something along similar lines in his honestly-written general introduction “Sanskrit poetry and Sanskrit Poetics” (from his translation of the Subhāṣita-ratna-kośa anthology):

As a result, Sanskrit is lacking in what is perhaps the chief force of English poetry: its kinesthetic effect. What I mean can be shown by an old ballad:

Martinmas wind, when wilt thou blow
and shake the green leaves off the tree…

One can feel the leaves shaking, and one shivers in the next line to the “Frost that freezes fell / and blowing snow’s inclemency.” One can find verses that produce this muscular effect in Bengali, and although I cannot speak at first hand of other modern Indian literatures, I imagine that one can find the effect in them as well. But it is only rarely that one finds it in Sanskrit. The powers of Sanskrit are of a different order.
[…]
[The following verse] is by Yogeśvara, an excellent poet who is capable of better things. In it he uses a strikingly elaborate metaphor:

Now the great cloud-cat,
darting out his lightning tongue,
licks the creamy moon
from the saucepan of the sky.

The effect here is gained by intellectual, entirely rational means. The metaphor is complete in every detail: cat, tongue, cream, and saucepan—cloud, moon, lightning, and sky. It is almost like an exercise from a manual of logic under the chapter “Analogy.” Compare the verse with a well-known passage of T. S. Eliot which uses several similar ideas, but uses them very differently:

The yellow fog that rubs its back upon the window-panes
The yellow smoke that rubs its muzzle on the window-panes,
Licked its tongue into the corners of the evening,
Lingered upon the pools that stand in drains, …

This from one who is often called an intellectual poet. And yet Eliot gets his effect in every line from the irrational, the strong but imprecise memory we have of fog and cats, the childhood associations of certain words and idioms. Consider the line: “Licked its tongue into the corners of the evening.” It brings to sudden flower certain homely and completely natural phrases: “licks his tongue around the bowl,” or “licks his tongue into the corner of the dish.” The idiom is suddenly transfigured by bringing it into juxtaposition with the last three words, “of the evening.” This transfiguration of language becomes impossible without a natural-language basis.

Is there a general point here that English poetry uses vague, fuzzy, but “kinesthetic” effects where Sanskrit (or classical Indian) poetry uses compressed metaphors that paint a precise and detailed picture? I think there is some merit to the idea that, by and large, Sanskrit poetry is “static”, not “dynamic”. It is not a stream in motion; it hasn’t any “flow”. It is more a pearl in itself, that dazzles as you read. If poetry is imagination and the evocation of something other-worldly, it seems to me that Sanskrit poetry in general / at its best, conjures a world that one can calmly dwell in for a while, not an evocative fleeting idea that escapes as you try to grasp it, one which has appeal more in the chasing. Consider the importance accorded ultimately to stability / sthāyī-bhāva in all Indian arts, from poetry to theatre to dance.

This requires more thought and elaboration, but one may as well quote the final lines of Ingalls’s introduction (emphasis mine):

One may argue today, as the Sanskrit critics argued in the past, the relative importance of the various factors of Sanskrit verse which I have discussed. Vocabulary, grammar, meter: these are all necessary. Figures of speech, both verbal and intellectual, furnish delight. Mood is what is sought, though the grand successes of Sanskrit I would say go beyond mood to a sort of universal revelation, to what James Joyce, drawing on the vocabulary of religion, called an epiphany. To achieve this success impersonality is a prerequisite and suggestion is the chief instrument. If I were to single out for admiration one factor above the others in this complex it would be suggestion, not because it is unknown in other languages but because the Sanskrit poets use it with such brilliance and because it seems to me the most intimately connected of all the factors with the excitement, the sudden rushing of the mind into a delightful, calm expansion, that one occasionally derives from Sanskrit poetry and that brings one who has once known it constantly back for further draughts.

Recall: To get a power of 2 that starts with a prefix (like ), we want such that the fractional part of lies between those of and (all logarithms here to base 10), and similarly to get a Fibonacci number starting with , we want (with some hand-waving) such that the fractional part of lies between those of and . The more general problem is:

Problem: Given an irrational number and an interval , find such that lies in the interval .

Here is one method, based on Edward Burger’s book Exploring the Number Jungle. Let be the midpoint of the interval . Then we are trying to find such that is close to .

• Find a fraction approximating , such that . (These are the convergents of the continued fraction of , but in practice it seems you can also get away with taking semi-convergents that may not satisfy this property.)
• Let be the closest integer to . Note that this automatically means
• Write with . This you can do quite easily with the Euclidean algorithm.
• Then for and , we have (it is a simple exercise to prove this)
  
• This means that the distance between and is small, modulo 1. If this distance turns out to be still too large, start with a bigger convergent .

I think I had some code to post as well (hey, what’s the actual Fibonacci number that starts with 2012?), but it needs to be cleaned up… probably this works (in Sage).

The thing we’re doing here is called inhomogeneous Diophantine approximation.

[Originally posted on math.stackexchange, here and here.]

The Day Before You Came is the last song that ABBA recorded. It is interesting for more than being their swansong: it is also highly atypical of ABBA.

Here is the song (Link is to Dailymotion because Youtube has videos only of live perfomances):

The music and the video are non-ABBAish too (gone are the exuberance and the outlandish clothes, the video is almost entirely Agnetha with the others getting only a few seconds of screen time and no action), but confining ourselves to the lyrics:

Must have left my house at eight, because I always do
My train, I’m certain, left the station just when it was due
I must have read the morning paper going into town
And having gotten through the editorial, no doubt I must have frowned
I must have made my desk around a quarter after nine
With letters to be read, and heaps of papers waiting to be signed
I must have gone to lunch at half past twelve or so
The usual place, the usual bunch
And still on top of this I’m pretty sure it must have rained
The day before you came

I must have lit my seventh cigarette at half past two
And at the time I never even noticed I was blue
I must have kept on dragging through the business of the day
Without really knowing anything, I hid a part of me away
At five I must have left, there’s no exception to the rule
A matter of routine, I’ve done it ever since I finished school
The train back home again
Undoubtedly I must have read the evening paper then
Oh yes, I’m sure my life was well within its usual frame
The day before you came

Must have opened my front door at eight o’clock or so
And stopped along the way to buy some Chinese food to go
I’m sure I had my dinner watching something on TV
There’s not, I think, a single episode of Dallas that I didn’t see
I must have gone to bed around a quarter after ten
I need a lot of sleep, and so I like to be in bed by then
I must have read a while
The latest one by Marilyn French or something in that style
It’s funny, but I had no sense of living without aim
The day before you came

And turning out the light
I must have yawned and cuddled up for yet another night
And rattling on the roof I must have heard the sound of rain
The day before you came

It is putatively a love song, but it makes no explicit declaration of love. The entire lyrics of the song are merely a catalogue of an average day’s events. The song is a timetable. You’ve got to admire the sheer cheek of this, if nothing else. :-) (a la Peter Cushing lives in Whitstable.)

Yet it is interesting. I think this could be argued to be a first-class example of svabhāvokti, the achievement of a poetic effect by simply and ably describing things as they are. The author of the song describes her usual boring routine, presumably to contrast against her much-changed life after meeting the “you” of the song. This is an inversion of the much more common poetic convention, that of recalling time spent in love, time spent together, etc. (Bilhana’s चौरपंचाशिका Chaura-panchashika comes to mind.)

It is linguistically interesting as well: with few exceptions, the verbs are all accompanied by “must have”, “I’m certain”, “undoubtedly”, “I’m sure”, or “I think”. [I'm not sure what this characteristic of the verb is called. In the old days I think we'd just call it verb tense, but now "tense" is reserved for verb forms that indicate time, and "tense/aspect/mood" is used instead. I don't know what this particular "must have"-type of construction is called: a Google search throws up terms like near-certainty mode, deductive, non-factual, evidential, presumptive, etc.] It’s as if the author isn’t sure. (It is remarkable that, in general, adding “I’m certain” or “undoubtedly” makes a statement less certain.) One interpretation is that the narrator after meeting her lover no longer remembers her life from before; so different it has become. But considering the level of detail, is this really possible? Besides, how much can a daily routine really change? The trains will still run at the same time, at any rate. A different possibility suggests itself: that the narrator is simply unreliable.

Suddenly a lot of things make sense: she is not describing her life “before you came”. She hasn’t met anyone at all, but is instead hoping to meet someone that will turn her colourless life exciting. The song is not reminiscences about a dull past (who would want to do that?), but she is instead imagining how different she will feel in the future after finding someone, yet so sad is her case that all she can imagine and describe is her present. The video lends credence to this idea: it starts with a scene of her daily commute, a guy appears and the video goes into a (presumably) imagined mode, before the guy disappears and she’s back at the same train station.

This would finally explain why the prevailing mood of the song, as experienced by the listener, is not one of love (it does not evoke śṛṅgāra शृङ्गार in other words): instead it is one of melancholy and weariness.

See also: Guardian article.

Future work:

• Extend this data to all pages in the dictionary (around 454/2 = 227)
• Write a web interface where you can type a word/prefix and be taken to the exact page

Feel free to take it up.

Some have even sought to assign Kalidasa to Kashmir, on no grounds stronger than that he was good at what he did!

Not for nothing is शारदा देवी called काश्मीर-पुरवासिनी.

If the answer is obvious to you (or you don’t care), you can stop reading.

The answer for both is:

• Yes.
• There are infinitely many such numbers.
• In fact, the fraction of (powers of 2 / Fibonacci numbers) starting with 2012 is exactly

  

Similarly with any other prefix p (of any length) in place of 2012. Proof follows.

A number x starts with a prefix p if and only if for some k ≥ 0,

Thus a power of 2, say 2ⁿ, starts with p iff

for some

Taking logarithms to base 10 and simplifying, this is equivalent to

for some

This is saying that the fractional part of lies between the fractional parts of and For example, if , this means that the fractional part of lies between and .

Similarly, for Fibonacci numbers, as is (or should be) well-known, the nth Fibonacci number F_n is the closest integer to , where is the golden ratio. So starts with iff

Taking logarithms to base 10 and simplifying, while ignoring the annoying which becomes irrelevant in the limit (this line is not rigorous), this is equivalent to

which means that the fractional part of lies between the fractional parts of and . For , this means that the fractional part of lies between and .

In either case, we are trying to make the fractional part of , for some irrational number , lie in some interval. The relevant fact is this:
Theorem 1: for any irrational number , the sequence (where denotes the fractional part of ) is dense in .
or, in other words,
Theorem 1: For any irrational number , the sequence is dense modulo .
Proving this theorem is a good exercise.

This means that for any interval you want, you can always find some such that the fractional part of lies in your interval. In fact, because the sequence is dense, you can find an infinite sequence of such that the fractional parts of converge to the midpoint (say) of the desired interval. This proves the first two facts of the answer, and for the third we need a stronger theorem:

Theorem 2 [Equidistribution theorem]: For any irrational number , the numbers are uniformly distributed modulo 1.

This means that for any interval of size (say), the fraction of integers for which lies in the interval satisfies

This proves the third fact. The fraction of Fibonacci numbers (or of powers of a number that is not a power of 10) that start with a prefix is exactly where log is to base 10.

That much is standard. And non-constructive. We are assured of the existence of such numbers, but how do we actually find one?

The answer (or one answer), as it so often does in these problems, involves continued fractions. Here is one method, [to be continued when I wake up :p]
Edit: Continued here.

Yesterday A couple of weeks ago Nearly three months ago, I attended an avadhana, by Shatavadhani Dr. R. Ganesh. Already (the very next day) my friend Mohan has written about it in great detail, but since I had started scribbling something down then, I thought I should write a post anyway: it is easily the most incredible feat of the human mind I have ever witnessed. (Unfortunately this may not be saying much, for I have not seen, say, George Koltanowski play 34 games of blindfold chess simultaneously. So suffice it to say that repeatedly we in the audience had trouble believing that what we were seeing was really happening!)

The word avadhāna, in common usage, means “concentration” or “attention”. In the specialised sense here, an “avadhana” is a performance of sorts, an exhibition of mental concentration, multi-tasking, literary skill, erudition and wit.

The basic format is this: there is a performer (avadhani) seated on stage, and also with him are several “questioners” (pṛcchakas). The performer has no access to pen or paper or any resources other than his head. The questioners give him various tasks in parallel, and he must answer them all, dividing his attention between them.

And these are no simple tasks! Some are harder than others, but all require great skill and concentration, especially to do them without any secondary memory (like, say, a piece of paper). Some are scheduled to happen in order, some are interrupt-driven, and all require concentration. This was an “Ashtavadhana”, so there were eight questioners/tasks (five of them had to do with composing poetry, and the rest were of a different nature):

1. Nishedhakshara (“letters forbidden”): the questioner gives him a topic on which to compose a verse in Sanskrit, and a metre to compose it in. Already a difficult task for mortals — metres in Sanskrit are to be strictly adhered to in every syllable; there is no amount of permitted variation as in English — but it’s nothing compared to the devilish twist here: the performer must compose the verse interactively, one letter at a time, and after each letter that he announces, the questioner imposes a constraint on what the next letter must not be. Thus for instance, each time the performer appears to be using a word, the questioner can prevent him from completing that word. He must find a way around this constraint, and so on till the entire line is completed.
This is done in four rounds: he composes one line at a stretch (along with the back-and-forth with the Nishedhakshari) in one round, and when the next round arrives, after some 40–50 minutes during which he has been facing other questions, he must pick up where he left off, relying on his memory with no external assistance. (E.g. he isn’t read back what he had composed as the first line.)

2. Samasya-purti: A traditional challenge, in which a line is given, and the performer has to compose a verse with it as its last line. Often the “problem” line will be nonsensical, or wholly inappropriate or even obscene, and the poet has to compose his “solution” poem such that the line makes sense in context. Usually, this involves clever tricks to engineer a radical reinterpratation of the line. Ganesh gave an example from one of his earlier programmes: a line like “Hari-worshipping atheists are numerous” was worked into a poem about music, describing a raga and ending with “Bila/hari-worshipping atheists are numerous”. (Bilahari is a popular raga in Carnatic music.)
In this instance, this round was in Kannada. Also done in four rounds, one line at a time.

3. Datta-pada (“given words”): Poem. Given topic, given metre. The catch: he is given four words that must occur in the poem, but the words are from another language. For instance, here the questioner wanted words like “ape” and “monkey” to appear in each line, and the performer’s task is to compose a poem in Kannada, with the English words occurring as segments of Kannada words. One line per round.

4. Chitrakavya (constrained writing): At the fringe of Sanskrit literature is an incredible body of constrained writing, of everything from palindromes to verses which satisfy difficult constraints on their letters, or which can be re-arranged into certain “shapes”, and so on. Here the performer is asked to compose a poem on a given topic, satisfying the constraint. One line per round.

5. Magic square: At the start of the performance someone from the audience (or the questioner) calls out a number, and the task is to construct a 5×5 magic square — a square of distinct numbers, such that every row, every column, and both diagonals sum to that number. This task is interrupt-driven: at any time during the performance — such as when he is composing a line of some poem — the performer is interrupted by the questioner who asks him for the entry in a particular row and column; the performer must give him a number and return to this task. (So 25 interruptions in all, throughout the performance.) Of all the tasks, this is the only one I feel even remotely confident of doing with a little practice, but it seemed to be the one that impressed the audience the most! Nevertheless, it is not trivial, and is definitely a distraction that can draw one’s full attention for at least a few moments. (Other avadhanas sometimes involve someone who, say, rings a bell at random moments, and the avadhani has to maintain a count of how many times the bell has rung, even as he concentrates on other tasks. A magic square is probably more impressive.)

6. Aprastuta-prasanga: Various meddling distractions and banter. This is interrupt-driven too. This questioner interrupts frequently, asking questions and making comments, and in general needling the performer and pulling his leg. This may include random humorous remarks, or the latest news, politics, celebrity gossip, whatever. The performer comes up with witty replies (well, Dr. Ganesh does, at any rate), deflects the question (or answers it if it’s a serious one), and moves on. I’ve heard it said that while most avadhanis treat this part as something to be endured, Ganesh actually grants this role a big part in the proceedings and even delights in it. This may be a sign of his wit and confidence, or (considering that there will be people in the audience who are impaired in their ability to follow the poetry, and who enjoy this part the most) a generous concession towards the modern-day audience. Either way, this role is a hard task for the questioner as well, and one fraught with danger: apparently, during a previous avadhana of Ganesh that was being conducted at the Bharatiya Vidya Bhavan with (I think) Dr. S R Leela in this role, at one point during the event Mattur Krishnamurthy who was in the audience stood up and yelled at her: “he’s trying to compose a serious poem; why do you distract with such trifles?” — but of course, that is precisely the job. And it appears Ganesh can handle any distraction. :-)
If one imagines the setting of erudite scholarship in an ancient language as a stuffy one, then this sits rather incongruously in that context. So this may serve as “comic relief” from the serious stuff. But actually, I think what this round suggests is that for the avadhani, unlike for us, even arcane metrical composition is at the same level of difficulty as small talk!

7. Ashu-kavitva: Compose a poem quickly. While the other four poem-composing tasks involved composing a single poem, one line in each round, here he is given a topic and must compose a complete poem on it immediately. Ganesh even offered to do it in any metre specified, but as the questioner in this case didn’t specify metres, he picked different metres appropriate to the topic himself. This is one poem per round.

8. Kavya-vachana: Identifying poems. The questioner reads out a poem, which could be from a rather obscure work in the literature, and the performer must identify where it is from. That already requires a deep knowledge of all the literature and a great memory besides, but apparently Ganesh finds that too easy. So what happened here was that the questioner would sing the poem, and instantly, as soon as the singing ended, Ganesh would reply, identifying both the poem and the raga in which it was sung, in verse and in the same metre as the original poem, and singing it in the same raga that was used!

Those are the tasks. So at any given point of time, the perfomer must remember and keep in his head, at minimum, the current state of composition of four poems-in-progress, and the constraints that were imposed on them in the first place, and also the state of the magic square, all the while responding to distractions, and this over a period of several hours — nearly an hour elapsing between working on one line of the poem, and returning to it again.

It is hard to describe how incredible this was to witness in person. For one thing, all the questioners are demanding and trying to trip up the performer, so there’s an elaborate cat-and-mouse game going on. On top of that, when even the audience, who don’t have to do anything but watch, have trouble remembering what has happened in the previous round — even those who have been taking notes — for the performer to resume everything from memory does make one’s jaw drop.

At the end of the performance, the questioners (2), (3), (4) and (7), who had asked for certain poems composed, read out their own creations, that they had composed before the performance at their own leisure. More than once, Ganesh’s compositions created in such a harsh setting were still more beautiful than the ones that had been composed with as much time as desired!

In an age where we’re beginning to feel in the face of technology that perhaps that we’re not so good at multitasking after all, a traditional performance like this feels a bit like the old world turning up in style and showing us how it’s done. Whatever happened to The Magical Number 7±2?

Other notes

* This was in a mixture of Sanskrit and Kannada, but he has given performances that have been entirely in Sanskrit (even the banter), those in which there are eight questioners in Kannada and eight in Sanskrit, etc.

* OK, all this is great, but this must be a once-in-a-lifetime performance, right? The culmination of a life of practice, that happens but once?
Nope. This was Ganesh’s 917th—NINE HUNDRED AND SEVENTEENTH—avadhana. He did another one two weeks later.

* EIGHT people! Four hours! Must be exhausting, and about the limits of what the human mind can do? Nope. He is called “Shatavadhani” because he has at least once performed a Shatavadhana, involving a hundred questioners in parallel rather than eight. Not only that, but he has said he is prepared to do a Sahasravadhana, with a thousand questioners, but it would take over a month to perform, and it is hard to find the people to ask the questions! (And an audience, I imagine.)

* How did he think of doing an avadhana in the first place? What I’ve heard is that he attended one, and felt “I can do this too”. Just like that.

* Of the eight “questioners” (pṛcchakas), only two were professionally related to Sanskrit (they were teachers/professors). The rest were from various fields — software engineers, hardware engineers, teachers of other subjects, and so on — who only pursue their love of Sanskrit in their spare time. (One of them has apparently read through the entire Apte’s dictionary several times, which is an activity I find hard to even imagine.) The audience, too, had a fair number of young people, which Ganesh commented positively upon. (“Gratifying to see a lot of black-haired heads, not just bald or grey-haired ones.”)

* [Other stuff which I had thought of then, but forgot to note down. Will expand if I remember.]

Further reading

* A detailed account of the entire proceedings is in Mohan’s post, as mentioned above. Besides the parallelism and concentration that I have described above, which is the immediately stunning fact to a newcomer, there was a striking beauty in the way he actually handled each of the problems. This is more apparent from Mohan’s post; I have intentionally emphasized the former to (sort of) complement that one. Do go and read it!

* Edit: See this post (“A Modern Day Ashtavadhanam”) by Venetia Ansell. As she notes, “Highbrow Sanskrit arts are far from dead.”
* Another post

* Dr. Ganesh has written a large monograph on avadhana in Kannada, for which he was awarded the first D. Litt. by Kannada University (Hampi).

* If you have trouble believing any of this, there are a few recordings of earlier avadhanas available, and you can try attending the next one.

* Update: The video of this avadhana is now online. The video cannot reproduce the atmosphere, but it’s something:

A few more Avadhanas have been uploaded online, on the Padyapaana YouTube channel.

(Always, while doing anything dangerous, have a gitk window open. Look, don’t guess. And if you’re sharing your repository publicly, you can forget about most of the below.)

Git reset

What I think git reset <commit> does:
* Reset HEAD to the given commit
* (If not --soft) copy this new HEAD to the index
* (If --hard) copy contents of index to working dir

Copy commits from another repository

# 1. Add the other repo as a remote
git remote add other_repo_nickname <other repo's path/url>
# 2. Fetch its data. (pull = fetch + merge, so we want only fetch, not pull)
git fetch other_repo_nickname
# 3. The rest should be familiar
git cherry-pick <commit>

Note that you don’t need to specify the remote’s name for cherry-picking. Once you have fetched, all commits, even those originally from the other repo, can be identified just by hash. (If you want to refer to commit by branch, then you can identify it with “other_repo_nickname/branch_name”.)

Swap commits (reorder top two commits)

 git rebase -i HEAD~2 

and in your editor, reorder the two “pick” lines. (See here.)

Recovering commits deleted with reset --hard

In general, these are garbage-collected after 30 days (or when you run git prune or git gc), so you shouldn’t use reset --hard at least without doing a stash first.
If the garbage-collection hasn’t happened yet, get the sha1 hash of the commit with

 git reflog 

then make sure the commit is what you want with

 git show sha1 

and get the commit back with

 git cherry-pick sha1 

(or rebase or merge instead of cherry-pick, if that’s what you want.)

Squashing commits together, to keep your history clean

Use rebase. To squash the last n commits into one, do

 git rebase -i HEAD~n 

and change all “pick”s except the first one to “squash” (or “s”). See here and here.

Delete a specific commit

Use rebase -i, again.

 git rebase -i <commit>~1 

Delete the line for the commit you want deleted. See here and here.

Amend a specific older commit

This is tricky, and I don’t think I’ve seen it anywhere, especially for the case where there are branches that depend on it.
My solution: Find the first branch X that’s downstream from (= later than) it. Keep track of the whole tree downstream from X (take a screenshot if you must); you’ll need it. Checkout X, and do “rebase -i HEAD~[large enough number to cover the commit you want to amend]“. In the editor that pops up, keep all “pick” lines, changing only that one line you want to amend to “edit”. Save and close. Now git has stopped, allowing you to amend that commit. Edit the file. Do “commit –amend” (don’t forget to add all files you want included in that commit!). Do “rebase –continue”. You’re back at X now. Now for the first branch Y that was downstream from X, checkout Y, do “git rebase X”, and recurse on Y.
This doesn’t seem work (gets into rebase conflicts). Need to try again, and ask.

The Ṛśyaśṛṅga episode appears also [i.e, besides the Ramayana] at MBh 3.110-13, PadmP, Bengali recension, Pātālakhaṇḍa, 13 (reprinted in Lüders 1897), Bhāratamañjarī 3.758-95, Bhadrakalpāvadāna 33, Avadānakalpalatā 65, Alambusā and Naḷanikā Jātakas, etc. The episode is clearly of great importance to traditional India…

Here is the story from the Vana Parva in the Mahabharata (taken from GRETIL), accompanied by a pleasant translation in simple rhyming verse, by Arthur W. Ryder. (Scroll horizontally to read the English text and/or compare. Or to read just the English text, click here.)

    lomaśa uvāca                                                                                                                                                              
    eṣā devanadī puṇyā kauśikī bharatarṣabha                                                                                                                          
    viśvāmitrāśramo ramya eṣa cātra prakāśate                                                                                                                         
    āśramaś caiva puṇyākhyaḥ kāśyapasya mahātmanaḥ                                                                                                                            
    ṛśyaśṛṅgaḥ suto yasya tapasvī saṃyatendriyaḥ                                                                                                                              
    tapaso yaḥ prabhāvena varṣayām āsa vāsavam                                                                                                                        
    anāvṛṣṭyāṃ bhayād yasya vavarṣa balavṛtrahā                                                                                                                               
    mṛgyāṃ jātaḥ sa tejasvī kāśyapasya sutaḥ prabhuḥ                                                                                                                  
    viṣaye lomapādasya yaś cakārādbhutaṃ mahat                                                                                                                        
    nivartiteṣu sasyeṣu yasmai śāntāṃ dadau nṛpaḥ                                                                                                                             
    lomapādo duhitaraṃ sāvitrīṃ savitā yathā                                                                                                                          
    yudhiṣṭhira uvāca                                                                                                                                                 
    ṛśyaśṛṅgaḥ kathaṃ mṛgyām utpannaḥ kāśyapātmajaḥ                                                                                                                           
    viruddhe yonisaṃsarge kathaṃ ca tapasā yutaḥ                                                                                                                              
    kimarthaṃ ca bhayāc chakras tasya bālasya dhīmataḥ                                                                                                                
    anāvṛṣṭyāṃ pravṛttāyāṃ vavarṣa balavṛtrahā                                                                                                                        
    kathaṃrūpā ca śāntābhūd rājaputrī yatavratā                                                                                                                               
    lobhayām āsa yā ceto mṛgabhūtasya tasya vai                                                                                                                               
    lomapādaś ca rājarṣir yadāśrūyata dhārmikaḥ                                                                                                                               
    kathaṃ vai viṣaye tasya nāvarṣat pākaśāsanaḥ                                                                                                                              
    etan me bhagavan sarvaṃ vistareṇa yathātatham                                                                                                                             
    vaktum arhasi śuśrūṣor ṛṣyaśṛṅgasya ceṣṭitam                                                                                                                              
    lomaśa uvāca                                                                                                                                                              
    vibhāṇḍakasya brahmarṣes tapasā bhāvitātmanaḥ                                                                                                                             
    amoghavīryasya sataḥ prajāpatisamadyuteḥ                                                                                                                          
    śṛṇu putro yathā jāta ṛśyaśṛṅgaḥ pratāpavān                                                                                                                               
    mahāhrade mahātejā bālaḥ sthavirasaṃmataḥ                                                                                                                         
    mahāhradaṃ samāsādya kāśyapas tapasi sthitaḥ                                                                                                                              
    dīrghakālaṃ pariśrānta ṛṣir devarṣisaṃmataḥ                                                                                                                               
    tasya retaḥ pracaskanda dṛṣṭvāpsarasam urvaśīm                                                                                                                            
    apsūpaspṛśato rājan mṛgī tac cāpibat tadā                                  SIMPLE DEER-HORN                                                                               
    saha toyena tṛṣitā sā garbhiṇy abhavan nṛpa                                                                                                                               
0543_01     sā puroktā bhagavatā brahmaṇā lokakartṛṇā                          I                                                                                              
0543_02     devakanyā mṛgī bhūtvā muniṃ sūya vimokṣyase                        Young Deer-horn was a pious youth                                                              
    amoghatvād vidheś caiva bhāvitvād daivanirmitāt                            Devoted to religious truth,                                                                    
    tasyāṃ mṛgyāṃ samabhavat tasya putro mahān ṛṣiḥ                            A hermit innocently good                                                                       
    ṛśyaśṛṅgas taponityo vana eva vyavardhata                                  Who grew to manhood in the wood.                                                               
    tasyarśyaśṛṅgaṃ śirasi rājann āsīn mahātmanaḥ                                                                                                                             
    tenarśyaśṛṅga ity evaṃ tadā sa prathito 'bhavat                                                                                                                           
                                                                               His mother left him at his birth;                                                              
    na tena dṛṣṭapūrvo 'nyaḥ pitur anyatra mānuṣaḥ                             He only knew one soul on earth,                                                                
    tasmāt tasya mano nityaṃ brahmacarye 'bhavan nṛpa                          His austere father; therefore he                                                               
                                                                               Grew up in natural piety.                                                                      
                                                                                                                                                                           
                                                                                                                                                                           
    etasminn eva kāle tu sakhā daśarathasya vai                                Now in a kingdom near at hand                                                          
    lomapāda iti khyāto aṅgānām īśvaro 'bhavat                                 No rain had fallen on the land,                                                                
0544_01     premoṣitāpacāreṇa tasya rājño yudhiṣṭhira                          Prevented by the magic skill                                                           
    tena kāmaḥ kṛto mithyā brāhmaṇebhya iti śrutiḥ                             Of priests the king had treated ill.                                                   
0545_01     daivopahatasattvena dharmajñenāpi bhārata                                                                                                                 
    sa brāhmaṇaiḥ parityaktas tadā vai jagatīpatiḥ                                                                                                                            
    purohitāpacārāc ca tasya rājño yadṛcchayā                                                                                                                         
    na vavarṣa sahasrākṣas tato 'pīḍyanta vai prajāḥ                                                                                                                  
                                                                                                                                                                           
    sa brāhmaṇān paryapṛcchat tapoyuktān manīṣiṇaḥ                             An aged priest advised the king:                                                               
    pravarṣaṇe surendrasya samarthān pṛthivīpatiḥ                              “Propitiate the clergy; bring                                                          
    kathaṃ pravarṣet parjanya upāyaḥ paridṛśyatām                              Pure-minded Deer-horn from the wood,                                                   
    tam ūcuś coditās tena svamatāni manīṣiṇaḥ                                  That hermit innocently good.                                                           
    tatra tv eko munivaras taṃ rājānam uvāca ha                                                                                                                               
    kupitās tava rājendra brāhmaṇā niskṛtiṃ cara                               “He dwells in purity afar;                                                                     
    ṛśyaśṛṅgaṃ munisutam ānayasva ca pārthiva                                  He does not know what women are:                                                               
    vāneyam anabhijñaṃ ca nārīṇām ārjave ratam                                 Fetch him, and then the rain will fall;                                                        
    sa ced avatared rājan viṣayaṃ te mahātapāḥ                                 Of this I have no doubt at all.”                                                               
    sadyaḥ pravarṣet parjanya iti me nātra saṃśayaḥ                                                                                                                           
                                                                                                                                                                           
    etac chrutvā vaco rājan kṛtvā niskṛtim ātmanaḥ                             The counsel pleased the king; he planned                                                       
    sa gatvā punar āgacchat prasanneṣu dvijātiṣu                               To entertain the hermit, and                                                           
    rājānam āgataṃ dṛṣṭvā pratisaṃjagṛhuḥ prajāḥ                               Invited women of the town                                                                      
0546_01     sa ca tāḥ pratijagrāha piteva hitakṛt sadā                         To go and bring young Deer-horn down.                                                  
    tato 'ṅgapatir āhūya sacivān mantrakovidān                                                                                                                        
    ṛśyaśṛṅgāgame yatnam akaron mantraniścaye                                                                                                                         
    so 'dhyagacchad upāyaṃ tu tair amātyaiḥ sahācyutaḥ                                                                                                                
    śāstrajñair alam arthajñair nītyāṃ ca pariniṣṭhitaiḥ                                                                                                                      
    tata ānāyayām āsa vāramukhyā mahīpatiḥ                                                                                                                                    
    veśyāḥ sarvatra niṣṇātās tā uvāca sa pārthivaḥ                                                                                                                            
    ṛśyaśṛṅgam ṛṣeḥ putram ānayadhvam upāyataḥ                                                                                                                        
    lobhayitvābhiviśvāsya viṣayaṃ mama śobhanāḥ                                                                                                                               
0547_01     niyojayām āsa ca tās tasya bālasya lobhane                                                                                                                
    tā rājabhayabhītāś ca śāpabhītāś ca yoṣitaḥ                                But they refused the royal plan,                                                               
    aśakyam ūcus tat kāryaṃ vivarṇā gatacetasaḥ                                Fearing to meet a holy man;                                                                    
    tatra tv ekā jaradyoṣā rājānam idam abravīt                                At last an aged crone’s ambition                                                               
    prayatiṣye mahārāja tam ānetuṃ tapodhanam                                  Drove her to undertake the mission.                                                            
                                                                                                                                                                           
    abhipretāṃs tu me kāmān samanujñātum arhasi                                “If you will give me what I ask;’                                                              
    tataḥ śakṣye lobhayitum ṛśyaśṛṅgam ṛṣeḥ sutam                              She said, “I can fulfill the task;                                                             
                                                                               But I require a rich reward                                                                    
                                                                               Of gold and gems, my royal lord.”                                                              
                                                                                                                                                                           
    tasyāḥ sarvam abhiprāyam anvajānāt sa pārthivaḥ                            With royal bounty richly laden,                                                                
    dhanaṃ ca pradadau bhūri ratnāni vividhāni ca                              She took her child, a youthful maiden                                                  
    tato rūpeṇa saṃpannā vayasā ca mahīpate                                    More known as beautiful than good,                                                             
    striya ādāya kāś cit sā jagāma vanam añjasā                                And so departed to the wood.                                                           
                                                                                                                                                                           
    lomaśa uvāca                                                               II                                                                                             
    sā tu nāvyāśramaṃ cakre rājakāryārthasiddhaye                              She waited till the coast was clear,                                                   
    saṃdeśāc caiva nṛpateḥ svabuddhyā caiva bhārata                            And then she sent her daughter dear                                                            
    nānāpuṣpaphalair vṛkṣaiḥ kṛtrimair upaśobhitam                             To interview the hermit who                                                                    
    nānāgulmalatopetaiḥ svādukāmaphalapradaiḥ                                  Had never learned what women do.                                                               
    atīva ramaṇīyaṃ tad atīva ca manoharam                                                                                                                                    
    cakre nāvyāśramaṃ ramyam adbhutopamadarśanam                                                                                                                              
    tato nibadhya tāṃ nāvam adūre kāśyapāśramāt                                                                                                                               
    cārayām āsa puruṣair vihāraṃ tasya vai muneḥ                                                                                                                              
    tato duhitaraṃ veśyā samādhāyetikṛtyatām                                   The maiden found the lad and said:                                                             
    dṛṣṭvāntaraṃ kāśyapasya prāhiṇod buddhisaṃmatām                            “I trust your pious life is led                                                                
    sā tatra gatvā kuśalā taponityasya saṃnidhau                               Without offense, and that your food                                                            
    āśramaṃ taṃ samāsādya dadarśa tam ṛṣeḥ sutam                               Of roots and fruits is sweet and good.                                                 
    veśyovāca                                                                                                                                                         
    kaccin mune kuśalaṃ tāpasānāṃ; kaccic ca vo mūlaphalaṃ prabhūtam           “I trust your father’s heart is blest                                                  
    kaccid bhavān ramate cāśrame 'smiṃs; tvāṃ vai draṣṭuṃ sāṃpratam āgato 'smi With deep religious peace and rest;                                                            
    kaccit tapo vardhate tāpasānāṃ; pitā ca te kaccid ahīnatejāḥ               For I am hither come to see                                                                    
    kaccit tvayā prīyate caiva vipra; kaccit svādhyāyaḥ kriyate ṛśyaśṛṅga      Your unpretending piety.”                                                                      
                                                                                                                                                                           
    ṛśyaśṛṅga uvāca                                                            And Deer-horn answered: “Sir, you are                                                  
    ṛddho bhavāñ jyotir iva prakāśate; manye cāhaṃ tvām abhivādanīyam          As radiant as a beaming star;                                                          
    pādyaṃ vai te saṃpradāsyāmi kāmād; yathādharmaṃ phalamūlāni caiva          I never saw a man like you;                                                                    
                                                                               Then tell me, sir, what shall I do                                                             
                                                                                                                                                                           
    kauśyāṃ bṛsyām āssva yathopajoṣaṃ; kṛṣṇājinenāvṛtāyāṃ sukhāyām             “To make you happy? Here are roots,                                                            
    kva cāśramas tava kiṃ nāma cedaṃ; vrataṃ brahmaṃś carasi hi devavat tvam   Water, a couch of skins, and fruits.                                                   
                                                                               What vows are yours, most holy sage?                                                   
                                                                               Where is your pious hermitage?”                                                                
                                                                                                                                                                           
                                                                                                                                                                           
    veśyovāca                                                                                                                                                         
    mamāśramaḥ kāśyapaputra ramyas; triyojanaṃ śailam imaṃ pareṇa              “My hermitage,” the maid replied,                                                              
    tatra svadharmo 'nabhivādanaṃ no; na codakaṃ pādyam upaspṛśāmaḥ            “Is three long leagues from here, beside                                                       
0548_01     bhavatā nābhivādyo 'ham abhivādyo bhavān mayā                      The river; there I practice now                                                                
0548_02     vratam etādṛśaṃ brahman pariṣvajyo bhavān mayā                     A fearfully ascetic vow.                                                                       
    ṛśyaśṛṅga uvāca                                                                                                                                                           
    phalāni pakvāni dadāni te 'haṃ; bhallātakāny āmalakāni caiva               “For I have sworn that I will greet                                                            
    parūṣakānīṅgudadhanvanāni; priyālānāṃ kāmakāraṃ kuruṣva                    Such other hermits as I meet;                                                          
0549_01     gṛhāṇa kāmād dhi mamopakārāt                                       And I must clasp and kiss you too—                                                             
0549_02     kuruṣva kāmaṃ yad abhīpsitaṃ me                                    So my religion bids me do.”                                                                    
                                                                                                                                                                           
    lomaśa uvāca                                                               She spurned the fruits that he had offered,                                                    
    sā tāni sarvāṇi visarjayitvā; bhakṣān mahārhān pradadau tato 'smai         And in their stead to him she proffered                                                        
    tāny ṛśyaśṛṅgasya mahārasāni; bhṛśaṃ surūpāṇi ruciṃ dadur hi               Confectionery sweet and good                                                           
                                                                               That she had brought into the wood.                                                            
                                                                                                                                                                           
    dadau ca mālyāni sugandhavanti; citrāṇi vāsāṃsi ca bhānumanti              She gave him fragrant garlands too,                                                            
    pānāni cāgryāṇi tato mumoda; cikrīḍa caiva prajahāsa caiva                 And brilliant garments, clean and new;                                                 
                                                                               She offered wine; and while he quaffed,                                                        
                                                                               She played and swayed and danced and laughed.                                          
                                                                                                                                                                           
    sā kandukenāramatāsya mūle; vibhajyamānā phalitā lateva                    She played about him with a ball,                                                              
    gātraiś ca gātrāṇi niṣevamāṇā; samāśliṣac cāsakṛd ṛśyaśṛṅgam               And oft coquettishly would fall                                                                
    sarjān aśokāṃs tilakāṃś ca vṛkṣān; prapuṣpitān avanāmyāvabhajya            Upon his bosom, until he                                                                       
    vilajjamāneva madābhibhūtā; pralobhayām āsa sutaṃ maharṣeḥ                 Took fire from her immodesty.                                                          
                                                                                                                                                                           
    atharśyaśṛṅgaṃ vikṛtaṃ samīkṣya; punaḥ punaḥ pīḍya ca kāyam asya           At last she saw the deed was done,                                                             
    avekṣamāṇā śanakair jagāma; kṛtvāgnihotrasya tadāpadeśam                   That she had charmed the hermit’s son;                                                 
                                                                               And, gazing o’er her shoulder, fled,                                                   
                                                                               To make her sacrifice, she said.                                                               
                                                                                                                                                                           
    tasyāṃ gatāyāṃ madanena matto; vicetanaś cābhavad ṛśyaśṛṅgaḥ               When she had left him, peace and joy                                                   
    tām eva bhāvena gatena śūnyo; viniḥśvasann ārtarūpo babhūva                Departed from the luckless boy;                                                                
                                                                               Sadly he sighed, by love distressed,                                                   
                                                                               An aching void within his breast.                                                              
                                                                                                                                                                           
    tato muhūrtād dharipiṅgalākṣaḥ; praveṣṭito romabhirā nakhāgrāt             His father, while he sighed, returned,                                                 
    svādhyāyavān vṛttasamādhiyukto; vibhāṇḍakaḥ kāśyapaḥ prādurāsīt            Whose eyes with fire ascetic burned,                                                   
                                                                               Whose life was one devoted prayer,                                                             
                                                                               Whose nails were overgrown with hair.                                                  
                                                                                                                                                                           
    so 'paśyad āsīnam upetya putraṃ; dhyāyantam ekaṃ viparītacittam            When he beheld his son distressed                                                              
    viniḥśvasantaṃ muhur ūrdhvadṛṣṭiṃ; vibhāṇḍakaḥ putram uvāca dīnam          With eye upturned and heaving breast,                                                  
                                                                               With longing written on his face                                                               
                                                                               And passion in contentment’s place,                                                            
                                                                                                                                                                           
    na kalpyante samidhaḥ kiṃ nu tāta; kaccid dhutaṃ cāgnihotraṃ tvayādya      “What troubles you, my dearest son?”                                                   
    sunirṇiktaṃ sruksruvaṃ homadhenuḥ; kaccit savatsā ca kṛtā tvayādya         He asked, “and are your duties done?                                                   
    na vai yathāpūrvam ivāsi putra; cintāparaś cāsi vicetanaś ca               Who has been here with you today?”                                                             
    dīno 'timātraṃ tvam ihādya kiṃ nu; pṛcchāmi tvāṃ ka ihādyāgato 'bhūt       And Deer-horn answered him straightway.                                                        
                                                                                                                                                                           
                                                                               III                                                                                            
    ṛśyaśṛṅga uvāca                                                            “A hermit youth with hanging hair,                                                             
    ihāgato jaṭilo brahmacārī; na vai hrasvo nātidīrgho manasvī                Not short, nor very tall, but fair                                                             
    suvarṇavarṇaḥ kamalāyatākṣaḥ; sutaḥ surāṇām iva śobhamānaḥ                 And bright as gold, with lotus-eyes,                                                   
                                                                               Some child of heaven, wondrous wise.                                                   
                                                                                                                                                                           
    samṛddharūpaḥ saviteva dīptaḥ; suśuklakṛṣṇākṣataraś cakoraiḥ               “He came in beauty like the sun,                                                               
    nīlāḥ prasannāś ca jaṭāḥ sugandhā; hiraṇyarajjugrathitāḥ sudīrghāḥ         Black eyes, sweet voice, his hair undone                                                       
                                                                               And hanging soft, dark, fragrant, and                                                  
                                                                               Encircled by a golden band.                                                                    
                                                                                                                                                                           
    ādhārarūpā punar asya kaṇṭhe; vibhrājate vidyud ivāntarikṣe                “A relic on his neck was seen                                                          
    dvau cāsya piṇḍāv adhareṇa kaṇṭham; ajātaromau sumanoharau ca              That danced like flashing lightnings keen;                                                     
                                                                               Below it, two soft swellings white                                                             
                                                                               That thrilled me with a strange delight.                                                       
                                                                                                                                                                           
    vilagnamadhyaś ca sa nābhideśe; kaṭiś ca tasyātikṛtapramāṇā                “Large hips he had, but slender waist                                                  
    tathāsya cīrāntaritā prabhāti; hiraṇmayī mekhalā me yatheyam               Which I could see was close embraced                                                   
                                                                               By a golden belt; I saw it shine                                                               
                                                                               And it was not at all like mine.                                                               
                                                                                                                                                                           
0550_01     anyac ca tasyādbhutadarśanīyā                                      “And on his ankles something stirred                                                   
0550_02     vibhāti mālā kanakaprabhāsā                                        That jingled like a cooing bird,                                                               
0550_03     kaṇṭhe sthitā vakṣasi ghūrṇamānā                                   While on his wrist there tinkled free                                                  
0550_04     yathākṣamālā bhavatā nibaddhā                                      A novel kind of rosary.                                                                        
                                                                                                                                                                           
    anyac ca tasyādbhutadarśanīyaṃ; vikūjitaṃ pādayoḥ saṃprabhāti              “And as he moved, the beads would sing                                                 
    pāṇyoś ca tadvat svanavan nibaddhau; kalāpakāv akṣamālā yatheyam           Like gay flamingoes in the spring;                                                             
                                                                               His pious robe was wondrous fair,                                                              
                                                                               And quite unlike the garb we wear.                                                             
                                                                                                                                                                           
    viceṣṭamānasya ca tasya tāni; kūjanti haṃsā sarasīva mattāḥ                “His face was beautiful to see;                                                                
    cīrāṇi tasyādbhutadarśanāni; nemāni tadvan mama rūpavanti                  His speech was kind and gladdened me;                                                  
    vaktraṃ ca tasyādbhutadarśanīyaṃ; pravyāhṛtaṃ hlādayatīva cetaḥ            His voice was like the nightingale;                                                            
    puṃskokilasyeva ca tasya vāṇī; tāṃ śṛṇvato me vyathito 'ntarātmā           It made me sigh and yearn and pale.                                                            
                                                                                                                                                                           
    yathā vanaṃ mādhavamāsi madhye; samīritaṃ śvasanenābhivāti                 “And as in spring the forest trees                                                             
    tathā sa vāty uttamapuṇyagandhī; niṣevyamāṇaḥ pavanena tāta                Wave beautifully in the breeze,                                                                
                                                                               So, father, when the wind blew, he                                                             
                                                                               Shed fragrance like a flowering tree.                                                  
                                                                                                                                                                           
    susaṃyatāś cāpi jaṭā vibhaktā; dvaidhīkṛtā bhānti samā lalāṭe              “His hermit locks— I wondered how                                                              
    karṇau ca citrair iva cakravālaiḥ; samāvṛtau tasya surūpavadbhiḥ           They parted on his noble brow;                                                         
                                                                               And dangling from each ear, there stirred                                                      
                                                                               And danced what seemed a brilliant bird.                                                       
                                                                                                                                                                           
    tathā phalaṃ vṛttam atho vicitraṃ; samāhanat pāṇinā dakṣiṇena              “A round, elastic fruit he had                                                         
    tad bhūmim āsādya punaḥ punaś ca; samutpataty adbhutarūpam uccaiḥ          That bounded from the earth like mad                                                   
                                                                               When he would strike it merrily—                                                               
                                                                               'Twas very wonderful to see.                                                           
                                                                                                                                                                           
    tac cāpi hatvā parivartate 'sau; vāterito vṛkṣa ivāvaghūrṇaḥ               “He moved and swayed with graceful ease—                                                       
    taṃ prekṣya me putram ivāmarāṇāṃ; prītiḥ parā tāta ratiś ca jātā           I thought of wind among the trees:                                                             
                                                                               A wonderful delight and joy                                                                    
                                                                               Came when I saw the godlike boy.                                                               
                                                                                                                                                                           
    sa me samāśliṣya punaḥ śarīraṃ; jaṭāsu gṛhyābhyavanāmya vaktram            “He held me in a tight embrace;                                                                
    vaktreṇa vaktraṃ praṇidhāya śabdaṃ; cakāra tan me 'janayat praharṣam       I felt his hair; he pressed his face                                                   
                                                                               Against my face and made a noise                                                               
                                                                               That waked in me the strangest joys.                                                   
                                                                                                                                                                           
    na cāpi pādyaṃ bahu manyate 'sau; phalāni cemāni mayāhṛtāni                “Our simple fruits he did not think                                                            
    evaṃvrato 'smīti ca mām avocat; phalāni cānyāni navāny adān me             Were good, or water that we drink;                                                             
                                                                               He gave me other fruits and rare,                                                              
                                                                               And said: ‘This is my humble fare.’                                                            
                                                                                                                                                                           
    mayopayuktāni phalāni tāni; nemāni tulyāni rasena teṣām                    “They were not like the fruits we eat,                                                 
    na cāpi teṣāṃ tvag iyaṃ yathaiṣāṃ; sārāṇi naiṣām iva santi teṣām           But tasted wonderfully sweet;                                                          
                                                                               They had a different sort of skin,                                                             
                                                                               And different was the pulp within.                                                             
                                                                                                                                                                           
    toyāni caivātirasāni mahyaṃ; prādāt sa vai pātum udārarūpaḥ                “A strange, sweet kind of water he                                                             
    pītvaiva yāny abhyadhikaḥ praharṣo; mamābhavad bhūś caliteva cāsīt         Offered with noble piety;                                                                      
                                                                               It filled me with an odd delight,                                                              
                                                                               And earth grew wobbly to my sight.                                                             
                                                                                                                                                                           
    imāni citrāṇi ca gandhavanti; mālyāni tasyodgrathitāni paṭṭaiḥ             “Sweet garlands with a careless mirth                                                  
    yāni prakīryeha gataḥ svam eva; sa āśramaṃ tapasā dyotamānaḥ               He wove, and scattered on the earth;                                                   
                                                                               Then, glorious as an ancient sage,                                                             
                                                                               Departed to his hermitage.                                                                     
                                                                                                                                                                           
    gatena tenāsmi kṛto vicetā; gātraṃ ca me saṃparitapyatīva                  “And since he went, I feel distressed;                                                 
    icchāmi tasyāntikam āśu gantuṃ; taṃ ceha nityaṃ parivartamānam             My limbs are burning and my breast;                                                            
                                                                               I long to go to him today                                                                      
                                                                               Or have him here with me alway.                                                                
                                                                                                                                                                           
    gacchāmi tasyāntikam eva tāta; kā nāma sā vratacaryā ca tasya              “Yes, I will tread the path he trod                                                            
    icchāmy ahaṃ carituṃ tena sārdhaṃ; yathā tapaḥ sa caraty ugrakarmā         And learn the way he worships God;                                                             
                                                                               With him I long to make a trial                                                                
                                                                               Of holy life and self-denial.                                                          
                                                                                                                                                                           
0551_01     cartuṃ tathecchā hṛdaye mamāsti                                    “I find no peace from him apart;                                                               
0551_02     dunoti cittaṃ yadi taṃ na paśye                                    Religious yearnings fill my heart.”                                                            
                                                                                                                                                                           
                                                                               IV                                                                                             
    vibhāṇḍaka uvāca                                                           “It was a devil, dear my son;                                                          
    rakṣāṃsi caitāni caranti putra; rūpeṇa tenādbhutadarśanena                 By foes like these we are undone;                                                              
    atulyarūpāṇy atighoravanti; vighnaṃ sadā tapasaś cintayanti                They walk the earth in conquering charm                                                        
                                                                               And work religious men much harm.                                                              
                                                                                                                                                                           
    surūparūpāṇi ca tāni tāta; pralobhayante vividhair upāyaiḥ                 “They win us with their cunning wiles,                                                 
    sukhāc ca lokāc ca nipātayanti; tāny ugrakarmāṇi munīn vaneṣu              Their wondrous beauty and their smiles,                                                        
                                                                               Then show themselves as demons fell                                                            
                                                                               And plunge us in the pit of hell.                                                              
                                                                                                                                                                           
    na tāni seveta munir yatātmā; satāṃ lokān prārthayānaḥ kathaṃ cit          “The man who seeks religious peace                                                             
    kṛtvā vighnaṃ tāpasānāṃ ramante; pāpācārās tapasas tāny apāpa              Should keep himself from such as these;                                                        
                                                                               To ruin us is their delight,                                                           
                                                                               My pious boy. Forget the sight.                                                                
                                                                                                                                                                           
    asajjanenācaritāni putra; pāpāny apeyāni madhūni tāni                      “And those sweet waters that you had                                                   
    mālyāni caitāni na vai munīnāṃ; smṛtāni citrojjvalagandhavanti             Are tasted only by the bad;                                                                    
                                                                               And we ascetics never wear                                                                     
                                                                               A perfumed garland on our hair.                                                                
                                                                                                                                                                           
    lomaśa uvāca                                                               “Resist the devil, boy”; he said                                                               
    rakṣāṃsi tānīti nivārya putraṃ; vibhāṇḍakas tāṃ mṛgayāṃ babhūva            And then he hunted for the jade;                                                               
    nāsādayām āsa yadā tryaheṇa; tadā sa paryāvavṛte ''śramāya                 Three days he sought without success                                                   
                                                                               And ceased for very weariness.                                                         
                                                                                                                                                                           
    yadā punaḥ kāśyapo vai jagāma; phalāny āhartuṃ vidhinā śrāmaṇena           Meantime, the tempting minx returned,                                                  
    tadā punar lobhayituṃ jagāma; sā veśayoṣā munim ṛśyaśṛṅgam                 And seeing her, young Deer-horn burned;                                                        
    dṛṣṭvaiva tām ṛśyaśṛṅgaḥ prahṛṣṭaḥ; saṃbhrāntarūpo 'bhyapatat tadānīm      “Come quick,” he said, “and let us roam;                                                       
    provāca caināṃ bhavato ''śramāya; gacchāva yāvan na pitā mamaiti           You see my father’s not at home.                                                               
                                                                                                                                                                           
    tato rājan kāśyapasyaikaputraṃ; praveśya yogena vimucya nāvam              “Your hermitage I fain would view”;                                                            
    pralobhayantyo vividhair upāyair; ājagmur aṅgādhipateḥ samīpam             So, hand in eager hand, they flew                                                              
                                                                               And found a boat and floated down                                                              
                                                                               The river to the royal town.                                                           
                                                                                                                                                                           
                                                                               No sooner did the hermit gain                                                          
    saṃsthāpya tām āśramadarśane tu; saṃtāritāṃ nāvam atīva śubhrām            The royal palace than the rain                                                         
    tīrād upādāya tathaiva cakre; rājāśramaṃ nāma vanaṃ vicitram               Fell, drenching every thirsty part                                                             
    antaḥpure taṃ tu niveśya rājā; vibhāṇḍakasyātmajam ekaputram               And gladdening the sovereign’s heart.                                                  
    dadarśa devaṃ sahasā pravṛṣṭam; āpūryamāṇaṃ ca jagaj jalena                                                                                                               
0552_01        samāyāte ṛṣyaśṛṅge 'tha rājan                                   The joyful monarch to the brave,                                 
       sa lomapādaḥ paripūrṇakāmaḥ; sutāṃ dadāv ṛśyaśṛṅgāya śāntām             Bewildered young ascetic gave—                                   
                                                                               Lest he should ever seek release—                                
                                                                               A princess—and her name was Peace.                                

Charles Dickens at 24 was writing his first novel The Pickwick Papers, which was being published serially like all novels of the era. Sales were chugging along decently for the first three months, until the character Sam Weller was introduced. The career of Dickens would never be the same. The novel became a publishing phenomenon and from that moment on he was a star, and new instalments of Dickens’s novels were often more eagerly awaited than any Harry Potter book has been.

Among the characteristics that made Sam Weller so popular with the masses were his linguistic charms, one of them a form of quotation known as a Wellerism. This survives in American popular culture as the rather lame and narrow-in-scope “…that’s what she said” (or the British “…as the actress said to the bishop”), but turning to samples from Dickens himself:

“out vith it, as the father said to his child, when he swallowed a farden.”

“How are you, ma’am?” said Mr. Weller. “Wery glad to see you, indeed, and hope our acquaintance may be a long ‘un, as the gen’l'm’n said to the fi’ pun’ note.”

“All good feelin’, sir—the wery best intentions, as the gen’l'm’n said ven he run away from his wife ‘cos she seemed unhappy with him,” replied Mr. Weller.

“There; now we look compact and comfortable, as the father said ven he cut his little boy’s head off, to cure him o’ squintin’.”

“Yes, but that ain’t all,” said Sam, [...] “vich I call addin’ insult to injury, as the parrot said ven they not only took him from his native land, but made him talk the English langwidge arterwards.”

“Sorry to do anythin’ as may cause an interruption to such wery pleasant proceedin’s, as the king said wen he dissolved the parliament,” interposed Mr. Weller, who had been peeping through the glass door;…

More examples not from Dickens, from Wikipedia and elsewhere:

“We’ll have to rehearse that,” as the undertaker said when the coffin fell out of the car.

“Simply remarkable,” said the teacher when asked her opinion about the new dry-erase board.

“Don’t move, I’ve got you covered”, as the wallpaper said to the wall.

‘It all comes back to me now’, said the Captain as he spat into the wind.

‘Eureka!’ said Archimedes to the skunk.

“Each moment makes thee dearer,” as the parsimonious tradesman said to his extravagant wife.

“Capital punishment,” as the boy said when the teacher seated him with the girls.

“I’ve been to see an old flame,” remarked the young man returning from Vesuvius.

“I hope I made myself clear,” as the water said when it passed through the filter.

“I’m at my wit’s end,” said the king as he trod on the jester’s toe.

“These are grave charges,” murmured the hopeless one, as he perused the bill for the burial of his mother-in-law.

“Notice the foot-note at the bottom of the page,” laughed the court fool, as the royal attendant’s shoes emitted a squeak.

“That’s my mission in life,” said the monk, as he pointed to his monastery.

“Oh, how blue I am,” mourned the poet, as his fountain pen spattered upon him.

“That’s an old gag,” said the cashier, as the bandit stopped up his mouth.

“My business is looking good,” said the model.

See also this post by Krish Ashok, which has a stream of examples culminating in

“Looks like we still have gaps”, he pointed out, like Aamer Sohail to Venkatesh Prasad.

A subgenre is the “Tom Swifty”, with a pun on the adverb:

“The doctor had to remove my left ventricle,” said Tom half-heartedly.

“The situation is grave,” Tom said cryptically.

“I’ve joined the navy,” Tom said fleetingly.

“I have a split personality,” said Tom, being frank.

“This is the real male goose,” said Tom producing the propaganda.

“I won’t finish in fifth place,” Tom held forth.

[See the paronomasia archives for more Tom Swifties from its members, like

"Let's put them in to bat now and bowl them out," Tom declared.

and of course everywhere on the internet.]

The invitation

Traveler, hurry your steps, be on your way:
the woods are full of wild animals,
snakes, elephants, tigers, and boars,
the sun’s going down and you’re so young to be going alone.
I can’t let you stay,
for I’m a young girl and no one’s home.

Translated from the गाहा-सत्तसई (= गाथा-सप्तशती) by Andrew Schelling:

Mother-in-law
sleeps over there
so does the
rest of the household but
  traveler
    this is my bed
    don’t trip over
    it in the dark

A non-rigorous argument: when is large enough so that is small, is roughly (hand-waving) the point on the unit circle at arc length (and hence angle) :

So multiplication by roughly corresponds to rotation by angle . Multiplication by , which is multiplication by n times, roughly corresponds to rotation by angle . As , “roughly” becomes exact.

Animation for :

Image generated from Python-generated SVG files; code available if anyone wants.

In particular, once one accepts the fact/definition that (for instance, show that the function satisfies ), it is true that is a rotation by π, that is,

document.getElementById('content').style.cssText += "font-family: sans-serif;"

or whatever it is that you want. Making this a Greasemonkey/Stylish/whatever extension is left for others; I just want something quick to fix this annoyance.

Monospaced is fine for code, but typical monospaced fonts lack so many non-ASCII characters that all the glyph substitution makes it really ugly here.

These are (not) a few of my favourite fonts: Medley by WordPress

Edit: Looking around two days later, you can see complaints (I guess… I haven’t read them) here, here, here, etc., and the userscript here.