Tu m’as dit “Je t’aime”
Je t’ai dit “Attends”
J’allais dire “Prends-moi”
Tu m’as dit “Va-t’en”

Rien!

Exactement!

(The anglais meaning)

The heiress

[Seldom have I seen a movie which has affected me more. And as is usual, there are a lot of reasons for not reading this post or other such ones of this kind, the chief of them being that they might spoil the movie for you.]

The following is little more than a more than brief synopsis of the movie, the latter which begins by introducing us to Catherine Sloper, the daughter of an extremely rich and cultured doctor and his extremely beautiful poised and elegant but also very dead wife. And inspite of such promising genetic material and all the finest training and education which money and influence can buy, Catherine  is, as her admirable father quotes “an entirely mediocre and defenseless creature with not a shred of poise” , who finds it hard to say anything except monosyllables in company. She is neither pretty not witty, neither accomplished nor dignified and awkward to a such a degree that it makes her lose her only unwilling dance partner procured for her by her considerate aunt.

And it is then that she meets Morris Townsend, a personable young man of such great charm and manner that he even manages to make her have a good time, and what is more, seems to enjoy it himself. Within a few short weeks, Catherine is very pleasantly fluttered when Morris, who might have any woman he chooses to have, chooses her, and despite her modesty, doesn’t find it hard to get over the shock and reconcile herself to the happy thought that she might soon have a loving husband in her happy home.

The elegant doctor on the other hand has a more cynical turn of the mind and is absolutely convinced that Morris is, as the unpleasant phrase goes, a fortune hunter,  chiefly influenced by the knowledge that the said Morris frittered away his inheritance in Paris getting himself educated socially and culturally which accounted for his current state of pennilessness. To assure himself of the correctness of his diagnosis, he meets the widowed sister of Morris whose sorry state of gloves in contrast to a more expensive pair possessed by Morris convinces him that he is more right than ever about the chap being a selfish idler.

Things grow uncomfortable as he refuses his permission for the marriage of the loving couple, inspite of being told by his relative that “this man may take good care of Catherine and her money and make her very happy as well” and grow even more so, when Catherine announces her complete faith in Morris. After a few rounds of dialogue, it is decided that Catherine and her father vacation in Europe for half a year, which would give enough time for either of the young people to change their minds. Months pass evoking no change in Catherine much to her father’s chagrin while back home,  her aunt attempts to console Morris and invigorate him by giving him dinners and telling him much pleasing stories about our heroine, while he helps himself to the Doctor’s wine after wondering about the similarity of their tastes.

The father and daughter return home and before the former goes to bed, he tells her that she has nothing but money to tempt Morris.           “I have known you all your life and am yet to see you learn anything, .. with one exception, my dear. You embroider neatly”. Waking up with a shock that she has lived for twenty years with a man who despises her very being, she takes refuge in Morris and they decide to elope in two hours. And just as he is about to leave to get the carriages, she tells him why she doesn’t want to see her father ever again, nor his house and nor his money.

And from this moment on, the movie becomes one of the best ones I have ever seen. And finally, three quotes which tell the tale, themselves …

Catherine’s  aunt : “Oh dear Catherine, why were you not a bit more … clever…Morris would not want .. to be the cause of your losing your natural inheritance “

Catherine : “I know now he did not love me, thanks to you.
Her (dying) father: ” Better to know it now, than  twenty years hence”
Catherine : ” Why ? I lived with you for twenty years before I found out you didn’t love me. I don’t know that Morris would have hurt me or starved me for affection more than you did”

Catherine: “He’s grown greedier over the years. Before he only wanted my money; now he wants my love as well. Well, he came to the wrong house – and he came twice. I shall see that he does not come a third time.”

Evaluated

Most of my ex-students in their evaluations said they had fun. Life suddenly doesn’t look all that bad. If you can make a compulsory math course fun for freshmen, well, there’s hope. I should do a re-evaluation.

Ninotchka

This picture takes place in Paris in those wonderful days when a siren was a brunette and not an alarm … and if a frenchman turned out the light, it was not on account of an air raid

One wonders how many movies of Lubitsch are set in Paris.

Kuch tho log

Yeh kya hua ? Kaise hua ?
Kab hua ? Kyon hua ?
Jab hua, tab hua
Oh chodo! ye naa socho

Hum kyon shikwa kar jootaa
Kya hua jo dhil tootaa ?
Sheeshe ka kilona thaa
Kuch naa kuch hona thaa, hua.

Hamne jo dekhaa thaa, sunaa thaa,
Kya bathaa woh kyaa thaa.
Sapna tho salonaa thaa,
Katham tho honaa thaa, hua.

Unnai kaanaadha kannum kannalla,
unnai ennaadha nenjum nenjalla,
nee sollaadha sollum sollalla
nee illamal naanum naan alla.

Phuloon ko taaron ka sabka kehna hai
Ek hazaaron me, meri behnaa hai
Saari umar hame sang rahna hai

Ye naa jaana duniyaa ne tu hai kyun udaas
Theri pyaasi aankhon me pyaar ki hai pyaas
Aaa mere paas aa, kah jo kehna hai
Ek hazaaron me, meri behnaa hai

Bholi-baali jaapaani guidya jesi tu
Pyaari-pyaari jaadu ki pudiya jesi tu
…

Jabse meri aankhon se ho gayi tu duur
Tab se saare jeevan ke sapne hain chuur
Aakhon me neendna mann me chahena hai
Ek hazaaron me meri behnaa hai

Dekho hum tum dhono hai ekdaali ke phool
Mein na bhoola tu kaise mujho gayi bhool ?
Aa mere paas aa, kah jo kehna hai
Ek hazaaron me, meri behnaa hai

Localization

All intelligent thoughts have already been thought; what is necessary is only to try to think them again – Goethe

And it comes to be that only at 2:20 AM on a Wednesday morning of  a surprisingly tolerable  Bostonian November that I finally realize that a ring R needn’t always sit inside its localization.  It’s discomfiting to know how one can have a “wrong picture” even when you can glibly recite the definition in the middle of your sleep.  Having given the climax away, let me begin at the beginning.

Age 5 :  Exasperated K.G teacher tries to teach counting. “One apple, two apples, many apples”

Age 10 : Tearful student grapples with the concept of negative numbers. “What is negative money ?!”

Age 15 : Having accepted that God made integers, students are drilled with the work of man – The rationals. “Irony ?”

Age 20: Rationals are just localizations with respect to the prime ideal (0) of ring .  “Whatever”

To begin at the beginning again (This is how a book on mathematics is read. You flip to the end and read the main theorem. It will generally resemble something like this : “ Image of a constructible set under a morphism of algebraic varieties is constructible “. Having understood not one word of this, you begin at the beginning (where generally most authors define set operations like union and intersection) again and again. Finally after having gotten thoroughly sick of the whole thing, you give up and watch a movie), there are the natural numbers. You can add two natural numbers and still stay within natural numbers, but you can’t subtract. 1-3 is not a natural number. So people threw in negative numbers and the zero and observed that now you could subtract and add without any qualms. Mathematicians promptly abstracted this out and fondly called it a group.

It turns out that even when you multiply any number with any other number, you still stay with the numbers. This makes the integers a ring. On a side note, one wonders how the word ring ever came about. A group is understandable, but a ring ?

And where there is multiplication, you’d like division to be present. Alas, you can’t divide two numbers and still stay within the integers. So you throw in elements of the form , b non zero (of – course) to get the rationals, where you can add, subtract, multiply and divide and so you’re happy. And if you still remember your high school math, you would know that . In fact, you say any two elements , if ad-bc=0.

The integers are nice rings.  That is, ab=0 would mean a=0 or b=0. And as is expected, things are not as hunky-dory as usual, but this process of “inverting elements” can be generalized as follows :

Let R be a ring. P is a prime ideal if  . Then you define localization at P to be the ring with an equivalence relation, namely if there exists an such that s(ad-bc)=0.

This is just saying that you take elements of R, throw in inverses of elements not in P and make it into a ring. And this is exactly where one should have realized that R does not sit in , the equivalence relation makes weird things equal.

Look at the ring Z/6Z, (ie) {0,1,2,3,4,5} with the usual operations + and * , where you go modulo 6 all the time. {0,2,4} is a prime ideal of this ring. Let’s localize our ring with respect to this prime ideal . So we get elements of the form where b is from the set {1,3,5}. Now, ladies and gentlemen, in our localized ring 2=0 —- [3*(2-0)=0]

So what ?

Well …Z/6Z is not a field (2*3=0) but the localizations at its prime ideals are fields. Yes, it’s trivial, but I just realized that. Now try this problem :

If R is a commutative ring whose nil-radical ({x| for some n } )is (0) such that any prime ideal is maximal, PT is a field for any prime ideal P.

Hint: Nil-radical of a ring is the intersection of all prime ideals of the ring.

..at a time when many eminent scholars, endowed with a great geometric talent, make a point of never disclosing the simple and direct ideas that guided them, subordinating their elegant results to abstract general theories which often have no application outside the particular case in question. Geometry was becoming a study of algebraic, differential or partial differential equations, thus losing all the charm that comes from its being an art.

- Henri Lebesgue