Nothing to be frightened of – Julian Barnes

Our lack of originality is something we usually forget as we hunch over our – to us – ever fascinating lives. My friend M., leaving his wife for a younger woman used to complain, ‘People tell me it is a cliché. But it doesn’t feel like a cliché to me.’ Yet it was, and is. As all our lives would prove, if we could see them from a greater distance – from the viewpoint, say, of that higher creature imagined by Einstein.

… there is something infinitely touching when an artist, in old age, takes on simplicity. The artist is saying: display and bravura are tricks for the young, and yes, showing off is part of ambition: but now that we are old, let us have the confidence to speak simply. For the religious, this might mean becoming as a chid again in order to enter heaven; for the artist, it means becoming wise enough and calm enough, not to hide. Do you need all those extravagances in the score, all those marks on the canvas, all those exuberant adjectives? This is not just humility in the face of eternity; it is also that it takes a lifetime to see, and say, simple things.

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The Salmon Of Doubt

By one and only Douglas Adams.

“A couple of hours later he had the answer, or at least some kind of an answer. Nothing that went so far as to make any kind of actual sense, but enough to make Dirk feel an encouraging surge of excitement: he had managed to unlock a part of the puzzle. How big a part he didn’t know. As yet he had no idea how big a puzzle he was dealing with. No idea at all.”

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Schur’s Lemma

SchursLemma

SchursLemma2

 

 

 

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Representation of finite groups – notes in pictures

Of course, we have to find sub-structure within a structure – that’s what we do! I present before you, ladies and gentlemen, submodules.

submodule

 

 

And some new structure. How about building the vector space from the group? Group algebra – vector space + ring.

groupalgebra

…and then ask the group to act on it.

regularfgmodule

 

 

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Representation of Finite Groups – Notes in pictures

A representation is simply a homomorphism between a group and the group of invertible matrices over a field, which is usually the field of complex numbers.

representation-defn

 

There are several approaches to developing the theory of representations, one of the popular ones is via FG-modules.

FGmodule-defn

 

The connection between FG-modules and representations is simple – it is that of siamese twins.

moduleToRep

 

 

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Basis of a vector space may not be strictly contained in it.

I thought that the basis must necessarily be smaller than the vector space itself. A colleague of mine gave me the following counterexample.
Let V be the direct sum of countably infinite copies of \mathbb{Z}_2.
V=\mathbb{Z}_2 \bigoplus \mathbb{Z}_2 \bigoplus \hdots=\{(x_1,x_2,\hdots)\mid x_i \in \mathbb{Z}_2, \text{only finitely many } x_i \neq 0. \}
Then cardinality of V is \aleph_0. Consider the set B defined as
B=\{(1,0,0,\hdots),(0,1,0,\hdots) \hdots\}.
B clearly forms a basis for V, but |B|=|V|=\aleph_0.

Of course such things cannot happen if finite dimensional vector spaces. One more proof that things get weird when they get to infinity.

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Notes from God’s own country

One of my teammates was tying the knot and we were cordially invited to grace the occasion. Since the venue happened to be in Kerela, plans were drawn, redrawn and then dropped. But Kerela did not give up on us; it beckoned us with renewed vigor and finally we had to give in. A few hasty notes scribbled on a hasty trip

Mumbai airport

I realize what’s keeping me air-borne is one man’s intelligence and his insistence on defying gravity. I trust this force as I board a plane or enjoy the backwaters on a motor boat. Men who made planes and boats and roads make being human something of a target for me. And it’s not because of what they did with their minds, but what they sought to do.

On the way from Kochi to Kottayam

Our driver is very chatty and instantly puts me at ease. Even though he’s speaking Malyalam and I obviously can’t follow a word, the sound of his incessant chatter is reassuring-it makes me feel welcomed. It’s past midnight but he’s not bothered about the lateness of the hour. We stop midway to drink black coffee from a roadside stall. Another day he brings us local liquor and serves us two courses in a glass kept in his car, I’m afraid for this very purpose. What a wonder words are, what powerful bridges! We ought to use them more lavishly. He poses for us as we click snaps and I’m wondering if all the people from this beautiful place are like him-simple, friendly, spontaneous. I know this is generalizing my limited experience. It is wrong, I realize, but it is human. I’m no patriot but I’ll remember this when I go to foreign land-not to bring bad name to the place I call home.

On the way to Munnar

I don’t want my snaps to be taken. This landscape minus me looks better. It looks better if I don’t look at the people.(Why is that, I am wondering)

There’s a waterfall on the way and we decide to play around a bit. Lot of people have stopped here. No matter how deep or shallow a person may be, how dumb or intelligent, this beauty spell bounds everyone. That, I think, is the mark of perfection.

For the past two days, we have done nothing but gaped in amazement over the hundreds of thousands of trees. What a place this is! The only embellishment it has to its merit is the green of the woods and the blue of the rivers and the shade of the azure skies. Yet, this alone is sufficient to qualify it as God’s own country for where else can you imagine God living? I wonder if it would be any less wonderful, any less magnificent if I saw more of it. I guess not. If it were not such a rare sight, I’d probably look at it less often but every time I did, I’m sure I’d be awestruck.

Munnar

There’s a flower here which blooms once in twelve years and when it does, the entire valley is painted with its vibrant violet hue. I want to lay supine on these mountains and feel the roughness of their surface against my skin, like the coarse hands of a lover. What a combination of chance factors this is-that this beauty exists and that I can enjoy it-see the colors, feel the winds, smell the fragrance; that I have someone to miss I look at this; that I’ve loved and have been loved back. People who do not have one or all of these far outnumber people like me and I’m eternally grateful for every bit of it. I’m imbued with a desire to live, to see more of this and show it to the people I love, to write and sing and be happy. May all of this and more come true, for me and for everyone else. Amen!

For a while I am bothered by the fact that everything that I am thinking of and want to say has already been said by someone, somewhere. But I shrug off this feeling. What does it matter? How can it be helped if this sight takes everyone to the same heights or depths? What matters is that I’m here today and what it makes me feel must be said. Originality be damned-I must write this at the cost of sounding clichéd.

Cochin airport

I blow kisses to this lovely place and promise I’ll come back; next time around, not in such a haste. I will come here and let the fragrances of this place fill my senses, the quietness of this ring through me. Some other time, surely, when I have more time to stand and stare.

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