$\tau: T \rightarrow 1$;

24 Oct

A twisted bundle map have a reversed base morphism; we have $(f’,f): E \rightarrow F$ where $f’: E \rightarrow F$ and $f: M \leftarrow N$.

We see that the identity bundle map has a twisted avatar by reversing the base map, which we can do because the map is invertible.

They form a category, since a composition of twisted maps is twisted; and there are twisted identity maps.

The natural example of the twisted category is the dual category of the tangent category. Recall a natural bundle is a transformation. Say $\tau: T \rightarrow 1$; and the tangent bundle is the standard example of this.

Hence, we can define a twisted transformation as $\tau: T \rightarrow S$ where T is a functor and S is a cofunctor.

Now given a natural bundle $\tau: T \rightarrow 1$, whose functor $T$ takes values in  vector space; we can define a twisted version by taking the dual, and we get $\tau^*: T^* \rightarrow 1$.

A little bit of Bengali Translation…

29 Oct




রোধেবাংলাদেশ অনেকখানি পিছিয়ে পড়েছে |

পারভীন;বিবিসি – বাংলা, ঢাকা |

রংপুরের মোসাম্ম মরিয়ম ঢাকার একটি বিপণি বিতানের সামনে রাস্তা পরিষ্কারেরকাজ | বলছিলেন কোন কিছু বোঝার আগেই একদিন জানলেন আজ সন্ধেয তার বিয়ে তিনি বলছিলেন সকালে এসে দেখে গেল আর সন্ধেয বিয়ে । আমার বয়স তখন ১২ অথবা ১৩। অত কিছু বুঝি নি । প্রথমে ভেবেছি আমাকে বেড়াতে নিয়ে যাচ্ছে । ২৫ বছর বয়সেই তিন সন্তানের মা হয়েছেন মরিয়ম । পড়াশোনার কোন সুযোগ আর পাননি । স্বামীর আরো কবার বিয়ে ও নির্যাতনের কারণে সংসার ছেড়ে চলে এসেছেন আর এখন তিন সন্তানের ভরন পোষণে রাস্তা পরিষ্কার ছাড়াও খুচরো যেখানে যে কাজ জোটে তা নিয়ে দিন রাত খাটছেন । আজ ঢাকায গার্ল সামিটে মরিয়মের মতো বাল্য বিয়ের শিকার নারীদের গল্প তুলে ধরা হয ।


রোধে বিপণি সন্তানের
চলে এসেছেন সন্তানের
ভরন পোষণে সন্তানের
ভরন পোষণে খুচরো
জোটে বাল্য


A woman from Rangpur, Miriam is cleaning the road in front of a shopping mall in Dhaka. She said before I had understood anything I found out that my marriage had been arranged for that evening. ” He came in the morning for the viewing and that evening was the marriage. I was then 12 or 13. I didn’t really understand anything. At first I thought they were going to take me on an outing. At 25 Miriam is the mother of three children 5 years of age. Schooling was no longer possible. Her husband marrying again left her. And now, in addition
to bringing up three children and besides cleaning work she takes whatever work she can get. at a ‘Girl’ conference women are talking on the problems faced by girls like Miriam who face marriage at such an early age.

Vocabulary – in depth

n age up to one’s sixteenth birth day; boyhood or girlhood, childhood, infancy



Bangladesh: Revolt & Fallout

1 May

Liz Phillipson analyses the political situation in Bangladesh after the general election in 2009 nd takes a close look at the BDR: http://www.opendemocracy.net/article/bangladesh-revolt-and-fallout

Purity, Danger & Dirt

2 Jan

“Should I not allow for the obsessional artist whose tolerance of disorder is practically complete? His studio is chaotic, he sleeps there, eats there, urinates in the hand-basin or out of the window when his passion for his work gives him no time to go to the WC. Everything look wildly disordered, except on his canvas: there alone do calm & quiet reign. For him the canvas is the only sacred space, where repleteness is compulsory and where the least signs of disorder would send him into fits of anxiety”.

– Purity & Danger, Mary Douglas

Santa is Dead

24 Dec

Someone asked me seeing that Santa doesn’t exist, and seeing that its Christmas, is there a philosophical reason that he could exist;  hence…with apologies to Nietszche…and Hegel…this:


Zarathrustra comes down from the mountain.

Have they not heard? Do they not know? I must hurry. Men in the market – they come and go talking of the loss and profit; men asleep yet walking; men asleep yet talking; the world darkly asleep. That draught of cool mountain air has awoken me – I shall awake them. This news keeps me most feverish awake; as a fever it runs through me; as a fever I shall speak out. The market-place beckons, and around all manner of men and all manner of manners – they dress fine these men

“Listen! And be alarmed, raise up thy voices and weep, and rend thus thy clothes and rub ash in thine hair as your fathers have done and their fathers before them! I have news and it hangs heavy in my heart, but also a fierce and subtle joy I know not how or where runs through me and makes me speak – a fever of subtle and unsubtle joy. Oh men, wish that I could be silent like the wise we have known and revered; Oh, men of the market place, Listen! SANTA IS DEAD! Oh tearful Men of the Market-Place, Santa is gone!”

[he outstretches both arms]

“Santa never here, never there & never everywhere – never seen; Santa missed! the Being of Santa escapes like Void; the Being of Santa escapes all totalising Logic. Thus: Santa is not an absolute free spirit; thus: Santa is a becoming-free-spirit; The world wills into existence free spirits – this is its purpose; ”

“Oh crowd of men, your faces up-turned to me and eager, Listen! Rejoice! Take good heed! Gladden hearts! Santa will exist and is the worlds purpose”