I have been studying Grigori Perelman's Poincaré proof these last few days, the so called Ricci Paper, and found it not only plausible, but also generally suitable to describe my own current state of mind. "So the limit turns out to be a solution" - it's pure genius. Read for yourself. And particularly Yu Ding's notes on Perelman's second paper here, are an interesting and eye-opening addition to this complex work.

The condition R(x; Tx) ? (Tx - T0)-1 says, if we rescale the time Tx - T0 to about 1, then R(x; tx) is bounded by Q. This is also an upper bound for Tx - T0, but it is not a very precise bound; we have in mind on this cap R should be at least h-2. The conclusion of II-4.7 gives a much better bond.

I agree. But I reckon that h-10 would be the more appropriate factor for cap R to guarantee the ultimate bond. Though you have to keep in mind that 0 is the smallest sectional curvature.

Isn't it terrible when people interview themselves? When politicians make statements and ask themselves yes/no questions before posing for an answer: "Did I expect this would get me into dire straights? No" "Have I ever thought about undermining the system? No" "Do I consider my position within the government stable and strong? Yes" - I wish they would answer the real questions with the same conviction and enthusiasm.

I have thought good and hard if I should touch this subject at all anywhere outside of the many intense discussions with friends and family and with myself, while following the deeply disturbing events in the Middle East. My own detailed understanding of the roots of the crisis is very basic and limited to say the least. Therefore my approach can only be lead by the blatantly obvious: That thousands of people are suffering. My reaction to the news is getting increasingly emotional. I find myself tearful in so many situations these days in which I am in one way or another indirectly touched by developments in Lebanon, Afghanistan and Iraq. I am drowning in questions, in helplessness, in hard-to-control anger and frustration... and I don't know where to put it.

A few weeks ago a catholic school in Britain was preparing for their annual stage show and one group rehearsed John Lennon's famous song "Imagine". The kids worked hard preparing for the show and were looking forward to the big day in excitement. A day before the performance the school's headmaster scrapped the song from the programme, claiming that the lyrics do not represent the values of the school. He did not want to promote a song that suggests that the world would be more peaceful without religion. The man could not have been more wrong.

Well, I wish the students had performed the song after all...

Imagine there's no heaven - It's easy if you try
No hell below us - Above us only sky
Imagine all the people - Living for today...

Imagine there's no countries - It isn't hard to do
Nothing to kill or die for - And no religion too
Imagine all the people - Living life in peace...

You may say I'm a dreamer - But I'm not the only one
I hope someday you'll join us - And the world will be as one

Imagine no possessions - I wonder if you can
No need for greed or hunger - A brotherhood of man
Imagine all the people - Sharing all the world...

You may say I'm a dreamer - But I'm not the only one
I hope someday you'll join us - And the world will live as one