Vanity of Vanities, all is Vanity

Its arriving early in Israel… It starts with a mini-war here, and lets hope it would not last. 2009 is definitely going to be an interesting year, potentially too interesting.

Books are what they are; readers that read nothing, who allow themselves to read books about nothing, have no place reading.

And so, with a similarly ridiculous construct, this book begins its tale of a nameless post-colonial country in eastern Africa. The hero is a Muslim-Indian from a family that lived for generations on the coast, and decides to move in land, to the city by the bend in the river. The book has vivid descriptions of life in such settings. Here is a quote:

Sun and rain and bush had made the site look old, like the site of a dead civilization. The ruins, spreading over so many acres, seemed to speak of a final catastrophe. But the civilization wasn’t dead. It was the civilization I existed in and in fact was still working towards. And that could make for an odd feeling: to be among the ruins was to have your time-sense unsettled. You felt like a ghost, not from the past, but from the future. You felt that your life and ambition had already been lived out for you and you were looking at the relics of that life. You were in a place where the future had come and gone.
— A bend in the river, V. S. Naipaul

The book is well written and worth reading. A bit short of a masterpiece despite the author quiet but determined hatred of his hero, his friends, the reader, Africa, women, men, people, and everything else (just to be on the safe side).

Soft words
Trying to convey what can
never be said.

Mundane words
carrying us through the day.

Tired words
For evenings and other occasions.

Empty words
To deny the silence.

Victory words
To celebrate defeat.

Words of loss
for future recovery.

Healing words
To cover the rift.

Once there was one,
now there are too many.

Since some person asked about it in the comments, here is one of Rachel most famous poems. Kinnert is the sea of Galilee.

AND MAYBE

And maybe those things never really were,
maybe
I never rose at dawn to the garden,
to work the earth in my fury?

Not once on those harvest days, so searing
and so long,
atop the cart that brimmed with fattened sheaves,
did I not give my voice to song?

Did I never cleanse myself in the innocence
and blue calm
of my Kinneret…oh, my Kinneret-
were you? Or did I dream it?

–Rachel (1927)

(Translation by M. Salomon.) Found here. And there is a really good performance of it here.

The interesting thing about this poem is the “modern” theme of it and its simplicity, considering it was written in 1927. At the time, she was slowly dying of tuberculosis, far from Kinneret, see here.

Here is a problem that occurred to me while doing nothing (i.e., writing a proposal). Consider a given set of segments S={s₁, …, s_n} in the plane:

We are interested in finding a maximum independent set of segments out of this set of segments. Naturally, two segments are independent if they do not intersect. A possible solution might be for example:

Since finding this set is probably NPC, we are looking for an approximation to the maximum set.

Currently, the only result I am aware of, is the cute but somewhat unsatsifying solution of Independent set of intersection graphs of convex objects in 2D, by Agarwal and Mustafa. They provide a roughly O(sqrt( opt )) approximation by using Dilworth’s theorem.

It is of course an interesting and natural open problem to improve the approximation or provide hardness of approximation for this problem.

But this seems somewhat challenging (it would require thinking and other headache-inducing operations). So, consider the following variant, which seems to be new. We would like to choose a subsegement t_i contained inside s_i, for i=1,…, n, such that:

1. They are interior disjoint,
2. and the total length of these segments is maximized (lets z denote the value of this optimal solution).

For example, a possible solution might look like:

I currently have an approximation for this that outputs a collection of segments of total length Omega(L / sqrt(n)), where L is the total length of the segments of S.

My question: Can you do better than this? Are you aware of any related work on this problem?

If you had to give up on sex, or internet access for two weeks, what would you choose? To make the question meaningful, assume that the two are of high quality: The sex is fast, and the internet access is safe.

Anyway, more details here…

A story of retribution. No simple answers – pretty depressing.

Made it to Israel. Flights were somewhat delayed but overall not too bad. Flew through Madrid with Iberia (ok minus overall). Its a huge airport (did not know), and Terminal 4 is new and has the most interesting architecture of an airport terminal I have seen. Except for a confused old man taking my suitcase from the airplane instead of his (but I caught up with him, and took my suitcase from him, so no big harm done, but it was strange), there is nothing to report.

I am jetlegged and a bit sick (to be expected).

As for Israel, it seems to be captured in a time bubble, replaying the same old themes again and again. Its a combination of groundhog day, but with t-shirt weather in the middle of December, with the neverending story, with the difference that the story is also never-beginning going back to the beginning of time. From the same politicians running with the same old, same old  ideas  that did not work 10, 20, 40, or 3000 years ago (the elections are in a month or two, also something that looks like it is always true in Israel). Or headlines decrying the deterioration in the education in Israel (all my life it was deteriorating – it must have been excellent at some point, because it is yet to reach the bottom). To the Gaza strip – poor, mostly unemployed, hextreme, and confused – with some people learning Hebrew, waiting for better times, that never seems to come. To people in the grocery store doing the standard shticks (like being in line, going away to get some extra stuff, and coming back to their old spot in the line). In short, the grave situation can only be compared to the situation a year ago, to whom it is completely identical.

The amazing thing is that there are still Israelies that get upset about all these things. You would think they would learn by now…

Its amazing what you can buy on ebay…

I will be in Israel starting this Thursday till January first. Lets hope this time the flights would go better than last time…