Saturday, May 20, 2006

是什么让我茫然?

科技发展有些时候匪夷所思。今天早上还在洛杉矶,现在就在家里上网。时空转变让人措手不及。身边的一切都变了,除了情绪还停留在原地。

从小离开家,渐行渐远。每次在一个新的地方,总有异乡的陌生感。虽说新鲜也是有的,但是当熟悉的东西不再出现的时候,人如同浮在空中一般,总有一种隐性的紧张情绪在缓缓增长。

我很小时候跟老妈东奔西跑,无论走到哪里都要带着我自己的枕头和褥子。到了陌生的地方,抑制着自己的恐惧,有什么吃什么,让做什么就做什么,是个很乖的表情严肃的孩子。只有在晚上睡觉的时候,打开行李,看到自己的枕头,才绽放出笑颜。

这次回到老地方,看到认识的人,老朋友,导师等等。真是奇怪阿,明明只待了一年,为什么现在这么留恋?也许是自己清楚地意识到,那一年是好的日子,而且这个好的日子,永远不会重复了。这次见到的许多人,马上就要各奔东西了。当时离开的时候也是有留恋的。这一次,是清楚的体会到,这种分离而且一去不复返的无奈。

时间留不住啊,在指缝中溜走。想要抓住影子,也许有一丝一缕,仔细看时,却分明没有当时的满心欢喜,只是茫然。

是什么,总让我觉得茫然?又是什么,让我泪流满面?

Tuesday, May 09, 2006

A math puzzle

A puzzle I learned from Joel, originated from Peter.

Given a deck of card face down on the table, now I flip the card one by one. Each time you can bet any amount of money from you have in hand. Say if you bet $50 for the first one to be red. If it is red, then you get $50 extra. Or, you lose $50.

You are given $100 to start with. Now the question is what is the maximum amount of money you can always win.

The answer is about $900, with a cute argument.

Saturday, May 06, 2006

小气鬼买机票

以前和沙和尚分居两地的时候经常要飞来飞去的,养成了找便宜机票的好(坏)习惯,找机票default是省钱。这次要买一个multi-destination的机票。晕哪。一共4段飞机,最后发现最便宜的就是买4个one-way,第一段飞jetblue,第二段southwest,第三段united,第四段american west。打印下来receipt一摞!

这样下去,估计我很快就可以跟那个网上的pizza hut的沙拉有一拼。

Friday, May 05, 2006

忽然之间的莫文蔚

我最近迷上了莫文蔚的这首歌,忽然之间。

每次听似乎看到,这个执著的女生,站在远远的天地下,自言自语般的唱着,真诚的感情缓缓的持续的涌现出来。

歌词朴素得很,歌声也很朴素。一个人审视自己,审视爱人。突然之间,天地万物都消失了,只有我和你。爱的感觉总是突然到来的,一件小事,一个场景,一句话,一件东西,一种颜色,一种味道,或者,仅仅是,一个时刻,突然就想起你。

人生的终点都是一样的,所有的所有的事情,我们的追求,事业家庭,一切一切,最终都会消失不见。佛说要修来世,耶稣说信他就会上天堂,世人却总在功名利禄里挣扎。忽然之间,一个声音唱着,其实生命的本质,就在那一个时刻,一个时间都可以消失的时刻,一个生命变成尘埃的时刻,只要有一个人可以牵手,一份情意可以怀念,一路走来珍惜的回忆。让时间的河流奔跑去吧,只有这一刻足以了。

附上歌词:

忽然之间 天昏地暗 世界可以忽然什么都没有 我想起了你 再想到自己 我为什么总在非常脆弱的时候 怀念你 我明白 太放不开你的爱 太熟悉你的关怀 分不开 想你算是安慰还是悲哀 而现在 就算时针都停摆 就算生命像尘埃 分不开 我们也许反而更相信爱 如果这天地 最终会消失不想一路走来珍惜的回忆 没有你 我明白太放不开你的爱 太熟悉你的关怀 分不开 想你算是安慰还是悲哀而现在 就算时针都停摆 就算生命像尘埃 分不开 我们也许反而更相信爱

Thursday, May 04, 2006

To-do list

1, book flight ticket for June trip.
2, a paragraph on secure localization.
3, a paragraph on geometry in sensor networks.
4, paper review.
5, read the papers about compressed sensing and gossip.
6, lower bound on brokerage.

Don't panic, calm down, and do it one by one.

Monday, May 01, 2006

High dimensions are tricky

I was bothered by a claim that seems to be trivial to argue. But I was stuck for a couple of days. It states:

If a d-dimensional convex body P does not contain a (k+1)-dimensional ball of radius r, then P can be enclosed in a k-dimensional flat with width (k+1)r.

This sounds intutively trivial. However when I try to write down the proof it is not easy. This also motivates me to read things about high dimensional space and polytopes etc. The thing is that high dimensional geometry is hard to visualize, and sometimes the results are counter-intuitive.

I have later been trying to use an old theorem called John's theorem to prove it. Though the theorem is very nice to know. My trials ended up in vain so far.

Anyway, here is the nice John's theorem (proved in 1938 or sth).

A convex body P in d-dimension contains an ellipsoid E such that E \subseteq P \subseteq dE, where dE is a factor d blowup of E. If P is symmetric, then P is enclosed in \sqrt{d}E. Both bounds are tight in the worst case. Examples are simplex and cube.