Lost

Last week I was in Budapest, Hungary for a conference. I got home Sunday evening. Monday morning I started grading exams and continued grading until 2am on Tuesday morning. Finally, I went to bed around 2:30am---I simply could not stay awake any longer. In the night I had a dream that I was back in Budapest, and it was dark. Suddenly I woke from the dream, looking around I could not tell where I was. I sat up in bed and tried very hard to think back to how I got in whatever place I was. My brain would not budge. This was a frightening experience---not because I didn't know where I was, but because I could not get my brain to process it. Lisa finally came into the room 30 seconds later, and when she asked "what is wrong?" it finally loosened the stuck gears in my head. I fell back down, comforted that I could think.

Déjà Vu

Every night I have many dreams. Right before I completely go to sleep, my brain starts a dream. I suspect that may be the reason I have a hard time getting to sleep since the dream process must start before I can really get to sleep. My dreams are very vivid and usually involve real life circumstances. I may dream about work, school, home, or anything. Sometimes, however, my dreams mix with my real memories. Sometimes distinguishing between dream memories and real memories is quite a challenge.

The most unusual feeling, though, is the one of déjà vu. Sometimes, in real life, I encounter a situation: a scene that seems to me to have come straight out of one of my dreams---as if in the past I had dreamt about a scene in my future. This past weekend it happened again, I was at a friend's house where he was having a gaming party. We started playing a game I had never seen before (Halo 3). We all took turns playing (two people could play at the same time), and at some point two of my friends were playing when they encountered a scene in Africa on a highway system. This triggered my déjà vu and I remembered having a dream watching both of them playing and encountering the exact same scene.

Now I suspect that I did not really dream exactly that, but the feeling of déjà vu is so strong that immediately when I feel it, I wonder if I am currently dreaming...

P != NP

I had an odd dream last night. I dreamt that I was giving a presentation at a conference, showing a proof that P doesn't equal NP. It seemed I had this closed box, which every year I would bring to the conference, and if someone could successfully complete my challenge, I would show them the contents of the box. It seems that inside that box was a secret set of numbers that helped me to come with all sorts of answers. This year, the answer I came with was that NP didn't equal P. To prove this I had a set of five objects. Each object was a set of tubes that were different, but precise diameters. These tubes were chosen with the help of the numbers in my box. The tubes were handcrafted, and on each object was drawn some sort of histogram. The histogram of each object conformed to certain properties, thus somehow proving that P != NP. The proof was simple to show, but hard to come up with. The proof it seemed (as I realized after I woke), was in the spirit of NP, easily verifiable, but not easily come by.