Your brain uses a triangular grid to map out space.

Some UCL neuroscientists have evidence that human (and rat) brains use triangular grids to represent locations in space.

That seems like a good idea for estimating distances. Manhattan distance is a very bad approximator to Euclidean distance. On a triangular grid, however, it's not so bad.

I wonder how this works in 3 dimensions.

A sleep paralysis experiment

After reading the Reddit comments on sleep paralysis and lucid dreams, I have just tried experimented with this stuff myself. First, some background. I've had sleep paralysis several times before. It's terrifying -- like being sucked into something, but not being able to move. Naturally, I fought it each time, successfully. After a few seconds of battle, I found the strength to open my eyes and wake up. The redditors suggested giving up instead and letting it take over you, so I wanted to try doing that.

The perfect opportunity presented itself this Monday morning. Normally, I go to sleep around 2am and wake up around 8:30. On Sunday, I had to get up at an unusual 5:30am to go to a volleyball tournament in a different city. The next day (today), I had to get up at 7:30 to run an errand, followed by a work meeting at 9:30. With all this sleep deprivation, by 10am, I was finding it hard to keep my eyes open during the meeting.

At 10:30, I was at my desk, tired, sleepy and ripe for a lucid dream experiment. I got comfortable in my chair, put my feet up, lay back, resting my head on the back of the armchair and tried to fall asleep.

It took about 30 minutes, and I had to be careful about keeping the delicate balance between relaxation and alertness to avoid actually falling asleep, but everything worked as planned.

I started feeling a tingling sensation in my limbs. My muscles got a little stiff with sleep paralysis, and I started hearing a loud high-pitched noise in my ears. I also felt a definite sense of fear. To test whether this was indeed sleep paralysis, I tried moving my fingers, but found that I couldn't.

I was wondering how difficult it would be to give in to the fear and stop fighting, but it turned out to be rather easy. I relaxed even more and let the fear take over. The noise in my ears got louder. Much louder. The muscle tingling intensified as well. I felt my heart rate increase. The screen went from black to white. It was like the "white light" or "light at the end of the tunnel" cliché that dying people talk about.

That experience lasted for only a second or two, and I started to wake up. I tried relaxing even more, but the whole thing passed, and I woke up feeling a bit agitated and excited. No lucid dreams, unfortunately. Instead of trying to do it again, I opened my eyes and decided to write down these notes.

I will definitely keep experimenting.

Sleep paralysis and lucid dreams

Here is a great example of the weirdness of the human brain.

http://www.reddit.com/r/AskReddit/comments/an86t/sleep_paralysis_anyone/

If you have ever experienced sleep paralysis (and most people have), you can probably relate to many of these stories. I've had this happen many times, but I've only once been able to experience a lucid dream, and it was awesome. I didn't know about the sleep-paralysis-to-lucid-dream connection though, and I can't wait to try an experiment next time I get a chance.