dreams of math and science
Nov. 3rd, 2006 06:45 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
guslApparently, my dreams are more visual than most people's. More mathematical as well.
Last week, I was thinking about model selection ideas, relating to the question of why Occam's Razor is useful. At my job, we do a search for production rules that explain a given problem-solving behavior. My dream had a person on a diagram, jumping from model to next-simplest model... reminescent of Levin search (incidentally,![[livejournal.com profile]](https://www.dreamwidth.org/img/external/lj-userinfo.gif)
jcreed recently told me that one of the problems in Rudich's Complexity Theory class was to find a program that will compute a given NP-complete problem in P-time, *IF* it is the case that P=NP. The solution is to (1) write a P-time reduction of the problem to SAT, and (2) to write an algorithm that will solve SAT in P-time if that it at all possible (i.e. P=NP), by searching through all algorithms.).
Yesterday,shaktool and I were discussing why milk is white. My argument was that this meant that milk couldn't be a pure substance (I believe it is a suspension), since white solids always become colorless when you melt them.
So tonight I dreamed that I was explaining to my mom something about the solubility of salts, and I predicted that Hudson Bay, consisting of cold polar water, would have precipitated salt at the bottom. In order to check my prediction, we walked over to Hudson Bay, walked in the not-unpleasantly-cool water, and to my surprise, we found salt crystals *floating*. Most of them were 5-10cm long and diamond-shaped but snow-flakish in texture, and tended to form clusters on the water's surface.
Another association to explain this dream is that I was speaking to my aunt in Alberta yesterday.
Last week, I was thinking about model selection ideas, relating to the question of why Occam's Razor is useful. At my job, we do a search for production rules that explain a given problem-solving behavior. My dream had a person on a diagram, jumping from model to next-simplest model... reminescent of Levin search (incidentally,
jcreed recently told me that one of the problems in Rudich's Complexity Theory class was to find a program that will compute a given NP-complete problem in P-time, *IF* it is the case that P=NP. The solution is to (1) write a P-time reduction of the problem to SAT, and (2) to write an algorithm that will solve SAT in P-time if that it at all possible (i.e. P=NP), by searching through all algorithms.).Yesterday,
shaktool and I were discussing why milk is white. My argument was that this meant that milk couldn't be a pure substance (I believe it is a suspension), since white solids always become colorless when you melt them.So tonight I dreamed that I was explaining to my mom something about the solubility of salts, and I predicted that Hudson Bay, consisting of cold polar water, would have precipitated salt at the bottom. In order to check my prediction, we walked over to Hudson Bay, walked in the not-unpleasantly-cool water, and to my surprise, we found salt crystals *floating*. Most of them were 5-10cm long and diamond-shaped but snow-flakish in texture, and tended to form clusters on the water's surface.
Another association to explain this dream is that I was speaking to my aunt in Alberta yesterday.