New Year's Resolution

I guess I missed a whole lot of posting opportunities over the holidays, but I am back now, doing a whole lot of nothing special.  Lately I have been trying to build a projective resolution, thus the post title.  As for actual New Year's resolutions, I don't really have any.  Fortunately I have built the desired resolution, and I am very close (I think) to proving it has a certain desirable property.  Other than that, I can't say I've been up to much or had any deep thoughts.  Perhaps I will come up with something to post about soon.

Back to Business

So, one holiday down, two more to go, I guess.  New Year's ironically straddles two years, so maybe we should say 3/2 for people who don't like to reduce (like me).  A big thanks to G & S for letting me stay for the weekend, etc.  I won't bother itemizing.  Now it's back to that weird stretch of the year that falls between major holidays, where you try to cram more learning into two weeks after just having been off for so long.  Good luck, professors! I'm pretty sure most students are just coasting at this point and won't fully regain consciousness until some time around January 4th.

I won't bore you with the details of my own holiday travels, since if you are reading this blog there's a significant chance you were there, and if you weren't, suffice it to say that it was fairly uneventful.  As for the shopping season which is upon us, I will add my usual request: don't buy me anything, and if you absolutely must throw your money at something, there are plenty of good causes out there, such as this guy, who probably has a donation link somewhere, but I couldn't find it in the first couple minutes of searching, so I gave up.

As for myself, I have research to do, although I just recently finished up what is basically my main problem, so now I have some other unrelated problem to work on.  It's kind of nice because it is so different and that gives me a break.  It also lets me think about functors like Cº: Top -> Rng and Spec: Rng -> Top.  Specifically, it is well-known that if you start with a topological space X, and look at the set Cº(X), the real-valued (although complex is fine) continuous functions on it, you get a ring, with multiplication and addition defined pointwise, i.e., (f + g)(x) = f(x) + g(x) and (fg)(x) = f(x)g(x).  In fact, it's a commutative ring with unity since R is.  It's also well-known, though by fewer people, that you can construct Spec of this ring to get a topological space, and that this space contains a "copy" of the original space.  Specifically, MaxSpec Cº(X) = X.

This isn't really crazy once you know the definitions.  Spec S for some ring S is the set of prime ideals of S, and it's easy to verify that px = { ƒ € Cº | ƒ(x) = 0 } is a prime ideal, and is in fact maximal. Because of the compact Hausdorff nature of X, it turns out that these are the only maximal ideals, and pushing through definitions the map that sends x to px is continuous and open, and so is a homeomorphism onto its image (there are other prime ideals, so Spec Cº(X) is actually more stuff than just X).  If you take away these nice properties of the underlying space, it may cause a failure of that map to be a homeomorphism.

As an example, if you take X = {1, 2} with the indiscrete topology, i.e., the only open sets are X and ø , then the only continuous functions will be constant functions, meaning that p1 = p2 = {0}, and you can see that this functor X -> MaxSpec Cº(X) sort of "forgets" that there were two points because from one point of view, there really weren't two points to begin with, since they couldn't even be separated by open sets.

That's just a dumb example I thought up on a train or something, but there are all sorts of still useful spaces that fail to be compact or even Hausdorff.  The usual topology on the real numbers, for example, gives a non-compact space. They are, however, locally compact, and even Lindelof, so maybe there's a hint.  The result I'm looking for is not actually homeomorphism, but that's a post for another day.  Ok, congrats if you got this far!

Bob

Whew.  I just got home (office, actually) from a Bob Dylan concert!!!  I'm still pretty excited so this probably won't be that coherent a post.  Anyway, the opening act was Mark Knopfler (formerly of the Dire Straits), who was pretty awesome and had a rocking band behind him.

Bob was awesome as ever, and did his usual changing around his songs so much from the album versions that it takes you a bit to figure out what he's up to.  It's great when the crowd catches up and starts woo-ing at one of their favorites.  In case you are wondering, here's an incomplete set list, not really in order:

You Ain't Goin Nowhere
It's All Over Now, Baby Blue (the arrangement on this threw me at first)
 Tangled Up In Blue (totally reworked, basically a new verse's worth of lyrics)
Early Roman Kings
Rollin' and Tumblin'
Chimes of Freedom (crazy different arrangement from anything I've heard before)
Things Have Changed
Highway 61 Revisited
Desolation Row (!!!)
Thunder on the Mountain
Ballad of a Thin Man (trippy echo effect going on this one)
Like a Rolling Stone
All Along the Watchtower (simply mindblowing)
and as an encore...
Blowin' In the Wind

I'm probably missing one or two.  But, by me and my friend's count, there were four (4!!!) tracks from Highway 61 Revisited.  That's pretty great, and each one was really a great version.   I have to say I was surprised that there were no tracks from Blonde on Blonde, but I can't complain about the set list at all.  It's almost surprising that there were no tracks from Infidels, since he had Knopfler with him, although they didn't play together.  Anyway, that's it for now.   :D

New Mac

Sorry for the long absence, everyone.  My mac laptop crashed on me a couple weeks back and so I haven't had regular access to the internet.  I think there was some massive hardware failure, but I don't know what it is.  Trying to boot it up at this point just leads to it asking for the os or some files, anyway.  It blinks a folder with a question mark at me, but I have no way of delivering it the goods since I don't currently know where the startup disk is, and even if I had it, the disk drive just stopped working for no apparent reason before the crash.  So, I had to get a new laptop.

By "new," I mean "used and almost the same model as the previous one" because it is much cheaper and all I want is a machine that will let me check email, use skype, and create latex documents, which the old one was doing fine until it just melted or whatever.  Hopefully I will be able to pull the files off the hard drive. I've been told this is relatively easy to do with older model macs because apple hadn't thought of making it nearly impossible to remove the hard drive yet.  I do have to say that while I like using a mac for some reasons, apple's tendency to make you do everything through them (for a fee, of course) is creepy and pretty awful.

Anyway, the new one is running fine thus far, but I want to vent on a couple things here.

1) The seller didn't send the CD, which wouldn't be that big a deal, if he/she had bothered to reset things to factory settings.  As it was, I had to search the internet for a method for resetting the administrator password, because a computer you can't install things on is basically just a (safari-using, ugh) web surfing machine.

2) The estimated time of arrival for this laptop was Tuesday-Thursday of last week.  The seller's only provided tracking information was "USPS," which is completely unhelpful and also turned out to be incorrect, since it arrived via UPS today.  I was really more annoyed by the inaccurate estimate than by the lateness, because I basically had to sit at home, waiting for the mail, as it is delivered in the afternoon here, all day, just to be disappointed when all that would come are coupon books and bills.  Meh, I will probably note that in the review.

Ok, next post will have something of interest to people in it.

Trip Pictures #3

Hey everybody! More trip pictures, but first I wanted to say that I was able to fix the last post, so if you wanted some context on the pictures of me eating various things, now you can read all about it.  Don't worry, I have more pictures of me eating things for those interested, but today is about a matsuri.

 

Here we are getting ready to go to Gaina Matsuri, Yonago's biggest festival.  Matsuri translates roughly to festival, and Gaina is Yonago dialect for big.  It's traditional for women to wear yukatas and men to wear jimbeis to festivals, which is what we were doing. The vast majority of people just wear their everyday clothes, but you'll generally see people dressed like this at any sizable matsuri. I bought the jimbei for pretty cheap and she already had the yukata. I opted not to buy geta, the traditional wooden sandals because they're not exactly useful or comfortable, while I can sleep in a jimbei. Women sort of get the short end of the stick here because jimbeis are basically just two part robes that are very comfortable, but Mie couldn't even get into hers without assistance because the belt mechanism is so complex.

 

Here are Mie's older sister and her kids, Misato (girl) and Tetsuya (boy). Misato decided to dress up, too, and I think it suits her, though apparently it was pretty tight. They're wearing the traditional crocs, if you can't tell.

 

And here is (for the time being) my only picture of the actual festival.  Generally festivals look a lot like you would expect, with tons of people selling festival food and drink. There are also usually taiko performances and other stuff like that. This picture shows a thing that is unique to Gaina, though, which is a sort of balancing contest.  It's hard to see, but that's a giant pole with lanterns hanging off it, and the people in the street there are trying to balance it. They balance it on their heads and hands and necks and all sorts of things, increasing the height of the thing every time they manage to balance it. It's pretty impressive.

Ok, so that is pretty much it for the festival stuff. Time to get back to research, I guess.

Trip Pictures #2

Update: blogger stopped being stupid, so I was able to put up explanations of the pictures. The ketchup and mustard face was my doing, by the way.

 

This is us eating takoyaki in Osaka.  Osaka has two foods that it is supposedly famous for, takoyaki and okonomiyaki.  Takoyaki is basically fried dough balls that have octopus (among other things) in them.  This place was really good takoyaki.  Okonomiyaki is basically cabbage pancakes, but actually Hiroshima style is better.

 

We had a barbecue with some of Mie's friends at her friend's family's house, which was pretty delightful.  Here's me eating something, probably meat.  It was very bright out, so that's why I was squinting.

 

Here's a picture of Mie's mom and me eating, mostly sashimi, but also some cooked fish and whatnot. That guy in the background is from some other prefecture and was of course interested in what the gaijin was doing in this little izakaya way out in the inaka.  Mie was there, too, but she was taking the picture.

 

Another one of the barbecue.  The guy's grandma was really nice and kept bringing us stuff to eat, including watermelon (gag). I was being polite and all but I would rather eat nothing than watermelon, and I think she felt bad that I couldn't eat it, so she went to all the trouble of making green tea by hand (like an improvised tea ceremony).  It was super nice of her and really good tea, too.  In this picture we are toasting using bamboo that we cut down and were using as sake cups.  Apparently this is a traditional way of drinking sake and I have to say that the bamboo smell really makes it better.

 

Here's more of me eating, probably mozuku, which is like a really slimy seaweed. Mie wanted me to eat it because I was saying that there's no way most Americans would even think of it as food. It really looks like pond scum or something, but it had a nice flavor (some kind of sauce), and at this point no food textures bother me at all.

 

Another toast, but this time with Mie on the left there.  New sunglasses, by the way.

Again, more delicious food. The towel around the neck thing is what I refer to as 超ジャパニーズ, "chou japaniizu" or very Japanese. You see people with towels around their necks all over the place during the summer because it is so handy to be able to wipe sweat off yourself in the oppressive heat and humidity. It also prevents sunburn, which is much appreciated.

Trip Pictures

Alright, here is the long awaited post with trip pictures.  I assume I won't get through all of them in one post because there are a ton. These are all pictures from Mie's phone. I actually have more pictures on my camera (thanks, Dan!) but I can't actually upload them directly to my Mac because it seems totally reasonable for a digital camera to have that problem nowadays (???).  Anyway, I will probably upload them to my work computer and then move them or some such thing.  Ok, here goes.

Here's a picture of me drinking some Green Dakara (warning: unbelievably cute commercial).  It looks like the road is slanting up because it is. This is Daisen (literally "big mountain"), one of the biggest mountains in western Japan, not too far from where we were. It's good for skiing in the winter and climbing in the summer.

And some more pictures of Daisen.  Sorry they are mostly of me, but, again Mie's phone.  It was a nice day, and we intended to go the shrine which is only part of the way up the mountain since my previous experiences at Daisen were all either skiing or beer drinking, but since it wasn't very far, we decided to go a little bit farther up the mountain before turning around.  Unfortunately, it turns out the path doesn't meet up with another path until most of the way up the mountain, which meant that we ended up climbing the mountain unintentionally.




That gate there is the entrance to the shrine, and that thing spitting out water is, well, a thing spitting out water.  It is for washing your hands before entering the shrine proper.  You can sort of make out on the sign, which was where our path finally crossed with another one.  To the left is the way to the top, 1.2 km up, to the right, the way down, 1.6 km, and you can barely see it, but the way we came was 2.3 km, I think. This was all done in just sneakers because we hadn't planned on actually climbing the mountain. There were tons of people going up and down the mountain with all their gear, which was kind of hilarious.  It's not like you can't do it without gear, though. There's no scaling a rock face or anything, just kind of hiking uphill.

Since blogger is weird with pictures, I think I will split this into multiple posts.