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.

只今！

So I just got back from Japan a little bit ago. Sorry for the lack of updates on that, but I had little to no internet access over the last couple months, but now I have good internets again and also a bunch of pictures of the trip, although they are mostly pictures of me making faces in front of stuff, so I will get to posting that tomorrow or later. As for now I must get my body back on EST.

Juneteenth

Happy Juneteenth everybody!  I had no idea that was a thing until I just looked it up on Wikipedia, but it's a nice way to open a post.  I just saw that some other people had updated recently, so I thought I would ride the mini-wave and let people know what's up with me.

The spring term is over here, and summer term doesn't start for another week or so.  It doesn't really matter to me, since I'm not teaching or anything during the summer term, which is when the math majors are on co-op, so there are few classes.  Not that there are many math majors, anyway, but summer classes are always in demand by the faculty so that they can continue to get paychecks all through these dog days.  Incidentally, it's probably not the dog days yet, technically, but it is awfully hot, so I'm going to pretend that the etymology is from dogs panting or something.

My research is going pretty well.  I typed up a giant (well, like 10 pages or so) document with a ton of computation on it, and now I'm just sort of reformatting and adding some signs (don't ask).  It's mostly a well-known computation, but nobody seems to ever write it out, or is ever even clear about what they are using the results for specifically, so it is good to be clear.  As you can imagine, making a bunch of little changes to a ton of code is not particularly interesting, so I won't bore you with the details, but it has given me a bunch of opportunities to take breaks, and since I'm not on campus, I use those breaks for things other than drinking coffee.  Things like making this:

As always, apologies for the weird coloration provided by the inadequate lighting here.  It's a strawberry-banana pie.  Actually I was short one banana, so I threw in a very ripe peach, as well.  I haven't actually tried it yet, except for a little bit of the crumble stuff on top.  Incidentally, it was also baked in a pi-tin.  Well, pi-plate.  That is, there's a big letter pi on it, and the digits around the rim.  It's not mine.  It just happened to be the only thing that looked like it would work for making pies.  The pie crust is also made from scratch, so haha!  I'm like a real homemaker or something.  Again, I haven't actually tried it yet.

In other news, there's not really any other news.  There are some shows that I've been watching, but nothing that anyone would be interested in.  It's too bad because Young Jutice (this is a children's cartoon) is actually quite good and the current storyline is pretty twisty and the creators were kind of bold in some of their choices, especially considering it's a cartoon running on Saturday mornings.  Unfortunately, I don't really have any friends who are that interested in amekomi = American comics, as Mie-chan calls it.  Ah, well.  Everyone else's loss.

I don't think anyone reading this has an iPhone, but I do want to mention that recently I got to play Ticket to Ride on one, and I have to say it is awesome and pretty much the only thing I've seen on them that really makes me want one at all.  I mean, siri is cool or whatever, but I can't see myself using much of the functionality.  Ticket to Ride is an awesome game, as you probably know if you are reading this blog, but it's even cooler when all the shuffling and whatnot is taken care of for you.  You can pass the phone back and forth to play with other people or play with multiple phones, but either way, it speeds the game up a ton.  I think only the America map is available, but there are some expansions and whatnot.  Anyway, I think it is pretty cheap to buy.

Alright, I guess that is pretty much all of my news.

Update: the pie is delicious (^_^)

Late Night Post

What's up?  Late night post is what's up.  So, I don't want this to just become my brog (this is a term I just made up for brag-blog), but I should probably mention that I was awarded, or at least informed that I would soon be awarded, another teaching assistant award, this time a department-exclusive one.  So that's kind of nice and will probably result in some more money coming my way.  So, real topics:

My research is actually going pretty well.  I am just finishing up a problem that I have been working on for basically ever involving homotopy categories of modules, blah blah, nobody really knows what that means.  At least I think I am in the home stretch.  There is some sort of connecting material which I am not totally clear on, but I think it is just classical results that I can adapt if need be.  It's odd that most of the time I have spent seems to be on simply understanding what the problem even was, and the second most time I spent was trying to decode the particularly French way that some stuff is encoded.  The French style can be, from what I can tell, generally summed up succinctly as "obfuscation."

I don't know if I have ever posted about this stuff before, but I probably did at least mention that based on my admittedly small (n=1) sample size, being in grad school has a weird sort of specialization effect to it, where people on the outside just see you and your peers as "doing math (or whatever you do)," but you each see what the other people do as completely foreign.  Maybe it is more exclusive to math, but I actually have the feeling that it is even less pronounced in math than in other fields, but as mathematicians, we don't really see outside of our own bubble.  Actually, a tree is probably a better model than a bubble, but I digress.  I only learned relatively recently that the number of, say, biologists doing research today is something like 10 times the number of mathematicians doing the same, so it is even more disparate.  I don't actually know if that is true; it's just what I heard.  Ultimately, I don't care that much if it is true, but it would be sort of interesting if it were.

The whole point of that last paragraph was that I got into some totally non-serious argument weeks ago with another student about how I act like my math is harder than other people's math, but it's really not.  I don't really think that's fair, because I usually preface talking about my stuff with "it's actually very easy," or "anyone could do this," or "it's just composing linear maps" if I am feeling fancy.  I do get to name drop a bunch of crazy sounding things like "total derived functors" and "supercommutative algebras associative up to homotopy" and "quasi-coherent sheaves of modules," for example, but this is just the benefit/curse of doing anything algebraic.  The field necessitates a bunch of terminology, which makes it very front-end heavy when learning.  That's compounded by the fact that a lot of the difficulty comes in actually understanding what result you are trying to get, as opposed to how to get there.  I can't really explain it without getting into more detail, which I don't want to do, but oftentimes the actual computational work is relatively simple, without analysis-like complicated inequalities, or crazy functions like ! or Gamma or zeta or anything because that's not algebraic by it's very nature.  Also, people tend to turn off if they don't immediately know the thing you are talking about because they (understandably) don't want to spend all their time wading through definitions they'll probably never use.

Just to contrast, the argument came up because I said sometimes I was jealous of her (she does combinatorics) because often you can just pick up a paper and read the intro or the initial definitions and say to yourself "ah, I see what you would like to count; that's a reasonable type of object," even if the actual work in getting the result is painstaking and, well, sort of awful to do.  It's just kind of nice not have to stop after the first sentence to chase down the ridiculous set of axioms that define a "triangulated category" or something.  She didn't really read what I was saying as that, but it all worked out, and, anyway, my other friend, who also does combinatorics-like stuff, totally understood what I was saying.  I think he only understands it better after slogging through ten weeks of algebraic geometry to get to the realization that it's mostly things like zeroes of polynomials.  Ha ha.

Ok, so I guess there's not much going on in my life outside of school?  I saw three, three, woodchucks in rapid succession on Monday.  They were definitely all different woodchucks, too.  I thought it was pretty impressive.  When I told my friend (the first one, above) about it, she said "do you mean groundhogs?"  I said, "yes, they are the same animal," and she said, "yes, but you are here, and here they are called groundhogs."  So maybe it's a regional thing?  I mean, I definitely have heard both, but I prefer the name woodchuck.

Oh, yeah, and another note about math.  My advisor once told me I was "kind of a weirdo for this school because you're the only one that likes algebra."  He also said in class that algebraic geometry was kind of a "crappy field to go into, because everyone else will be publishing papers and you'll still be trying to figure out what's going on" or something to that effect.  I just thought that was kind of funny.

BOA

I just want to rant about how stupid bank of america is.  I only got an account with them so that I wouldn't get charged for using ATMs, by the way.  I keep trying to set up direct deposit for my paychecks, but, understandably, I need the account number.  You would think in the 21st century that this would be easy to get via ATM or the bank's website, but, no, BOA insists on hiding my number from me at ATMs, for what reason I cannot fathom, and their website refuses to let me sign in because I don't know the passcode that THEY NEVER GAVE ME and I can't reset because "security purposes," even though I've already given them my debit card number, my PIN, and my SSN.  There is literally NO WAY ON EARTH that I could have all this information and not be me.  Why not just look on my bank statement, you ask?  Well, they keep sending my statements to my old address, and I can't tell them to change addresses because I would need to sign on to the website to do so.  In what universe does this security system make any sense?  I just want to know my account number so that I can put money in the account, something which I am able to do via LESS INFORMATION than I have already given them.  Just to belabor the point, with LESS INFORMATION than I have already given them, I could take all the money in the account out in cash and close it.  These people are morons.

Lemon Chicken

Before I get around to the meat (haha) of the post, I just want to vent that Google changed their layout a few weeks back and it is very frustrating.  I don't really know why it's so difficult to get from the sign in screen to the new post screen.  There should just be a button saying 投稿 as soon as you sign in, but instead I have to dig through a couple pages to get here.  It really makes no sense, because writing new posts is pretty much the most important thing.  I don't really care about some page view statistics or all this other integrated crap that Google thinks I will want to see on the front page, and I don't really know why anyone would.  And while I'm ranting about Google, I'll also mention that I wish they would stop asking me for my phone number.  I didn't want to give it to them before and I still don't.  Why is there no option to make that annoying message go away?  There should definitely be a "I will never give you this information" button.

So I made lemon chicken the other day, using a recipe from an actual cookbook.  That's the result.  Pretty delicious looking, right?  The lighting is bad in the kitchen; it always looks much more yellow than it really is.  Coloration aside, it was pretty good, but if I make it again I will probably double the lemon juice that goes in the sauce.  I made orange chicken the night before and it was even better, but I don't have a picture of that, unfortunately.

And in other, possibly more exciting, news, I won an award for being an excellent teaching assistant recently.  It's sort of funny because I'm currently not teaching anything, just "grading" for a linear algebra class.  I actually just write solutions to homework problems for the students to use as a guide, and what's even funnier about it is that the guy actually teaching the class is a first year grad student who should really be studying for his qualifying exam.  He's a nice guy and doesn't ask me to do much, so I don't resent it or anything, but it seems like kind of a waste of "teaching excellence."

There were something like five winners of this award, but I'm the only one from the college of arts and sciences, I think.  The CoAS is kind of the low man on the totem pole here because engineering is what built the school and what it's most famous for and the business school brings in the big bucks.  It seems like the main job of the math department is teaching future engineers how to take limits without knowing what a limit is and trying to get business students to add fractions.  Probably needless to say, a lot of people don't seem to hold other schools/departments in high regard and don't really like having to teach baby math because the more important schools/departments don't want their students to learn, you know, actual math, but just how to do whatever they will need.  Sigh...

Anyway, it's nice to win an award, and there's some money that comes with it, which is even nicer.  I probably won mostly because some people in the department were pulling for me because I had to fill in for a couple sections of the class I was assisting with in the fall because the professor got seriously ill all of a sudden.  It's kind of weird because even if I were a terrible teacher, I probably would have done it anyway because nobody else has the experience in that subject and the department didn't really have any other options.  Also, aside from the actual teaching time, it was not really much additional preparation other than making more copies.  But, whatever, a win is a win and I'm happy about it.  Alright, that's enough bragging.

Pork Chop Blues

I was messing around on the keyboard the other day, doing one of my favorite tricks for playing the twelve bar blues, which is sort of mashing the flatted third and then the non-flatted third in rapid succession, and I noticed it sort of sounds like an oinking in the lower register, so I sort of threw these lyrics together (it's actually a slightly modified twelve bar blues):

This little piggie went to market
And this little piggie stayed home
This little piggie had pork chops
And this little piggie had none
And this little piggie went
Wee wee wee wee wee
Stick to your bones

Oh, this little piggie likes sausage
Oh, this little piggie likes ham
This little piggie get some bacon
Gonna fry it up in the pan
Gonna make a pig of myself
Gonna eat up all I can

Don't gimme no chicken
That stuff's no good to eat
Don't gimme no turkey
Can't even compete
Just gimme some of that
Other white meat

If little pigs had wings
Away they'd fly
Up to that big old
Mud hole in the sky
But if you wanna get to hog heaven
First you gotta fry

Better not build your house of straw
I'll blow it down on you
Better not build your house of sticks
You know I'll wreck it, too
Ain't no more bricks for houses
I used 'em for my barbecue

So hopefully that's a mildly entertaining post.

And He'll Be a Good Man

I'm not going to focus too long on this, but I'm sure you have read somewhere that Levon Helm of The Band died a couple days ago, which is sad.  Here's a link which is probably unnecessary for anyone who is either American or Canadian, which should cover pretty much my entire audience, since you've no doubt heard the song, but it is still one of the best ever, and no doubt it is getting tons of views lately.

Anyway, what's new with me?  Well, not a whole lot.  There's a lot more going on over at JLink's blog, so why not head over and check it out?  I'm pretty much just grinding through math and getting up to my usual boring hijinks when I'm not doing that.  In my math life, I am taking a class in algebraic geometry while slowly progressing on research, so have two more paragraphs on that:

Algebraic geometry is all about schemes and varieties and whatnot.  It's very terminology heavy, as you can probably guess from that last sentence.  For example, a scheme is the spectrum of a ring, equipped with the Zariski topology, and its structure sheaf.  If you don't know what those are, don't worry, I won't explain, but suffice it to say that each will require a couple more sentences just to tell you what they even are.  It's quite complicated to say it all, but in some sense is just formalizing geometric notions as algebra.  It's also highly unintuitive to just look at and I doubt anyone would be interested in it, but tell me this isn't a convoluted way of building stuff:

ring -> prime ideals on the ring -> topological space on the set of these ideals -> sheaf of rings over this space

My research is, well, my research.  I'm currently trying to show that the cohomology of the cone of the inclusion of a certain module category into another module category is acyclic, which will show that the two categories' homotopy categories are equivalent.  That seems quite out there, but the actual calculation is basically just trying to find the preimage under a certain operator of a given pair of sets of linear maps.  Even that sounds confusing, but it's really just saying if I know d(f,g) = 0, how can I find h and k so that d(h,k) = (f,g).  So, it's a lot like guessing at stuff and seeing what happens when you apply d.  I won't explain further.

Outside of that, not much is happening.  I substituted for a class last week and that earned me $100.  My one friend bought Risk 2210, which is like Risk with extra territories, a currency system which is used for buying cards and special units that affect the game, and a 5 turn limit.  It seems quite complicated at first glance, even compared to usual Risk, so I think it will be hard to find many people who would be willing to learn to play it, but it turns out that it is actually quite simple, and also quite fun.  It's his birthday soon, so I bought Risk: Godstorm off the interwebs, and we'll see how fun that is to play.  Don't worry, he doesn't read this blog, so I'm not giving anything away.

My roommate and I recently finished watching Star Trek: Voyager, so I'm kind of out of stuff to watch.  I don't really like getting involved in tv dramas and they end up being boring to me after a while, and there's only a small subset of comedies that aren't terrible and I'm already watching/have watched all of them, I think.  I may post some more thoughts on Trek, since probably one person out there enjoys those shows.

I originally started watching The Next Generation when it popped up on Netflix, and it was quite enjoyable, if very dated and full of stupid crap that makes no sense all the time.  I also basically had to skip watching seasons 1 & 2 since they are painful, but from there on out, it is mostly pretty great, with a few egregious examples in the final season.  Then we started watching DS9, just to keep watching something.  It's another one of those shows that takes a while to really find its groove.  I wasn't really much of a fan of it for the first couple seasons, but by the time Sisko shaves his head, it's fairly consistently watchable, if not good.  It's also extremely dated and sort of strange to watch now, since apparently tv drama has improved quite a bit since then.  Things that seemed good at the time now come off as really cheesy or bland.  Another thing I noticed is that Jadzia is one of the most annoying characters of all time and every time she refers to something Curzon did as something she did, I just want to throw her out the nearest airlock, but I don't want to spend a whole post talking about this show.

Then we finished that show (incidentally, despite the huge run-up to the finale of DS9, it feels quite underwhelming and simultaneously rushes and drags, while All Good Things is a standalone classic of an episode), I was going to stop forcing my roommate to watch Trek, since even TNG doesn't really hold up to the test of time and Voyager wasn't even considered any good when it was on.  But, my roommate decided to watch it anyway, so we plowed through that as well.  I think a lot of it was made more enjoyable by my tendency to be doing something else while it was on because its ultimate failing is that it's really just not compelling at all.  The characters are almost uniformly featureless and most episodes are just a forgettable technobabble problem with a technobabble solution.  Like I said, I may post about this again, but I do want to mention that Kate Mulgrew is such a terrible actress that it's actually sort of interesting to watch her.  It's like she doesn't really know how people actually behave, so she's constantly mugging inappropriately to the point where I sometimes would just laugh at the random reaction shots that seemed to be almost omnipresent in the show.  And since I mentioned the finales for the other two sequel treks, the finale of Voyager is pretty much complete garbage, like the guys making the show realized that it didn't matter what they did at that point, so they just crapped out something that barely qualifies as wrapping up the story.

Alright, now that I've probably lost everyone, I'll end the post with note that the last time I posted, I posted twice in one day, so unless you are observant, you may not have seen the first, much more substantial post.  I only mention it because nobody commented on it, but one person (thanks!) commented on the shorter post.

Bonus Pork Post

The other day, my housemate and I made pulled pork, which it turns out is very easy to make. It's basically just waiting for pork to cook in a crock pot, and then pulling it apart and adding barbecue sauce. But we ran out of bread, so I hadn't actually tried any of it till tonight, after buying some bread from the Wawa, because it's the closest place. We did, however, have a head of cabbage, so I did the sensible thing and made coleslaw. I learned the trick of putting coleslaw on a pulled pork sandwich from Saga Dave, weirdly enough, but what a delightful trick :)

Alpine Spring Break

My spring break started officially some time this weekend, but since I wasn't taking any classes, it doesn't really matter when it actually started. I had a final to give on Thursday, but it was an optional final. Fortunately, most of my students are academically very lazy and unwilling to take a test at 8am even though it can't possibly hurt their grade and might possibly help it. So, only about 3o of the 130 students in the class bothered to show up, which made grading go quickly, and we were able to finish around noon of the same day. Friday there was a board game night, which I went to and had fun at, but that was the only thing I actually did at school. I'm feeling pretty lazy, so just this post will just be a few thoughts without a ton of structure.

The games that I played Friday were Incan Gold, which is a simple but fun exercise in expected value, and Risk, which we all know I love. Usually I can't get other people to play, but this time there was no problem with that. In fact, we had seven people playing, with two people working as a team. I think of myself as being relatively expert at the game, given how much time I've spent on it, but I try not to be obnoxious about telling people what they should do or over-explaining the rules because I hate when people do that. My one friend always asks me for advice on what he should do, which is funny, since we are ostensibly enemies for the purposes of the game. Anyway, the one guy in our department who we basically all dislike because of his lack of social/hygiene skills was also playing, and he kept trying to lecture people about what to do, so we were all sort of silently relieved when he was actually the first one eliminated. Full disclosure: I did recommend eliminating him to the couple that then promptly did so when he was down to three territories, but it was a strategically sound decision that garnered them a few cards (we were playing the usual rules where cards become obscenely valuable obscenely quickly), and they were soliciting advice.

If you are curious, I did not win, though I will attribute this partially to not really trying due to my terrible starting position and the fact that I wanted to do some other stuff at the time, so I kept leaving and coming back just for my turns. If you are even more curious, my starting position was something like three territories in northern Asia, a couple in North America, one in Australia, and I think one in Africa (?). Normally I consider North America the place to be, but the couple playing got more and better distributed territories there to start with, and built those up at the cost of their other territories, so I didn't have any options. My housemate also started out with a territory in Australia, and put all his armies there, so I really had no options, but such is life when you randomly select territories. So, I just sat back most of the game, accumulating territories one per turn and hoping to build up large armies. Alas, it was not to be.

Alright, so enough Risk. Last night I noticed that Netflix recently added the amazing(ly terrible) 80's horror movie "The Stuff," so I had to watch it. For anyone who doesn't know what that is, and I assume that includes pretty much everyone, it's a movie about people eating some kind of ice cream/yogurt/marshmallow goo out of the ground, which turns out to be an organism that turns people into zombies and then maybe explodes them or something. It has the worst acting I've seen since Troll 2, and dialogue that is almost as out of left field at times. But get this: some of the actors appearing in it are Michael Moriarty, Garrett Morris, and Paul Sorvino! Yeah, two Law & Order actors from the early days of the show and the most under-appreciated SNL alum I can come up with off the top of my head. None of them really seem to know/care what they are doing in the movie, though, so it is kind of extra fascinating. Michael Moriarty spends about half his time with a southern drawl and half his time just kind of reading lines, Garrett Morris explodes, and Sorvino, well, I don't know. He's a militia leader or something? His motivations and dialogue are baffling, like there were pages missing from the script. Anyway, check it out.

The "Alpine" in the title is because I bought a Sam Adams variety pack the other day, and Alpine Spring is one of the new brews that is included. It's not actually any good. I get really annoyed with Pennsylvania's stupid alcohol laws that basically force you to buy variety packs if you want to try new beers. See, you can only get beer from distributors, which have to sell it by the case, or from restaurants, which can sell you six packs, but always mark it up to ridiculous levels because, hey, it's not like you can get it from anywhere else. Supply and demand and all that. So, if I see something that looks interesting at a beer distributor (prices are also higher at these than at comparable places in, say, New Jersey, but not as bad as at restaurants) I have to buy 24-30 bottles of it, which is ludicrous, especially because I don't know if it's actually going to be good or even palatable. So, variety packs are the way to go, since at least then you are getting a few kinds and are guaranteed that at least one of them will be decent. But then you have less selection overall, because not every company makes such things, and for instance, Sam Adams always includes their Boston Lager as one of the varieties, and it's pretty much garbage. I'd rather drink one of the low-end American-style lagers like Bud or Miller than Boston Lager. Yards, which may be sort of local, I don't know, usually has variety packs, but they're often full of IPAs, which to me is meh. I'll drink IPAs, but I feel like they're just the snob version of crap beer. Like when this whole craft beer trend started, people learned that fancy beers have hops in them, so now they're in a stupid space race of seeing who can cram more hops into their own brew. I don't find hops to be that amazing, so I'm pretty put off by such a strong and not nuanced flavor. Any thoughts, beer drinkers?

Now for the only part of the post that may be sort of interesting to people. I probably shouldn't bury the lead, but here it is. A while back, a caring soul sent me the book American Ballads and Folk Songs by Alan Lomax. It's kind of a classic reference book in its field, I think. Anyway, it's an invaluable resource if you are interested in folk music, and full of gems that sadly time has forgotten. There's a short section on war songs, in which I found a catchy little number, and I'll reproduce some of the lyrics for you:

Damn, damn, damn the Fillipino,
Cross-eyed, kakiack ladrone!
And beneath the starry flag
Civilize 'em with a Krag
And go back to our own beloved home!

Lovely, isn't it? I actually copy-pasted that from another website, but the book has the same lyrics. For people who don't speak 19th century, which includes me, "kakiack" basically means yellow, a "ladrone" is a thief, and "Krag" refers to a type of rifle used by American soldiers in the Spanish-American war. I doubt that anyone of my readers is old or racist enough to remember this song, but maybe you will recognize the alternate lyrics:

Jesus loves the little children
All the children of the world
Red and yellow, black and white
They are precious in his sight
Jesus loves the little children of the world

One of the things I love about these old folk songs is how if you liked a song, it has generally been cool with everyone if you just took the melody as your own and added different lyrics. It's not parody or anything, just different lyrics. The vast differences in this case just point out how crazy the switch can be at times. So, I guess the first little bit got me interested in brushing up on the history of the Spanish-American/Philippine-American War, since AP US History was a long time ago, and who can remember anything about them but the Maine? Haha, get it? So, I was reading the Wikipedia page, and the little bit about the "fighting" in Guam made me laugh. I'll copy paste this for you, too:

On 20 June, a U.S. fleet commanded by Captain Henry Glass, consisting of the armored cruiser USS Charleston and three transports carrying troops to the Philippines, entered Guam's Apra Harbor, Captain Glass having opened sealed orders instructing him to proceed to Guam and capture it. Charleston fired a few cannon rounds at Fort Santa Cruz without receiving return fire. Two local officials, not knowing that war had been declared and believing the firing had been a salute, came out to Charleston to apologize for their inability to return the salute. Glass informed them that the U.S. and Spain were at war. The following day, Glass sent Lt. William Braunersruehter to meet the Spanish Governor to arrange the surrender of the island and the Spanish garrison there. Some 54 Spanish infantry were captured and transported to the Philippines as prisoners of war. No U.S. forces were left on Guam, but the only U.S. citizen on the island, Frank Portusach, told Captain Glass that he would look after things until U.S. forces returned.

How ridiculous is that? Alright, that's enough for me for today.

CB&C

Not much to say or any pictures to upload or anything. My housemate/landlord/coworker made corned beef and cabbage last night, presumably because it's almost St. Patrick's Day. That's a thing, right? Anyway, it was delicious, of course. But it's one of those things that's even better the next day when you can just take it out of the fridge and heat it up for a minute or so, or just make a sandwich. I looked it up on Wikipedia, as I do all interesting foodstuffs, and found a suggestion of cider vinegar as a condiment, which I have to say, turned out to be excellent, at least on the cabbage. I don't know why it's just called corned beef and cabbage when there are also potatoes and carrots and whatnot, but whatever. As for the beef itself, spicy mustard is awesome.

These are the only thoughts I've had lately.

Lack of Updates

Hello, all. Sorry for the lack of updates. To tide you over, have this nice picture of sushi that I made. Since I have a request for math updates, perhaps I will do something about that soon enough. I can't go into too much detail about it, though, I guess, since then someone will steal all my precious research.

This is an actual thing to fear, I think. My advisor and I have some constructions and some preliminary results, at least, by trying to emulate what has been done in some papers for our extension of their cases, and we have enough stuff that we could probably publish a paper without too much more work, I guess, but he doesn't want to do that because he thinks that somebody, like the people who wrote those papers we are emulating, might see them, figure out what we are doing, and then do it faster. It's so weird how the academic world works.

So, I've been busy with that research, although I feel like I'm actually contributing very little. Mostly I attempt to do some calculation, and then my advisor does it faster, but at least it gets done. The next step is supposedly all me, though. This is proving that strict modules over a curved algebra are equivalent on a homotopy level to all modules over that algebra, if anyone is curious. I think it's mostly just finding the usual result and seeing if it applies, which I think it does.

Anyway, other than that, what has been going on in my life? Well, yesterday I got food poisoning or something, so I felt terrible all day, but still taught four hours of class and two of tutoring. After getting home, I slept for about 13-14 hours, so I'm feeling much better now. This past weekend, I went to a conference in Ann Arbor, MI, about homological mirror symmetry. This may lead you to ask, what is homological mirror symmetry? I wish I could tell you. It's some very deep conjecture about certain algebro-geometric or topological constructions having some sort of dual construction that carries the properties or something, but I guess it's not even convenient to state what the conjecture is in full generality.

My advisor was giving a talk there, so he wanted me to go, and learn things "by osmosis" because I wouldn't understand most of the algebraic geometry, and anyway, they would "explain it wrong" anyway. He's kind of hilarious, the way that he thinks a lot of people approach problems the wrong way because of some bias they have or desire to demonstrate something on the most abstract level. He told me once that if you're not doing math that's meaningful, you might as well "be a social worker." So, he's often at odds with other people, who go about things in backwards ways, which even I can see without totally understanding what's going on. Ann Arbor is nice, except the bus terminal, which is terrible. I took buses both ways, partially out of a dislike of the TSA, and partially because I like traveling where I can see out the windows, and partially because apparently you can't fly direct to Ann Arbor, anyway. If you are curious, the route was basically this:

Philadelphia --(Harrisburg)--> Pittsburgh ---->Cleveland -- (Toledo) --> Detroit -->Ann Arbor

Place names in parentheses are places that the bus stopped but that I didn't have to change buses. Reverse the arrows to get the route back (haha, it is just like my research!!!)

It's interesting how the bus terminals are different. Philadelphia's is sort of middling size, but relatively well organized, and there are always people arguing about how their bus was late and they should be getting a refund, despite Greyhound having never once given a refund to anyone. Their buses are late a ton of the time, by the way, and if you ever need to be on time, you should not take them.

Pittsburgh's terminal is very long and thin, which seems like how these places should be set up. I've yet to be there earlier than midnight, so I wonder if that colors my impression of the place. They have a bunch of TV's that are always playing the scifi channel. Syfy, I guess they call it now. There are a bunch of generic arcade games, like this last time, there was a cabinet for a racing game called "Fast and Furious," clearly trying to bank off the popularity of the movie series without paying any of the royalties.

Cleveland's seems nice, like it was repurposed from some other building. The walls are all lined with wood, and all the doors are crammed down on one end of the building. There are two TV's with chairs surrounding them, and now chairs anywhere else, like a midwestern house built around the television.

Detroit's is like Detroit: sad. I heard one of the workers saying that there used to be fifty-four employees or something, but now there are only two. They're nice enough, but the place is full of bums and the half-hearted attempts at keeping the place clean are failing miserably. It was funny to hear a guy going home to Cleveland complaining about how terrible Detroit is, and the woman he was talking to laugh about how Cleveland is only the second worst city in America.

Ok, I guess this has become a massive update, so there you go.

Heart Growing Fonder, Anyone?

Sorry for the long absence, but I had basically no internet access for the last month. Although, from the looks of the comments, nobody really noticed. Well, back to the mathzzz.