Crescat Scientia

Not that the United States is particularly keen on protecting civil liberties or not arresting people willy-nilly, it does happen elsewhere. At least it beats being shot to death by the same scared, incompetent police department.

I can now attest to the fact that a ride home in a Chicago police car is much faster than taking the route 55 bus.

You decide:



(Found on flickr via a blog. Click on the image to go to flickr.)

I had a weird dream the other night. The whole dream was unusually vivid. The dream started at a store, very much like a bookstore, with lots of shelves, everything a light brown color. The place reminded me of Barnes & Noble or Borders. It was generic. It could've been a Hallmark store just as easily. I was there to get a greeting card, so I used a computer display in the store to make a personalized card. I don't remember why I wanted a greeting card, but it seemed an important enough reason at the time.

Once I secured the card, I had to go upstairs to buy stamps. This store was on the 28th floor so I got into the elevator to go up one floor. Unfortunately when I got in the elevator, it was but a shell of a car. Its walls were the plain metal exterior of the car. Its wiring was exposed. Its lights didn't seem to work. I began to worry. As it turns out, it was not a working elevator, and I plunged all 28 stories down to my death.

Now, although odd, at this point the dream's not entirely shocking. I've had my share of dreams where I die, or come close to dying, both at the hands of others and of purely natural causes. I've been shot at by a sniper, I've been chased down by anthropomorphic lightning... But I usually wake up--breathing heavily. It's supposed to be a nightmare. Not this time!

Although dead in the elevator, I did not wake up. The dream calmly continued. I--now dead--was suddenly back in the store. My sister was there and I was attempting to say goodbye, although she was rather bored with me and walked away. My mom was also there. Then quite suddenly I was no longer in the store. I was walking out of a house, through a patio. The patio had a covering with wooden supports, painted white, and thin wooden lattice work between the supports. I was walking with other people in a single-file line. The only recognizable person in the group was Jesus! Although he was not what you may imagine of Jesus. He was white, middle-aged, with short brownish-grey hair, wearing glasses, sandals, and a robe--a bath robe. He had a small face with tight muscles. I could see the veins near his temples and the wrinkles near his eyes.

I said to him that I couldn't recall if I had repented before death and apologized if I had. He said I had. We continued walking in silence. Then I woke up.

Although overly idealistic, I've long liked this quote:

What, if some day or night a demon were to steal after you into your loneliest loneliness and say to you: "This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence--even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again, and you with it, speck of dust!"

Would you not throw yourself down and gnash your teeth and curse the demon who spoke thus? Or have you once experienced a tremendous moment when you would have answered him: "you are a god and never have I heard anything more divine." If this thought gained possession of you, it would change you as you are or perhaps crush you. The question in each and every thing, "Do you desire this once more and innumerable times more?" would lie upon your actions as the greatest weight. Or how well disposed would you have to become to yourself and to life to crave nothing more fervently than this ultimate eternal confirmation and seal?

I like this theme.

Meanwhile, this is getting to be a very small Debian installation. 134 packages installed, 197 MiB used. And still it could get better.

Ok, so this linode setup is pretty neat. The whole thing is based on UML, so several "hosts" run on one box. You essentially get your own computer coexisting with others on the same hardware. They have multiple distributions to install, etc. Installing and formatting the disk are done with their web interface. Once installed though, you have your own box esssentially. You can even ssh into the box your host is running on, and get console access!

So far a great experience...


You can, through their web setup, correctly set up your reverse DNS mapping. That's one of the first things I did. You have to successfully have a forward mapping setup first though. This was one of the things I would've had to bug WS to do before. Apparently some (few) mail servers will reject mail based on incorrect reverse lookups and I had run into one or two of these already. I think this is a questionable practice, but it's of no concern to me anymore. :-)

You can also through their web setup, deposit your ssh public key(s) at the box your host resides on. This means the ssh console access alluded to above can use public key authentication. It'd be nice if you could disable password based authentication here, but I don't see a way. The website also uses the same password, so it is not worth it anyways. Just use a good password for this. I tend to use pwgen to create long passwords and they get stored in an encrypted file on my laptop. So hopefully this would never be an issue anyways.

There are other implications of the ssh console access. The first of which is, if that gets defeated, your box is vulnerable. So use a good password for this, don't use password based authentication which is more vulnerable than PK, and don't leave yourself logged in, especially as root, at the console. This means that hopefully, they'd have to get through another cryptographically strong password.

The second implication is a very good one. You do not have to run your own ssh daemon unless you need to. So for those who don't keep up with security focus mailing lists as they should, you don't have to worry about the off-chance that someone finds a vulnerability. Presumably in this case the host-based ssh daemons would get updated pretty quickly. :-)

At the moment, I'm running an ssh daemon since I have to set up things, and have multiple shells going at once, and it does seem a little bit faster than the console access, although this could be psychological. I don't know if I'll continue. I took the time to set it up appropriately anyways. In the install offered, password based authentication and root logins were allowed. I set up my PK authentication and sudo and then quickly turned those off.

It was set up generally well for such a system. However, inetd was running with a few services turned on. The security tips part of the linode wiki suggests replacing it with xinetd, but I prefer to remove it all-together. :) Most of the services I wish to run will bind to their port themselves, and I've never really seen the value in a complex tcpd configuration. This is a web and mail server, so I have to be generally open to traffic. There's more value in setting up a good firewall and IDS that will detect hanky-panky before it gets out of hand. The security tips on the wiki are pretty good.

There are still a few things to do. One of them is remove unnecessary dependencies.

Ok, so modified it a bit. Dates appear below posts, with categories. This bugs me less. :-)

Ok, so a little backstory... My friend WS has an excellent job as network architect/engineer for some web hosting company. He set himself up a little private box on their network, and that was hosting jgarrett.org. The purpose of my little vanity address itself is questionable, but I'd like to think of it at least as giving itself to a stable e-mail and web server. Turns out that the e-mail went down on that machine about a month ago, and I was completely unaware. I'm not so fond of e-mail. :-)

The reason for the failure was a rather questionable apt-get upgrade, shortly after Debian 3.1 was released. Anyways, this gave me the incentive to relocate. This way, (a) I'm not mooching off of WS' bandwidth, (b) he was going to need to move that machine sometime anyways, leading to trouble, and (c) I can task the machine exactly right. :-)

Linode.com was what I settled on. Seems like a great little UML based virtual hosting place. Anyways, right now I'm in the process of getting everything set up the way I like, and batting down the hatches as it were.

In more personal news, you may or may not know that my brother intends to become a fireman. He is taking some classes to this effect. Anyways a week ago, his equipment worth nearly $1500 was stolen out of his truck. The real downside more than anything else it seemed, was that this would put him very far behind in his class. See, he originally ordered the coat specially, to get the sleeve length right, and it took 2 weeks to get the coat in. Fortunately though, this time he had no problems at all. He has already got his equipment replaced and only had to make up about 30 minutes worth of instruction.

Yay for that!

I have acquired for my own nefarious purposes the domain jgarrett.org.

My blog is therefore moving to http://jgarrett.org/blog.

My livejournal account has not yet been discontinued, despite my nearly 2 year hiatus. (I think my gmail account has!) This warrants new entries. Unfortunately the math will not be as restrained, although not quite as evident as in Ian's blog.

A geometer friend Ben from college is visiting. He told me about a process through which you can associate a curve to a knot. One can then ask if infinitely many curves of genus 0 show up, etc. Apparently to do this, one starts with a knot, look at the complement in S3, give this a hyperbolic structure, look at the associated group in PSL2C, and take the character variety. There is a distinguished component, and it is 1-dimensional. Smooth this and you get a smooth proper curve defined over a number field from your knot. My first response to this was to consider the analogy between 3-manifolds and number fields. By this analogy, one would have a process which associates to each rational prime a smooth proper curve over some number field. I would be curious to know what this is. Then one could guess what the appropriate answers are to questions about the curves.

In relation to something else he brought up, the question arose if the rank of an elliptic curve over a number field is independent of the number field. That is, is it stable under extension. This is a pretty stupid question, but I don't know the answer. Another question: given an elliptic curve E over a number field K, can the set of points over K be dense in E.

Another Ben told me while ago that étale K-theory is just the étale sheafification of algebraic K-theory. Although this should've been obvious to me, it wasn't. Algebraic K-theory gives a presheaf of spectra on the small étale site of a scheme X, and one should sheafify to get a sheaf of spectra. The global sections of this of this on X is the étale K-theory spectrum. One can make sense of the sheafification with model categories and Bousfield localization. Ben suggested that the theory of Kan extensions means you can make sense of sheafification whenever you have a theory of homotopy limits. Unfortunately, I don't know anything about Kan extensions.

A more naïve approach to sheafification might be solved as follows. For a “triangulated category” D, there should be a notion of presheaves and sheaves with values in D. These should also be “triangulated categories.” One should have notions of exactness and localization. An example of both should be given by sheafification. One should have an exact global sections functor from both presheaves and sheaves to D. There should be a descent spectral sequence, etc.

Unfortunately, trying to do this naïvely with triangulated categories fails due to the nonuniqueness of the cone. One should use DG-categories, or better A_∞ categories.

This perhaps explains why one has to go through the model category structure above when D is the category of spectra, and likewise why Thomason has to work so hard to work with appropriate models of the derived category.

One can likewise introduce algebraic K-theory this way. Define it first for affine schemes, and then sheafify in the Zariski topology. I should write this all up soon.

Another example of this, would be with D the derived category of abelian groups. Then sheaves with values in D would essentially be the derived category of sheaves. The global sections functor is the usual one, and the descent spectral sequence specializes to the hypercohomology spectral sequence.

So tomorrow is the last class day of the quarter. Mohammed and I have a deal: I bring a Jack Daniels bottle to class (containing whatever I like) and drink from it, and Mohammed shaves his head and beard. Sounds like I've got the easy end of the deal. I don't know if there will be alcohol, I don't have that much left. We'll see.

Meanwhile, the quarter is coming to the end. I've got to write up all the homework I neglected to previously, and generally I'm screwed. I wonder if I'll pass or not. And then I get to make up the P* in geometry, and there's a move coming up, and of course finals...

And all we seem to do lately is play bridge. Every time there's 4 people. And Robert always is frustrated when he's my partner. I think I might eventually drive him to suicide. His suicide note will read "4 clubs ?!?!".

Oooh, and I've got to pick an advisor soon. And tomorrow is my last chance to get Kate to skip class. And Karen and I never bowled again this quarter despite us both wanting to at the beginning. And Mike G and I and Boris and the like never went out to the city and found ethnic food and such... This quarter has been hectic.

But all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon, all will be over soon...

Como estas?

A recent post of rjyoung's got me thinking, and even though it is really a response, I prefer to post it here rather than there (partly because it is long, partly because of my dearth of posts)... My visit to Chicago was exactly a year ago. It was rather uneventful. I didn't contact too many people about it, so I didn't get taken out or such things. I talked to a few people, and they were nice, but this was the only place I was considering, and I probably would've come here no matter what. I am glad I came here though.

The classes have been ok, but that's not the point as far as I'm concerned. The material in the first year is all classical enough to be found in books, and although classes/professors offer insights and intuition and examples that are harder to find purely by reading, one could get by. As Robert mentioned, the first year forms social bonds, through the workload, and the common location, and perhaps the fact that all the first years are excellent people. I love Karen's statement to one of the prospectives, that we are all like an old married couple. It's amusing but true... The people are wonderful. And I think we did well advertising the place. My perception was, that for most prospectives, the more we hung out with them, the more they seemed to enjoy themselves, and the better disposed they became to this place. Perhaps this was a bit of projection, as I enjoyed it, but I still think it's true. And my reason for thinking it is true, is again the people are fun to hang out with...

It also occurred to me that in a way, the social atmosphere is artificial in a way, in much the same way grade/high school is. One spends so much time together in a small setting. There is no effort required to contact people. I hardly ever talk on the phone, and there is no need; I see most of the people I'd like to see almost daily... But then I like getting phone calls, so perhaps I should call people. Much the same way that getting a letter is always fun, but no one writes letters these days...

I feel trusted. I feel loved. Everything is copacetic because it is.

And in response to some friends' posts: snow is great, I agree that Robert is hilarious, and I'm glad that Matt is liking Hartshorne (I think H's exposition is wonderful).

Everything is copacetic because I declare it to be so.

I need to see a good movie. One that I haven't seen before. I had an idea a long time ago to visit one of the Landmark Theatres in Chicago. However, that requires an investment of time and effort. Seems like that's in short supply.

In a similar vein, I may have enjoyed the ice-skating event tonight. However it seemed like it'd be cold and I was a bit out of it. On the way home I ran into Anne and Keith. Anne and Dani will be around for spring break, as will I. Possibly others will as well. We will have to do something.

I changed my fiction to Henrik Ibsen's A Doll House. I can finally see whence Elizabeth got her name. It should be (slightly) more cheery than my previous choice of the Death of Ivan Ilych which I am currently abandoning. That book could well have contributed to that Black Thursday I had earlier this quarter. I didn't feel like coming in, but I did, because a day is not the same without seeing all my first year friends. And I started to read DOII, but II had died and his friends didn't care. They thought about their obligations and what they would have to do. I mean the death seemed to be beginning to have its effect at the point I got to, but the (realistic) phase where it wasn't quite real yet, was depressing. Anyways, I'm sure if I continued in DOII, it at least wouldn't continue to be depressing for that reason. Tolstoy always seems to convey a realistic human feeling... On a similar weird/related note, for some weird reason, I find the "On Star" radio commercials moving...

Oh, and I should probably ramble about math for a bit. I am supposed to be doing that 16 hours a day. It's boring. I do it all the time, and I get only a bit of it ever written up, and so on and so on. I always feel weird writing these things, because people will read them, and it seems like my entries seem depressing, but it's just a perpetual state of ennui.

One thing however which is nice, and happy and so on is my friends. Yay. We've celebrated two birthdays (each twice :)) in the past two weeks... The most memorable part about the dinner sunday aside from overdoing it with the green habanero sauce, was a weird conversation about porn. And Deepam &c. picked on me a bit. That was less pleasant. But I had a good time I guess. I liked the Georgian food better than the Mexican, but such is the state of things. This is probably unintelligible to most people (i.e. those who weren't there)...

Mike was/is considering another place. And that gives me occassion to think of the program if it were less social. I don't think it'd be bearable ...

Anyways, the cycle goes on, the phoenix dies and rises alive again to live another 500 years...

Snow is supposed to accumulate today. How wonderful, it has already done so more than in the past this winter. It is beautiful, sparkly, powdery, white, snow. People say the novelty of this will wear off, but I'm not so sure. It seems magical every time. Today will be an excellent day. Beautiful snow.

Just so it doesn't seem like I'm turning into a weatherman, I should add more... but it seems that the number of things which I would like to mention which I cannot in this venue has grown of late. I understand ever more why sugardickdaddy opted for a real journal. I've contented myself to writing random thoughts on pieces of scratch paper rather than maintaining a separate real-life type outlet. It also occurs to me my recent posts have been so infrequent, I doubt anyone reads this anymore aside from those few who have livejournals themselves.

As for school, I feel unfulfilled lately. Everyone's always busy and with the same old stuff. All people talk about is math. Granted I don't always have great other things to talk about but...

C'est la vie.

Anyways, beautiful happy snow. Who could ask for anything more?

I walked home about an hour ago. Late night and all with some of the analysis and such things. But it was snowing. The snow sparkled on the ground, as if it were glittered with bits of shiny silvery glitter. I can tell this will be a wonderful day.

And regarding my last entry, it wasn't so bad. Apparently only 2 first yrs attended the party. Rob says I was missed at happy hour. But a lot of my favorite people showed up at the office this weekend.

All is copacetic.

This week was less eventful. Since my last entry, I did get my hair cut, we had the presentation, which went very poorly for me. We followed with a pub outing, which was definitely fun. Then everyone scurried about preparing for the algebra midterm Thursday which was worse than anyone's worst nightmare. After that we then sat through a little lecture thing, a lot of us ate dinner together at Hutch, and then 4 of us stayed at the office all night doing homework and playing worms. Interestingly enough, Karen and Anne stayed at the office late that day. It was noted later that if you put Anne and Karen together you have Anna Karenina... That was my favorite book in high school, even though I only got halfway through. Anyways, it was fun staying at the office, but I was too tired and thus went home and slept and missed happy hour and Haris' party, as well as whatever fun transpired in the office and class before that. For that reason, I feel sad. Anyways, I woke up recently, and I'll head to the office in a few hours and spend most of Saturday there. If other happy people show up, it will redeem the day.

In short it seems as if this week didn't even happen.