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Every once in a while an earth-shattering event happens to me. A representative sample of these events appears below in reverse chronological order.
Graduate school starts this week. I have an office in Avery Hall and a fall schedule. I also have a math home page.
Well, the GRE Subject Test in Mathematics never happened. I couldn't get the wonderful Educational Testing Service to tell me where any tests were being held (read the ridiculous story). So I am attending the University of Nebraska–Lincoln this coming year. This actually turned into a good thing, though, because UNL has a joint Ph.D. program in math and computer science, into which I was accepted. I'm the second person ever to be in this program, so no one really knows how it should work yet; I'm hoping that this means I have quite a bit of say in what happens.
This summer I am doing some research in complexity theory under Dr. Vinod Variyam, and continuing my research in graph theory under Dr. Jamie Radcliffe. This latter research ended up producing an honors thesis this spring.
In other news, one of my old computers finally died. It was the one hosting the database for Sentence, so until I get a replacement up and running I'm afraid you can't generate things from context-free grammars here. You should still be able to do everything else, though.
The unbelievably surreal GRE saga continues. If you haven't read it yet, start with the beginning.
I called the math professor at Briar Cliff this morning, just to make sure he got the e-mail I sent last night. He had, and said he would investigate and send me a reply by the end of the day.
After my algebra class, I related this whole story to my combinatorics professor, who couldn't believe that Sioux City was the only test site in three states. So she actually started making some phone calls on my behalf. She called some ETS number which I must have called at some point in the past, because I remember the recorded message she described that said "Please call back after July 1, 2005." So she gave up on ETS (a wise choice) and placed some calls to the actual test centers themselves. She found out that the subject tests are normally given in Omaha, but not this Saturday, since no one registered. So far this matched up with what the last ETS guy I talked to had said. She also called Kearney, but whoever would know about the math test wasn't in today.
After that I got a reply from Briar Cliff, telling me that they weren't sent any math tests. So Sioux City is now out of the question.
When I got back home, I called ETS again. I once again explained that I wanted to give them $165 to take the GRE Subject Test in Mathematics on Saturday, and asked where exactly I could do so. The woman on the other end started to repeat the same list of test sites I'd heard several times before: "Chadron, Kearney—" I explained myself again, explaining that yes, these are the sites where tests might be held, but I needed locations that actually were giving the test. I got back "Chadron, Kearney—" Once more I tried to convince her that she needed to make sure that these sites actually had tests to give, but she responded, "Here are the sites I have: Chadron State College, in Chadron; University of En-Ee in Kearney; and the University of Nebraska at Oklahoma."
(Keep in mind that, as mentioned before, ETS representatives are barely literate. The "University of En-Ee" is the University of Nebraska; apparently the abbreviation NE was too much for her. And, of course, the University of Nebraska at Oklahoma isn't in Oklahoma at all. It's really the University of Nebraska at Omaha. She read "Omaha" as "Oklahoma" once more during the call, and thereafter just spelled it out letter by letter, referring to the "University of Oh-Em-Ay-Aitch-Ay.")
So then I told her that I had been told twice before (once by GRE Guy, and once when my professor called Omaha) that there was no test in math being given in Omaha this Saturday. She put me on hold.
When she got back, she claimed that whoever I talked to probably wasn't allowed to say how many people were registered for the test, and so they just told me that there was no test being given. (This was, of course, baloney.) She then reassured me that the test would be given in Oh-Em-Ay-Aitch-Ay this Saturday, and then gave me a room number and an address.
So I'm in the same boat I was in yesterday at this time. I called Omaha, but apparently whoever it is that knows which tests will be given there on Saturday had already left for the day, so I need to call back tomorrow morning.
I can't believe how ridiculously absurd this whole situation is. Any respect I might have had for ETS has been demolished.
The story of my life is the story of the last minute.
I only became a math major sometime in September, and hadn't made up my mind about going to graduate school in math until about the first week of November. At that point I registered to take the GRE, and started to look at some entrance requirements for various schools. It was then that I learned that some schools require the GRE Subject Test in Mathematics, so I went to register for that.
As it turns out, this subject test is given three times a year. I needed to take it on the December 10 test date; the next test date is in April. But the registration deadline for this test was November 4. I had missed it by a day.
So I called the wonderful ETS help line (they're the folks that administer the GRE), waited on hold for a while, and finally got some representative. I explained my situation, and he told me that I could test on a standby basis. I asked him if I needed to get on some list, and he said no, I just needed to show up at the test site with identification, my registration form, my test fee, and a $35 standby fee. I asked him if he could tell me which test site in Nebraska had the most open seats available, so that I could see where I would have the best chance of getting into the test. He said that that information wouldn't be available until people dropped their registrations. I said okay, but surely there were some sites that hadn't filled up? He said no, everything was full, but if I called back three days before the test date, I could find out how many people had dropped, and figure out where to go. This sounded ludicrous to me, but I clearly wasn't getting anywhere, so I quit that line of questioning.
Then I asked if I really should be taking the December test, or if I could wait for the April test instead. He then told me that the December test was for people who wanted to start graduate school in the winter, and the April test was for those who wanted to start in the fall. So I was temporarily relieved. Maybe I hadn't missed the deadline after all.
The next day I talked to one of my professors about it, and she pointed out that I'll need to decide which school I'm going to in March, so an April test would be pointless. This admittedly made a lot more sense than the ETS guy's claim. So I was back to having missed the deadline.
Then came today, three days before the test date. I called the ETS help line again, and was put on hold. Here I listened to their very faint Christmas hold music for fifteen or twenty minutes—there were two songs in the loop, and they alternated back and forth over and over again. When I had thoroughly tired of this, I finally got another ETS representative on the line. I once again explained that I needed to take the GRE Subject Test in Mathematics on a standby basis this Saturday, and asked which of the sites in Nebraska had the greatest number of open seats. Wouldn't you know it, this information still wasn't available! Apparently such things aren't known by the ETS reps; the only thing they can tell you is which sites are giving the test. This was news to me. I had assumed that all of the sites gave all the tests. So I told him I was in Lincoln, and asked which sites in Nebraska would be giving the test I needed to take on Saturday.
Two or three minutes of typing noises later, he asked if he could put me on hold. Of course I didn't really have any choice in the matter. This time there was no hold music of any kind, so I sat in silence for maybe five minutes. He eventually came back and told me that the closest site he could find was Omaha. This was fine. I asked him where exactly in Omaha the test would be given, and he typed some more, and then informed me that the Subject Test in Mathematics wouldn't be given in Omaha this Saturday. I was baffled. So then he asked if Lincoln was anywhere near Wayne. I said yes, I could get to Wayne. So he typed some more and told me that the test wouldn't be given in Wayne either; how far away would Kearney be? Well, that would be a little bit of a drive, but I could make it. Some more typing revealed that the test wouldn't be given in Kearney. What about Chadron? Now, Chadron is clear across the entire state, so I told him I couldn't make that. Maybe there was something in Kansas?
He started listing off a bunch of towns in Kansas I had never heard of, so I told him he could just give me a list of places in Kansas where this test was going to be given, and later I could figure out which was closest. He said that it would be too much work for him to look at every town in Kansas. So I told him that maybe Topeka or Manhattan or Kansas City would be within driving distance. Then the cycle repeated itself a few more times: He would name off some town, I would hear some typing sounds, and then he would inform me that the test wouldn't be given there. This started with Topeka, Manhattan, and Kansas City, and then continued with random towns he picked from his list. Eventually he stumbled across Lawrence, and found that, lo and behold, this test was going to be given there this Saturday! But, he said, there were only two people registered for it, so the chances that one of them would fail to show up were pretty small. So I gave up on Kansas and asked about Iowa.
Several more rounds of town-naming and test-denying happened, and then he discovered that the test was scheduled to be given in Sioux City. This worked out pretty well; of all the cities in Iowa, Sioux City is about as close as I could hope for. He then told me that I had a much better shot at taking the test in Sioux City, since there was no one registered for the test. Now I was even more baffled. I asked him to clarify what I thought I had heard: There was no one registered to take the test in Sioux City, but copies of the test had been sent there anyway, and the test was actually scheduled to take place. Yes, he said, that was what had happened. So I really have no idea how the hell ETS decides where tests are to be given.
Anyway, after recovering from shock, I asked him to tell me where in Sioux City I should go. This is when I learned that ETS representatives can't read very well. He said it would be given at "Blair Cliff University" (actually Briar Cliff University), in room 105 of "Helene Hall" (actually Heelan Hall). Then he spelled out "Sioux City" for me letter by letter, just in case I was confused and thought maybe he was talking about Dubuque. The test starts at 8:30 a.m., but he recommended I arrive an hour early, since standby seats are given out on a first-come-first-served basis.
So I've sent an e-mail to a math professor at Briar Cliff, asking him to confirm or deny the rumor that a GRE Subject Test in Mathematics is going to be given there this Saturday. I can hardly believe that such a thing is actually going to happen. If he says that it really is, then I get to make a three-hour drive up to Sioux City this Friday afternoon in possibly crappy weather (it is currently snowing, and has been doing so on and off for a week). What an exciting adventure.
The thing that seems most startlingly odd about this whole mess is that apparently there are only two people in all of Nebraska, Kansas, and Iowa who have registered to take this test. That's one I can't figure out.
I think I know which classes I'm taking next semester.
Last week we had an assignment in my modern algebra class. One of the things we were supposed to do was to explain the RSA encryption algorithm in our own words. I wrote this:
There once was a girl from Great Bend
Who wanted to hear from a friend.
But to her disgust
There was no way to trust
The network, beginning to end.She needed a way to encrypt
Message X before it was shipped.
"It needs to be true
That it's easy to do,
But hard to do backwards," she quipped."I can multiply numbers with ease—
Numbers as large as you please.
But to go in reverse
Is very much worse.
So I'll pick two big primes to make keys."One is p, other's q. Next step, then,
Is to find out their product, called N.
Now choose e: This time,
It's a relative prime
To the Euler φ-function of N."This function is easy to do:
Find pq less p, minus q,
Plus one. So we see
It's not hard to find e.
Now the last thing we need is called μ."In Greece, long ago, Euclid taught
A way to find μ, which is sought,
So that 1 less μe
Will turn out to be
A multiple of φ(N) less than nought."So I have μ and e. Now I may
Keep μ private, but give e away.
My friend gets the key,
Computes X to the e
Mod N, and sends that my way."This new message Y seems complex.
To decrypt it, what to do next?
Well, all that I do
Is find Y to the μ
Mod N; the result will be X."This encryption is hard to undo
Without knowing q, p, or μ.
The 'security guard'
Is that factoring's hard,
Unless there's a brilliant breakthrough."
On our first day in China, we needed to cross to the west side of the Huangpu River, so we decided to take a ferry. After finding ourselves lost in the midst of heavy construction in an industrial zone, we pulled out a map. (This would have been a foolish thing to do when lost in an American or European city, for it would have marked us as ignorant tourists. In China, however, we were clearly ignorant tourists anyway, so it wasn't a big deal.)
The map showed a ferry north of where we were, so we circumnavigated the construction sites and found the place to board. Here we found our first sign with no English. After comparing some Chinese characters on the map with other characters on a timetable, we inferred that a ferry was about to arrive at the east bank. So we went up to the ticket booth to buy our passage.
We couldn't find any prices on the sign, so Kaiser walked up and handed the cashier a ten-yuan bill. The man looked at us quizzically, so I pointed exaggeratedly to the west, across the river. He seemed to understand, because he handed Kaiser three yellow plastic tokens and four yuan in change. Tokens to cross the river were two yuan each, apparently (about 24 U.S. cents). We walked ten feet, dropped our tokens in a bin, and boarded the ferry.
I understand now how ferry accidents in Asian nations cause hundreds of deaths. The ferry was a simple boat with a concrete floor, packed full of pedestrians and people on bicycles and motorcyles, that crossed the busy Huangpu River, dodging ocean-going ships as it went. Luckily for us, there weren't any storms or strong winds during our week in China, so the ferry rides were much less eventful than they might have been.
On our return trip, we felt like veterans of the ferry. Kaiser strode up to the ticket booth and plunked down his two yuan. Much to our surprise, the man behind the counter gave him three yellow plastic tokens and some change. We began to realize that the money-taker at the first ticket booth had ripped us off royally.
That night at our hotel, we opened a map of Shanghai and found a ferry much closer than the one we had taken. We had walked about a mile north of our hotel to board the first ferry, when we could have walked a quarter-mile south and taken a ferry to reach a point closer to where we wanted to be. So we never took the industrial-construction ferry again. (And we never put down more than two yuan for our three tokens.)
Just now I opened up a Shanghai guidebook and happened to see a little box that gave advice about ferries. Apparently eastbound ferries are supposed to cost eight yuan, but westbound ferries are free! If this is true, we got some cheap eastbound trips, but overpaid going west. It doesn't matter too much to us, though; after all, one yuan is about twelve U.S. cents.
I have finally returned from 上海 and 杭州. We woke up this morning about 4:20 a.m. in Hangzhou, which was followed by a three-hour drive to Shanghai Pudong International Airport, two hours of Chinese customs, and a three-hour flight to Tokyo. After a short wait in Tokyo, we began our flight to Detroit.
Sometime around 11:00 p.m., we crossed the International Date Line, so we went back to Friday for a while before starting Saturday all over again. It's now almost 10:00 p.m. the second time around, so I'm exhausted.
I'll probably post miscellaneous China stories as I feel like it.
I'm in Shanghai for the ACM International Collegiate Programming Contest world finals. Finally, my years of sitting in front of computers have rewarded me with a trip to an exotic foreign country.
The flight over here was ridiculously long. We flew out of Lincoln at 11:00 a.m. on 1 April to Minneapolis, and then boarded a 747 for Tokyo. From my 45 minutes in Japan, the complete list of differences from the United States seems to be the following:
Upon landing in Shanghai around 8:00 p.m. on 2 April, we found our way through customs and took a van from the Pudong airport to our hotel. Apparently all Chinese traffic laws can be summarized as "try not to hit anyone intentionally."
The first thing I noticed when I woke up this morning was the huge amount of traffic on the river here. Since the contest doesn't officially start until tomorrow, we spent the day wandering around the city. The Pudong district, east of the river, is very new; our hotel is considered old, and it was built in the late 1990s. We got lost in some construction before finding a ferry to cross the river. This was our first strong reminder of our foreignness. We walked up to the ticket booth, handed the man a ten-yuan bill, and gestured wildly in the general direction of the river. He handed us four yuan in change and three plastic tokens, which we carried ten feet and dropped in a bin. Then we walked down a ramp and boarded the ferry along with about fifty other people, many of whom were riding bicycles or motorcycles.
On the other side of the river was the "real" Shanghai, the older part of town. The Bund is the strip along the western side of the river, with old European colonial-era buildings. We began to walk west, to see what we could find.
One thing we found was an attractive little park, with hills and rocks and trees and a pond. Some giggling girls from some Chinese university asked us if we would answer a questionnaire, which turned out to be simply asking what we thought of the park. I told them it was more beautiful than most American parks, which are boring plots of grass. She said in surprise that she thought American parks were more beautiful. I wonder if that's a cultural difference or whether she had somehow seen much more beautiful American parks than I had.
It seems as though Shanghai is divided into districts. We found ourselves on Beijing Road, which is the hardware district. For blocks and blocks, every single store we passed was selling hardware: steel rods, ball bearings, electric drills, valves, pipes, multimeters, electronic components, and so on. These weren't American hardware stores—the things for sale were unbelievable. In the United States, if you wanted to buy any of those kinds of things—centrifuges, specialized electronic switches, little metal parts of all sizes and shapes—you would have to open a thick catalog and order it from a big company. Here in China, when you need any kind of hardware at all, you just go down to Beijing Road and try the shops. The other incredible thing was how identical all these shops were. They all seemed to be selling more or less the same variety of things. And these shops went on forever. Several times we left Beijing Road and walked west on some other street, but whenever we found ourselves at Beijing Road again, there were the hardware shops.
It was about this time when I began to notice myself thinking, "Wow, they have that item in China? We have that same thing in the United States," and then remembering that everything we have in the United States is made in China.
We wandered around for a couple hours trying to figure out where to eat lunch. We didn't want to walk into a restaurant and be utterly unable to communicate, so we decided to choose a restaurant from a book we had. But on every attempt to find one of these places, we were distracted by an interesting side street. Finally we gave up and saw a McDonald's. On our way there, however, we passed a small restaurant. Two women standing outside said "English menu!" to us, so we did an about face and went inside. It was a good choice; the meal was excellent, and the owner had a great sense of humor and a tenuous grasp of English (which was better than no English at all).
Another fascinating fact about China is that a full 37 percent of the population is engaged in the sale of watches to American tourists.
So it was a fascinating day. We're now back in our hotel, exhausted, but we're all registered for the contest. Tomorrow we begin the things they have planned for us. The contest itself is on Wednesday.
Eventually I might have some pictures available, but at the moment I don't have any way to transfer them from my camera.
The number 2095·283166 + 1 is prime. It contains 25039 digits.
Here's the relevant section from my Proth log:
Mon Jan 31 08:56:44 2005 : 2095*2^83166 + 1 is prime! (a = 3) [25039 digits] Mon Jan 31 08:58:22 2005 : 2095*2^83166 + 1 is prime! (verification : a = 7) [25039 digits] Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any Fm. Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any GF(3, m). Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any GF(5, m). Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any GF(6, m). Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any GF(10, m). Mon Jan 31 09:03:38 2005 : 2095*2^83166 + 1 doesn't divide any GF(12, m). Mon Jan 31 09:03:38 2005 : 2095*2^83166 - 1 factor : 3 Mon Jan 31 09:03:38 2005 : 2095*2^83167 + 3 factor : 7 Mon Jan 31 09:03:38 2005 : 2095*2^83167 + 1 factor : 3 Mon Jan 31 09:03:38 2005 : 2095*2^83165 + 1 factor : 3
Assuming that I'm the first person to have ever known this fact, the philosophical question could be raised: When exactly was this prime number discovered? Sure, Proth "knew" about it at 8:56 a.m. on 31 January, but no human knew until 1:47 p.m. the next day, when I happened to notice it. (This is similar to the question of whether M4253 or M4423 was discovered first; Hurwitz knew of the larger prime first, because of the way the output was stacked.)
My spring 2005 schedule is available. Don't be misled by all that blank space, though. I don't know where my Design Studio team times will go, and they'll eat up around ten hours a week.
On another note, I now have an interesting little thing called Sentence that you can play with. (This has actually been up for a week, but I failed to say anything about it, except elsewhere.) I made this as my final project for my linguistics class this past semester. It generates random "sentences" based on a set of rules and a vocabulary. I find it rather addicting. If you come up with an interesting language model, save it, so that others can play with it.
I think I might try to have some more content, and move a lot of things off the main page. It would be nice to have some organization around here. Too many things are randomly located (consider the /stuff directory, for example). So I've started a page about me, in order to put all that boring nonsense away in a corner.
I'm also rather sleepy. I think I should go to bed soon.
I finally got my computer up and running after moving back into Kauffman. During the moving process, I picked up my computer and heard a "clink" noise inside. This is never a good thing, so I opened it up for a look. Lo and behold, my northbridge heatsink and fan had fallen off. Apparently this is a not uncommon occurrence for my motherboard (an ABIT IC7-G).
So, after considering several alternatives, I ended up slathering some thermal compound on the thing and super-gluing it back on. I hope it remains adhered.
In other news, I have my fall 2004 schedule available. At the moment it looks pretty bare, but it will soon fill up with things like Design Studio Team Time.
Last night I spent about four hours writing the following piece of code. It's Perl, believe it or not, and is my first attempt at its genre.
($a='%Q$yW0se3%qhggfIi')=~s,([f-y]),qq;"\\c$1";,ege,@l=unpack'a5a5a*',$a;for$i( @l){$$i.=sprintf"%lx",$_ for unpack'C*',$i;push@n,$$i;}$"=',',$_="\c`",$p=eval" pack'VVN',@n",@b=unpack'C12',$p;$m=4054314,$a=96;(++$a,$m>>=1)&1?s@$@chr$a-!($a %6-4)*32@e:$;while$m;@z=split m &&;for$j(@b){print$z[$j&15|($j>>=4,0)]for+z,j;}
I challenge anyone to figure out how it works. (Ask me in a couple days and I may not know any more.)
Originally I was going to do something via the calculus of finite differences and Newton's forward difference formula, but I ran into problems that appeared to be floating-point goofs, like roundoff error. These problems caused the function to become rather chaotic after a certain point, so the output of my test program was
Just anotheu-}ñÇ·O¼à¬ªá_ƒä,?éZ?d"<~dªº^ñs»?
So that was a no-go.
I was just handed this advertisement by My Yahoo!:
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I decided my old index page was a bit too out-of-date, so I did some housekeeping.
I hope to get FreeBSD running on Upsilon one of these days. Once I do that, everything will magically become much cooler and I will suddenly have far more time to work on this Web page.
On a side note, I registered zifyoip.com, so maybe I can have a URL whose availability doesn't change like the seasons depending on my at-UNL status.
I've decided that I really need to be proactive about getting a new computer instead of just griping about it, so here's my list of computer components that should hopefully help me decide what I want.
Well, I have a ticker up so everyone can track my point total. All year my roommate has been saying things like "Ten points for you!" or "Minus five points for you!", the latter being far more common than the former, so I finally decided I was a big enough nerd to keep track.
But as a much larger expression of my nerddom, I embedded a copyright notice
into the up and down
arrows in a way that's probably never been done before, simply because it's way
too stupid. Both of the images happen to have 12 unique colors, but the palette
is a 16-color palette. This means that there are four unused colors in each
image. If you take the red, green, and blue components of each of the four
unused colors, in that order, and translate them into their ASCII equivalents
(here's an ASCII table if you need it), you'll
find that the message encoded is "(c)2003BKell".
If you have some amazing story of nerdiness that surpasses this, you must let me know immediately.
I just banked a Slinky off a door handle across the room, off my roommate's head, and hooked it on an electrical cord under his shelf. I rock.
Update: Shortly after, I dropped a honey-roasted peanut, which fell to the floor, bounced, and landed perfectly on the toe of my left shoe. I had to go for it. So, after eating the rest of the peanuts in my hand and clearing the area of breakables (namely, my roommate), I kicked the peanut in the air. It described a perfect parabolic arc, but unfortunately the y-coordinate of the vertex of this parabola was not great enough for me to catch it easily in my mouth. So I dove for it. I missed. I then had to find the peanut again, which by this time was hiding under a backpack. It was still good, so I ate it.
