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| Saturday, November 7th, 2009 |
jcreed
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1:16p |
An observation on researching problems you are not an expert at, or, "Why I am not a kook". This happens to me occasionally that I get interested in a cute little problem, (e.g. graph reconstruction) think about it for a while, come up with some partial results, and then poke at the literature and quickly go ohhhhh shittttt people have really studied this, and a single section of their papers has way more insight than I could expect to generate if I slogged away at the problem for a month. Which is okay, since I'm not going to slog away at it for a month, but rather go back to working on problems I can make headway on. But it's still fun to play with such things, and a good sort of exercise to wrestle with new problem domains. I think all it takes to go off the deep end into kooksville is to forget this last step of being at least a token amount of welcoming to other people's ideas. Anyway, case in point (of other people doing awesome work, not of people being kooks) is David Rivshin's master's thesis which has some algorithmic cleverness that let him computationally determine a whole ton of statistics on graphs that are sort of "trying to be counterexamples" to the reconstruction conjecture. In particular on page 19 there are a few pairs of graphs that have 7 "cards" in their "deck" (i.e. vertex deletions) in common! I managed using some dumb perl scripts to find a pair of 8-vertex graphs with 6 in common, and determined that there were no 9-vertex graph pairs with 7 in common but after that bumped up against the fact that there are like 12 million 10-veretx graphs, and finding pairs of things in a 12 million member set that satisfy some property sounds very 72 trillionish, and that's no good for anybody. Also, Bowler, Brown, Fenner's " Families of Pairs of Graphs with a Large Number of Common Cards" [sorry, I can't find a copy not behind a !@#$ paywall] has a nice construction on page 16 that yields as many overlaps as you want; if you want n nonisomorphic co-occurring vertex deletions, you need a pair of graphs of (asymptotically) 5n vertices. (note the paper says effectively 5n/2, because it's thinking about multisets of vertex deletions, whereas I'm thinking about sets, and the deletions come in isomorphic pairs) You basically take a line graph with a pair of dangling degree-1 vertices hanging off it every three vertices:
o o o
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o--o--o--o--o--o--o--o
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o o o
and the other graph is a ring graph with, again, a pair of danglies every third vertex of the ring except exactly one of the danglies (just one, globally) is missing. This is harder to ASCII-ize, but imagine:
o o
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...-o--o--o--o--o--o--o--o-...
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o o o
where those outer two half-edges are supposed to wrap around and connect. The way this generates lots of different common vertex deletions is this: imagine cutting the ring graph on one of the ring vertices without bits dangling off of it. This creates a line graph with one danglie-thing missing somewhere, but all of the somewheres are non-isomorphic to one another, and the original line graph can be made isomorphic to this one by chopping off exactly one dangling vertex. There's something I really like about both of these works that seems ubiquitous and useful in dealing with really hard conjectures about the existence of mathematical objects --- that is, looking for a quantitative sliding scale at the one end of which the conjectural thing might or might not exist. The win is that (at least in this case) you can write programs to hunt around for the almost-counterexamples, the close calls, the weird outliers, and hopefully learn something from them. Looks as if graph reconstruction is still quite tough after all this data has come pouring in, but it's neat to think about. |
daemonv
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12:10p |
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mdrnprometheus
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6:11a |
On a happier note...
Much wailing and gnashing of teeth in my friends list over Prop 1 in Maine. Understandable. Note, though, that not everywhere is filled with jerkitude. Washington state appears to have approved Ref 71 (referendum vote to certify our new domestic-partnership law) by about 5 percentage points, with the yet-uncounted votes coming mostly from King County (where Seattle is, i.e. where most of the "yes" votes are living). We also are on track to reject our version of TABOR by about the same margin. It's quite pretty and really doesn't rain as much as you think. (About as much as Pittsburgh.) And we have tasty fishies. And killer whales. And coffee. Feeling depressed about living with bigots? Come over here! Current Mood:  tired |
qatar
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9:08a |
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| Friday, November 6th, 2009 |
sorenlundi
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10:34p |
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jcreed
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11:23a |
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bluekirby
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10:20a |
rewards
Check out my new grill apron / dexter knife kit holder, courtesy of the red cross:   Not pictured is a brush, already in the sink from coating fish. |
leon
|
4:34a |
Illustration
The illustrations accompanying my columns in The Phoenix have been pretty consistently awesome, so it’s probably worth reposting them here. The most recent two:
 
Originally published at yoyoel.com. You can comment here or there. |
| Thursday, November 5th, 2009 |
jcreed
|
5:41p |
I do so love Lipton's blog. The linked entry mentions the graph reconstruction conjecture which is a beautiful little open problem in graph theory. In one sentence, it is: A graph (on at least 3 vertices) is uniquely determined by the multiset of all possible vertex deletions of it. Determined up to isomorphism, that is. A vertex deletion of a graph is the graph you get out of deleting some vertex and all the edges incident to it. You have to say at least 3 vertices because it's just not true for 2! There are only two graphs on 2 vertices, * * and *→*, which both have {*,*} as their multiset of vertex deletions. There's a related (stronger) conjecture, A graph (on at least 4 vertices) is uniquely determined by the set of all possible vertex deletions of it And there you can see the 4 is necessary, because the multiset of vertex deletions of * *→* is {* *, * *, *-*}, and that of *-*-* is {* *, *-*, *-*}, and these collapse to the same set if we ignore multiplicities, {* *, *-*}. Here's a question I thought of: Given n, what is the smallest pair of graphs G and H such that ||D(G) ∩ D(H)|| ≥ n, where D(G) is the set of vertex deletions of G? I can't even think of graphs such that ||D(G) ∩ D(H)|| ≥ 3! I sort of expect they must exist, though. The thought of there being a constant upper bound on ||D(G) ∩ D(H)|| for all G and H seems absurd. I bet this could be refuted by playing with the output of Nauty, which contains tools for generating all nonisomorphic graphs over n vertices, and testing graph isomorphism. --- Ah, thought of a pair over four vertices just by pencil-and-paper brute force.
o--o
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o--o--o
o--o
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o--o--o
both possess vertex deletions
o--o o--o
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o--o o
o
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o--o--o
and then each has one more that distinguishes them. --- Another example that is smaller with respect to jointly how many distinct vertex deletions exist of of G (3) and H (4):
G H
o---o o---o
/ \ / \ / \ / \
o---o---o o---o o
Maybe the right question to ask is how small you can get the distinct sets of vertex deletions of the pair such that their intersection is at least n big. In this case (||D(G)||,||D(H)||) = (n,n+1) for ||D(G)∩D(H)||=n is as close as you can get without violating the second conjecture above (which violation would require (n,n)), and this does in fact obtain for n=1,2,3. |
jcreed
|
5:27p |
Some things that have gone wrong lately but are more or less acceptable: My office is at a pretty steady temperature of 85 degrees now. I complained about this a week ago-ish when it hit 80 and, allegedly, gears are turning, and maybe eventually it will be fixed. My bicycle's tires started to get a little low on air, and I thought, hey I'll by a cheap little pump and pump them up a bit, and promptly did everything wrong and let all the air out of my back tire. After ![[info]](http://l-stat.livejournal.com/img/userinfo.gif) escargonaut heroically helped me a lot over the phone, I still couldn't get any air to apparently get into the tire and I finally gave in and went back to the bike shop and they just air-compressored them back to normal shape. The moral here is that when you are a Educated Person and fancy yourself an Adult at least and on a good day Generally Quite Clever, and it's just about the most painful thing in the world to have --- and not only to have, but to display in front of an entire store full of people who know what's what --- the sort of obliterating, flailing, not-even-a-rudimentarily-correct-mental-m odel ignorance (the sort that you can just hardly fathom any non-troglodyte human having when it is about your own favorite problem domain), it is actually a good idea to just suck it the fuck up, ask for help when you need to, and try to observe and by observation learn a couple of things if you can. Now I know, for instance, that there are two types of air valves, one common in low-pressure mountain bike tires, one in high-pressure road bike tires. |
sorenlundi
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4:03p |
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daemonv
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12:10p |
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| Wednesday, November 4th, 2009 |
daemonv
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12:10p |
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matthewljacobs
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9:26a |
The greatest thing in the history of ever
In my Earth Science class today we were watching the Bill Nye episode about heat. In one part of the show, they do a mock talk show called "Heated Debate" between three "panelists" of 12-year olds: Ray D. Ation Connie Vection and Conrad Duction (you can see where this is going) Anyway, during that part of the video one of my students shouts out, "Yo, dis is a real show! I saw Muhammed Ali come on dis show once!" I totally lost it. I broke down laughing hysterically and couldn't stop. Kids say the craziest things. I love being a teacher. Current Mood:  amused |
leon
|
4:52a |
Frozen turkey
I’m posting a lot about cooking lately, but considering I’ve taken to procrastinating my actual work by preparing meals that I don’t need, I figure it’s at least worth mentioning. Anyway, here’s the somewhat disastrous tale of my meat sauce:
After going to the big supermarket nearest Oxford (Sainsbury’s) on Sunday and finally finding ground turkey, something I thought didn’t exist in the UK, I decided to spend Monday afternoon cooking meat sauce. So, I chopped an onion, peeled and chopped some garlic, put on some cooking music, started sauteeing… and then realized that the turkey was still in the freezer.
Once I opened the package, I encountered my first problem: the frozen turkey had a piece of paper stuck to the bottom of it that, no matter how hard I tried, wasn’t coming off. So, being a fairly intuitive individual, I ran the turkey under some scaldingly hot water, which caused the paper to come loose. Crisis averted! But, the turkey was still completely frozen, and by this point, my onions and garlic were beginning to burn.
I now realize that I should have put the turkey in the microwave for a few minutes to defrost it, and then cut it up and put it in the pot with the onions and garlic as normal. My brain, however, wasn’t operating on that level of culinary prowess, so I put a huge frozen brick of turkey in the pot and let it sizzle. After a few seconds, I saw that the outer layer of the turkey could be scraped off. So, over about 20 minutes, I alternated sides of the turkey, scraping off tiny layers of meat each time and trying to break up this huge clod of ground meat.
Which was all well and good until the wooden spoon I was using to finesse the turkey snapped. I broke a spoon with my ineptitude.
Fortunately, we had a replacement so the cooking went on, and ultimately, the sauce came out really well (I had one of my flatmates taste it to confirm). But it was a traumatic process, as well as one that further reduced the stock of available cookware in my kitchen.
Originally published at yoyoel.com. You can comment here or there. |
andres_s_p_b
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12:51a |
Reversing the Wheel of Time
Echoed from Words: the typings of a madman:Gordrog finished his chant. Traveling to the distant grave had taken all day. There had been hours of preparation. The candles had been placed at the precise locations to funnel the spirit of the dead back into its abandoned body. The incense had been checked to be just right. The skull of power had been polished and placed upon the ground. The long chant had left his throat dry and cracked. Now, as he uttered the final black syllable, lightning tore open the sky and struck the grave before him with an ear-splitting roar. In response, a leathery hand shot out of the ground and pulled back downwards, establishing its grip. Inches away, its twin did the same, and together they pulled free the rest of the mummified corpse, clods of earth crumbling away. The hollow sockets turned towards Gordrog, silently demanding his reasons for reaching across the veil. "In life, you undertook a great task, old man, but you overreached your grasp, and death took you before you could finish. I, foolishly, have followed in your trail and run it to its end, but I will not be stymied. By the black arts I have summoned you to the lands of the living to complete your work. Do you accept the terms of your binding?" The dead man faced Gordrog for a moment, then his shruken jaw ground against his skull and rasped out a single parched word. "Advance." Gordrog stepped forward, but the corpse shook its head. "No, I want an advance." "Huh?" The necromancer was at a loss for words. "An advance. Hundred thousand. If you're bringing me back from the dead for this, demand has gotta be outrageous. Sales are gonna be through the roof." Gordrog could get the gold, though he was loathe to spend it. Still, it would pay itself back many times over. "Very well, but I get to be your publisher." "For the lands of the living. I keep rights of first publication in the realms beyond." "Done." As he clasped the dead man's hand, a smile spread over Gordrog's face. At long last, he would know how his favorite tale ended… |
| Tuesday, November 3rd, 2009 |
daemonv
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12:10p |
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| Monday, November 2nd, 2009 |
leon
|
2:53p |
Stress cooking
I think I’ve developed the dubiously positive habit of stress cooking.
This past cycle of tutorials, I’ve been feeling particularly overwhelmed because of an upcoming group trip to Bath that the Sarah Lawrence program is taking us on. Ordinarily, my paper-writing routine goes something like this:
Monday: Political theory tutorial; researching film essay
Tuesday: Researching and writing film essay
Wednesday: Finishing and submitting film essay
Thursday: Film tutorial
Friday: Researching political theory essay
Saturday: Writing political theory essay
Sunday: Proofreading political theory essay; researching film essay
The trip to Bath, in and of itself, isn’t a huge issue, except that I wasn’t nearly productive enough last week. As a result, I didn’t have time to even begin working on my film research until today. Which means that I’ll still be researching for most of tomorrow, which means that my essay won’t be written in time to submit it before I leave for Bath on Wednesday morning. I’m awaiting a response from my tutor to the rather frantic e-mail I sent him this afternoon, but in the mean time…
…I’ve been cooking basically nonstop. I’ve made baked eggplant, a turkey-based meat sauce (many stories of cooking catastrophe associated with that one), some roasted potatoes, a bunch of tuna salad, more peanut butter and jelly sandwiches than I know what to do with, rice and lentils, and, in the oven now, baked apples.
I have absolutely no use for all this food! I’m not even actually hungry, and the fridge is so full of my roommates’ stuff that there’s no room for all the leftovers that my mania is generating. At the very least, though, I’m going to have an easy time, food-wise, for the next week, because between what I’ve purchased and what I’ve managed to cook, there’s a pretty incredible quantity of stuff waiting to be eaten.
Time to check on my apples to make sure they’re not detonating (we lack a corer, so I’m skeptical about whether they’ll actually be successful)…
Originally published at yoyoel.com. You can comment here or there. |
daemonv
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12:10p |
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leon
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3:41a |
Maintenance
About five minutes into my shower this morning, I noticed that the shower drain was clogged and the water from the shower was overflowing in a pretty significant way out of the shower and into my bathroom. This joins a number of other maintenance issues on the list of Shit That’s Wrong With My Apartment:
- The lock on the front door no longer locks
- The toilet in one of the bathrooms requires a certain level of persistence re: flushing
- The door on the other bathroom either doesn’t lock, or locks you in
- The door to my balcony doesn’t stay closed
- The light in one of the bathrooms only works intermittently
- One of the refrigerators has a puddle of water inside it that reforms no matter how often you wipe it up
- The kitchen sink will occasionally decline to produce hot water
- The bathroom showers will occasionally decline to produce hot water
- Two of the burners on the stove are broken
- The handle of one of the pots snapped in half yesterday, rendering the pot more or less useless
- The wireless router needs to be reset every two or so days or the Oxford VPN stops working
And these are just the issues in D4. There are six flats in this building of the complex, each with five rooms and each with a litany of problems.
At first, I thought putting all the Americans in the building with all the defects was just the British way of saying, “Thank you for declaring your independence!” But after talking to a friend who lives in another building in the complex about his persistent hot water issues, I’ve come to realize that these problems are a bit more widespread than just the D-block.
The apartment manager, Lindsay, has an interesting repair strategy when it comes to maintenance problems. Namely, he reverses whatever problem you report to him. When our front door wouldn’t unlock, he came, banged on it for a few minutes, and then declared the problem solved — and indeed, our original issue was; the front door no longer stays locked, but nor does it do anything but stay unlocked anymore. When my flatmate Madeline’s window wouldn’t open, he corrected that issue and she now has an open window… that won’t close. The un-flushing toilet (disgusting), overflowing shower (disgusting), broken bathroom door (irritating), and leaky refrigerator (wet) are, presumably, all on the list to be inverted (into a toilet that won’t stop flushing, a shower that doesn’t work at all, a bathroom door that doesn’t exist, and a refrigerator that isn’t cold), but we haven’t heard any updates on them yet.
Every once in a while, the manager will reply to an e-mail you send reporting some maintenance problem with the observation that the Americans in the D building send about four times as many complaints as the British students living in every other building in the complex. What I’m trying to figure out now is: is that because American college students don’t have the keep-calm-and-carry-on mentality of our British counterparts, or because we really did get the dud apartments?
Originally published at yoyoel.com. You can comment here or there. |
| Sunday, November 1st, 2009 |
stepleton
|
11:51p |
Today I ran a half marathon. I did not train. A friend injured her ankle a while back, and this week we all had the idea that I would take her tag. (It said "Laura" on it in large letters. I told the race organizers afterward so I wouldn't interfere with prize-giving, although there was probably no great risk.) My time was 2:00:00 to the second, a 9:10 mile pace. I'm pretty happy with that. |
recsrainbow
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4:42p |
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jcreed
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9:42a |
Ew, flies on my toothbrush and a weird-ass beetle thing on my towel. Why so many bugs? Why hel lo bag of trash that I neglected to throw away two months ago when I moved out of this room. Oh I see that y---ewwwww. Well, that explains it. |
leon
|
5:35a |
Definitely not a Nashville party
Sorry, again, for the prolonged silence; it’s been a busy week or so. My latest Phoenix column is going up here, but expect more blog-exclusive stories soon.
Note: This column will appear in the November 5 issue of The Phoenix.
If history serves as any example, this past weekend Swarthmore was overrun by the annual Halloween party. I’ve always put a lot of weight on Halloween at Swarthmore because, ignoring the Hootenannies and Disorientations our Greek friends put on each year in the hopes of sleeping with the freshmen while they’re still fresh, it’s the first big party of the semester. And for first-year students, it’s the first time in their experience that a vast majority of the campus is brought together in the singleminded pursuit of getting crunk.
Moreover, if the Daily Gazette is to be trusted, I’ve heard that the party was, blessedly, moved out of Mertz Marsh and back into Upper Tarble, a change that continues the administration’s tradition of struggling to figure out where the least number of people will get injured at this infernal party. While the mud of Mertz Marsh has obvious appeal with its magical ability to eat shoes and turn your entire life into a colossal load of dirty laundry, I guess the administration and SAC decided that Upper Tarble’s convenient steep staircase was somehow less dangerous. To that, all I have to say is: tell it to the three people who fell down the stairs my freshman year. You know, the ones who were screaming really loudly about wanting to go home right around the time when the Party Associates barricaded the doors and wouldn’t let anyone leave the building because, supposedly, the Swarthmore town police were preparing to send in SWAT teams to bust underage drinkers, which I maintain was a colossal joke Peter Gardner ’08 played on the student body as a way of saying, “Thanks for making me class president! Punk’d!”
For me, anyway, Halloween was a big deal my freshman year because it represented the first time I went to an event at Swarthmore that wasn’t academic or organized by the Orientation Committee. At the urging of my Mary Lyon hallmates, I went as Waldo of childhood puzzle favorite Where’s Waldo?, wearing a red beanie, dark-rimmed glasses, a striped sweatshirt, and a nametag reading, “Hi! You found me!” What I also found that night was the understanding that attending any large party at Swarthmore inevitably means carrying around nightmares of it for the rest of your life. As every columnist in The Phoenix’s Living and Arts section has noted in the past twenty or so years, partying at Swarthmore is a horrific experience.
Coming to Oxford, I wasn’t sure what to expect from the party scene. It seems somehow improper to envision debauchery on the order of a Paces par-tastrophe in the setting of a university founded in the 11th century. My all time worst Paces experience — witnessing a line of gyrating men at least ten people long, one of whom I had class with two days later, grinding in sync to Rihanna’s “SOS” — seemed like the sort of thing that just couldn’t exist here. Even now, looking around the Bodleian Library, the people studying near me just don’t seem like the make-love-in-this-club type. How wrong I turned out to be.
During orientation, the Sarah Lawrence at Oxford program director, Deborah, made a point of telling us that the way British students approach drinking is very different from what we, as Americans, might be used to. With a drinking age of 18, university students presumably have worked out their youthful indiscretions with regards to alcohol by the time they arrive on campus, and, as it was put to us, “Brits enjoy alcohol. They don’t drink to get drunk.” And, the moral of the only slightly condescending story was, neither should you.
Well, Debbie, tell that to Felicity (or as she calls herself, Fliss, an abbreviation I can’t even begin to process and only wish I was making up), a Wadham College second-year and bona fide Briton, who, the night of the second big party of the semester, threw up all over a friend of mine. British students, it turns out, are exactly the same brand of sloppy drinkers as Americans. The only difference is: in the UK, you have to pay a pretty significant amount of money for the privilege of drinking mediocre alcohol, whereas you get it for free at Paces with Tri-Co ID.
(In Fliss’s defense, she did inter-college mail my friend a bracelet as a token of apology the next day; but honestly, I don’t know if even an infinite quantity of kitschy homemade jewelry could make me get over being vomited on. Maybe I’m just heartless.)
Organizationally speaking, parties at Oxford are a much bigger deal than your run-of-the-mill night out at Swarthmore. For one, being an Oxford student means you can’t call a party a “party,” a word reserved for townies and ignorant Americans; instead, a party is known as a “bop,” a word that is as uncomfortable to say in public as it is to read. Moreover, these bops all have exceedingly complicated premises that require — not just suggest, but actually require — “fancy dress,” a British phrase that, improbably, translates to “dress like a complete and utter fool in accordance with an ill-conceived theme developed by the party organizers to make people unhappy.”
Bop themes thus far this term have included “back to school” (I’m embarrassed to admit that I dressed as a schoolboy having an affair with his teacher; I’ve never felt so dirty in my life) and the London Underground, while some more colorful examples from previous years include “golf pros and tennis hos” (I swear I’m not making this up) and “P is for…” a theme that leaves open such exciting avenues for costumes as “porn star,” “Presbyterian,” and “pumpkin.”
And all this while writing two 2000-plus word essays per week, attending lectures, eating, sleeping, and trying to maintain some semblance of hygiene using British showers that alternate at will between scaldingly hot and unbearably cold. It’s amazing that Oxford students don’t explode from the excitement of it all. At Swarthmore, it seems like the operating philosophy is “work hard, party harder.” Spending days locked in the basement of McCabe can be rationalized by the anticipation of screaming a drink order at a surly Deshi member tending bar and getting stuck to the floor in Paces. At Oxford, the hard work is there, as is the drinking; but when it comes to the primal gratification of partying, at least for now, it’s all just a bit too weird for me.
Originally published at yoyoel.com. You can comment here or there. |
missytas
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12:03a |
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