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Ben Babcock

I read, write, code, and knit.

25 Articles Tagged with “mathematics”

  1. Happy Ada Lovelace Day, now dismantle the tech patriarchy

    I just started writing my review for Broad Band: The Untold Story of the Women Who Made the Internet, by Claire L. Evans. If I had timed things better, I could have written this review earlier and published it today, on Ada Lovelace Day. As it is, I’ve paused writing my review of this amazing book for a quick blog post about this day and women in STEM in general.

    Ada Lovelace, by the way, is often called the world’s first computer programmer. This is because she designed the first algorithm for Charles Babbage’s never-built Analytical Engine, which was itself the first stab at a mechanical computer. Additionally, Lovelace was a kickass mathematician—although she was reluctant to draw attention to herself by publishing her own work, she ended up translating a bunch of other work and adding annotations of her own that were often longer, in total, than the original work!

    Lovelace, and the many women who follow her (read Evans’ book for more!), demonstrate that women have always been a part of tech. Women don’t just belong in STEM; women are an essential component of STEM and have been from the very beginning.

    Yet we have what…

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  2. Algorithms are not the answer

    Oh, look! It’s another article about discovery vs rote math! Here we go again….

    I thought I had solved this back in 2011 (twice!), but apparently a couple of people in the world didn’t listen, so now here I am, back at it again. It seems like every five years when the latest round of test scores shows that the sky is falling we’ll be doomed to have the same arguments over and over about how to teach, and in particular, how to teach math. It’s tiresome. I’ve only been a teacher for four years, and I’m already tired of it.

    Let me qualify that statement of fatigue: I never tire of talking about how to teach. Education is serious business, and having a healthy debate over the best and most effective strategies is important. I am not out to label anyone in any of the camps as wrong or extremist in their views, and I believe that most of the participants in these discussions genuinely want what is best for our children. When I say that I’m “tired” of this discussion, I’m not here to say, “I’m right” (even though I am) and, therefore, we should shut down…

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  3. Modelling epidemics to learn about probability

    My major focus in my work at the Adult Education Centre has been adapting online courses for the Hybrid Learning Project. Basically, these are high school courses adult learners can complete online, but there is also an in-person tutorial component to them. I’ve been adapting the e-Learning Ontario MDM4U (Grade 12 Data Management) course. I’m almost done.

    I could write an entire post about this assignment and how I feel about it, but that’s for another time. Instead I want to share something cool I made for the course.

    When I hit the lesson on experimental probability, the assignment was basically, “Create an experiment and perform it ten or twenty times and then estimate the experimental probability.” Yeah. As if someone doing an online course would really do that.

    So I searched for some kind of interactive resource—and I found this NRICH activity on modelling epidemics. It’s a neat Flash applet that lets you adjust variables and then simulate an epidemic in a village. After each epidemic finishes, the simulator calculates the mean and standard deviation for a few different variables. The idea is that students should adjust one variable at a time and then hypothesize what effects this…

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  4. Things I wish I had done or seen

    I tweet a lot, and that includes links to interesting things I see on the Web. Twitter is an interesting medium with a lot of advantages—but one of those isn’t really permanence. It’s not easy to go back and look at one’s previous tweets, or to collect and categorize one’s tweets.

    Since I’d like to blog more, I thought I’d try sharing here some of those things (and other things) I’ve encountered over the week.

    • You can use math to become better at Monopoly. Well, you can use math to help you out with any game of chance, but Walter Hickey does an excellent job actually analyzing, step-by-step, the different probabilities involved. You don’t have to be well-versed in math to get something from the presentation, though familiarity with probability will definitely help.
    • I’m stoked that the Large Hadron Collider has detected what is most likely a Higgs boson. It would have been exciting to have to tweak the standard model even more, but now we have some interesting evidence in its favour (especially because it wasn’t quite the mass of Higgs we were looking for). That being said, discovering what you are looking for, instead of something entirely

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  5. More on math from Margaret: Arithmetic should be boring

    Once again Margaret Wente, my favourite Globe and Mail columnist, has delved into the gritty underworld of math education to expose the truth. This time she is concerned that we’re not teaching basic arithmetic in schools any more. She takes issue with recent trends in math education, which emphasize discovery-based learning over drill or rote-based learning. As a consequence of this shift, the standard algorithms for addition, subtraction, multiplication, and division are no longer a core part of the curriculum. Wente, as well as some parents and teachers, thinks this is a bad idea. And while I agree with her on one point—it’s essential for students to know basic arithmetic as they go on to high school—once again I have to protest how she has chosen to argue that point.

    Before I discuss Wente’s arguments, I think it’s important to mention one thing that Wente does not make explicit. Education falls under the mandate of the provincial governments. Hence, every province and territory in Canada has different math curricula. There are similarities, but we still have to be careful when we are talking about math education across the entire country as if it were some uniform curriculum.

    Canada is “Behind…

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  6. Why Wente is wrong about math education

    I woke up on Friday to see a page from Thursday’s Globe and Mail on the living room table. My dad had flagged an article by Margaret Wente as something that I might find relevant. You can find it online under the title “Too many teachers can’t do math, let alone teach it”, but in the paper itself it was published with the headline, “Go figure, because teachers can’t.” I encourage you to read the article, but the gist goes like this: elementary teachers, according to Wente, are failing to teach students the basics of math, because faculties of education don’t take their responsibility to prepare those teachers seriously enough.

    By way of disclaimer, I am preparing to teach at the Intermediate/Senior level (I/S), or grades 7–12. As an I/S teacher, and as a formally-trained mathematician, I have to admit to a bias when it comes to this subject: I do worry about how well-prepared elementary teachers are to teach math. I’ve marked for a course that teaches elementary concepts to prospective teachers, and some of the answers to the assignments are … creative. However, my concern isn’t so much with their knowledge of content; I worry more about…

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  7. Now the summer begins

    Jessica displays her raspberry pie

    Last Friday marked the end of my summer research term. For reasons I don't entirely understand and don't need to understand, Jessica made a pie to celebrate the milestone. It was raspberry (my favourite fruit) and, more importantly, it was delicious. This summer feels like it has gone by extremely quickly, and I'm not yet eagerly anticipating school. I have two weeks off now, returning early on August 29 to begin the intense final year of my concurrent education degree. My schedule does not seem all that bad, as far as classes go, but I'm not sure what the workload will be like—I hear it's heavy but not difficult.

    As far as my research goes, I can't help but compare this summer to last summer. Overall, I was not as interested in my project this time around—it's the same project, so it is no longer fresh. Working on it on a full-time basis for 16 weeks was intense. This year was also quieter around the office; Jessica was not around as much, and Rachael had a research project, but it only lasted eight weeks. Aaron came in pretty consistently several days a week, despite not being on any kind of…

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  8. Good books and a sleepy conscience

    Sunday was mostly an odds-and-ends day. I cleaned my room, organized things, and finished some books. Although the threat of rain hovered constantly in the air, I even managed to do some reading outside. So I had a pretty good weekend.

    I managed to finish both Persuasion and the Iliad. My to-read shelf was finally empty, which meant I could restock it with books from the rather oppressive overflow stack. I have forty more books on the shelf now, and the overflow now fits comfortably inside that blue milk crate! My goal is to empty the shelf again by the end of July--this is ambitious, I'm aware, and made even more so by the fact that I also have to get through the Hugo Voters Packet by the end of July.

    I'm voting in the Hugo Awards again this year. I first voted last year, when John Scalzi alerted his readers to the fact that the Worldcon organizers distribute a packet containing electronic copies of most of the nominated works. This year, the attending membership at Renovation is only $50. That is a small price to pay for access to all these wonderful works, not to mention…

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  9. I'm at it again!

    So I've finished my first week of summer research, which I began on Tuesday (as Easter Monday was a holiday). I am re-revisiting the spreading and covering numbers, those devilish little fiends from combinatorial commutative algebra that plagued me last summer. You can read about last summer's research here. I shall try to blog often about this summer's efforts as well.

    This week was very much about settling in and trying to get my mind into a math research mode. I am starting earlier than I did last year, because I will be returning to school in late August. We professional year students have to start early to finish classes in time for student-teaching in November! Unfortunately, this means that I didn't get much of a break between the end of classes and starting research. I have tried to seize as much downtime as I could. Still, as far as summer jobs go, I won't complain about doing research. It's pretty choice.

    I'm in the same office as I used last year, and you can see photographs in this blog post. I'm in the desk in which Aaron is sitting in those photos, as my former desk…

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  10. Next year I kind of enter the adult world

    I'm almost finished my fourth year of university, and with it, my HBA in Mathematics. It doesn't feel like four years! It feels like barely yesterday I was a nervous first-year student trying to figure out how to get around our campus (which I now realize is tiny compared to other campuses).

    I won't be graduating at the end of the year, because I'm actually in a five-year concurrent education program. For those of you unfamiliar with it and with teaching certification in Ontario, let me give you a brief run down. Instead of completing my mathematics degree and then doing a one-year education program ("consecutive education" or colloquially known as "teacher's college" around these parts), I have for the past four years been enrolled in concurrent education. As the name implies, I'm taking education courses concurrently with the courses I need for my math degree. So at the end of the five years, assuming I complete the program, I'll have an HBA in Mathematics and a BEd. In Ontario, teachers are certified to teach in a specialization defined by grade level. Mine is "Intermediate/Senior," or I/S, which means grades 7-12. I really want to teach high school, but…

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  11. I can haz conference?

    This Friday, Saturday, and Sunday I attended the eighth annual Combinatorial Algebra meets Algebraic Combinatorics Conference. No, I didn't record awesome video diaries as I did when I attended the 2010 Canadian Undergraduate Mathematics Conference. I did meet many experts in these fields, listened to interesting talks that I didn't really understand, and gave a talk of my own!

    Combinatorial algebra and algebraic combinatorics are, as the conference's title and purpose expresses, two sides of the same mathematical coin. They are areas of mathematics that combine techniques from combinatorics and abstract algebra (notably, commutative algebra) to solve a variety of problems in algebra, combinatorics, and even algebraic geometry. Now, these fields are specialized. I got the impression that even among the thirty or so graduate students, postdocs, and professors in attendance, many of them were struggling to keep up with some of the talks, because the topics in this area, as with any specialized field, can get pretty esoteric. One fellow gave a talk on cluster algebras, and the room was rather silent when it came time for questions.

    Still, it was exciting to attend the conference even though I, as an undergraduate student with only two courses…

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  12. Summer endings, September beginnings

    Hello September. I have missed you. You might be my favourite among all months, but don't tell the others. And no, it's not because my birthday is in September (although that helps). Nor is it because September signals the start of fall television, with new episodes of Castle, Chuck, House, Stargate Universe, etc. More than any other month, even that notorious January, September is a month of changes and new beginnings. For those of us biased in our perceptions by our position in the northern hemisphere, summer will soon be a memory; the leaves will change colour; and I'll be back in school, where I belong.

    I spent this summer doing research and quite enjoyed it. We didn't make as much progress toward a solution as I had hoped, but I learned a lot, both about mathematics and research in general. I'm comfortable using LaTeX (which is sexy) and have had some experience with Macaulay2 (also pretty hot). I even went to a conference, something that surprised me.

    With my research finished, I have these two weeks off before school begins on September 13. Next week I return to work at the art gallery. I don't…

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  13. CUMC 2010, Days 3 and 4

    It is Saturday, but it doesn't feel like Saturday, mostly because I'm . . . at school. This is the last day of the CUMC. I'm in the last talk of the day, having chosen to attend "Perfect Matchings and Shuffling." Afterward, there is the final keynote, which Ram Murty will deliver on the Riemann hypothesis.

    Yesterday I went to a talk on fractal image compression. The talk itself was not stellar, but there were some good questions on the applications of this type of lossy compression, and the speaker addressed those well.

    In the afternoon Aaron, Rachael, and I took a bus--yes, a bus--down to King St. This was my first time riding public transit, and it wasn't in my own city! Aaron wanted to visit a small record store, Orange Monkey Records, and then i checked out a used bookstore known as Old Goat Books. I bought more books than I should have, considering they need to fit in my sparse luggage--but I couldn't resist.

    The final keynote of the day was delivered by Greg Brill, of Infusion. Although titled "The Evolution of Technology," Brill's talk was not what I expected. He has a…

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  14. CUMC 2010, Day 2

    It is Thursday, July 8.

    After the first talk this morning--on set theory, particularly ZFC--I spent time caressing the lovely wireless network by way of uploading some photos to Flickr. When attempting to geotag them, however, I ran into the slight problem, in that typing "University of Waterloo" into the Flickr map's location finder produced no results.

    So, Yahoo!, in case you are wondering why people drool over Google and its products, here is a hint: we are lazy. When I type in the name of a major university, your map should be able to find it for me. I should not have to go find a postal code on my own, enter that, and wind up in the general vicinity of the campus. (I used Google Maps to find the postal code too, which just seems wrong). It is not that I am a Google fanboy, Yahoo!--they just do it so much better.

    At lunch, I did something completely out of character and chose to be adventurous, purchasing bubble tea for the first time. My less adventurous self was soon vindicated. We went to a fast food place called "The Grill" for food. I attempted to…

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  15. CUMC 2010, Day 1

    It is Wednesday, July 7. The CUMC talks began today.

    I went to four talks today. Rather than summarize them all--I enjoyed them all--I'll mention some highlights. The first talk of the afternoon was both my least favourite and most favourite talk. Entitled "The Ontology of Mathematics: Do Numbers Exist?," the presenter read from dense slides, which did not make for the most riveting experience. There was some lively discussion among the audience, however, and I enjoy talks like that.

    Comparing CUMC to the Combinatorics & Optimization workshop that preceded it, I prefer the student talks of the former. The topics are so varied--there is so much choice within each time slot, that it is difficult to decide which talks to attend. The atmosphere is less intimidating, because it's undergraduates talking to undergraduates. I almost regret not giving a talk myself--almost, for it would involve public speaking, and long gone are the days when classes made that mandatory.

    There were two keynote speakers, one at lunch and one at the end of the day. First, Frank Morgan, from Williams College, gave a talk on densities and the Poincaré conjecture. As I have never studied differential geometry, most of the mathematics…

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  16. Combinatorics and Optimization, Day 2

    It is Tuesday, July 6.

    Today's four talks began with electrical networks and random walks. That is, suppose you have a graph that describes a network through which electricity flows. Starting at a vertex x, what is the probability that, when walking at random along the graph, we will arrive at a vertex s instead of a vertex t? This talk was very easy to follow (for which I am thankful), even though I don't have any engineering or physics background with which to understand the electrical current aspects (like voltage law).

    Unfortunately, the second talk involved probability. Probability is great, but I find it very difficult, so this talk was hard to follow. The third talk was about embedding locally-compact metric spaces on surfaces (it is not as scary as it sounds). Finally, the fourth talk was about matching polynomials. The speaker went rather briskly, so it was difficult to take detailed notes, but I enjoyed the subject. Before this summer, I had no idea that polynomials and graphs went so well together. Now it seems like they're inseparable.

    And that concludes the Combinatorial and Optimization workshop. There was a banquet for CUMC at the Huether Hotel,…

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  17. Combinatorics and Optimization, Day 1

    I wrote this last night at my grandparents' house, which has no Internet connection I can feasibly use (dial-up does not count), so I had to wait until today to post it from the University of Waterloo campus. All references to "today" refer to Monday, July 5.

    This week, Rachael, Aaron, and I have travelled to Waterloo, Ontario for two math conferences. The first is the Combinatorics & Optimization Summer School, a two-day event consisting of several talks and, yes, food! The second is the Canadian Undergraduate Math Conference, which also entails much talking and eating. I was reluctant to attend at first, because I dislike travelling. However, my grandparents live in Waterloo, so this was a convenient way to visit them for a week while still getting paid. With that incentive, I managed to convince myself that these conferences would be interesting and probably even useful to my research. This was only the first day, but so far I remain convinced in those respects.

    I've been up since 4:30 in the morning. Let me take a moment to reflect on the fact that we flew from Thunder Bay to Toronto in an hour and a half, traversing--or…

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  18. No sugar tonight

    Stanley, prior to a paint job

    Last week, I discussed how maths is hard, but I spent plenty of time solving a Rubik's cube anyway. At this rate, you are going to get the idea that I don't do any work at all. Nevertheless, a desire for accuracy and lulz requires me to remain truthful regarding how I spent this week in the office.

    We made a piñata.

    We named him Stanley the Resurrection Pig.

    I don't recall who came up with the initial idea. As with all good, crazy plots, it starts off as an innocuous hypothetical scenario: piñatas equal fun, fun equal good, we could make a piñata! This is the last week all four of us will be in the office together--Aaron, Rachael, and I are going to Waterloo next week for a conference, and Jessica is off to Ireland, returning only after Aaron and Rachael's contracts are finished. So if ever there was a time to set aside the math papers and construct a papier-mâché animal, then savagely beat it to a pulp, this was that time.

    None of us are piñata-making experts, and that was probably for the best. Rachael had some experience with papier-mâché--also for the best--so we made…

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  19. Music must change

    I like to joke with my friends about how easy I have it this summer. I'm sitting in a cozy little office with a fan, proximity to a kettle, and a high-speed Internet connection. Unlike a summer research student in, say, chemistry or biology, I don't have to manipulate lab equipment or sex fruit flies (Cassie :P). The extent of my experimentation will involve uploading programs to a high-powered computing network and asking it kindly to compute a few more numbers for me. I Google math papers relevant to my problem, try to understand what they say, and see if I can come up with my own ideas. One thing I love about math research, especially in my area of interest, is how much it's thought. All I really need is a blackboard and chalk, or pencil and paper. (That being said, the high-powered computing network does help when I get to the computation step!)

    Of course, it's not all fun and games (even though I did learn how to solve a Rubik's cube last week). Maths is hard! And right now, even though I've been in university for three years, I feel like an amateur groping around an unsolved…

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  20. Guitar and pen

    Yes, yes, I know. At this rate, my weekly recap will become bi-weekly. I didn't do a lot the week before last, owing to Victoria Day making for a shortened week. So rather than two very short blog posts, I decided to forbear and write one short blog post instead.

    The last two weeks have been more reading, more learning, and a little thinking. I hesitate to ascribe a label like "productive," since it's hard to quantify. I think I understand my problem now, but there remains a lot for me to learn in order to start trying solutions.

    I tried running the original algorithm for computing the spreading number, which was written in CoCoA, on my computer. I had hoped that my 2 GB of RAM and 1.83 GHz processor would have enough memory to compute some additional numbers. Alas, CoCoA stubbornly crashed (after several long hours) each time I instructed it to do so.

    So I ported the code to Macaulay2. It's even slower, which makes me suspicious that I'm missing something--after all, I am learning both languages, so I'm sure that in transliterating the code I managed to miss an obvious way to make it…

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  21. You ain't seen nothing yet

    Shorter entry this week, as I didn't do much new and exciting in week 2 of my research project. I'm still having fun, but because it's so early in the summer, that fun mostly takes the form of reading.

    As tweeted earlier, the secret to reading (and understanding) math papers is simple. First, always read it twice. Then read it again. But to make sure you really understand, you need to take notes. Write down what's implicit in the paper, the steps the author leaves out because "it is obvious" or "it is clear to the reader" or, even worse, "this has been left has an exercise for the reader." Once you've done that, the final step is to read the paper again.

    I spent all week reading two papers, one of which expands on the findings of the other. The first investigates the spreading and covering numbers in relation to the ideal generation conjecture. Much of the paper goes over my head. Nevertheless, there were some very useful figures, and the use of graph theory in one paper and set theory in another helped improve my comprehension of what these numbers are. The second paper, in particular,…

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  22. Start me up

    Chalk board in my office

    I am now into the second week of my NSERC summer research project. So far, I'm having a lot of fun. The subject of my research is interesting and exactly the type of mathematics that I want to study. The "daily grind," such as it is, does not grind at all--it helps that there are three other undergraduate students doing research this summer, and we all share the sessional lecturer office. We can distract each other, when needed, and pick each other's brains for help with particularly puzzling proofs.

    So what exactly am I doing? Well, it's esoteric even for those who enjoyed math up until the first years of university. I'm going to drop some math jargon in the next few paragraphs, so don't worry if your eyes start to glaze over. Photos and hilarious video will follow!

    Since my prof was leaving town at the end of the week, we met several times so he could give me some lectures and we could discuss my project. The work I'm doing relates to ring theory, which is a course I took nearly two years ago, so I have a lot of review to do. Most of the week,…

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  23. Summer scoop: I have an NSERC grant!

    This January, I applied for a summer Undergraduate Student Research Award (USRA) from the Natural Sciences & Engineering Research Council (NSERC). Lakehead University has 20 such awards to give to applicants this year, and on Monday, I learned that I am the recipient of one!

    I was (still am) a mixture of elation and trepidation. Part of me is still in a state of shock and can't quite believe that this is real. I spend a good half hour after learning I got the grant just trying to calm down so I would not run up to everyone I encountered and yell, "I GOT A GRANT!" Another part of me is saying, "What do you think you're doing, Ben? You don't even understand what it is you're going to be researching!" As anyone who has ever looked at a higher math textbook knows, the language is just scary sometimes.

    I applied for the NSERC grant for two reasons. Firstly, it's a different summer employment opportunity than my default, which is the art gallery. Don't get me wrong: I love working at the gallery. You can't beat the hours, and I have an awesome boss--she took the news that I wouldn't…

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  24. Bring me your math! All your math!

    Tonight Stargate Universe premiered, and I wanted to share my thoughts on it. However, I feel guilty blogging about a television show when I haven't blogged about arguably more important matters, such as life.

    With a month behind me, I feel good about the school year so far. I only have four courses this year: Introductory Analysis, Partial Differential Equations (PDEs), Introduction to Mathematical Probability, and Speculative Fiction. Three math courses and an English course. All of my math courses are interesting, and I was excited to take the English course the moment I saw it offered. I'll discuss it first, since the rest of the post will be about math.

    My Speculative Fiction course is covering only science fiction this section--which is fine. Although I love literature in general and would gladly have taken something like Victorian Literature if this course hadn't been offered, the chance to read and discuss science fiction for credit is not something I was going to overlook! We're reading The Time Machine and The War of the Worlds, The Left Hand of Darkness, Do Androids Dream of Electric Sheep?, Neuromancer, Dawn, and Singularity Sky. We also have to…

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  25. Avatars, zombies, and nephews, oh my!

    More Reasons to Love the Guild

    I've already preached my love for The Guild, a webseries by talented comedians and actors, including Felicia Day. Well, even as they work on a third season, they've released a fantastic music video:

    Who Said Math Can't Be Fun?

    Well you were wrong, whoever you were. Mathematicians from Carleton University and the University of Ottawa modelled different responses to a zombie apocalypse and concluded that the best way to survive a short-term zombie apocalypse is to impulsively eradicate all zombies. Ladies and gentlemen, load your engines and start your shotguns.

    I'm an Uncle

    Baby Clark

    In July, my sister, Tara, gave birth to a very little boy named Clark! So I've got a nephew, which makes me an uncle, and that is sublime. I got to meet Clark today for the first time, which called for the typical point-and-shoot photos that wind up on Flickr somehow.((I blame the gnomes, if only because they haven't unionized yet like the orcs did.)) If I'm short on words about Clark, it's only because I don't really know him yet--he doesn't know himself yet, since he's only a month old and still new to the world.…

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