Putting The Pieces Together Is Tough For Some

I've seen a lot of examples in recent months of students who can learn Math skills in one (often rather rigid) context but then be quite lousy at figuring out how to use them in other situations. To understand what I mean, let's look at an example.

Suppose you knew that the formula for the area of a rectangle was length times width, and had known that for years. Also assume that you learned in Grade 9 how to multiply binomials and since then have even acquired the ability to solve simple quadratic equations. All of that knowledge would seem to position you perfectly to answer the following question:

"A rectangle is x + 6 units long and x - 4 units wide. If its area is 56 square units, what are the dimensions of this rectangle?"

Someone who's comfortable with Math at a high school level or higher will quickly realize that they need to solve the equation:

(x + 6)(x - 4) = 56

which is to say, solve:

x**2 + 2x - 24 = 56, or x**2 + 2x - 80 = 0

Factoring that quadratic yields:

(x + 10)(x - 8) = 0

meaning that only x = -10 and x = 8 will solve it. Since a value of -10 gives us negative values for the length (-4) and width (-14), we can safely discard it, leaving x = 8 as the only reasonable answer.

Sure enough, if we use 8 for x, we get a rectangle with a length of 14 and a width of 4, good for an area of 56 square units. Problem solved!

Every step in this solution involved Math of a sort that a typical high school student in Gr 10 or higher would know how to do. But because it starts off as a word problem (Strike 1!), has dimensions that involve variables as well as numbers (Strike 2!!) and requires the solving of a quadratic equation "out of the blue" (Strike 3!!!), it's just a full stop for many of them. I think part of the problem is that some students aren't willing to just try stuff in order to see where it leads them, in addition to a general but deep-rooted aversion to applying what's been learned for one type of problem to questions that don't initially seem similar.

I'm always shocked and dismayed when one of my Math tutoring pupils has all of the tools necessary to solve something like the example used here and yet can't even get going on it, without someone like me to push them in the right direction. I can't help but feel that some essential ingredient has been missed in their education up to this point... I'm just not sure yet what exactly that omitted component is.

No Del Toro For The Hobbit

Bad way to start the week: Guillermo del Toro has stepped down as director of the two part adaptation of The Hobbit. I can't believe how much strife and conflict this film project has had, considering that the Lord of the Rings trilogy ruled the world for three years, achieving the rare feat of both critical and box office mega-success!

My Weekend As A Math Teacher

Most of my free time this weekend has not been spent swimming (no pool!) but rather preparing Practice Sheets for a couple of high school Math students of mine, both of whom fortunately are in the same course (at different schools).

I decided to break the material down along the same unit lines that are being used within the curriculum, allowing me to focus on one aspect of the course at a time. In each case, the first page covers "Key Concepts" and instructs the student to get these clear in his/her head before proceeding on to the actual practice (i.e. questions). A typical "practice sheet" has turned out to be about 4 or 5 pages in length, and I've done two and a half of them so far (out of what I expect to be a total of four). Since final exams are now less than 4 weeks away, I want to get these completed and into the students' hands very soon, in order to give them time to spend on them before the big crunch time right before the finals begin being written. My goal is to have all four sets ready to go by the end of this week, and to get the first set or two out and being worked on sometime this week.

Hence, I've felt like a high school Math teacher all weekend. I think I could probably ace the final exam for this course right now, too.

Pool Sometime Soon, Maybe?

Despite being told that we'd have our new liner by the middle of last week, and suffering through one of the hottest May weeks I can remember, we still don't have anything but cement in that hole in our backyard. However, pool-type people are scurrying around in it right now, so maybe we'll be at the "just add water to make fun" portion of the proceedings later tonight or tomorrow. It's been a long, long wait for this, thanks to an overly-optimistic estimate and one heck of a heatwave.

[Update later that evening: After a few hours of trying, they've decided they can't fit the new liner in without fixing the "broken corners" (coping) first, which they'll do tomorrow morning. So the saga continues...]

A Good Avengers Comic For A Change

Last week I railed against the re-launched Avengers title, sorely disappointed that it was the same talking heads baloney that's turned me off that franchise of late. This week's debut of Secret Avengers was quite a different tale, however.

Writer Ed Brubaker and artist Mike Deodato were in fine form as they kicked off what I hope will be a long collaboration on Secret Avengers. Steve Rogers, the recently-resurrected Captain America, has told former sidekick Buckey Barnes to continue as the current Cap, while Rogers functions more as a Mission: Impossible operative out of costume. He's also the head honcho at S.H.I.E.L.D. in the post-Siege version of the Disney Universe (replacing Norman Osborn who took Nick Fury's job), which is probably what gives him the resources to form his own, covert group of Avengers: Black Widow, the Beast, War Machine, the Valkyrie, Moon Knight, Ant Man and Nova (an eclectic group if ever there was one).

Brubaker packs more plot and action into this first issue of Secret Avengers than I imagine we'll see in the first five- or six-part Avengers "epic". He's just so good at mixing up the characterization moments with cool stuff actually happening, making him something of a throwback in the modern era of comic plotting. This is definitely the Avengers title that I want to follow now.

Does This Make Sense To Anyone Else?

I'm reviewing the actual unit tests completed by one of my high school students right now, in order to be able to make up Practice Sheets for the student that reflect what was previously tested as well as focus on whichever areas the student was weakest in. This is all in preparation for the final exam, late next month.

The first thing I noticed is just how full of errors the tests have been. Usually it's just poorly worded sentences in which you can fairly easily guess which word was left out or what wrong word was used. But the following question absolutely stumped me (as to its meaning) when I first read it over:

If f(x) = 3x - 4 and g(x) = 2(x - 1) + 3, find the value of x.

To my understanding of function notation, this makes no sense whatsoever. The values (plural) of x for each function, otherwise known as the function's domain, are whatever subset of the set of real numbers that you can legitimately substitute into each function wherever x appears. (In this case, the domain would be all real numbers.) Therefore asking what the value (singular) of x is seems ludicrous.

After thinking about it for a minute or two, I decided that they probably meant to ask "... find the value of x where f(x) = g(x)" but there's no indication of that in the question itself. I can see that a value of 5 for x would yield the same answer for the two functions: f(5) = 11 = g(5). But who knows if that's what was even meant, when the question is so ambiguously worded. (My student had no idea at all, and got 0 on this particular part of the test.)

I'm starting to wonder about the standards being applied to some of these courses.

Bugged By Bad Dreams? Play More Video Games!

Well, at least that's one possible way to interpret this report of a study into whether those who play video games are more likely to have lucid dreaming or even take control of their dreams (I've experienced both on many occasions in my life).

2010: The Year Of The Bonobo?

We know a lot about chimpanzees, including how closely related to us they are. According to this article by Research Scientist Vanessa Woods, this may be the year in which our other closest animal relative, the bonobo, finally gets some mainstream coverage.

Why haven't we heard more about bonobos before now if they're such close neighbours of ours on the evolutionary tree? As Ms. Woods explains, talking about a species that actually exhibits gay sex and uses sex in general to relieve stress just doesn't play into the ideologies of the day (especially in the U.S.). Here's hoping scientists like her can succeed in changing that in the coming days.

A Very Nice Improvement

I was looking over the test results of one of my students today, with the school year almost complete. Because this is an elementary school child, the marks from unit tests have by far the most weight, as contrasted with the high school experience in which final exams come into play. For this particular individual, who last year (before getting tutoring) was a solid B student in Math, I discovered that 12 different test results in the 2009/10 academic year yielded an average of 90%! In other words, a jump of about 15% has been realized in the span of a single year. That's the sort of thing that makes a Math tutor's day!

Worried That You're A Bad Parent?

Check out this story about a 2-year-old who smokes 40 cigarettes a day, and you'll almost certainly feel at least a little better about your own parenting missteps!

Want To Lose Yourself In Lost?

Re-watching the entire series on DVD is one way to immerse yourself in all things Lost. (Season 6 is due out in August). Another option involves reading up on the mysteries of the show, both resolved and otherwise. Lostpedia has a great site for that, which I've just begun to explore, thanks to Tammy and Vicki.

A Comic Strip You Simply Must Read

Thanks to a friend on Twitter, I got directed to this terrific, graphically-illustrated tale which aptly summarizes the Immunization/Autism controversy that's raged for the last decade or more. I encourage all of my readers to check it out.

This Doc Has All The Answers

If you're a Lost fan and haven't read "Doc" Jensen's two-part write-up of "The End" (Lost's two and a half hour series finale), then you're just plain nutty.

Part One is here and Part Two is here. I've read a lot of reviews and reactions to "The End" in the nearly 48 hours since it aired, and Jensen's is easily the best. That guy's a fan's fan, through and through, and also incredibly insightful. I just hope he turns his watchful eye onto Fringe next, because I like that show a whole bunch but mostly because I know that I'd miss Doc's humour, intelligence and attention to detail if he simply disappeared from my life.

No Jury Duty For Me!

Unlike Liz Lemon, I didn't resort to dressing up as a famous Star Wars character in order to get out of jury duty when I headed downtown this morning. Fortunately, though, my number was not called, despite the court system going through a lot of the 120+ candidates who were nervously gathered with me.

I imagine I'll get another summons before too long, but for now: I'm dismissed!

Some Folks Just Have No Patience

Our new pool liner is still at least a couple days away, but that didn't stop these two chipmunks (and another friend of theirs, not shown in the photo) from checking out the premises. You may want to click/enlarge the picture to get a better look (or not).

There was just enough water in the bottom of the deep end to allow one of them to go for a dip at one point. We managed to get them back out of there through a combination of Vicki's nylon ladder trick and me lifting the final intruder up, up and away with a tennis racket.

Lost: The Mo(u)rning After

When I go to bed and my head is still processing the day's events, it's usually not a good night for sleeping. Last night was an absolutely lousy night for sleeping.

During the few hours in which I managed to get any sleep at all, I naturally dreamed about Lost. In one of them, I was sitting at a table with two or three other people (I don't remember who) and started weeping at the thought of SPOILER ALERT! what happened to Jack in the finale. Then I woke up to discover that, sure enough, there were tears running down my cheeks and onto my pillow! That's the kind of night I had.

One of the most interesting aspects of the wrap up, for me, was learning the meaning of the so-called Sideways world. Once it became clear what it was, it immediately reminded me of the sleight of hand that the creative team pulled on us at the end of Season 3. There, it was the "flashback" with Jack that turned out to be a flashforward, revealing that at least some of the castaways actually do get off the island. Here it was a twist that relied upon us buying into Daniel Faraday's crazy notion of blowing up an atomic bomb over the island's electromagnetic "hot spot" in the hopes of rebooting reality from 1977 forward. This assumption was further amplified in Season 6 when Desmond seemed to connect with his Sideways counterpart, although now we know that that particular juxtapositioning was either a red herring or a reflection of Mr Hume's unique ability to perceive time differently (my memory's on the former). Probably the revelation of that world's true meaning has left some fans even more disenchanted with its existence, but for me it actually gave those Season 6 vignettes greater poignancy, not less. The Sideways glimpses provided a denouement to those characters' stories in a way that spoiled nothing while still moving them forward, in a fashion.

I'm sure the hating on the finale is already is full voice by now (12 hours after it concluded), but Vicki and I absolutely loved it... from start to finish. It provided both a realistic ending, in which some lived and some died, and a more emotionally satisfying conclusion in which long-lost lovers were reunited and the promise of something "new" for them was dangled, albeit only for our imagination to enjoy. I can't think of any way the creators could have finished the six year run that would've left me more appreciative of all they accomplished. As I told Tammy over Instant Messenger last night, Lost has probably bumped Babylon 5 out of my Favourite Show of All Time spot. I'll be mourning its passage for a long time to come, I suspect.

Tonight It All Ends

It was almost six years ago now that Vicki and I sat down to watch, with some skepticism, the premiere of a new drama that TV Guide, in their Fall Preview issue, had given a very strong recommendation to. They'd managed to make somewhat intriguing what had initially sounded like a cross between Survivor (a complete waste of time which I've never had any interest in, then or now) and Gilligan's Island (something I'd long since outgrown). If I remember correctly, they predicted that viewers would be truly shocked by what they saw. And they weren't wrong. Lost's pilot episode (all 2 hours of it) blew Vicki and I away.

By the time Walkabout aired, a week or two later, I was officially hooked. The characters who crashed on the island certainly weren't proving to be the one-dimensional caricatures that inhabited other prime time dramas, as each subsequent flashback in Season One provided new insight into Jack Shepherd, Kate Austin, John Locke and the rest. This attention to character-building was something fairly new, at least within the realm of TV science fiction.

Tonight, we get the final installment of the journey that is Lost. There have been numerous and undeniable clues all season long that this isn't going to be the sort of wrap-up that many of us had expected and even hoped for; we weren't going to get closure on dozens of mini-mysteries that had been launched throughout the show's six years. I've read many articles and posts lately that seem to celebrate that fact, but I'm still sitting in the section of the arena that believes at least some of that is simply bad planning, execution or writing. Maybe I'm wrong; maybe Lindeloff and Cuse, the show-runners of Lost, always intended it to be this way. But at times it strikes me as a little like a murder mystery in which the writer loses interest in who the killer is after setting up a delightful locked-room crime.

Regardless, we'll get what we get. For all the thrills, twists and turns, and wonderful character development, not to mention the many hours of thinking, talking and writing about the show that ensued since the pilot aired, it's been time well spent following this little island adventure. I hope there's a big finish that encourages us to re-watch earlier seasons through a new lens of understanding; but that may or may not be delivered tonight. In just a few short hours it'll all be over, and every generation of fans who discover the show from now on will have a very different experience of it than we, the "live viewers," ever did. In that sense, while one era ends tonight, another one is just about to begin. And that's pretty awesome to consider.

How Much Do You Think This Is Worth?

This page of original artwork, Frank Miller's cover to Daredevil # 188 from 1982, recently sold for over $100,000 at auction. Now, it is a gorgeous image, and Miller's name has achieved elevated status among the general population thanks to the Sin City and 300 films, but still...! That's a lot of cash for a not-quite-30 year old piece of art!

You can read a few more details about this monster of a sale here.

I've said it before: if original comic book artwork starts to really take off in value, I may just have to part with some of mine. It's awfully nice having it framed and up on our walls for us to enjoy, but if any of the stuff I own becomes worth as much as a new car, I may just have to find it a new home!

New Title, Same Old Crap

I really wanted to believe that the relaunch of Avengers this week was going to be worth reading, but unfortunately it's just a fresh coat of paint on the same wreck of a car. In this version, like the last one, the heroes mostly stand around trading quips, all sounding like they're the same person (which I assume is writer Brian Michael Bendis). Something that should've occupied about 3 to 5 pages is instead the entirety of this product. Also not working in its favour is the fact that it's a $3.99 title despite having no more story pages than a $2.99 comic, padded out with text pages that aren't of the least interest to me.

It's painful to see how far my once-favourite team-title has fallen, but that seems to be par for the course with Disney Comics anymore.

OK, That's Pretty Cool!

Colour me impressed (in green or red!).

Here's a cover from my childhood... one of my faves, in fact:


This amazing image ushered in the Dennis O'Neil/Neal Adams/Dick Giordano era of Green Lantern/Green Arrow, which featured a focus on relevant topics of the day (overpopulation, racism, drug abuse, etc). That GL/GA run, which lasted about a dozen issues, is one of the high water marks of comic books in the early 1970s.

Yesterday, DC Comics teased us with a strangely familiar and yet not-quite-right image:



Many of us in the comic blogosphere wondered just what this could possibly mean. On the one hand, it could be tied to the recently-completed Blackest Night series, which did in fact feature some Red Lanterns in it (though not Hal Jordan as one, as shown in that preceding cover). On the other hand, Green Arrow's former sidekick, Roy Harper, has been appearing as a sort of "Red Arrow" of late (actually codenamed "Arsenal"), but of course that's clearly Oliver "Green Arrow" Queen in that cover shot, not his beardless protege.

So WTF?

Well, today, word arrived on just what the deal is, and it's a good one: tonight's episode of Fringe, dealing with an alternate universe, will somehow feature that very-crimson variant on the famous Green Lantern/Green Arrow # 76 cover, showcasing at least one crucial difference between that other Earth and ours! How awesome is that? Pretty darn, I think.

Oh, and by the way: that 40-year-old Adams drawing kicks the tar out of the new version, showing just how far ahead of his time old Neal really was!

[Update May 21/10: Here's a link to the rest of the alterniverse DC covers shown on last night's Fringe. Nice side-by-side display here.]

Is It Time For A Last Lost Lust List?

OK, so maybe the "lust" in this case is simply my deep desire for answers. But I'm really starting to worry about which answers we will and won't be receiving as Lost finishes up in a 2.5 hour spectacular on Sunday night. I'm OK with the fact that many of the smaller unresolved puzzles won't be dealt with, but there are still a fair number of large-ish ones hanging in the breeze.

Here's an example: Who was in Jacob's cabin when it was visited by Benry and Locke (Season... 4, maybe?)? It seemed like whoever was in there could be seen, at least partially, by Locke (as a dim figure sitting in a chair), and was heard - again, by John Locke but not Benry - to plead, "Help me!" It makes no sense that it would be Jacob, since we know he had the run of the island, and why would he act so directly, anyway? It could have been Man in Black (messing with Locke's head), if we accept that he wasn't really trapped in there. He couldn't have been trapped, after all, as we've seen the Smoke Monster roaming free and wreaking havoc all throughout the show's run (all the way back to the pilot episode, for crying out loud!). But if he wasn't a prisoner of the cabin, then what was the deal with the ash perimeter that was up around it, and why had it been partly erased when Jacob's acolytes arrived there in Season 6? At the time of each of these various incidents, we were led to believe they were significant... was that just subterfuge, or bad writing/planning? I'd hate to think that something like that is going to be left unanswered, but I'm beginning to lean heavily toward just that outcome. And there are dozens more just like it.

As I get ready for Sunday's finale, I keep thinking that there's a great risk at this point that Lost is going to be remembered for promising more than it delivered. Not on the order of magnitude of, say, Twin Peaks... but maybe more like an X-Files or an Alias. I hope that doesn't prove to be the case, as in most other regards Lost has been a vastly superior product to either of those earlier shows. But it is somewhat depressing to think of all the acres of soil we tilled over 6 years only to have most of it bear little or no fruit.

[Just as an aside: Has it seemed strange to anyone else that the Sideways world and the Island world seem to be converging and yet are separated in time by 3 years? Happy Jack and nice Benjamin Linus are still back in 2004, shortly after the Oceanic 815 flight, whereas their Island-world counterparts are operating in 2007. I can't help but think - hope? - that there's some significance to this. Vicki posited an interesting theory last night as we watched "What They Died For": what if someone, possibly Eloise, created the Sideways reality as a place to hide the "source" that's supposed to be at the center of the island? That would explain the other world's existence and why we've been shown it all season long, as well as the generally well-off nature of the people there (it's full of light!). It would also imply that Island Jack (the new Jacob) and Fake Locke are headed to a confrontation over something that isn't even there anymore... which would be a Hell of a twist, no? Still not sure how Desmond would fit into that, as he obviously now has enlightenment toward what's really going on... so is he going to merge the various dopplegangers together in the sunny Sideways world, or what?]

Leading The Green Energy Revolution: Texas?!

This kind of story gives me hope: Texas is actually one of the major producers and consumers of wind and solar energy among the 50 states. It's not exactly what we'd expect to hear out of the Longhorn State, given its long love affair with oil and gas, but it's good news, nonetheless. The article is a good read that I predict may surprise you.

Make Your Own Superhero

The Periodic Table of Superpowers is a lot of fun! It also brings back lots of memories - good and bad - of working with the less-jovial version that has something or other to do with elements...

So Much For Privacy

A Twitter friend linked to this CBS News report about digital photocopying machines and the way they store their document images on a hard drive... seemingly forever! They've apparently become goldmines for criminals who can buy used copiers and then experience Christmas morning (for crooks) as they get to quickly and easily "unwrap" their new gifts and discover just what treasures are waiting for them on each discarded drive. Examples from the report included health records, police reports, payroll information, and more.

I was a bit frustrated that no one asked the manufacturers: why is retention of the data a standard feature? What's the value in having digital copies kept, such that a $500 security feature is considered an "add-on" in order to clear the info after it's been scanned, printed or faxed? Why isn't that the default behaviour, maybe with a built-in delay of some short period of time? Given how litigious Americans are, this sounds like a lawsuit (against the copier companies) waiting to happen.

Fire First, Then Re-Hire Later

This story just gets weirder and weirder!

I mentioned, back in March, that a Rhode Island high school in which students had historically done very poorly in standardized testing had seen its entire teaching and administrative staff fired in an effort to improve things there. Now it turns out that all of those fired are being re-hired, following some negotiated changes to the teaching format there!

I've heard that some teachers' unions are traditionally difficult to get concessions out of, but I really hope this sort of approach doesn't become the new norm in such situations.

Come On Over For A Swim?

If you're planning to drop by anytime soon for a refreshing dip, I'm afraid we can't offer much in the way of scenery... or even water, for that matter. Here's the eye sore that's currently occupying the area where our pool used to be. Hopefully within a couple of weeks it will have been magically transformed into something beautiful.

Almost Enough To Cheer Me Up

Beautiful, full-colour Neal Adams artwork on Batman: Odyssey!! Sweet.

Pool Ownership Sometimes Sucks

Tammy was kind enough to assist us in getting the winter cover off the pool this morning, which was extremely helpful. Unfortunately, the operation itself was pretty much a disaster - not Tammy's fault in the least - as the cover appeared to be letting a whole lot of water through in both directions. This meant that we couldn't get the last billion litres (or so it seemed) of water off the cover but were instead lowering the water level beneath it by trying. Eventually we had no choice but to cut some holes in it, letting the oily-black water flow into the pool before it was light enough to be lifted off. We we were pretty sure this 2009-edition winter cover was somewhat permeable after last year's adventure, but it seemed even worse this time around (I think some of the dirty water on top had flowed through it even before today, as the pool water was disgusting under there). When we had to resort to desperate measures to get the cover off without draining the entire pool, we'd already invested a couple hours into the effort (all for naught, as the dirt spread through the pool).

At that point we also discovered that the liner was pulling away from the coping in a significant way, meaning that we'd never be able to get away with opening it anyway. So now Vicki's been calling around to get quotes on a replacement liner, which is going to be a $3000 expense that wasn't planned for 2010. Good thing I've got a great job to cover such -- oh wait, scratch that. Good thing we save lots of money for things like this... but still. I'm not a happy man right now.

How Classy People "Handle The Scandal"

You may or may not have heard about the big bruhaha involving Neil Gaiman this week, but I can almost guarantee that you'll be impressed by how he handled it (all of the details can be found there, including links to various pieces of it if you want more context than Neil provides). When the story first broke, I have to admit that I had the expected reaction: "He charged $45,000 for a library appearance that lasted part of a day?!" It just didn't match my opinion of how Neil operates, considering that he's a big supporter of libraries and is the last person I'd expect to gouge one for a fee (Sarah Palin, on the other hand...)

Of course, once I heard the full story (details at the aforementioned link), the planets resumed their normal orbits and all was right in the universe again. But that hasn't stopped others from misusing the facts in this story for their own political agendas.

Success Is In The Eye Of The Beholder

It's interesting to me how some of the companies that my former coworkers are applying to or even having interviews with are in various stages of adopting/trying out Agile. I've been contacted by a few people this week who are therefore experiencing a renewed interest in the topic, which is understandable considering how much of the previous enthusiasm was killed by that office's corporate ownership.

I've been ruminating lately on the question of, how successful was our Agile adoption? No one would be foolish enough to brand it as highly successful, I imagine, since it was ultimately reversed to a large degree. But when I measure it in terms of the changes that were accomplished, especially in the areas of empowerment, adaptability, automated tests, code reviews and test coverage, I have to think we made some pretty impressive progress. And it's those achievements, more than anything else, that my ex-colleagues now forced to seek employment elsewhere may be able to bring with them into a new organization. Even just as concrete proof that those practices really are possible and not just theoretical goals that never materialize, they're very valuable, I think.

It should be an interesting next couple of months.

The Real Smoke Monster

This BP oil disaster will likely end more lives than the nasty ol' Smoke Monster on Lost ever could (unless Fake Locke really does destroy all of reality, that is).

At Least It Was Only Four Issues Of Crap

Disney Comics' latest "event", called Siege, wrapped up today. It was a 4-issue miniseries that had lots of spin-offs and one-shots to accompany it, none of which (thankfully) I was foolish enough to purchase or read. I decided to take a flyer on Siege itself, but even that was $15.96 more than I really should have wasted on this story.

The intent of Siege, I believe, was to transition in a dramatic fashion away from the cynical stories of the past several years (Civil War, Secret Invasion and Dark Reign) and into what Disney is touting as "The Heroic Age." That's all well and good.

Unfortunately, what they accomplished was a ridiculous story involving the destruction of Asgard (home of Thor and the Norse gods) as well as one of their Superman-analogues, the Sentry, going nuts and having to be put down (thrown into the sun, in this case... which I personally had no idea Thor was anywhere nearly capable of doing, but I guess that just shows how dumb I am!) Along the way, Thor's evil half-brother, Loki, was shown to be repentant for his part in the proceedings and shocked - yes, shocked! - that Earth's superhero community had such unbridled power as the evil persona of the Sentry demonstrated.

OK, let's think about that last plot point for just a few seconds (meaning, a few seconds longer than writer Brian Bendis apparently did): Loki's been around for centuries or more, and has interacted with the Disney (nee Marvel) Universe for the last several decades. Over that span, he's seen various members of that super-fraternity defeat Galactus, the Planet Eater, at least a dozen times; he's watched them repel alien invasions, overcome enemies who can alter reality with a mere thought... and yet he "could not see that this monster was so all-powerful" (yes, that's an actual quote). Yup, he thought they were a bunch of pikers who, when pushed, couldn't possibly be capable of doing something truly destructive. Sigh.

And then, to top it off, when the Sentry's disposed of, all of the heroes who were at each others' throats through Civil War, Secret Invasion and Dark Reign, get together for a party at Avengers Tower and decide to be buddy-buddy again. Yeah, that's some fine character development, that is!

Anyway, I can take solace in the fact that I didn't invest more than my $15.96 into this. I'm sure others got soaked for a whole lot more.

Why Can't The Jays Beat The Bosox?

I know it's still early, but this is ridiculous! Check out the following win-loss records for the Toronto Blue Jays and Boston Red Sox so far in 2010:

Toronto vs Boston: 0-5
Toronto vs rest of MLB: 19-11

Boston vs Toronto: 5-0
Boston vs rest of MLB: 13-16

There's something horribly wrong with results that out of whack!

[Update later that same day: Just to spite me, the Jays won the series finale this afternoon, 3-2.]

Counting Down On Lost

Going into tonight's episode, there are 4.5 hours of Lost left to be broadcast. However, that figure is somewhat misleading because it counts commercial time, which is useless at best and distracting at worst. Since a typical one-hour show on network TV actually contains about 42 minutes of true programming content, what we really have is 42 x 4.5 or 189 minutes of Lost left. Let's be generous to ourselves and round that up to 190 minutes. That's still not very much time in which to resolve or otherwise put to rest a whole lot of unanswered questions. How many? Well, I wouldn't pretend to be able to list a complete set, but here are just a few of the ones rolling around in my head (in no particular order, as should become amazingly obvious as you read it over):

• What is the "Sideways" (alternate) world that we began to see vignettes of in Season 6?
• Was the Man in Black (MIB) playing the part of every dead person shown on Lost (except for the ones Hurley sees), including those like Christian Shepherd who appeared off of the island?
• If MIB was all those dead people, what was his motivation in appearing as each and how does he know what they knew (in order to impersonate them)?
• Who was in Jacob's cabin all those years (as viewed by Locke and Hurley), how did he get trapped there, and if it was MIB then how was he able to wreak havoc as the black smoke at the same time?
• What are Charles Widmore's true intentions, and why (if he's good) does he seem to do so many evil things (including sending a mercenary death squad to the island)?
• If Benry thought he was following Jacob all the time that he was with the Others, and Widmore is fighting the MIB (Jacob's arch nemesis), then why are Benry and Widmore enemies?
• Did the Dharma Initiative/Hanso people just stumble upon the island by accident, or did Jacob "bring" them there, and if so, for what purpose?
• If the people on the island are so important (candidates), then why did Jacob allow something as potentially dangerous as "the incident" to happen in the first place, such that someone had to push a button every 108 minutes to avoid catastrophe?
• Was Desmond "special" before he was exposed to the effects of the whiteout event (end of Season 2), and if not, then why did Widmore (or whoever) arrange for him to receive Libby's boat in order to get him to the island (had someone seen the future?)?
• Was "the list" that was mentioned by the Others way back in Season 2 supplied by Jacob, taken off the cave wall, or something else?
• Why was Kate's name crossed off the cave wall?
  
• If Anthony Cooper (Locke's dad) is "good" in the Sideways world (i.e. not a con man), then who swindled Sawyer's mother back when he was a child, resulting in both of his parents' deaths?
• What the heck was Sideways Desmond doing running over Locke with his car?
  
• How did the Others know to build a runway in 2004 that would be needed in 2007 for the Ajira flight?
• What brought Saiyid back to life in the temple after the Healing Pool failed?
• In the island version of history, what happened in 1977 when Juliet banged on the bomb at the bottom of the hole? If it went off (sending the castaways forward into 2007), why weren't the people at the site killed (including Dr Chang, who went on to make Dharma videos afterward, with a prosthetic arm replacing the one he lost at the site)?
• Where the heck have Benry, Richard and Miles been for the last few episodes? And isn't Desmond getting pretty hungry and thirsty down in that well all this time?
• If Jacob can appear to Hurley, why isn't he helping more? Is that against the rules, or is he really just so laid back that he'd let everything go to Hell rather than interfere?
• If MIB gets his wish (all candidates dead), does he really get off the island, or does reality end, or what?
• If MIB believes that mankind simply corrupts (as he told Jacob), then what does Jacob believe? For hundreds of years, it seems like neither of them was capable of proving their point-of-view on the island, so why is now any different?
• Who built the giant 4-toed statue on the island?
• Is the island really "alive"/"sentient", or has everything that's been attributed to the island since the first episode really been the work of Jacob or MIB?
• Who constructed the "frozen donkey wheel" (turned by Locke, and then Benry), and for what purpose?
• Who's the boy (or boys) seen haunting MIB twice so far this season?
• Was the lighthouse mirror array (destroyed by Jack this season) really looking into the past, or the present, or into the Sideways world? What was its purpose?
• What's the real story with Eloise Hawking, and why does she always seem to exist outside of time and space somehow (as seen when Desmond was time traveling and she knew that fact, or in the Sideways world where she appeared to realize that that reality was manufactured for a specific purpose)?
• What happened to Christian Shepherd's body, both on the island (where it disappeared from its coffin) and in the Sideways reality (where body and coffin disappeared or were lost by Oceanic)?
• What happened to the Dharma Initiative back in Ann Arbor, Michigan, such that they never sent anyone to the island after Benry and the Others wiped out the island group? What have they been up to in the years since then?
• Was the psychic who warned Claire about letting her baby be raised by the wrong people (suggesting it would be calamitous if it happened) just running a scam on her, and if so, why was he so freaked out when he saw her later?
• Why did Walt have special, seemingly supernatural abilities (not including the ability to keep the actor playing him from aging, unfortunately)? Was that just a coincidence, or was he supposed to go to the island in order to play some important role?
• Why did all the women (after 1977, anyway) always die in their second trimester if they got pregnant on the island?
• What grand plan did Benry really think he was helping to orchestrate if he'd never actually had any contact with Jacob, and Richard Alpert wasn't even aware of Jacob's end game?
• Why did Locke become so super-competent (hunter, tracker, master planner, etc) once he got to the island? He seemed to be a mess before that (according to the flashbacks).
• What was the significance of the numbers (4, 8, 15, 16, 23, 42)? Why did they "curse" Hurley when he used them to win the lottery? What do they mean?
• Who were the pair of skeletons found in the cave early in Season 1?
• Why did Juliet think "It worked" when she died (as reported by Miles shortly thereafter)?

OK, I could actually go on and on and on, but we all know that many of these mysteries are unlikely to be dealt with in the short time left. There are probably already websites devoted to capturing every puzzle from the show, and presumably new ones have been added just in the last couple of weeks. As Vicki says, maybe the show's creators will eventually realize they have to make a theatrical release or two just to put some of the head-scratchers to bed. We can only hope.

Re-Discovering Trig

One of my students started the Trigonometry portion of Grade 11 Functions recently, necessitating my re-acquainting myself with that slice of the Mathematics spectrum. Thanks to Tammy's experiences in high school, I already remembered SOHCAHTOA and its usefulness with right-angled triangles. However, I quickly found that I needed to look up both the Sine Law and Cosine Law, as neither of them were in the easily-accessed part of my memory banks from my own school days.

Those two laws each open up what you can do with triangular shapes quite significantly. First of all, you get to use them on any 3-sided shapes, not just the right-angled ones. Also, you can fairly quickly become familiar with what pieces of data lead you to use which law, as well as recognizing when you simply don't have enough information to proceed.

My student has been doing very well in this unit so far in the exercises he's done with me, which hasn't always been the case with previous topics. It's interesting to see how different topics in Math resonate differently with each student. For people who relate to diagrams or pictures better than words, Trig can be quite a welcome relief. It's also a good combination of memorization (of a few theories and laws) and application (figuring out which formulas to use in each new situation).

I'm quite enjoying it so far and look forward to working through Trig with other students, now that I'm (back) up to speed on it (again).

Busy Weekend

So I did 3 things in the past 24 hours that aren't exactly typical for me on the weekend:

1. Went to a play (Strangers on a Train) last night; it was good but didn't feel as tightly written as the classic Hitchcock film version from the 1950s
2. Did some Math tutoring this morning for a student who had to cancel his regular session earlier in the week
3. Went out to a movie (Iron Man 2); I liked it but wouldn't put it at quite the same level as its predecessor (a little too much "Oh, we're doing that again, are we?" for my liking)

It feels like the weekend just flew by, but that's always easier to take when your work week is only about 8 hours long.

The Lost Wrap Up

In my Internet travels tonight, I happened upon the titles of the remaining episodes of Lost. I don't think they're overly spoilerish in and of themselves, but just to be safe, I'll put them under whiteout and you can decide for yourself whether or not you want to know them ahead of time:

Episode 15 (Tue, May 11): Across the Sea

Episode 16 (Tue, May 18): What They Died For

Episode 17 (Sun, May 23, 2.5 hr): The End

I don't think most of us have sufficiently prepared ourselves for the void that's going to form once we've seen the finale on May 23rd. It's going to be great to re-watch the entire show once we know what it all means, but it'll never be the same as having new episodes to look forward to. Hard to believe anything will ever top this experience, but I'd love to be proven wrong on that front... eventually.

One Of The Great Pleasures Of Comics

Just like with other forms of entertainment, comics are sometimes best evaluated when you revisit them years after they originally appeared. As I've mentioned here before, I've probably read Watchmen, by Alan Moore and Dave Gibbons, something close to a dozen times in the 25 years since it debuted. When you can have that kind of experience, you feel confident in saying that a work is something special.

Today I decided to re-read the Kurt Busiek and George Perez JLA/Avengers crossover from 2003. I was inspired to do so by a page of original artwork from the series that Vicki and I recently had framed. I'm about 1/4 of the way through the story so far and it's every bit as thrilling as it was the first time I read it. I'm enjoying the oversized edition that I bought a couple years ago, which I recommend to anyone who's as much a fan of the two superteams as I am.

One of the things I've always loved about this hobby is the fact that I can often get just as much pleasure out of a comic (or series of comics) on a re-read, years after the initial encounter. It's the gift that keeps on giving!

Put Away Those Brooms

Much to Boneman's dismay, the first 2 rounds of the 2009/10 NHL Playoffs will feature no sweeps. The last time all 12 series in the Conference Quarters and Semis went at least 5 games was 2001/02 (not all that long ago), and it's certainly a lot more common to see at least some lopsided results across that many matchups. Not this year, though.

Detroit and Philadelphia, the only 2 teams to head into a Game 4 in 2010 down 3-0 (so far), avoided the brooms in diametrically-opposed ways: Detroit took a 5-0 1st period lead over San Jose last night and eventually won 7-1, whereas the Flyers needed overtime tonight to avoid elimination at the Bruins' hands.

It figures that the Rangers would miss a playoff year where no one got swept... although I suppose if they'd made it in this year, then that particular statistic might not have held up anyway!

Science Versus The Agenda

While its eventual effectiveness is questionable at this time, I really applaud this open letter created and signed by over 200 members of the U.S. National Academy of Scientists recently. I think it strikes exactly the right note in response to the so-called ClimateGate "scandal" and its continuing fallout. The current persecution of climate scientists is sadly reminiscent of attacks in earlier centuries whenever a new discovery clashed with either long held religious beliefs, vested interests or simply popular opinions.

There's such an essential difference between followers of Science and those who always choose to believe what they want to believe: while an individual scientist might, in some circumstances, be resistant to the truth because of issues of pride or reputation, the community that he or she exists within is generally wired to accept new data with open arms in search of the truth. On the other side of the fence are people who band together to push their own agenda, utterly united in their desire to discredit or even cover up anything that threatens to overturn their point of view. How any intelligent member of our species could ever choose the latter perspective over the former confounds me, and yet it clearly continues to be a popular choice, even as we move through the 21st century.

A Tale Of Two Summers

I think I've mentioned before now that I quite like comics, yes? And perhaps I might have dropped a hint from time to time that I've got a reasonably good memory for trivia, as well, right?

Well, back when I was just barely out of my teens, Uncanny X-Men by Chris Claremont, John Byrne and Terry Austin was one of my favourite comics. It seemed to be the pinnacle of comic greatness back then, and maybe it even was. I just know that my tastes have changed over the ensuing decades, and now I find that material overwritten and crudely drawn. I suppose that's to be expected, as so many highly-regarded childhood artifacts fail to hold up when scrutinized from the vantage point of time. That's just one of the many sad realities that goes hand in hand with growing up and getting older.

But that lowered opinion of those old X-Men comics still didn't stop me from getting a big chuckle out of one of the two covers for this week's Buffy the Vampire Slayer # 35, for a reason that should be fairly obvious by now: Yes, it's an homage to Uncanny X-Men # 138's cover, shown above. Interestingly, both of the big figures on the right side of the cover are named Summers: Scott "Cyclops" Summers and Buffy "Vampire Slayer" Summers! I wonder if they planned it that way? (Vicki had the nerve to ask me, "How did you know it was an homage? Did you read it on the Internet?" Please. I immediately spotted it for what it was, sitting on the shelf in the comic store on Wednesday! Mind for trivia, remember?)

Fun stuff like this is sometimes all that's holding my interest in the comics field anymore...

Math Blind Spots

As a Math tutor, you'd expect that I'd be pretty good at Math. And, in fact, in primary and secondary school, I was. I routinely sported Math marks in the 90+% stratosphere, sometimes finishing first in my grade and pretty much always in the Top 3.

When I got to university, however, I discovered Math of a tougher sort. My first year Calculus mark at the University of Waterloo, for example, was a very humbling 58%. (In Algebra there, at least I managed something like a 75%.) That Calculus result, more than anything before or since, convinced me that I was no Math genius. Compared to the general population of Canada, I'm quite good at Math... but once you narrow the sample set down to just those who can actually handle the post-secondary version of the subject, I'm probably average, at best.

With the virtue of hindsight all these years later, I can see where some of my struggles hailed from. I didn't study like I should have; I didn't form alliances with fellow students who might have been strong in the areas in which I was weak; and I wasn't humble enough. At 19 years of age, I entered university convinced that I was a top Math student (thanks to ridiculous Grade 13 marks) and it took me most of that first year to work that undeserved hubris out of my system. I like to think that, were I able to go back in time and take that Calculus course over again, I'd do at least somewhat better today. But I may once again be fooling myself.

Regardless, I've also come to another revelation on this subject: I, like virtually all of my tutoring students, have the odd "blind spot" when it comes to Math. Some kids just don't "get" fractions, for example. And so the operations of adding, subtracting, multiplying, dividing, and reducing or reformatting fractions typically involve the student guessing at strategies until they get the right answer. Others didn't learn how negative numbers work when the topic was introduced in or around Grade 7, and so their Algebra in the later grades always falls apart if they can't manipulate the terms sufficiently to eliminate any negatives.

In reading up on one of the Grade 12 Math courses, I realized that logarithms were and are one of my blind spots. Unlike most high school Mathematical concepts, log functions don't come to me naturally. In fact, when faced with a question involving log (or ln when dealing with base e) I have to stop and remind myself what a logarithmic function really is. Fortunately, I'm wired to react that way in such a situation, because I can usually then carry on with the problem once I've re-established my frame of reference. (For anyone who cares, the log of X base B is that number Y such that B raised to the power of Y is equal to X. Got that? In other words, log of 100 base 10 is 2, because 10 raised to the power of 2 is 100.)

For many students, though, they just completely hit a wall when they're not sure how something works. I've tried to teach a few of them mitigation strategies, like the following:

"Suppose you don't remember what to do when multiplying with exponents. You know there's some rule about what to do with the exponents if the bases are the same, but you can't remember if you're supposed to add them, multiply them, or what. So when you get to that point, do a simple example, where you can actually work out the numbers to see what the right answer is. For example, try 2 squared times 2 cubed. You know that 2 squared is 4, and that 2 cubed is 8, and you know that 4 x 8 is 32. So now all you have to do is figure out what power of 2 equals 32. Once you see that it's 2 to the power of 5, then you'll know to add the exponents when multiplying the bases."

The kids who have the potential to get good at Math usually embrace that kind of approach... eventually. Getting them there, though, can be half the battle. Which is one of the reasons I so liked that quote from the Freakonomics site yesterday: it speaks to the value of being willing to work through a tough problem, instead of just giving up on it when the answer isn't immediately obvious.

One Lost Question From Last Night

There was way too much in the fourth last installment of Lost Season Six last night to fully digest after just one viewing, but here's the question that nagged at me toward the end of it:

Was Jack right about Fake Locke (aka Man in Black) being unable to kill the candidates directly? Had faithless Sawyer not pulled the wires out, would the bomb have simply fizzled when the timer ran out, just as the Black Rock dynamite did when Richard tried to get Jack to kill him with it? Granted, that was a different scenario - "the island's not done with you yet" - but we've heard and seen a few instances where the Man in Black appears bound by rules of some sort that prohibit him from knocking off candidates. Therefore, was it Sawyer's actions that resulted in the death of so many regulars? And if that's the way things work on the Island, then how did the Man in Black know that Jack would find the C4 in his backpack before the timer ran out? If Jack doesn't find it, then Sawyer doesn't pull out the wires and the sub sails merrily on its way to freedom and salvation... right?

I hope this (admittedly small in the grand scheme of Lost) mystery gets resolved in the few remaining hours we have left. It does seem rather central to the conflict that's at the heart of Season Six, after all.

Great Advice For Parents

Reading this interesting Freakonomics article about "the science of genius", I really loved the concluding Q&A:

"Q: What does this new understanding of genetics and intelligence mean for parenting? What can parents do to help their kids achieve greatness?

A: In this limited space, let me just stick to one point, which is that parents need to model a life of delayed gratification and persistence if they want their kids to embrace those values themselves. Show your kids how hard you work, how often you experience disappointments and how you respond to those disappointments. If you blame others for your failures or simply give up, that’s what your kids will learn. If you take on a long-term challenge, show a deep commitment to the process and a refusal to give up in the face of adversity, your kids will pick that up instead."

I wish all parents could read this advice and take it to heart. I've run into some parents, while tutoring, who want quick fixes for their kids' lack of basic Math understanding, or who've taught their children the instant gratification game by living that way themselves. While some students are naturally good at Math, there's no solution quite as effective for the rest of them as simple hard work: do the homework exercises, ask questions about whatever you don't understand, and look for connections between the various bits of info that you're encountering. My tutoring students who are willing to put the effort in always improve their Math skills; the ones who don't usually continue to struggle.

Have You Been Very Good Lately?

If so, you can consider the following news your just reward: Lost finale to be expanded by 30 minutes! That's right, the finale will now actually be two and a half hours long (minus commercials, of course). As the remaining minutes of this great show continue to shrink away, it's fantastic to find out that there's going to be more 30 minutes more than we all expected.

There's next Tuesday's episode, another one the following Tuesday, and then the 2.5 hour finale on Sunday, May 23rd. After which we'll be discussing it for the rest of our natural lives.

Some Buttons Just Beg To Be Pushed

Tonight's episode of Lost really pushed a lot of buttons, including a brief reference to the second season version of precisely that! I had to think that semi-conscious Locke's "must push the button" delirium was inserted to remind us of the confusion and back-and-forth debate that developed in Season Two around that every-108-minute duty: should they or shouldn't they? In tonight's episode, that was echoed by the scene with the C4 countdown (to pull the wires or not to pull them), but also at a higher level: which reality (Island or mainland version) should we really care about? It's been assumed by most of us all season long that it's the Island universe that matters, but now that the grim reaper is riding roughshod through it we have to wonder if maybe we've emotionally backed the wrong horse. Is the so-called "sideways world" the one where our favourite characters are going to live happily after?

Great episodes are the ones that really make you think... and tonight's "The Candidate" will likely be discussed and dissected for a long time to come!

Death To Typos! (And Typo'd Almost To Death!)

The quality of the resumes I've seen in the past couple of days has been better than was previously the case, so that's something. But when I was seeing typos in the ones being passed to me, I really wondered how anyone could ever proofread something of their own quite that badly.

Then I read the 7 Most Disastrous Typos of All Time and realized: 'twas ever thus!

Halo: Reach Multiplayer Beta Arrives (Sort Of)

Monday May 3rd has been marked on many XBox 360 owners' calendars for months now. Today is the day that the Halo: Reach multiplayer public beta begins, open to anyone who owns a copy of Halo: ODST. I'm not among the super-fanatic followers of the Halo franchise, but I've certainly gotten my fair share of enjoyment out of several of the games (ODST, I must say, was underwhelming). Because of that, I'm busy downloading the beta onto my machine right now.

In the video promoting this beta, the Microsoft representative talks about how important this step is to them, as they'll analyze the stats generated by our online play in order to fine tune the game before it ships for real. I hope that's more than just spin, as that sort of thing can make the difference between an OK game and one that's absolutely addictive. We'll see how close Halo: Reach comes to the current benchmark of such matters, which has to be Call of Duty: Modern Warfare 2.

Download's now complete, but my first attempt at playing has resulted in a never-ending "Loading..." screen that says "Playlist data pending download..." Not off to a great start so far, MS!

Canadians' Debt Load Increasing Through Recession?

This afternoon I was reading a Maclean's article (admittedly from 3 months ago) that described how Canada is virtually the only country in the world whose citizens added on more debt over the last two recessionary years. This increase came in the form of higher mortgage principals and larger balances being carried on credit cards and lines of credit. I always like to believe that most Canadians are - like me - fairly conservative when it comes to finances compared to our Wild West neighbours to the south, but this article highlighted how that's just not proving to be true at the moment.

Now, I can think of a few mitigating circumstances that might explain some of those increases in forms more defensible than simple runaway spending. First, the renovation tax credits that were made available in 2009 no doubt provided a good incentive for some debt to be taken on toward improving many Canadians' home (a reasonable, strategic decision). Also, some may have been forced to either pile on line of credit expenses or take out a second mortgage on their home when faced with a job loss or reduced hours courtesy of the recession. And finally, budding entrepreneurs, many of them created by the current downturn, are no doubt taking on new debt in the hopes of realizing revenue from those loans over the long run.

However, I can't help but worry that there may be some of my countrymen and women out there who are simply continuing to live like there's no tomorrow, much as the Americans did right up to the collapse of their economy two years ago. As an incurable saver, I can't relate to that attitude at all; but it's starting to look like Vicki and I may be exceptions in that regard.

That Can't Be Right... Can It?

On TSN just now, they said that the Boston Bruins and Philadelphia Flyers are meeting in the playoffs for the first time since... 1978?! How could two Eastern Conference teams who make the postseason on such a regular basis possibly go more than three decades without encountering each other in the playoffs? That's pretty weird!

In the first year that I followed hockey - 1973/74 - my Rangers played in a thrilling 7-game Semi-Final series against the Flyers in which the home team won every game (unfortunately the Rangers only got 3 home games). Game 7 finished 4-3 for the Broadstreet Bullies and featured one of the most exciting final few minutes I've ever seen, with the visitors doing everything but tying the game up.

The victorious Flyers then went on to meet Boston in the Cup Final, and took home their first of two back-to-back championships (their only ones, to date). It's hard to believe those two teams had not matched up against each other since a mere 4 years after that memorable playoff season. And yet here we are.

Sometimes You Just Get Lucky

A friend and I headed downtown for Free Comic Book Day 2010 just a little while ago, and we saw a lineup outside the main comic book store that had to be 100 - 200 people strong. Gulp! Given that it was raining or threatening to rain on the drive downtown, we expected the worst. We then continued on to the store that I frequent, only to discover that it had almost no lineup at all! Just as we finished picking up our stuff - both free and otherwise - a fresh wave of comic-seekers arrived and we realized that we'd inadvertently timed it perfectly!

Just to show how connected everything is, the store owner asked about my former workplace shutting down, and it came out that he has a couple of friends there who I know well enough to have managed one of them and gamed with both of them (a big Hey! to Damian and Boomer).

It looks like this will be another successful Free Comic Book Day, if the turnout we saw at each of the downtown stores (and in the rain, yet) is any indication.