komplexify!

03.3.2010

Movie review: Next

The movie Next has been on TV a lot lately. To say it’s a bit repetitive might be an understatement. Here’s the movie summarized in psuedocode.

movie NEXT ()
{
  set audience-satisfaction = 0;
  set plot-points-resolved = 0;
  set creepy_factor = 0;

  do while (creepy_factor < 2) {
    for (i = 1 to 100) {
       show << the mall-escape sequence from
               the movie "Minority Report";
    }
    audience_satisfaction ++;
    plot_points_resolved ++;
    show << creepy scene with 40-something Nic Cage in bed
            with 20-something Jessica Biehl;
    creepy_factor ++;
  }

  show << previous movie events invalidated
          as an extended dream sequence;
  plot_points_resolved --;
  audience_satisfaction = 0;
  return 0;
}

Filed under: Math musings, Reel life —

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03.2.2010

Fundamental theorem, part II

After Calc III, student C pulled me aside.

“Dr K,” he said, “I think I finally figured out calculus. Check this out.”

C grabbed a piece of chalk.

“At first you think math is all about functions and curves. Functions are like ‘I can do anything I want.’”

He drew a plane curve meandering across the board, strutting its stuff.

“But then calculus comes along and gives the derivative, the velocity right? And the derivative’s all like: Dude, I control you. Once you pick a starting point, I force you to go where I want you to go.”

C drew several velocity vectors along the curve’s periphery, including one at the end, effectively forcing the curve on.

“See? This function is the derivative’s bitch.”

“…..” I said.

“But then the second derivative is all like ‘Velocity, I control you! I decide where you go! You’re my bitch!’”

C sketched some acceleration vectors along the curve as well, to illustrate the point.

“And it keeps going,” C said. “Each derivative makes the derivative that came before him his bitch.”

“That’s calculus,” C concluded.

Filed under: Math musings, School daze —

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03.1.2010

Fundamental theorem

After a lecture introducing the cross product of vectors in $\mathbb{R}^3$ , student R countered me thus: “Dr. K, I’m a little worried about this cross product stuff.”

“How so?” I asked.

“Well, check this out,” R said. He then proceeded to diagram the determinant expansion formula for the cross product:

$\mathbf{u} \times \mathbf{v} = \left| \begin{array}{ccc} \mathbf{i} & \mathbf{j} & \mathbf{k} \\ u_1 & u_2 & u_3 \\ v_1 & v_2 & v_3 \end{array} \right| = \left| \begin{array}{cc} u_2 & u_3 \\ v_2 & v_3 \end{array} \right| \mathbf{i} - \left| \begin{array}{cc} u_1 & u_3 \\ v_1 & v_3 \end{array} \right| \mathbf{j} + \left| \begin{array}{cc} u_1 & u_2 \\ v_1 & v_2 \end{array} \right| \mathbf{k}$ .

H continued: “When we work it out, we have to work out each of these little boxes of numbers–”

“2 x 2 determinants,” I offered helpfully.

“Right, each of these determinants by multiplying these two together and then subtracting these two multiplied together, like so.” He indicated each with a swooshing motion:

“Is it just me,” R said ,”or does that look just like a Jesus fish?”

“Er,” I said. The terms coincidence and conspiracy nut briefly flashed in my mind.

“And you get the cross product,” R continued, ” by computing three of these little things. And you said that any two perpendicular vectors can be crossed to get a third vector to form a ‘local frame of reference.’ So the cross product is one of three things that together form your frame of reference. Doesn’t that sound just like the Holy Trinity?”

“Huh,” I replied. I hadn’t really ever thought of that.

“And even the name of thing — the cross product? The symbol of Christianity?”

I was speechless.

“So,” R concluded, “isn’t all this vector stuff really just a plug for Christianity? And if so, shouldn’t I be excused from being forced to take calculus on First Amendment grounds?”

The next day in class, I pulled R aside.

“You raise an interesting point yesterday,” I admitted. “However, your fears are entirely unfounded. If you go on a little further in mathematics and take a course in Advanced Calculus, you’ll discover first that all the basic operations of calculus are justified using so-called $\epsilon$ - $\delta$ proofs, which are more or less arguments built up by comparing things to almost nothing. Go a little further, and you’ll even discover that all of the numbers we use in calculus are built from the empty set, which is quite literally nothing. Hence, calculus is really teaching you that one of the most effective ways to understand the world around you is to accept that it’s inherently based on nothingness.”

R considered this a moment.

“So,” I concluded, “I’m actually apparently plugging Buddhism instead.”

Filed under: Math musings, School daze —

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02.27.2010

Grammar

From a conversation between Ladybug and I about her crush on Alex, a boy from her preschool:

The Ladybug: Don’t. Tell. Anyone. It’s a un-prize.

Me: Do you mean a surprise?

The Ladybug: No. When you wait to tell everybody, that’s a surprise. When you don’t tell anybody, that’s a unprise.

I was particularly amused by this, and related the story to the Queen B

The Queen B: You know, you’re pretty good with vocabulary.

The Ladybug: Yes. Yes, I are.

Filed under: Ladybuggin' —

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02.20.2010

Newsletter: month forty-seven

Dear Ladybug,

This week you turned forty-seven months old. While you’re still a month away from becoming the Big Four, that doesn’t much seem to matter anymore, as this month you became a Big Sister, which to you is infinitely better.

You’ve been excited about being a big sister for some time now, which has been a little stressful at times since your mom and I were trying to keep the adoption relatively quiet. You are terribly excited about being able to hold her close to you. You can’t wait to hug her and kiss her. You are brimming with excitement about feeding her milk from a bottle. You are, however, entirely uninterested in changing her diapers, my claims to its importance notwithstanding.

As a result, you were positively thrilled when the first packet of information about your baby sister arrived in late January. You brushed past the pages of medical forms (pausing only to note that some of them were in Chinese, which you found oddly surprising) to see the three pictures of the Butterfly. “Oh!,” you squealed, “She’s cute!” Moments later you disappeared in your room, emerging seconds later with ladybug backpack crammed with shirts, socks, and snacks and announcing you were ready to go get her.

It’s going to be a loooooonnnnnnnng four-to-eight months.

Eventually we convinced you that (a) we wouldn’t need to pack for China for several months and (b) when we eventually did, you would be better served by packing pants and underwear rather than trail mix and craisins. Nevertheless, you remain excited about the prospect of finally, officially becoming a big sister.

It’s already become the new chronological benchmark for you, replacing your previous measure via units of annual age. To wit, nowadays you preface statements such as “When I am a big sister, then I can sit in the front seat,” or “When I am a big sister, I can chew gum,” or “When I am a big sister, I will rule the world with my minion, muwah ha ha haaa!” I may be exaggerating a little bit.

Of course, I’ve also been trying to explain the logical consequences of the “When I am a big sister” antecedent to you, namely, When you are a big sister, you will not longer be the only child in the family.” The concept of no longer being the daughter, as opposed to being a daughter, has troubled you of late. I suppose this is true of all first siblings, but I’ve been particularly impressed by the way you’re handling it: not with quiet grace and acceptance, but neither with tantrums and tears. Instead, as is often your way, you’ve approached this not as a problem, but as the starting point for negotiations:

You: So Dad, how about this?

Me: I’m listening.

You: How about I be your daughter, and the Butterfly by my little sister?

Me: Well, that is how it’s going to work. But the Butterfly will also be my daughter, too.

You: No, no, that’s not what I mean. I mean how about I be your daughter, and the Butterfly by my little sister, and that’s all.

Me: Well, if the Butterfly is your sister, then she has to be someone’s daughter, right.

You: Okay, okay. How ’bout I be your daughter, and the Butterfly be mommy’s daughter, and she be my little sister.

Me: But then you wouldn’t be mommy’s daughter anymore, right?

You: Oh, yeah… Maybe we could take turns.

Me: Sometimes your my daughter, and sometimes your mommy’s daughter?

You: Yes. I think that would work.

Me: But that means sometimes you won’t be my daughter, but the Butterfly will instead.

You: Oh, yeah… Okay, okay, here’s my final offer: I be your daughter and mommy’s daughter, and the Butterfly be’s my daughter.

Me: The Butterfly will be your daughter and your sister?

You: Yes. How about that?

Me: I think that’s illegal outside of Arkansas.

You: What?

Me: I’ll explain it to you later.

You: How about when I’m 6?*

Me: How about when you’re 16? In any case, the answer is still “No.”

You: You drive a hard bargain.

…And then you’ll go off to your room and furiously begin scribbling out master plans and complicated calculations in the attempt to find that perfect combination of attributes that will allow you be the an only child and, simultaneously, and older sister. I’m not exactly sure what progress you’ve made, since most of your calculations take the following form:

However, if volume of calculations is any indication of progress, I expect you’ll have a publishable result any day now.

* Unrelated to issues of the Butterfly, you’ve taken to asking questions that require explanations of increasing complexity or maturity to understand. When such questions arose, I would usually preface my response with “Well, that’s a little difficult to explain,” before launching into a (usually incomprehensible to you) answer. However, lately when I make such a proclamation, you’ve been responding with “Why don’t you tell me when I’m older,” and then specifying a particular age at which you’d like to be informed. For example, as noted above, you’ve requested to be informed of the inbreeding stereotypes of the Deep South when you’re six.

As a second example, the other night we were watching the kid-friendly time-traveling movie Meet the Robinsons. Near the end of the movie, the protagonist Lewis and the antagonist Goob fly through a disruption in the film’s time-line, and watch the effects of one potential future (a grim industrial one) change into another potential future (a retro-utopian one) through a cascade of bubbles. “Dad,” you asked, “what’s happening to the city?” “That’s a little hard to explain,” I replied, and mentally began the process of distilling the A- and B-theories of time at a level appropriate to a 3-year-old pretend princess. “Why don’t you tell me when I’m older. When I’m 5, I think.”

So there you go: my current docket for back-logged explanations

Temporal causality and paradox — age 5

Southern stereotypes — age 6

So, yes, you’re full of love this month. I guess that’s particularly timely, what with this month also including Valentine’s Day, which you celebrated by passing out (and thereby collecting) cards and candies at preschool. This year you opted to give out Phineas and Ferb valentine cards and heart-shaped lollipops, which was fine. You also wanted to give each valentine your own personal touch, which meant signing your name by yourself and affixing heart-shaped stickers on each card of various sizes indicating the relative degree to which you liked the person to whom the card would be given. The upshot of this is that it took me about ten seconds to properly label attach a lollipop to each of the 24 valentines we needed to make; it took you the better part of a hour to sign your name and stickerly bedazzle each one afterward.

I should have paid particular attention to the size of the heart you stuck on “Alex”’s card, because the day after Valentine’s Day you announced that Alex was your new boyfriend, and that you loved him. When I asked why Alex was your boyfriend, you replied “Because he said he loves me.” Then you danced up into the clouds on a sea of hearts and rainbows that unexpectedly burst forth from your head.

On the one hand, I was relieved to hear that bad-boy Jevon was out of the picture (literally, apparently — he was bad enough to be removed from daycare); on the other hand, I’m still not ready to deal with this particular brand of drama. As a result, I laid down the following edict:

Me: You’re not allowed to love any boys.

You: But Dad, I love you, and you’re a boy.

Me: Good point. Okay, you’re only allowed to love one boy.

You: Oh daddy, sometimes one boy is not enough. Sometimes you just have to love two boys.

Me: And why is that?

You: Oh, it’s a little hard to explain.

Okay, kiddo. Why don’t you explain it to me when I’m older, like when I’m 40.

In the mean time, I love you!

–Ba ba

PS. NO BOYFRIENDS!

Filed under: Newsletters —

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