Doodle #3 and Rotating Calipers

I got a sketchpad and am fooling around on it, practicing sketching motions and emotions. Motions are easy, emotions are hard. So far, this is my favorite from the motions sketches:



If you're looking for some mathy updates, perhaps you should consider reading Geoff's very technical blog. He recently put up an implementation of the Rotating Calipers algorithm for finding the minimum bounding rectangle around any polygon. (The algorithm finds the best rotated rectangle, not just the best right-side-up rectangle, which would have been too easy.) His tech blog is super dry like the stock market books that he reads in his leisure time, but he likes it that way. :) He says he just wants to dump information on the internet to facilitate other people who might come across the same issues, so reader-friendliness isn't one of his main concerns.

Anyway, if you read through his implementation, you'd see that there's a lot of vectors math in there. It's neat... He's a computer programmer who actually uses high-school math on a regular basis to solve problems!

Ah, winter break...

I miss drawing. I think this Christmas, I'm going to buy Geoff and myself some charcoal and drawing pad, so that we can be drawing hippies on Saturday mornings. I made this today because I was bored and the art store was closed. It's based loosely on this picture, but of course I messed up on the arms since I was drawing with an ink pen (one I normally use for grading) and I hadn't made anything in years.



Hello, winter break. :) It's only Day 2, and we have already: partied a good bit, finished hanging all kinds of things up in our apartment (Geoff measured/built three art frames from scratch and stapled the canvasses to them! It was awesome watching him sawing and banging things together while I laid back, ate chocolate, and watched TV... but I'm extra happy that finally all of our Salvadoran art is hung up), and we rode our bikes today to eat yummy breakfast in the park. In about 5 days we will be off to Turkey. I can't wait!!!

PS. Geoff's parents sent us chilled champagne in the mail. Two bottles. I managed to convince Geoff to immediately crack open one bottle upon receiving them, because hey -- how often in your life would you get chilled champagne in the mail?! That seems like as good an occasion as any to enjoy them. :)

PPS. Our Christmas tree/bush is coming along. It's crooked and small (that's what she said?), but it's filled with holiday spirit! :) I am so excited about our first jointly owned Christmas tree ever!! (Last two years we lived in the tropics, and before that we each lived separately in NYC.)


Anyway, I hope your holiday spirits are bright. Setting up the Christmas tree made me all sorts of sentimental. It was the first time I had actually set one up without my sister around (even though it has been 7 or so years since we've spent Christmas together). Made me miss her extra much.

PPPS. You know that Australian claymation movie Mary and Max? Please watch it. It's phenomenal (although not really suitable for children) and made me both laugh and cry.

Engagement Thoughts

During the summer, when I was away from Geoff for 5 weeks, I thought about writing down some things that I loved about Geoff that even our friends may or may not know. Since we recently got engaged, it seems like an appropriate occasion for such a post! So, here we go. :)

I love Geoff because he is authentic. The first time I stayed over at his apartment, in the morning he put on a pair of circular, coke-can glasses. I politely pointed out that it's fairly unusual for someone to be so not self-conscious so early on in dating someone else. He shrugged and replied that people are either going to like you for who you are, or not. For that I liked him more.

I love Geoff because he has traits of a real gentleman. I know it's old-school, but he opens doors, carries my stuff, and plans a helluva good date. I also love that he is romantic and that we still hold hands everywhere we go. :)

I love Geoff because he is fiercely loyal. I see it in the way he treats his family and his friends. Even if things happen that show him that other people aren't as good to him as they maybe ought to be, he continues to give them 120% of his loyalty and goes out of his way to take care of them. I know that he does the same with me, and that sometimes I'm not as considerate as I ought to be. Geoff forgives because he is generous.

I love Geoff because he's hilarious. When you talk to Geoff, you never know when something phallic will seep into the conversation. (Usually within the first 30 minutes, if he really hits it off with a dude.) When we met my cousins for the first time (who are older than me and whom I had always looked up to as a kid), he was rubbing his nipples and sticking his tongue out at the lunch table. When he came back from Israel for the birthright trip, he told me that he had right away figured out the circumcision status of everybody in his birthright group. It's just the kind of thing he shares, and then people reciprocate; he's very disarming in a strange sort of way.

I love Geoff because when you talk to him, you feel like his attention zooms in on you and nothing else in the world matters for the moment. He's genuinely interested in what you have to say, and it's evident that people love talking to him.

I love Geoff because he's the only person I know who tries to make people underestimate him. Everyone else I know is out to prove themselves to the world -- how smart they are, how much money they make, how talented they are at XYZ. Geoff? You'd never hear him talk himself up at anything, even if he might be better than you at XYZ.

I love Geoff because he's the most methodical and disciplined person I know. He has so many checklists, that he has built entire software systems to keep track of the things he needs to do and his systems yell at him when things fall through the cracks or run behind schedule. Before he buys anything, he looks at hundreds of options, reads books, and creates entire spreadsheets and software systems to track things. Because of it, he makes superb life decisions and achieves big goals efficiently (even though only a few people know about these things).

I love Geoff because he has a creative soul. He's not the best guitar player, but every time he plays, he's writing and discarding new tunes. He thinks of our experiences in metaphors and sings about simple stories that have beautiful messages that are opaque unless you talk to him about them. I love that when Geoff sings, he sweats up a storm and you can picture a little Geoff singing out of a garage rock band.

I love Geoff because he is fearless. I've jumped off a cliff with him. I've slid down a steep volcano with him. I've climbed 7 floors of ladder-stairs with him. I've seen him stick his hand into a pot of hissing roaches. I've eaten live crickets with him. I don't think I would have done those things myself. He pushes me to always go a little bit beyond my comfort zone.

I love Geoff because he balances his wander-lust with his career ambitions. We've had numerous conversations about this, where we think it's quite amazing that neither of our careers suffers from our lifestyle, and that we have each other to share it with.

I love Geoff because he is a true optimist. He's so damned positive that I call him Positive Pedro (or just Pedro) most of the time, and he calls me (Negative) Nancy. He thinks everything is do-able, and doesn't stress out about anything. When Geoff's around, he sucks out all of the negative energy in the room and replaces it with the human equivalence of sunshine. :)

I love Geoff because he believes that what I do makes a difference in the world. At the end of a hard day, it's so good to come home to someone who believes you to be better than you are.

I love Geoff because even if I travel all the world, I may not find another person like him. We could never predict what things may come, but I am happy that we have decided that we will be in it together for the long haul.

A Little Shoutout to Our Favorite Cafe

Apparently the best barista in the world is Salvadoran and works at the local coffee chain that we frequent. I guess I shouldn't have made fun of Geoff all of those times when he claimed emphatically that Viva Espresso has the best cappuccinos he has ever tasted in his entire life. Turns out that his taste buds are quite sophisticated.

My boyfriend has sophisticated taste buds and is willing to eat anything that has not been rotting for too long. That's dangerous.

Anniversary!

Today's the 1461st day that Geoff and I have been officially dating. :) (That includes a leap day somewhere.)

Since it's easier to celebrate on Saturdays than on Sundays, we went out last night to one of the fancy Japanese restaurants we've only seen but never tried. It's on top of Torre Futura, which has an amazing night view of the city from all sides. The dinner turned out to be delicious! :)

Birthday Thoughts

I turn 28 today. :)

It feels brilliant to be this old, because I am doing exactly what I want to do (and I had thought that it would take years more to feel this way). Geoff and I are so blessed; we travel, we love our jobs, and at the end of the day, we are still saving money! I also have no doubt that Geoff is the person I want to spend a really long time with, and when we look back on the four years that we have already shared and look ahead at the life that we hope to still build together, it astounds me just how blessed we are.

So, I am turning 28, and I feel absolutely, utterly fantastic.

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...On a not-so-fabulous tangent, yesterday I stepped through mud on the way to school, and by the time I had realized this, it was way too late. (Why was there mud right outside of the school, even though it hadn't been raining??) So, the entire back of my long WHITE skirt was covered in mud stains, along with my legs. Yikes for a first impression upon the kids.

That was non-fab. Fortunately, my skirt had a lot of folds (it's a convertible skirt/dress, so there's definitely extra fabric), so I just folded some of the worst stains (quarter-sized) under other cleaner parts, to minimize the visible damage. But, yikes!

Holes in the U.S. Education

Oh, so here's a funny thing that happened in Peru that I forgot to relay: At some point, we were hanging out at Machu Picchu and the guides wanted us to list all the things we knew about the famous ruins or about the Incas. Out of a group of 13 of us, guess how much we knew? ...Next to nothing.

Those guys were shocked. They said, "What do you guys learn in the U.S. schools?" ...Yeah, if only I had a dollar for every time I heard that.

Being a teacher, that's a pretty sad thing to hear. My Taiwanese friend (who is really smug about a lot of things, whether rightfully so or not) is quick to point out that Americans don't get geography jokes about other countries, because given a random non-Western-European country name, we can't really tell you anything specific about that country's geography, besides roughly where it is located in the world.

Sad.

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So, I'm back in El Salvador. I had thought I would be relieved to be home after four weeks of consecutive traveling. And, I am. But I miss Geoff already, and it's only Day 1. :(

Work starts tomorrow for me. I feel a fair amount of anxiety about returning to work (for reasons not to be discussed here -- but suffices to say that this is a rare occurence for me) and about the fact that Geoff will remain in the States for at least another 2 weeks. (Maybe longer, if he needs to close a deal on a house.) So, I am home, yes, but calm the way I normally feel at home? That's still a work in progress...

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In other news, recently I've been telling people stories about how Geoff and I went about planning out the next few years of our lives together. Everyone's been choking on laughter when I say matter-of-factly that Geoff wants to make babies at some point, and that I have told him that that shouldn't happen when we're, say, 40.

It's funny how men have nesting instincts but are clueless about fertility rates. How come people always talk about women having mothering instincts? :) I think Geoff's fathering instincts far exceed my own nurturing instincts. I can't even hold babies! (I am scared of breaking them.)

Anyway, I thought I'd put it out there, so you can all tell him that you now know he has a sensitive side. ;)

Math in Science

Before I decided to try this teaching-abroad thing, I used to work at a really great 6th-through-12th-grade public school that believes in teaching applied mathematics and sciences. They try to make everything hands-on and real for the kids. And I mean, everything! You would walk through the halls and see giant pulley setups, or see kids practicing pitching tents in preparation for their upcoming camping trip. In math classes, you see kids doing debates about tax policies and hosting probability game carnivals. (In fact, they are doubtlessly one of the best schools in NYC, and possibly one of the best schools around the country. They take in regular Bronx kids -- some of who can't read and have never done any math and many who come from broken homes -- and do magic to them; this year, 2010-2011, AMS will be having their first graduating class of seniors, and of the entire class of about 90 or so kids, only a handful is at risk of not graduating with their peers. The rest of them have passed their Regents and class requirements with flying colors.)

So, that's a long-winded way of explaining why I am always on the prawl for ways to integrate science into my math curriculum. (The science teachers at my current school sometimes make fun of me, because I am always going in and out of their classrooms and borrowing scales, beakers, thermometers, and whatnot. Some days they let me borrow their entire lab space, and those days are extra awesome!) One of the things I did somewhat recently is an RC circuit lab, to help the kids see that exponential data does occur naturally in physical space. They collected a bunch of data about charging and discharging capacitors and then did regression on their calculators to see that the exponential curve fits the data almost perfectly! Then, we ripped the equation apart to discuss every bit of it and how it related to the physical thing they saw.

Today, I spent some time looking at the skeletal lesson ideas at a NASA-sponsored site called PUMAS. Silly name, I guess, but they had some neat stuff. In particular, what I liked were:

• Launching something off of a rotating Earth is trickier than you might think.


• The trig of landing an airplane, which seems slightly better than the contrived trig problems in our textbooks. (...For some reason, the older I get, the more nervous I feel about airplane-landing. Geoff recently explained to me that they reverse the engines during landing, and that the noise you hear isn't really from friction of the brakes but from the engine reversal. That has helped to put me at ease during the subsequent landings...)


• Doing multiplication using parallel number lines. Can we extend this to help our kids who might still be struggling with certain multiplication pairs (such as 8X7 or 6X7)?


• Going from topographical maps to cross-sectional graphs and back!


• Doppler Effect and trigometry (of planets).


• Not sure why, but I am particularly amused by the premise of this one (albeit really unrealistic): If everyone in the world decides to jump into the ocean at once, would low-lying Bangladesh become submerged?

...Anyway, these are just skeletal lesson ideas, so maybe they won't work well in the end, but I like them as raw ideas!

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On an unrelated note, I finally went to the restaurant from Seinfeld yesterday! It's so funny that I had never been inside, even though I used to live four little blocks away on Broadway and 108th! The inside doesn't look like the show set, which was a bit disappointing, but the food was pretty decent for a diner! (Geoff was disappointed that I didn't order a Big Salad. heehee)

...And, in between looking at apartments, contacting realtors, following up on building regulations, and hanging out with family/friends, my boyfriend hasn't properly rested in days. :'( I can't wait until all of this madness is over and we get to finally, Finally be back at home, just the two of us. (That won't likely happen until end of August, if even.)

When You Go Budget...

I was reminded yesterday of something silly that had happened in Peru, and I thought I'd jot it down for future reference. It goes to illustrate how budget Geoff and I are, and the general ridonculous nature of our travels.

(As is the norm when you are or date a redhead...) G and I decided to buy some wine for the four-hour train ride between Aguas Calientes and Cuzco. Because we didn't have a bottle-opener, boxed wine seemed to be a natural choice. The tienda we went to only had a (dusty?!) box of WHITE wine (named Gato, or Cat), so whatthehell, we decided to get it even though room-temperature white wine in a box seems even more suspicious than red wine in a box.

About 20 minutes into the train ride, we realized that we didn't have cups. So, no worries, we emptied our plastic hiking water bottles and poured the white wine into them. We shared a round of drinks with our hiking mates, and while partaking in this first round, Geoff discovered the expiration date on the box: January 2009.

...Needless to say, hilarity ensued, during which we made several tipsy bad puns such as, "The cat is out of the box!" and "Hey, cats are supposed to have 9 lives," and other things I can't remember now. I'm half-amazed that we didn't die from bad chemical reactions.

That night, Geoff and I went to some local restaurant in Cuzco, where Geoff orderd a dish that looked like someone had literally thrown up all over his plate and brought the puke out as a dish. Hysterical in hindsight, but we were really worried about food-poisoning when it was all happening (especially because there was trash all over the floor of the restaurant and everything -- and I mean everything -- tasted recycled). I know it has been days since, but I am still banned from choosing a restaurant.

(Geoff was most traumatized because Peruvian food is super delicious, and this restaurant was damaging our impression of their national cuisine.)

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In other news, Geoff and I have arrived in Jersey/NYC! I am SUPER excited for Fram tonight (especially because Heather and Ryan will be DJing!). :) Oh, how I've dearly missed swing-dancing in the city!! (Not to mention the awesome ethnic foods galore... YUM.)

...I love how in NY, ya never know whom you're going to bump into, where, and how. When Geoff and I got out of Customs at JFK Airport a couple of nights ago -- at 2:30am -- I saw my old student Pamela V. waiting to pick up her uncle at the airport. How funny!

And, randomly, here are a couple of hysterical photos of Geoff's one day of mustache following our trip to Peru. (He thought that since he already had a full face of beard from 10 days of not shaving, he might as well shave it into a mustache look for a day.) ...As you can tell, I am just thrilled by the idea of his upper-lip decor. (--I will, until the day I die, never figure out why men think mustaches are cool. That night he wore this look to dinner with our Escuela Americana amigos; the gals all winced, and the dudes were all ready to start a new mustache trend! Ri-donc!)

Triangle Area - Simple

Tech Tangent: I fiddled a bit with iFrames this morning, in trying to embed a java applet directly into my blog. It worked (functionally), except it (aesthetically) messed up all the other elements that are part of the default blog layout. So, forget it for now; you're stuck with the regular web links until further notice.

Here is the GeoGebra visual of the day, accompanied by a math question. You'll notice that it says "Simple" next to the description/header, because I am ultimately interested in a more complex (but definitely related) problem. Eventually, I am interested in exploring how an area of a triangle changes as more than one of its vertices rotate around a circle.

A snapshot (but you should click on the link above to see the animation):


...By the way, in solving this problem, I had to try to figure out how to model a piecewise function in a piece of Geometry software. It looks like GeoGeobra does not have a way of doing this (at least when I searched in the Help index), and Geometer's Sketchpad makes it a helluva pain to get piecewise functions to work. Boooo. In the end, I still couldn't figure out how to get the individual pieces to merge into a single graph in GSP. This is the best that I could do, for now, in GSP. So, if you're a GSP expert and you happen to come across this post, please help!

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PS. I did a lot of math on the flight over to Peru. Can you tell? :) Geoff and I also proved the differential formulas for d(x^n)/dx, like the couple of nerds that we are. It's amazing how much math he remembers, even though it has been years since he has seen any of this stuff! (He is 29 this year, so that is at LEAST 7 years since college, and probably more since he has seen any form of Calculus! He uses a bit of math from time to time, both on his job -- graphics-related programming stuff for his Google-Maps type of mapping interfaces a while back -- and for understanding mortgage, interest rates, etc. in his investment-related leisure reading. But, still! I was surely very impressed.)

Our Peruvian Adventure

I am back home!! But, not for long. We just returned from our Peruvian trip yesterday (after some logistical snafoos), and we will be leaving again tomorrow. The day before we were leaving for Peru, Geoff found out to his HUGE disappointment that the house he had been looking to purchase in Jersey had fallen through. So, while we were in Peru, we each bought a round-trip ticket to Jersey. We leave tomorrow evening; I will be in the States for two weeks, visiting friends(!) and swing-dancing(!!), while Geoff looks around at other properties in NJ. The plan is that he will be in Jersey for four weeks total, but this way at least we are not apart for the entire time. (I will have to get back to San Salvador within two weeks, because that is when all returning teachers will start to prepare "officially" for the year. In truth, I have been on-and-off doing all sorts of prep this summer, but it will be nice to finally get a class schedule, finalized room assignment, meet the new hires, etc.)

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Peru took my breath away, both literally and figuratively. On our 5 days / 4 nights trek, the highest point we reached was about 4600 meters, or over 15000 feet above sea level. That is an astonishing feat! The temperature dropped below freezing on the first night of the trip -- in the 20s Fahrenheit range. What had happened to Geoff and me was that we had only arrived in Cuzco the day before our trek was due to start, so our bodies didn't have enough time to adjust to the altitude before beginning the climb into even higher altitudes. I threw up twice on the first day while ascending the mountain, and my chest hurt the entire time as I was walking / breathing, because my lungs were constricted. We passed by a couple of tombstones along the way, and the guide explained that one of them belonged to a gal whose asthma had flared up in the high altitudes, but who pushed on obstinately until things went from bad to worse. (I'm highly asthmatic, so that story got Geoff and me both a bit worried.) Finally, after about 9 or 10 hours of hiking, I gave up and hopped onto an emergency horse for the last hour of hike of the day.

On day 2 of the hike, the guides put me on a horse on the way up to the highest point, since the air was so thin. Geoff, too, was having a lot of trouble breathing -- and he runs marathons!! He was very pale by the time he finally got to the top of the mountain. I hopped off the horse and took a few steps on completely flat ground, and I already could not catch my breath. I had thought that descending would be easier for me to walk (even though we were still at an altitude > 4500 meters), but I clearly was wrong, because after walking for about 15 minutes, I threw up again. The guide insisted on me getting back onto the horse, and I threw up once more that day. Not my strongest showing, and I was super disappointed in myself that day. :(

That night, we got back to a lower altitude (in the 2000s meter-wise). By the time I woke up the next morning, the tightness in my chest had subsided. I was able to walk the rest of the trip, and even raced my way to the entrance of Machu Picchu to be one of the 400 people each day to receive a ticket to hike Wainapicchu (a nearby super-steep but stunningly beautiful mountain; you can see it in the picture above)! I was so proud of myself, because we had started hiking at 3:30am, in pitch darkness, and we were ascending these steep stairways that seemed to never end. Geoff was eager to be one of the 400 people, so he ran up the entire stairway and left me to climbing by myself. It was a tough mental game, but I was able to outrace a lot of people in similar (or better) physical condition than me, because I really wanted to get one of those tickets to Wainapicchu!

I can't describe how amazing Wainapicchu was, and our pictures do not do it any justice. It was like climbing up to a city in the clouds -- you have to use your hands and feet, rock wall-climbing style, in order to get up the narrow and VERY steep stairs. (I was really freaked out, naturally, because I'm terrified of heights. But, I tried not to focus on the fact that if you missed a step, you might very well tumble down the mountain and die. On the way down was much scarier, because you couldn't avoid looking at how high up you are.) When you look down from the top of Wainapicchu, even the immensity that is Machu Picchu is entirely dwarfed at the base of this mountain. It was definitely the highlight of our entire trip!

In Lima, Geoff and I also spent some time going to discotecas and bars. We also checked out a peña, which is essentially a local Peruvian cabaret, where traditional dancers come out in fancy outfits and dance during your dinner. Geoff and I found a place called "La Brisa de Titicaca" (the Breeze of Titicaca), which was cheap and you can get up in between the dance numbers to dance to traditional music! It was super fun. And, while walking around Lima during the day, we decided on a whim to go paragliding, since we had never done it before! It was awesome to fly over the cliffs of the Peruvian coastline. And, of course we also checked out some delicious Peruvian cuisine -- including cuy, or guinea pig!!

My only (HUGE) annoyance from the entire trip was that when we arrived at the Lima Airport yesterday, 3 hours before our scheduled flight back to El Salvador, the Copa Airline guy told us that the Salvadorean rule is for you to be deported from El Salvador (back to Peru), unless you can show proof that you have been vaccinated against the Yellow Fever more than 10 days BEFORE your scheduled flight from a country with active cases of the disease (ie. Peru)! In fact, the only reason that Copa eventually allowed us to check in to our flight was because the doctor on-site at the airport did Geoff and me a huge favor and wrote "Revacunado" ("Re-vaccinated") on our immunization record cards, after administering the vaccine to us! Otherwise, we would have been literally stuck in Peru for another 10 days!! Ridiculous!!

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Anyway, that's it for now. Ciao! I've got some errands to run (as is the nature of things when you keep leaving the country), but I'll leave you with this cute picture of us from our Peruvian trek. There was purple chalk on our faces and confetti in our hair, because it happened to be our hike-mate, Kate's, birthday, and that's how the Peruvians helped her celebrate!


How can you not love this country??

Student-Art Combinatorics

Pretty momentous: Yesterday, after Geoff's morning run, he came back in and said nonchalantly while laying out his towel for doing situps, "Happy 1 year in El Salvador!" --Wow! He's totally right!

On a funny expat note, just the other night when I was making tea for the both of us, I had asked Geoff what type of tea he would like. For a brief moment, his face went blank and he mumbled after a bit of hesitation, "Manzanilla." I started to giggle because I realized then that he had remembered the Spanish word but not the English word for chamomile!

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I don't teach combinatorics, but a fun lesson idea occurred to me while I was skimming through a discussion online, and I thought I'd sketch it up for the possible benefit of others.

The idea involves setting aside a day when the kids would each create/bring in a full-body, colored cartoon drawing of a person, and we would cut them into three parts (head, torso + arms, legs), and make three piles in the front of class, one pile for each "body part".

The kids would then each randomly pick a head, a torso, and a pair of legs out of the respective piles, and paste them together on a page, no matter how funny it looks, and write about the combinations / probabilities involved in this problem:

Assuming that no student has yet gone up to pick from the piles...


• How many combinations of body parts are possible?


• What are the chances that you would pick out an "entire" (contiguous) paper person, with all three parts that belong together?


• What are the chances that your paper person would have at least one mismatching body part?


• What are the chances that your paper person would have exactly one mismatching body part?


• What are the chances that you would get all three parts of your own original paper person back?


• Let's say that Jenny is the first student to go up to the front of class to pick out three parts at random, and James is the second. Explain why and how the results of Jenny's paper person might impact the probability of James to then pick three parts that belong together.


• Compare the chances of piecing together an "entire" (contiguous) paper person for the first student of the class (Jenny) vs. the last student of the class (you). If you go last, will it be "unfair"?*

*This question is my favorite, because it sounds deceptively simple but it begs an intuitive wrestling between what is commonly perceived as unfairness ("I am the last person to go up; by the time it gets to me, I've got no influence over whether I can piece together a contiguous person!") and a different story told using numbers (All participants, regardless of eventual order, had an equal chance of winning prior to the picking).

It could be a fun and light activity, while still keeping the rigors of a combinatoric lesson -- and it may also contribute towards decorating your classroom! ;) Obviously, the kids would write an explanation for each question in addition to showing the math work...

--But, sadly, I don't currently teach combinatorics, so if you have stumbled upon this entry and happen to enjoy this idea and decide to implement it in your (future?) classroom, I would love to hear how it goes! Let me live vicariously through you.

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Off to the highlands of Peru! WOOHOO. :) See you back here in 10 days or so.

Cameras, Shutter Speeds, and Suspicious Half-Chickens

In the interest of taking motion-blurred pictures of rotating objects (a la this, this, this, this, or this), I did some mini-research about my digicam and about the iPhone. I'm not one to be particularly bogged down on electronics or to be nitpicky about what tools I own, etc. But, the results of my research have spurred me to want to get another camera (or one of the newer iPhones)!!

It turns out that the Canon Digital Elph -- which Geoff and I have and love -- only has two modes: one being instantaneous exposure (with flash) and the other being long exposure (1 second or longer). For the purposes of math-teaching, if I were to take motion-blurred pictures myself, the exposure should be somewhat variable in the 0 to 1 second range. And, more depressingly, it looks like because Geoff has an older iPhone (iPhone 3G, with OS version 3.0), its built-in camera does not have all the spiffy features that I would need, either. --Doh!! I'll have to keep looking around for another solution, I guess. In the meanwhile, the Flickr photos will have to do (provided that their owners are kind enough to share their shutter speeds with me).

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By the way, it's pretty amazing that Geoff and I have not gotten really, really sick from food poisoning in our 12 months of living together. Case in point, two nights ago I decided to try cooking a new chicken dish. Now, I'd say that I'm a pretty decent Chinese-food chef, but whenever I try a new dish, it's still really nerve-wracking because my mom's recipes are hand-wavy at best. In this case, it was something like, "You boil half a chicken with some salt, and then when that's done, you scoop out the oil at the top of the broth, and you add the oil to some chopped ginger, scallions, and you add some salt to the dip. You take a big butcher knife to chop up the chicken into slices, and -- tada! You'll have what's called the Scallion-Oil Chicken." Sounds pretty easy, but it turned out that for some reason, part of the chicken we boiled was pink even after a while of cooking (and we were pretty sure, by the way, that this chicken was well-defrosted before cooking). We sliced it up pretty well and threw it back in the broth for some more time, and then took it out. After a couple of bites, Geoff and I decided to be safe and to microwave the chicken before eating.

I'll never know if that chicken was fully cooked or not. It tasted oddly tender and looked oddly pink even after the microwaving. But, I'll say that this is the first time I've topped off any cooking feat with microwaving! It's royally sad. And, amazingly, Geoff and I didn't get sick from that meal; we just might have stomachs of steel!

Next steps

Geoff and I are quickly approaching the end of our fourth year of being together! :) September 2010 will be that next milestone. I could not have imagined, even a year ago, where we would be right now with our relationship. Moving together abroad was an excellent decision, because we had to learn tolerance, communication, and compromise in order to live together and to be able to rely on each other day in and day out. I still love Geoff for all the same reasons as before -- his goodness, his love of adventure, his career ambitions -- but I have also learned to appreciate his relentless patience and protective love.

So, what's next??

(Since I know this is on all of your minds, all three of you that read this blog...) We do want to get married and to start a family, EVENTUALLY! We're just not in a big hurry to do it yet. I also want to go back to school to get my PhD, not for the name of the degree, but because I really want to someday help math teachers to be better at their craft. Thus, Geoff and I looked at our timeline for the next five to ten years, and decided that if we still wanted to live somewhere else (ie. Europe), we would have to do it relatively soon, before our lovely future arrives and we are slammed with raising a family and possibly my going back to school all at once!*

*And yes, I'm well-aware of how impossible/crazy that sounds to try to play both roles at once. But Geoff and I have discussed it and are hopeful that we will find a way for it to work, somehow. Even if I have to be the oldest PhD student ever and/or Geoff has to be a part-time stay-at-home dad! haha

So, our gears are turning. Stay tuned... (Don't get all over-excited though. Remember the last time we had decided to move abroad, it had taken us close to two years to get everything in order!)

Movies and Down Time

Geoff and I have been watching a lot of movies, because he has recently cut back (ie. temporarily stopped) drinking, in hopes of getting back on track with a healthier lifestyle before Christmas. As a result, neither of us has been too excited about hanging out at bars the last couple of weeks. Instead, over the weekend, we went to the movie theatre twice and watched Julie and Julia and Unglorious Bastards.

Unglorious Bastards was an excellent film about the Nazi occupation of France (set during WWII, but it's actually historically inaccurate, so it doesn't matter). The entire film kept us on the edge of our seats, and the plot twists were clever and intricate. To add to the experience, much of the movie was spoken in either German or French, and Geoff and I had to rely on our ability to read the Spanish subtitles to follow the plot. Fortunately, reading is always easier than listening, and we were actually fairly surprised by our ability to follow most of the film! (Our Spanish is getting better, for sure, but when native speakers begin to speak fast, we still have trouble understanding sometimes. Thus, watching dubbed movies is still very challenging.)

Julie and Julia is a much slower film. It got me thinking, however, about the blogosphere. I used to read various blogs written by friends. Over the years, as everyone got busier, the frequency of both their writing and my reading of their blogs had waned. Once in a while, I still go through short phases where I would follow blogs of some random teachers or swing dancers, to keep me in the loop of what others with similar interests are finding and exploring. But, there is nothing out there that really keeps my interest consistently as a reader. I would, however, be interested in reading in real time about someone else's ambitious undertaking of a task, similar to what Julie had set out to do in the movie. Are you familiar with some such blog? (Google seemed to fail me in finding anything of interest. But then again, I couldn't think of good keywords to use to help filter out the bloggers who blog mostly about their careers.)

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Anyway, as for my own life, things are going slowly. School has almost slowed to a halt, with kids taking midterms and teachers grading only idly before the holidays. I'm looking forward to having a few days off between school and going back to the States to unwind, read some books, watch some Law and Order, and maybe even get a haircut. :)

Anniversary weekend

Geoff and I celebrated our third-year anniversary this weekend. :) It was kind of a big deal, since I think we had hit a few big milestones in this past year (ie. moving in together and moving to another country), and everything had been as smooth and fun as can be. We don't eat at expensive restaurants much (since we cook decently well during the week, and we also enjoy eating at mom-and-pop Salvadorean places that cost only a few bucks for the whole meal), but we decided that for this particular occasion, we would splurge a little...

Colleen and Eric had highly recommended an Italian restaurant in Zona Rosa called "Vittorio's", so G and I decided to start our night there. It was by far the most expensive meal we have yet had in this country! A bottle of wine, a fabulous calamari appetizer, two entrees (fish and pasta) muy ricos, and two cappuccinos all added up to be about $70, but we thought it was well worth the price. The food at the restaurant was fantastic, and the ambiance was also lovely. Even though it had rained on-and-off throughout the night, Geoff and I sat in a covered section of the garden outside, surrounded by decorative wine, wooden wine racks, and lush tropical plants.

After dinner, we went to a couple of different spots, eventually landing in the "Jungle", which is now officially Geoff's and my favorite dancing spot on the Zona Rosa strip! We were already pretty tipsy when we started dancing there, and after a short while, the DJ offered us a free bucket of beers! --WHAT?! We were really surprised and a little confused; we never quite figured out what the free beers were for, but we were told it had something to do with our dancing. Anyway, we had a pretty great time there; a few of the locals were talking to us and being very friendly, and by the time we finally got home, it was already past 2am! For partying by ourselves, we didn't do too badly. :)

The rest of the weekend was also deeply relaxing, complete with naps in our two hammocks and some old-school video game-playing. (Geoff and I have been downloading old Nintendo games and playing them on my laptop, with the $7 game controllers we bought. It feels pretty silly to be playing games from the 80s, but G gets really excited about them. The only caveat is that I have short attention span and can barely sit still through a game, if we last through multiple levels...) I think I am almost ready for a full week of work. Almost.

Nature? Yes, I've read about it...

Last night, I saw a big pink iguana dart across our bathroom after it had entered through the window. I was freaked out! Geoff had to grab our pot in order to catch it and to put it outside. It was scaling the wall at a crazy speed, and even jumped during the Geoff vs. Iguana hand-to-hand combat.

Then, an owl was stuck in my classroom today! It was small, and apparently couldn't find its way out. I wish I had a camera with me, because it was the cutest thing I had seen in days. It kept eyeing me suspiciously by turning its head to a weird angle to follow me with its eyes. Eventually, it let me get close enough to open all of the windows to let it out. SUPER CUTE!

--This place is crazy. There are iguanas, armies of ants, killer mosquitoes, (dead birds on our porch,) and now an owl!

A Weekend to Remember

We had our goodbye party in Geoff's parents' garden on Saturday, and it was a blast! The weather was beautiful, even though it had been predicted to rain for part of the evening. A steady stream of guests came and went throughout the night, and I think everybody had a good time mingling. Geoff and I were surprised by the turnout of New Yorkers, actually, since it was definitely a bit of a trek out of their way. Even our friends who came solo seemed to be having a great time. And, as a special treat, I got to see an old college friend (Dan) for the first time in five years, because he had just arrived in NYC for the summer! All in all, we were more than grateful for all the friends and family who came out, and we will be spending the rest of our time here catching up with the rest of them...

Earlier in the day, when I had realized that my friend John wasn't going to be able to make our party (because he and his girlfriend were busy doing last-minute packing for their own summer trip), I made a hasty decision to rush uptown to meet him for coffee. As a result, I had to take a cab and sprint through midtown Manhattan to get to Port Authority on time for the bus -- TOTAL CHAOS! -- but it was totally worth it, because I got to say goodbye to my dear friend before he headed off for the airport today. yay. :)

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Then, this morning I came back into the city to meet up with the dancers for brunch at our troupe director, Laura's, apartment. There was an incredible spread of food, and we played Apples to Apples for a while before heading over to Central Park to enjoy a live jazz band. The afternoon wrapped up with some awesome music and dancing, before I had to say my goodbyes.

I am terrible at saying goodbyes, and I felt very sentimental to be leaving the troupe... But, it was definitely the perfect afternoon to remember. :)

30 days!

It is unfathomable that I will be moving out of my apartment and getting rid of all of my stuff in the next 30 days! I think that time will really fly by, now that we are actually in June. (--A surreal notion, in and of itself.) It is a two-week sprint from now until my high-schoolers are done with instructional days, and then another week until my 8th-graders take their Regents exams. And another week until those middle-schoolers, too, will finish school. Following that will be a busy weekend of: dance performance; our going-away party; and hanging out with the lovely dancers for the last time. Then, finally, I will have a couple of days of packing, throwing crap out, and MOVING!

Meanwhile, I'm teaching the next two Saturday schools (because I am a sucker) and Geoff is trying to organize a weekend trip to Pittsburgh to visit his pal's upcoming new baby. Our lives are caught in a centrifuge, and it's about to get crazy.

Departure date!

We finally have a projected date of departure: July 15! --Or at least, that is when I will be leaving; hopefully Geoff will be able to book a flight on that same day as well. :) The rest of the new international staffers will be arriving around July 23, which means that we have roughly one extra week to find an apartment and to settle in before my orientation starts.

In other news, Geoff has sent out evites for our goodbye party, which will be on the last Saturday of June. Seeing that both Geoff and I are playing-by-ear types, I am truly amazed by how early these are going out, but his mom -- the hostess of hostesses -- had been anxious about not knowing how many people will be in attendance, so some parental pressure was definitely involved in making this early evitation happen. :) I don't know how many New Yorkers are going to trek out to Jersey to party with us, but it is going to be a good time regardless! At the Coxes', drinks are always flowing merrily...

Translation: I'm going to throw up on someone's foot, and my boyfriend is going to piss on my leg. Just sayin'.