Wednesday, February 02, 2011


3 oz. rice soju
juice of 1/2 navel orange
juice of 1/2 lemon
0.75 oz. simple syrup
0.5 oz. egg white
3 drops Angostura bitters

Shake vigorously over ice. Pour very slowly through strainer into chilled cocktail glass.

Fruit juice should be around 1.5 oz. total.

Thursday, March 25, 2010

Gladwellian musings on love and infinity

There are as many even integers as there are integers.

We're used to being able to see a collection of objects, line them up, and count them all. But the even integers and the integers are infinite sets, and infinite sets can't be counted in the same way as finite sets. No matter how many elements of the set you've collected and decided to count in the traditional sense, there are always more elements to be counted. (All of the math here should be taken as a vast oversimplification.)

Georg Cantor showed how to compare the size of different infinite sets. The even integers and the integers are equal in size because their elements can be put into a one-to-one correspondence with each other. Why I'm writing about this, though, is because Cantor solved the major headache of infinity in mathematics by redefining infinity from the ground up.

Cantor said that something is infinite if you can remove a portion of it and what remains is just as large as the original. That, and not the fact that you'll always have more elements to count, is the definition of infinity.


I've struggled with the definition of love, and the connection between love and logic. I didn't understand why logic can poke so many holes and yet love does not diminish. But perhaps that is the purest definition of love. When logic gives you reasons not to, but you still care every bit as much about the person. Love is that infinity.

I can't wrap my head around transfinite math, and that's okay. It's beyond real-world perception. I can't wrap my head around love, either, and maybe that's okay, too.

Wednesday, March 03, 2010

Am I writing again?

"I am not a religious man, but I find there is no contradiction in my mind when I say that God is within these walls."

Sunday, March 15, 2009

Shamrock & Coke

This infused vodka took me three days to make, although the vanilla beans may not really need that long to contribute their flavor. My first test batch (in smaller quantity) was way too minty, so I reduced both the amount and time for the mint.

Shamrock Shake vodka

  • two 1-liter glass bottles (I used these)
  • Fine mesh strainer
  • Funnel
  • 1 liter of decent vodka (I used Smirnoff)
  • 6 vanilla beans
  • 1 teaspoon of dried spearmint
  1. Place vanilla beans in glass bottle.
  2. Fill bottle with vodka, close bottle, shake vigorously, then set aside.
  3. Shake a few times per day for three days. (Not sure how much the shaking really matters.)
  4. After three days, add mint to bottle, close bottle, shake, then set aside for three hours, shaking occasionally.
  5. After three hours, set up the strainer (to catch the mint) above the funnel above the second (empty) bottle.
  6. Slowly pour the vodka from the first bottle through the strainer (into the funnel and second bottle). The goal is to transfer the liquid to the second bottle with as few solid bits as possible, and the strainer's job is made easier if you keep as much of the mint in the first bottle as possible. (Pouring slowly works well enough that I have no interest in using a coffee filter, paper towel, cheesecloth, etc.)
  7. Store at room temperature.
Interesting when sipped. My preferred concoction, however, is...

Shamrock & Coke

Do you really need instructions? Take glass, add ice, add desired amount of vodka, add Coca-Cola. Drink. Tell your friends how awesome it is. When they respond unenthusiastically, pour yourself another one.

Friday, March 13, 2009

UCL quarterfinal draw - English odds

The sun rises in the east, and all four English clubs make the Champions League quarterfinals. Now that we're here, what are the odds of none of the four facing each other in the quarters? What are the odds of all four being placed in the same half of the bracket? I'm sure I could find this on the web somewhere; I do my best thinking in the shower, however, so the numbers below are brought to you by Johnson & Johnson shampoo and Dial soap. Let's dive in...

I'm mainly going to consider how to group 8 teams into 4 pairings, without regard for home and away legs or position of the pairings in the bracket. There are 8! ways to arrange 8 objects in order, except we don't care about the 4! ways in which the 4 pairs can be arranged, and we also don't care about the 2! ways in which each of the 4 pairs can be ordered. This can be expressed as

4! * (2!2!2!2!)

which equals 105. So there are 105 possible pairings for the quarterfinals. (Note that I've ignored the position of the pairings in the bracket, and I'll continue to do so for the most part.)

Starting over, if we only consider each club as English or not, there are three cases for possible pairings:
  1. EE EE xx xx
  2. EE Ex Ex xx
  3. Ex Ex Ex Ex
Case 1 has each English club facing another English club. Within this case, each English club may face any of 3 opponents, although once that selection is made, the other all-English matchup is determined. Likewise, there are 3 possible matchups for the 4 non-English clubs. There are 3 * 3 = 9 pairings with two all-English matchups. Please note that if Case 1 occurs, there is only a 1-in-3 chance that both all-English pairings will be placed on the same side of the bracket.

Case 2 has exactly one all-English matchup. Selecting this matchup requires choosing 2 objects from 4, and there are 6 possibilities. There is also exactly one non-English matchup, for which there are also 6 possibilities. We then know the clubs for the remaining two games, although there are 2 possibilities for selecting which English club will play which non-English club. There are 6 * 6 * 2 = 72 pairings with exactly one all-English matchup. Please note that if Case 2 occurs, there is a 2-in-3 chance that the all-English matchup and the non-English matchup will be on opposite sides of the bracket.

Case 3 has no all-English matchups, so that each pairing includes one English club and one non-English club. For each English club, we need to select the non-English club it will play, which is simply arranging 4 objects in order. There are 4! = 24 pairings with no all-English matchups.

Note that 9 + 72 + 24 = 105; two different methods, same result.

A couple of calculations to sum up:
  • Chance of at least one all-English matchup in quarterfinals:
    81/105 = 77.1%
  • Chance of all English clubs being placed in the same half of the bracket:
    9/105 * 1/3 = 2.9%
  • Chance of Liverpool knocking out Chelsea:
    (no math required)

Thursday, December 25, 2008

In Closing: Fah Who For-aze, Dah Who Dor-aze

Intro: The 12 Days Of Christmas Memories
1 2 3 4 5 6 7 8 9 10 11 12 Closing

Well, that was fun! Let's close it out with some Dr. Seuss:
Welcome, Christmas, bring your cheer.
Cheer to all Whos far and near.
Christmas Day is in our grasp
So long as we have hands to clasp.
Christmas Day will always be
Just as long as we have we.
Welcome, Christmas, while we stand
Heart to heart and hand in hand.
Merry Christmas!

Wednesday, December 24, 2008

Day 12: The Most Ridiculous Thing I've Ever Done

Intro: The 12 Days Of Christmas Memories
1 2 3 4 5 6 7 8 9 10 11 12 Closing

Early in the grade school years, at my birthday party in February, my friend Andy gave me the space Lego set Shuttle Craft. And so it began. Space Legos were the perfect toy for me -- I have a gift for three-dimensional awareness, I was starting to become mystified with astronauts and outer space, and there was something magical about the way that just a few hundred nondescript little blocks could transform into something much more than the sum of their parts, and in an infinite variety of ways.

My Lego collection grew rapidly, but my hunger for Legos grew at an even higher rate. I had already taken to studying the Lego catalog as my bedtime reading, and there simply weren't enough events in the year where I was guaranteed to get more Legos. One year in March, with my birthday just behind me, I realized that it would be Christmas before I could expect to receive more Legos. But my Lego mania knew no bounds, and December was further away than I could stand to wait.

On a sunny March afternoon, I sat down at home at my little wooden desk, took out a sheet of red construction paper and some Crayola crayons, and wrote a letter to Santa Claus. In true kindergartener fashion, this letter obeyed no rules of letter writing. Most of the letter consisted of the list of Lego sets that I wanted for Christmas; when I ran out of room wherever I was writing, I found a blank spot on the page and continued with the next item on the list. But this wasn't merely a wish list. I told Santa that I couldn't wait until Christmas, and I did so with these words:


That's right, I made a threatening bluff to Santa Claus, just because I didn't want to wait nine months for Christmas to arrive. So when I handed this letter to Mom and asked her to mail it to the North Pole...what could she have thought? I mean, perhaps it's funny now, but if your supposed little angel threatens a munificent stranger who brings joy to kids all around the world...out of mere impatience...I mean, how the hell are you supposed to deal with that?

Mom probably did the best thing -- she took the letter and told me she mailed it. Then about a month later, Mom suggested to me that maybe it wasn't very nice for me to have threatened Santa like that, and that perhaps I owed Santa an apology. Overcome with the feeling that I may have screwed myself out of presents, I sat down to write Santa another letter, this one on light blue construction paper. I apologized to Santa for threatening him, and I told him I could wait until Christmas to get my presents. Then I used the rest of the sheet of paper to list all of the other Lego sets I hadn't been able to fit into the first letter.

Shortly thereafter, my parents told me the secret of Santa Claus (his suit is laser-proof), probably so they didn't have to deal with this shit anymore. And as we know, that went well.

Tuesday, December 23, 2008

Day 11: The Snapparellas

Intro: The 12 Days Of Christmas Memories
1 2 3 4 5 6 7 8 9 10 11 12 Closing

Throughout my whole life, Dad has been an anchor to me in the cognitive sense, because he serves as my first estimate of where I may end up, and who I may become, in the future. Dad's a lawyer, so in seventh grade when Mr. Downey gave us an assignment to write descriptions of our life at various distances into the future, I naturally decided that I would have become a lawyer, too. (I think I did my undergraduate work at Princeton before moving on to Harvard Law. Go ahead, it's okay to laugh.)

Dad is also quite the storyteller, so that's something I've always shot for as well. I try, but it turns out I'm more like the Horace Grant of entertainment -- I'm usually good for a tip-in at a critical moment, but I'm not going to average 30 points per game or knock down six 3-pointers in one half. Maybe storytelling is just one of those things that skips a generation. And I'm okay with that. Dad is a great storyteller. I still have all my hair.

Dad's best storytelling was something that no one outside our immediate family ever got to hear. Dad had created a family named the Snapparellas, and as our family grew, so did the Snapparellas. As our family comprised me, Ben, Teddy, and Allison, our respective counterparts in the Snapparella family were Snoopy, Snappy, Rooty, and Zooty. (In a very "Peanuts"-like sense, I'm not sure we ever encountered Mr. or Mrs. Snapparella.)

The Snapparella kids were not the most socially adept. At one point Dad drew a series of cartoons, similar to "Goofus & Gallant", that highlighted the differences between us. For example, one cartoon showed me swinging a 9-iron, with the caption, "Robin goes for the green in two." The opposite panel had a similar caption, "Snoopy goes for the green in two," showing Snoopy with a finger up each nostril.

Listening to stories about the Snapparellas became a holiday tradition for our family. Each winter, we would have a few nights in the lead up to Christmas where we kids would each grab a blanket and stake out some space on a couch in the family room; Mom and Dad would put on a pot of coffee and dim the lights; and Dad would spend close to an hour telling one chapter of that year's story of our family and the Snapparellas. The centerpiece of the tale was usually Snoopy's annual attempt to catch Santa Claus.

Snoopy obviously never learned the secret of Santa (that he has bodyguards, whom he considers expendable -- seriously, the most important person on the planet is really going to jump down a billion chimneys and not have someone else go in first?), but that didn't stop Snoopy from concocting some rather amazing traps over the years, things that put Wile E. Coyote to shame. One year Snoopy used miles and miles of string, not just to set trip wires all over the house but so that when anyone was caught, everything in the house that could possibly make noise would go off at once. I don't remember exactly how this plan fell apart, but it wouldn't surprise me if a household pet were involved.

Mom adds: "What I liked was how Dad would think out the stories in detail ahead of time and he would leave a cliff-hanger for the next night. But what I really thought was cool was you and Ben (maybe Teddy, too, although I think Dad may have stopped telling the stories by then) would try to guess and tell your own versions of what was happening in the story."

Snoopy carried out so many plans that I have a hard time separating them in my memories from the general ridiculousness of all the cartoons I watched. (Did Snoopy really ice down the roof of the house so the reindeer would skid off when landing?) But there must really be something to the mystique of trying to catch Santa. On Christmas Eve in 1986, when Teddy was just four-and-a-half years old, he woke up in the middle of the night to use the bathroom. Teddy decided that he would catch Santa on his way back to bed. He finished up in the bathroom, and then headed right back to bed, completely forgetting what he had intended to do. It turned out to be his last chance, because the very next year, Teddy learned the truth about Santa (he knows when you're on the can).

Monday, December 22, 2008

Day 10: While You Were Sleeping

Intro: The 12 Days Of Christmas Memories
1 2 3 4 5 6 7 8 9 10 11 12 Closing

On Christmas Day a few years ago, while Allison was still in high school, one of her friends -- a boy -- came over to the house to give her a present. As the white room (capitalized?) served not only as our center of Christmas operations but also as, well, the room with what was technically our front door, the rest of us retreated from the room when Allison's friend arrived to give them some privacy. All of us, that is, except for Dad. No, he wasn't being overly protective like Teddy and I were. Dad was asleep.

I should point out that this kid was a friend of Allison's boyfriend, so even though he obviously had a crush on her, nothing was going on in that room. He gave her a toy from a Pixar film, they chatted for a while, he left. All the more reason why it was so wrong, later, for Teddy and even Mom to riddle Dad with innuendo about what had taken place in that room while he was asleep.

Mom: "I can't believe you were sleeping right there the whole time."
Dad: "Wait, a boy came over to give Allison a present?"
Teddy: "Oh, he gave her something, all right."

This went on for a while. I'm trying to get them to stop: "Come on, this isn't's his little girl...I mean, it's--"

And then something in my head clicked. "Dad...Dad...I'll tell you what he gave her."

"He gave her the one-eyed monster."

Sunday, December 21, 2008

Day 9: Early To Bed And Early To Rise

Intro: The 12 Days Of Christmas Memories
1 2 3 4 5 6 7 8 9 10 11 12 Closing

It is now four sleeps until Christmas. Wait, don't I mean days? No, I mean sleeps. I realized long ago that the most difficult part of waiting until Christmas wasn't the days, during which I could play with my brothers, but it was having to clear my mind and fall asleep each night. Thinking about the Lego sets or Sega Genesis games I was hoping to receive, well, it kept me up at night! So I was painfully aware of how many times I needed to conquer those thoughts and get to sleep.

On the last day, Christmas Eve, I would find my excitement peaking, and the puzzle-solver in me realized that if I could achieve that last sleep earlier, Christmas Day would effectively arrive sooner. So I started to go to bed early on Christmas Eve. Really early. What was surprising about this is that it actually worked -- as I resolved to do, I did fall asleep earlier. What was not surprising is that, as a consequence of falling asleep earlier, I also woke up earlier. Much earlier.

Like everyone has, at one time or another I've made the joke, "I didn't know there was a five-o'clock in the morning." The truth is, of course I knew there was a five-o'clock in the morning, I just didn't know it was soooooo long. What was I supposed to do at 5:00am on Christmas morning? I couldn't do anything that made noise, because I would wake people up, and as a kid I had very few things in my repertoire that didn't involve making noise. So I did the only thing I could think of: I read. And what I decided to read was the dinosaur book.

Our dinosaur book -- out of print, but if you're interested, ISBN 9780307137647 -- stands out because of its vivid drawings; its timeline at the bottom of each page that, across the entire book, spans the entire Mesozoic Era; and its depiction of all dinosaurs as cold-blooded...yeah, so it's a little dated. It seems it has just the right amount of science nerdage to keep me mildly captivated through the entire book...which would take me a surprisingly long time to get all the way through. Perhaps I would daydream in the middle of the T-rex battle scene.

These days I still get teased on Christmas Eve -- "It's 9:30, shouldn't you be in bed?" -- and on Christmas Day, Mom may ask whether I read the dinosaur book. I keep it at my place these days, so when I'm out at Mom and Dad's for Christmas, I don't have that option. If I want reading material, I have to choose from among whatever has accumulated at the house over the years -- classic literature and books on programming. Hmmm...maybe Allison has something I could borrow. Harry Potter once fought a dinosaur, right?