Career Day

Thanks to everybody for all your advice on career day. I gave a 30-minute presentation full of slides with interesting pictures. I began by asking who liked math. I got a show of a few hands. Then I said, "I'm glad that some people here like math. But for the rest of you, I have bad news. Any career is going to involve math to a greater or lesser degree. And generally speaking, the more math that's involved, the more money you'll make."

I had some pictures from popular television shows to get them interested. I asked them if anybody watched "Gray's Anatomy." There was a show of a few hands. "Well," I said. "What if you're a doctor and you prescribe 200 mg of a very potent medicine instead of 200 µg?"
I also had a picture from the show "CSI." Again, I asked if anyone liked that show. And then I asked what would happen if you were working on the very last DNA sample and you added 5 mL of solvent when you meant to add 50 µL? In both of these cases, knowledge of math is vital for job success.
Then I talked about my job. I told them about our supercomputers, giving the really cool numbers about how many flops* the machines do; our huge, expensive cooling system (capable of cooling 640 large houses); how much our power bill is ($5-7 million/year), etc.

And I told them about the science. I showed some pretty pictures of various applications, starting off with combustion. I asked who got to school today thanks to the power of internal combustion. There was some confusion, but after it was established that I was talking about engines, just about everyone raised their hands. Then I asked who had heard their parents complaining about the high price of gas lately. Everyone raised their hands for that one. Well, I said, that's because some of the best cars, such as mine, get maybe 30-40 mpg. But wouldn't it be cool if we could get more like 300 or 400 mpg? That's why we study combustion.

I ended the presentation by talking about my educational background and then what they could do if they were interested in a career like mine. I told them what sort of educational activities they should do but above all encouraged them to be persistent and don't let other people discourage them. I also showed a slide with pictures of some of the youngest and most attractive people I work with. In addition to being more visually appealing, they are more diverse, and it is part of my mission as a member of an underrepresented group in computer science to encourage students from underrepresented groups to join us. (I showed pictures of three people, two of whom were women, and two of whom were African-American.)

After my presentation was over, I got quite a few good questions. One joker asked something about my advanced age, but otherwise the students were genuinely curious. I felt that career day was a success and I'm grateful for all your advice.


* A flop (in addition to being a bad joke that nobody laughs at)** is a FLoating-point OPeration -- basically, any arithmetic operation involving numbers with decimal points, such as 1.1+1.1. Our big machine does 263 teraflops per second, or 263 trillion floating point operations per second. If everyone in the world were capable of doing one floating point operation per second, and we all worked together, it would take us nearly half a day to do what it takes this machine one second to do.

** Standard leadership computing facility tour guide joke.

Memorial Day Fun

My plan for Jeff's Father's Day gift was to get him a nice grill. I know nothing of grills, however, so I wasn't sure what to get. Luckily, my boss is quite knowledgeable about the subject, and found a good one in the newspaper circulars. It was on sale for Memorial Day, though, so I decided to go ahead and get it early.

Seeing as it's impossible to hide a grill, and that even if it were possible, Jeff has psychic powers that give him the ability to discern the contents of any gift package, box, or envelope, I decided to just let him know what he was getting. My boss graciously helped me go pick up the grill in his enormous truck (it wasn't going to fit in our VW Beetle or even our Chevy Impala), and he and Jeff unloaded it and put it on our deck.

Here's a link to what I got him: it's a Kenmore gas grill with 770 square inches of grilling space. It also has a side burner that you can use like a normal stove burner. (I paid less than they are currently asking for it.) He is really enjoying it so far. He grilled out twice during the Memorial Day weekend, so I consider it a successful gift.

On the Bright Side, He Does Understand Verb Tense

A (sadly, all-too-) typical scene in our household:

Vinny: "Fart!"

[He passes gas.]

"Farted!"

Professor Henry Jones Denied Tenure

An appropriate link for the opening of the latest installment of the Indiana Jones franchise...

That Amazing Little Boy

Vinny, despite his painful mouth, continues to be quite cheerful most of the time. He has come down with a cold courtesy of his generous mother (who got it from a generous friend at work) but is still a happy boy overall.

This afternoon, instead of napping, he was singing. Here's a transliteration courtesy of his father:
blug-bo-blug-bo-goobar-goo.... dug-do-dug do- hi hi hi hiyea yo yo hiyea yo yo hieyeah dooo gooo blug goobar goo

(Pure poetry, don't you agree?)

He has an interesting sense of humor and tells you when something tickles his funnybone, by declaring it "Fuuunny!"

One of the most hilarious things in the world is to peer at Mama through something (e.g. the hole between the handle and the body of the toy toolbench, or through a translucent cup). "Ahseeeooo!" he shouts. "Fuuunny!" he announces, and laughs.

Another funny thing is to touch his foot to mine and wiggle the toes. This warrants a big grin and the statement of "giggle giggle giggle."

Other humorous highlights include smacking my belly and watching it jiggle, beeping my nose or pinching it and making a Model T horn sound ("ga-HOO-ga"), and pointing out my eyebrows (when he says it, it sounds more like "eyeball" than "eyebrow", but he's definitely talking about eyebrows).

He's extremely ticklish in the armpits, so it's pretty easy to get him making that deep belly laugh. That's a sound I will never grow tired of.

He loves this book called Hand, Hand, Fingers, Thumb. He calls it "Thumb" when he pushes it into my hands. "Wead? Thumb?" he inquires. I think I've read it to him approximately 8,257,913 times, so I have it memorized by now. The thing he loves about it is the rhythm. And since I read it more rhythmically than Daddy, he prefers my rendition, and so I am cursed blessed with the opportunity to read it quite frequently.

He continues to just amaze me with his vocabulary. Thanks to Jeff's efforts, he knows the word for just about everything that he encounters on a daily basis. He learned the word monkey from the aforementioned book, and interestingly, believes that Cookie Monster is a monkey, as are the faces depicting various emotions that are on this magnet on our fridge. He also learned the word plum from that book. I told him that prunes (one of his favorite foods) are made from plums, but I will have to get him some actual plums before long.

Happy World Metrology Day!

I hope that you all had a wonderful World Metrology Day. Today marks the anniversary of the signing of the Meter Convention, which created the International Bureau of Weights and Measures.

The theme for this year's celebration is measurement in sports. I discovered this (and the existence of World Metrology Day) back in October when I wrote a critique of the techniques used to measure downs in American football.
Anyhow, I hope you're all enjoying the fruits of metrology today as well as every day!

Tooth Update

Thanks for all your kind words in the comments of the previous post. It meant a lot to me. I really appreciated hearing from all of you, even those of you who are complete strangers to me. Thank you for taking some time out of your busy life to comfort someone you don't even know.

I took Vinny to the dentist yesterday morning. He's a pediatric dentist who was recommended by my (extremely young, fresh out of school) dental hygienist, who went to him when she was growing up.

Anyhow, the dentist took a look at his tooth and told me that it was unlikely that the baby tooth damaged the bud of the permanent tooth growing above it, and if it did, it probably didn't do much damage. The baby tooth could take up to a year to descend back to where it belongs. At this point, we don't know if it's going to die or not, but I'm to bring Vinny back in a month and we'll reevaluate then.

I felt relieved by the visit, but it was a bit traumatic for Vinny. The nurse and I held him down while the dentist checked his tooth and squeezed out some gooey white substance from under his gum. "Is that pus?!?!" I gasped in horror. But he said he didn't think it was, because not enough time had passed for so much pus to form. But just in case, he wrote a prescription for amoxicillin. And Jeff and I are to wipe Vinny's front teeth with a piece of gauze with peroxyl mouthwash solution on it, twice a day. It feels so cruel to do because it makes Vinny weep and beg for us to stop. But it has to be done.

Anyhow, I'm feeling better about the whole thing and Vinny is getting better. He's able to sleep through the night now (unlike the first two nights) and his appetite has returned. The mouth is still tender, though; tonight, he was goofing off and waving his arms around and accidentally bonked himself in the mouth, which clearly hurt a lot. But in time, it will be better.

The Worst Mother Ever

I am the Worst Mother Ever.

We were having a pleasant morning. Vinny and I were horsing around on the bed. Jeff was in the kitchen making his own breakfast.

Vinny loves to tumble. I try to be very careful and make sure he doesn't tumble off the bed. But he was closer to the edge than I had thought, and I didn't catch him in time. He tumbled another full rotation and landed on his face.

He was screaming. I grabbed him and held him to my chest, trying to calm him down. Then I noticed that there was blood coming from his mouth. I thought he had cut his lip or bit his tongue, but he screamed bloody murder when I tried to take a look and I saw that his front left tooth was pushed up into his gums. I called to Jeff and said we'd better take Vinny to the doctor. He called the doctor's office and they said we should take him to the emergency room. We decided to take him to the Children's Hospital because they seem better equipped to handle children than does our local emergency room.

I tried to hold some ice to his mouth while we were going there, but any kind of pressure on it made poor Vinny scream bloody murder. After what seemed like an eternity, we arrived at the hospital. I took him in while Jeff parked the car.

His tooth got pushed up into his gum, and it should descend on its own, according to the doctor. We need to take him to a dentist sometime within the next week or two, to determine the extent of the damage and whether the baby tooth has damaged the permanent tooth bud. He said to give him tylenol and ibuprofen, and a soft diet for seven days.

I looked to see what Dr. Google says the prognosis is for our sweet boy's smile. According to this site, if it's pushed up more than 6 mm (which I think it is), it's pretty much hopeless. The tooth will die and will probably need to be extracted.

I feel like the worst mother in the world. I should have stopped him from tumbling so close to the edge of the bed. Thanks to me, he's probably going to have a huge gap where his front tooth belongs for the next 5 years. I will take him to the dentist next week and find out for sure.

A Landmark Decision

I was ecstatic when I heard the news that California's State Supreme Court has struck down the state's ban on same-sex marriages!

This is a very important issue to me, because half of the members of my first family (excluding myself) are gay. I have always been a proponent of marriage equality, but the fact that it directly impacts my loved ones raises its importance to me.

I am pleased by their decision because it underscores the fact that marriage, in the eyes of the government, is independent of religion. The only objections to same-sex marriage are religious in nature, and therefore irrelevant when making the decision on whose commitments can be granted legal recognition.

I got goosebumps when I read the wonderful news in an email from the ACLU. Here are some particularly poignant excerpts:

Simply having the California Supreme Court say that constitutional principles demand that marriage be open to same-sex couples is an enormous win. This Court has a remarkable history of leadership on civil rights and civil liberties. It made landmark decisions on race and sex discrimination, on freedom of speech and privacy, and on treatment of the disabled and poor people long before the U.S. Supreme Court. No court in America has more authority to say that marriage for same-sex couples is an issue of basic freedom than this one.

...

Marriage in California will transform the discussion of marriage nationwide. California has one of the largest economies in the world. Given the state’s economic clout, the fact that California is marrying same-sex couples will put considerable pressure on the rest of the country to recognize those marriages.

Even more important, the rest of the country recognizes that California is America’s cultural trendsetter, that cultural change in California is usually a preview of what is to come in the rest of the United States. Most Americans already believe that marriage for same-sex couples is bound to happen sooner or later. I think marriage in California will help persuade many of them that this is an issue of basic fairness, and that the time for it is now.

...

Thank you, California, for giving those of us who value equality a little hope for the future! With a lot of elbow grease and a little luck, the committed relationships of same-sex couples such as my own family members could be legally recognized within a decade, which pleases me to no end.

Vinny's Latest Obsession

• In the house, pointing at the front door: "Opeeeeeen! Opeeeeen! Moon!"
• In the car, looking through the sunroof: "Moon!"
• Upon seeing a streetlight: "Moon!"
• Upon seeing a cookie, a coaster, a croissant, a Boppy pillow, nearly anything round or crescent-shaped*: "Moon!"
• The only thing that can cheer the inconsolable little lad, who was sobbing late at night before he spiked a fever: Google image search for moon
• The top three entities in his life: "Mama, Daddy, Moon!"

*You might think that a pizza would also elicit this response, but pizza (or, as he calls it, either "piZAAAAAA" or "miZAAAAA") is fourth on the list of important things (beating out prunes, shoes, and refried beans), and is therefore generally not conflated with the moon.

Sickness Strikes the Family

It's virus central here at Casa Rebecca. Vinny had a temperature of 103.5ºF and spent most of the day moaning yesterday. We took him to the doctor and while he did not have strep, he did have a nasty sore throat. But today he bounced back and is doing fine, just in time for me to feel miserable. I'll probably be fine by tomorrow, just in time for Jeff to get it.

There are some foods that I crave when I'm sick. A big one for me is canned fruit with cottage cheese. The most comforting is canned plums, but I have to admit, I have a weakness for canned peaches and canned pears too. In fact, I just snarfed down a can of peaches that was rightfully Vinny's. Jeff always needs a grilled cheese sandwich when he's sick.

What's your comfort food?

May Scientiae Carnival

The May edition of the Scientiae Carnival is up at my blogfriend Flicka Mawa's place, A Cat Nap. The topic of the carnival is "career paths, perspective, and changing self-image." Flicka Mawa was kind enough to include my graphical interpretation of my ever-evolving self-image.

Go forth and read it! It's really great! Thanks, Flicka Mawa, for putting together such a fascinating carnival!

In Which I Solicit Advice from My Vast Readership

O Vast Readership, maybe some of you will be able to help me figure out what I should do with the latest opportunity I have been afforded!

Later this month, I will be speaking at my local middle school's career day. My topic is "Math Careers," and I have a half hour allotted to me during each math period. My target audience is 8th graders (13-year-olds), I believe, but the school goes from 5th-8th grades.

I'd like to engage them and keep them interested in what I'm talking about. I could drone on and on about things that they will probably find boring, but what I was thinking was that quite honestly, every job they will ever have will involve math to a greater or lesser degree. I thought I might inform them of that fact, give some examples (e.g., cooking, which requires knowledge of fractions, multiplication, division, addition, and subtraction) before proceeding on to more math-based careers (such as scientist, engineer, computer scientist, and mathematician). But I'm not really sure what specifically to say and I'm not sure how I'm going to fill a half-hour, or maybe let's say 25 minutes with five minutes for questions. ;)

This is where the expertise of my vast readership comes in. I was an atypical 13-year-old in that I would have actually been fascinated by anything an actual mathematician had to say, so I am lacking a certain perspective. Any suggestions?

Lilly Ledbetter Fair Pay Act

Sometimes I think I live in the land of dinosaurs! Neither of my senators voted for the Lilly Ledbetter Fair Pay Act. Oh sure, there are misinformed people who believe that by allowing someone to sue for back pay after 180 days, there would be a catastrophic ten percent decrease in everyone's pay, but quite honestly, this does not follow. (If you believe that one, I've got some waterfront property to sell you -- it has a view of the water from all directions! Very lovely!) What it would do instead is make employers that much more careful about systematically discriminating against anyone.

Anyhow, here's what I wrote to my senators:

Dear Senator:

I was disappointed to see that you voted against the Lilly Ledbetter Fair Pay Act recently. I cannot understand why you would vote against a bill that would remedy unfairness in pay.

Senator, I am a woman and the breadwinner of my family. It is a well-known fact that due to bias (both conscious and subconscious), women do not get the recognition that they deserve for their hard work, and this includes promotion and raises. I am a scientist, and there have been peer-reviewed, double-blind studies that have shown that a woman scientist has to be more than twice as productive as a man scientist in order to be considered equally competent. If a man must publish ten papers a year, then a woman must publish twenty in order to be considered his peer.

Therefore a woman who works as hard as her male counterpart will not receive the same reward, and fall behind in pay. It takes time to ascertain the pattern of iniquity, and this bill seeks to allow women and others subject to this type of discriminatory practice the time necessary to do so.

Senator, I encourage you to change your vote the next time this bill comes up. My family deserves your support in making sure that I am remunerated as much as I deserve.

Sincerely,

[me], Ph.D.
Computational Scientist

My Awesome Husband

My husband is the coolest guy in the world. Here are a few of the myriad of reasons why:

• He is very brave. Like me, he defies gender stereotypes in his chosen vocation. It takes a lot of courage to be a stay-at-home dad and face gender discrimination every day. I admire him for doing what he wants to do despite the pressure to do otherwise.
• He is very loving. I love to watch him play and interact with Vinny. It brings so much joy to my heart to see the way they interact! Most of what I know about parenting, I've learned from him.
• He is a really good cook. When we first got married, he didn't know much about cooking. I taught him everything I knew, but he took that knowledge and ran with it. He has a knack for combining flavors in just the right way. Last week he made this catfish with lime and some combination of herbs and spices, and it was just superb. He didn't get the recipe from a cookbook; he just made it up! He has a blank book in which he writes all his special recipes, and I told him he definitely needs to add that one to the list.
• He is amazingly artistic. He has more artistic talent in his big toe than most people have in their entire body. He's recently taken up drawing. Most of the time, people start with simple compositions, such as a still life. But Jeff started by drawing portraits and figures. He is getting really good. The drawings are becoming more realistic every time. I am amazed by how well and how quickly he has picked up this ability!
• He is incredibly creative. In addition to his artistic talents, he has a knack for storytelling, which he uses for role-playing but also to develop plots for books. He has several books of fiction all planned out in his head. I keep telling him to write one down already so that we can live off all the money it will bring in! ;)
  
• He is empathetic. There's nobody in this world who understands me as well as he does. He really gets everything I say. I think he's also the perfect feminist boyfriend. He sees the damage that our patriarchal society does to women and to men. There aren't too many men who really get it like that.
• He loves me. I am continually baffled by the fact that despite my numerous character flaws, he really cares about me and wants to spend his life with me. I try not to let on about my bewilderment, but I always keep in perspective how fortunate I am to have him as my partner in this journey through life!
  

Game Theory and Human Behavior, Part II

Remember the post Game Theory and Human Behavior, Part I? What, you don't? Okay, so I posted it back in February. Obviously it was meant as the first of a series of posts. You might want to read that one again before reading this post, because this one uses some of the concepts I explored in the first post.

The practice of torture is another signaling game. This one is a bit more complicated than the good employee signaling game or signaling in contract bridge, but the premise is the same. Let's call the person doing the torturing the investigator, and the person being tortured the detainee. (I refer to them both as male, since they always are on television and in the movies.) The idea is that the investigator seeks truthful information from the detainee. The investigator doesn't have the same knowledge space as the detainee, although the two may overlap. (If the investigator knew what the detainee knew, he wouldn't have to talk to the detainee at all!)

The detainee, on the other hand, seeks to provide the investigator with only enough information to satisfy him and stop the torture. So the detainee wants to give the investigator the very minimum amount of information that would satisfy his curiosity.

Economist Roger Koppl performed a thorough evaluation of the efficacy of torture in a 2005 paper entitled "Epistemic Systems." In this paper, he determines that torture works only if the following two conditions are met:

1. The investigator must be able to recognize the truth when he hears it.
2. The investigator must be able to credibly commit to stopping the torture upon hearing the truth.

If the investigator cannot recognize the truth when he hears it, then he won't find the truth regardless of the method of questioning. If the detainee doesn't believe that the torture will stop upon telling the truth, then he has no incentive to tell the truth.

Here's the problem: These two conditions are both necessary for torture to work, but they almost never occur together in real-life situations.

Consider the first condition. The more the investigator knows about the knowledge space of the detainee, the better he is able to recognize the truth. But how can he recognize the truth when he hears it, if he isn't privy to everything within the knowledge space of the detainee? This is how the detainee can get away with providing the least useful information out of the set of relevant information that he knows, or even worse, information that sounds truthful to the investigator but turns out to be false upon verification.

The second condition is similarly difficult to satisfy. Consider the case of a Chilean rebel, who broke down and confessed the names of the nuns and priests who had sheltered her. Her devout interrogators didn't believe that these holy men and women were involved, and continued to torture her.

Even if torture were effective on actual "bad guys," the consequences of using it on people who are actually innocent bystanders are the things nightmares are made of. In Discover Your Inner Economist, Tyler Cowen discusses the nightmare situation of being mistaken for a spy when you are nothing but a clueless American on vacation. How can you signal to your captors that you are not a spy? Anything that you do, from protesting your innocence, to providing them with information that sounds promising but turns out to be false, is indistinguishable from what a real spy would do in that situation.

There's always the situation in spy movies and political thriller TV shows such as 24, in which the entire population of New York City is in imminent danger from a ticking time bomb, which was set by a fanatical terrorist of some sort. The hero has to beat the information about the location of the bomb out of the bad guy. Usually it's a renegade cop played by somebody like Bruce Willis -- a guy who goes against the rules and saves the day, much to the chagrin and grudging gratitude of his superiors.

While these sorts of movies and shows are entertaining, they are not reality-based. Dr. Jean Maria Arrigo, a social psychologist with a mathematics background, refutes the ticking time bomb scenario in her papers "A Utilitarian Argument Against Torture Interrogation of Terrorists" (Science and Engineering Ethics (2004) 10, pp. 543-572) and "Torture, Terrorism and the State: a Refutation of the Ticking-Bomb Argument" (Journal of Applied Philosophy (2006) 23(3), pp. 355-373), co-authored with Vittorio Bufacchi. I focus upon this second paper.

Bufacchi and Arrigo first formalize the scenario. The dominant elements in the story are that first, a great number of lives are at stake; second, there is a time at which the catastrophic event will occur if it is not prevented; and third, a person privy to knowledge that will allow authorities to intervene and prevent the catastrophic event has been captured. Under these circumstances, some philosophers and legal experts believe that torture may be justified. A naive utilitarian argument might go something like, "we're causing one person some pain so to prevent that person from causing millions of others even more pain."

But this is an argument based on fiction. First, it assumes that torture is necessary for the captive to give up his information, when the opposite is more likely to be true. Consider the case described in Bufacchi and Arrigo's paper (p. 359):

Five foreign terrorists were captured by the local [counterterrorist police team]. All were found under arms with explosives and maps of targets....The question of how many [terrorist] cells were to be sent to the country to other targets was of interest. The first three terrorists were not even questioned, only shot. The next two were asked the question separately. One shot was heard. The officer said to the last terrorist, ‘Do you also want to remain silent?’ The guy began to lay out the entire operation, the training the cells had received, where they were to meet, where the weapons depots were located, and the route that the terrorists were to take to exfiltrate the country....The other cells were picked up along with in-country support personnel.

How was the fifth man chosen, you may wonder?

The group was searched and then fed and given tea as per the Shariat law of the Koran. Those who refused to eat or drink and made intense hostile eye contact were selected as the first three. The body posture decided who went fourth. The youngest, who ate the bread, drank tea, and thanked his captors was determined to be the least experienced. His AK rifle was not even clean...and he did not appear committed to the jihad.

So, they simply profiled the men they captured, picked the one who was most likely to confess first, and just asked him. No torture was necessary to obtain the information they needed. Once he was free from the influence of the more senior terrorists, and felt well-respected by his captors' adherence to local custom, he readily gave the police all the information they needed. Like the majority of "ticking-bomb success stories, the efficacy of torture interrogation is demonstrated only if the case is framed on that premise."

There are several premises upon which the argument for forward-looking interrogational torture is based. I will use Bufacchi and Arrigo's outline of the argument to explain this (Notation: P = premise, C = conclusion).

• P1: The terrorist has been captured.
• P2: Torturing the terrorist will make him reveal crucial information about the catastrophic event.
• C1: The terrorist must be tortured.
• C2: The crucial information will be revealed.
• C3: The catastrophe will be averted, saving the lives of many innocent people.

Unfortunately, the conclusions C1, C2, and C3 do not follow from premises P1 and P2. There are some hidden premises that must hold true before C1-3 can follow, and none of these premises are legitimate "from an empirical point of view" (p. 360).

P1 has an invisible, companion premise:

• P1A: This terrorist possesses crucial information about the catastrophic event.

Remember the overlapping knowledge spaces of the torturer and detainee? Well, they don't completely overlap; if they did, we wouldn't need to extract information from the detainee. So this premise is an assumption, and we could end up torturing some innocent bystander who was indistinguishable (based on our knowledge space) from a real terrorist.

P2 is problematic, too, as I have discussed above. But even if we assume that Koppl's conditions are both met, there are other problems. Many American POW's in Vietnam (e.g., John McCain) withstood a great deal of torture without confessing anything. Similarly, most victims of the Inquisition confessed to no crimes. Countless torture victims in the Algerian Civil War went to their graves with their secrets undiscovered. Terrorists are more than likely trained in the art of withstanding torture, making it even harder to draw any information out of them with this means. Finally, terrorists could be provided with false information to "confess" in order to deliberately throw their captors off the trail -- this tactic was recommended by Sun Tzu more than 2500 years ago!

And even if torture did yield information from the terrorist, what is to say that it will happen in a timely fashion? After all, if the time bomb is going to go off in 24 hours, anyone sufficiently devoted to the cause would use every ounce of their fortitude to resist for that length of time. Furthermore, torture interrogation is not a "quick coercion" -- it is a lengthy "degradation of the subject's resistance" over the course of months, not minutes (p. 361)!

According to Koppl, "It is a fair, but approximate, summary to say that, as a means of extracting information, torture works best when it is needed the least."

I couldn't have said it better myself.

My Ever-Evolving Self-Image: A Mathematical Perspective

The topic of this month's scientiae carnival is "our changing views of ourselves and our careers as we pass through time."

Since I am more mathematician than wordsmith, I thought I might express these changes in graphical form. The x-axis represents time, and the colored, dashed lines represent major life events that have exerted influence upon my life.

First up, the amount of change for the better I must bring to this world (or else face certain doom):
A few data points from the previous graph: {(4, President of the United States + Nobel Peace Prize), (8, Nobel Peace Prize), (12, Nobel Prize in Chemistry/Physics/Medicine), (18, Professor at top-ranked Research I University), (32, Best second-rate mathematician in the world)}.

Next, my level of self-confidence:
A few data points from this graph: {(4, I can never do anything right), (12, Junior High -- need I say more?), (23, Grad School is Hard!), (27, My family -- putting the fun in dysfunctional), (29, I made it out of grad school! I made it!), (32, I got a real job!)}.

Third, how convinced I am that I'm doing the right thing with my life:
A few data points for this graph: {(4, I'll never be able to stop being a total screw-up), (12, I have to be a violinist but I'll never make it), (16, I want to be a scientist even though my mother thinks my talents are best spent elsewhere), (21, Physics is hard!), (27, Why did I ever take my mother's opinion of what I should do in life as my own? WTF was I thinking?), (32, I am definitely in the right place.)}.

scientiae-carnival

Power of Two Cake

I know you've been long awaiting a post on my powers-of-two themed cake.  Now that I'm less swamped by work, I can oblige.

But first, a little math.  (I know you all come here for the math!)  Astute commenter Rico mentioned his fascination with the sum of the series 1/2ⁿ (where n = 0, 1, 2, ...).  If you add 1 + 1/2 + 1/4 + 1/8 +..., the sum approaches but never reaches 2.  For a given n, the sum of the series equals 2-1/2ⁿ.  So for n=4, the sum equals 2 - 1/16 = 1+15/16.

I decided to represent this sum in cake.  In order to do so, I needed to bake two square cakes.  I had one 8" square cake pan, but I needed another, so I did as The Joy of Cooking suggested and squared off a rectangular cake with aluminum foil, putting dried beans on the other side:

The cake was my favorite cake recipe: cocoa devil's food cake from The Joy of Cooking.  You've seen me make this cake twice already, so I won't duplicate it here.

Here's how it turned out: the foil edge is a little uneven, but not bad.  I decided to use it as the base of the cake, to hide the unevenness.

My dad and Marvis were visiting, and Dad helped cut the cake into the proper pieces.  You can see him measuring the fractions with a measuring tape.
Here are the pieces after he was done.  So, if the other square represents one, then we have a 1/2, a 1/4, 1/8, and two 1/16s (one of which will not be used), concretely (or maybe, more aptly, chocolately) demonstrating the sum I showed above.
The frosting is a simple buttercream: butter + milk + powdered sugar + vanilla.  Here's the 1 + 1/2 + 1/4.
And here is the completed cake.
Next I decorated it with chocolate chips, to illustrate positive powers of two.  I put four chocolate chips on the smallest piece, four more on the part of the next sized layer that's showing, eight on the part of the next sized layer that's showing, etc.
So that ideally, if you look straight down on the cake, it just looks like it has 64 evenly-spaced chocolate chips on it.
Here's the cake from its most photogenic angle, complete with tissue paper flowers in the background:
I ate the leftover 1/16th piece while I was decorating the cake.  Then, when I served the cake, I had the 1/16th piece, Jeff had the 1/8th piece, and Dad and Marvis split the 1/4 piece.  We all had equal portions of cake and equal numbers of chocolate chips.  How cool is that?!?

I took the leftover cake to work with me the following Monday, so that Jeff and I wouldn't eat it.  I told everyone it was made in celebration of powers of two.  One of my colleagues emailed me with a message of "Great cake -- terrible reason!"  I had to laugh.

I hope you all enjoyed this mathematically-inspired cake as much as I did!

Busy Busy Busy

I have been so busy for the past two weeks that it's just not funny. I have been burning the candle from both ends, and probably the middle too.

I'm the PI (principal investigator) for a proposal that's due the Monday after this coming Monday (or, as the British call it, Monday-week). This means I am in charge of writing the proposal, figuring out the budget, and filling out all the dumb paperwork. And because we are soliciting money from the gubmint, then there are all kinds of crazy hoops to jump through too. Adding to the confusion is the fact that this is the first time I have ever had these responsibilities, so I don't know what I'm doing at all.

I worked on the proposal all day on Sunday, and it looks like I'm going to need to devote some more time to it this weekend. I hate doing work on the weekend but it doesn't seem like I really have a choice in this case.

Last week, I taught a one-day course on supercomputing to students and professors from colleges and universities in the region who were attending a conference put on by my division. I had to add some new content to the course, unfortunately, so I couldn't just dust of the old slides and reuse them. It was kind of a last-minute thing and I had to make all the slides the day before. But it was a success and I got a lot of positive ratings. My colleague, who organized the conference, declared that I was amazing for daring to do a live demo of writing a parallel program on the fly. He was especially impressed because it compiled and ran correctly on the first try. I attribute that to the excellent audience members, who found my syntax errors so that the compiler didn't have to.

This week, we had our users' meeting. I gave a presentation on how to use our supercomputer. My boss, his boss, and a very important person from the gubmint thought that my presentation was really good. Personally, I thought it was so-so. But hey, if they were pleased, I was pleased!

I'm really glad that the worst of the busy times are over. I still have to finish up the proposal and jump through all the proper hoops, of course, but it's manageable. Now I can get back to my other projects (work-related and other).

Power Winners!

Sorry, my vast blogging audience, for my involuntary hiatus. I had intended to announce the winners of the contest on the 8th (=2³) but then my life and my job got in the way. So I decided that the 16th, which is two squared, squared, was a good alternative date. I'm future-posting this at 2:32 am, just to get a few extra powers of two in there. I may be awake at that time, but doing all the work I'm supposed to be doing rather than writing this post.

Anyhow, there were some terrific entries in the contest, and it was hard to decide who should win. In keeping with the theme, I will announce them in terms of powers of two.

2² place: A tie between Lost Clown and Rico, who describe their geektastic obsessions with cyclic groups and sums of 1/2^N, respectively. You are my kind of people! When I get around to it, I will post pictures of my powers of two cake, which illustrates concretely (actually, chocolately) the fact that the sum of 1/2^N is finite.

2²-1 place: Rachel, with the bimetalic Toonie, her favorite coin. If you bring those coins south of the border, they'll be worth more than $2. Heck, at the rate the dollar's plummeting, they might be worth $2² American sometime soon!

2¹st place: Laura, who shared a favorite song featuring the powers of two. See, math and music share a special relationship!

and...

2⁰th place: Pete, whose father, mother, and he are each twins. 'Cause that's just cool.

All those of you who are not my family members or colleagues have won a very exciting prize: your choice of a Tennessee ball cap or t-shirt.

Why? Because a) I live in Tennessee, and you don't, and b) Tennessee is a power-of-two themed state name. It has four (=2²) unique letters, each of which appears in it a power-of-two times (T -- once; e -- four times; n and s -- twice each). And, depending on where in the state you live, it is pronounced with either two or four syllables (TEN-see or TEN-uh-say-ee).

If you want to collect your prize, simply leave a comment with your choice, the size (if applicable), and a mailing address to which I can send your prize. The comments are moderated, and I promise not to publish your contact information. If you don't feel comfortable claiming your prize, don't worry about it; that's less work for me.