Grammatical and Mathematical Tip of the Day

The local Humane Society is running an ad on the radio asking for help taking care of all the pets that have been abandoned by people who have lost their jobs and/or homes and can no longer afford to keep them. While this is a very important message, their phrasing really irritates me every time I hear the ad.

They say "a countless number of pets" have been abandoned. This is wrong on many levels:

1. You cannot say "a countless number." It doesn't sound right. Go with either "countless pets" or "a number of pets."
2. If you're going to say "a countless number" and ignore the grammar, then I'm going to get pedantic on you and say that the number of pets cannot be countless. You see, countless means "too many to be counted," and it is impossible to have a number of pets that is too large to be counted. Too large to count easily or quickly? Sure! But it can't be too large to be counted. Here's why:

There are only non-negative integer numbers of pets. That is to say, you can't have 3.7 pets or √3 pets or -28 pets. Therefore, the number of pets must be countable.

In other words, if you took all the pets and lined them all up, you could map them one-to-one with the set of natural numbers (non-negative integers), kind of like this: {(Fido, 0), (Goldie, 1), (Muffin, 2), (Fifi, 3), ...}. Therefore, we could take the size of the set of one-to-one mappings of pets and natural numbers, and determine the number of pets.

I understand that what they really mean is an unknown and probably very large number of pets that need help. But they should express it in a more mathematically accurate way, especially if they're counting on the support of mathematicians.

FYI

This is what happens when you leave a two-year-old with markers and a coloring book while you go to take a shower...


Luckily, they're washable markers, so his new navel décor should come right out in the next bath.

My Daily Scenic Drive

One thing I really like about living here is how beautiful the scenery is. There are breathtaking landscapes just about everywhere you look.

Inspired by my budding supercomputer supermodeling career, I decided to snap a photo shoot of my own: the scenic things I see every day as I drive to and from work. Enjoy!

This is a view from the parking lot where I park my car. The area behind the parking lot is full of trees of all kinds.
This is a closeup of part of the previous picture. You can see the dogwood in bloom. Unfortunately, the redbuds were pretty much done by this point, so you can't see them here.

There's a beautiful scene that I encounter every day, on the property of my workplace, where a lake inlet comes right up next to the road and the tree cover breaks. You can see this inlet surrounded by trees on either side, and it's just gorgeous. Unfortunately, it's hard to get a picture of it without stopping by the side of the road and I didn't really have the time to do that the other day. Maybe I'll capture that image for you later. All my subsequent pictures were taken at stoplights when I was stopped.


At a stoplight, where I'm about to turn left.

This is another view of that clump of trees up the hill from the previous picture. Okay, yes, I did take this when I was driving. But actually, I wasn't looking at the camera -- I had begun to take a picture right as the light turned green. It took several seconds (thanks to the red-eye preventive flash sequence) for the picture to be taken. By the time the picture was snapped, I'd already turned left and was driving up the hill.

This is a typical view at a stoplight in town. Notice the hills in the distance. In the evening, when the sun is setting, they are positively spectacular!

Adventures in Coupled Differential Equations

If you ever took a differential equations course in college, you probably encountered the fox and rabbit (predator/prey) paired differential equations. They looked something like this:

R'(t) = 2 R(t) - 0.01 R(t) F(t), R(0) = R₀
F'(t) = - F(t) + 0.01 R(t) F(t), F(0) = F₀

where R(t) and F(t) are functions representing the rabbit population and fox population, respectively, at time t. The initial conditions (starting values for R and F at time zero) are R₀ and F₀, respectively. R'(t) and F'(t) are standard notation indicating the derivatives of R and F with respect to t: in other words, the change in R and T per unit time at time t.

If you think about it, you can understand that if we neglect constraints such as food supply and predation, the more rabbits there are, the faster the rabbit population will rise, which is indicated by the first term on the right-hand side of the first equation. Conversely, the more foxes there are, the more the fox population will decrease, because the foxes have to compete with each other for food, as modeled by the first term on the right-hand side of the second equation. The encounters between rabbits and foxes have a deleterious effect on rabbits and a population raising effect on foxes, as you can see by the opposite signs on the coefficients of the final terms in both equations.

This turns out to be actually a pretty good model of population dynamics. An important question in ecology is what population levels can be sustained at a constant level (equilibrium)? If you look at the effect on the predator-prey populations of different initial conditions, you can find this out using trial and error. (There are legitimate mathematical ways to figure this out without graphing a bunch of guesses like this, just so you know.)

I used Matlab to solve the pair of differential equations with different initial conditions. I didn't graph some of the more boring initial conditions: if we start off with all rabbits and no foxes, the number of rabbits grows exponentially. Similarly, if we start off with no rabbits and all foxes, the foxes go extinct. On to more exciting initial conditions.

First, let's suppose that we start off with equal rabbit and fox populations. How do the populations change over time?
(Click the graph to embiggen.) As you can see, the populations vary in a regular, periodic pattern. You can see that the populations return to the starting state every so often, but the numbers of each species vary by a factor of 3 or 4. What happens then if we start off with 200 rabbits and 5 foxes?
Observe the dramatic swings in the populations of the two species. Again, the result is periodic, but the period is longer and the change in population from the maximum to the minimum of each species is quite drastic.

As it turns out, I know what the starting populations must be for the two species to remain at constant population. Look what happens when we start with 100 rabbits and 200 foxes:


You might wonder, what if we vary the numbers slightly? So I set the starting population of rabbits to 110 and kept the starting fox population at 200, and here's what I obtained:

So, as you can see, if the ratio of rabbits to foxes is close to 1:2, the populations will remain relatively stable, while if it gets out of balance, the populations will swing wildly.


Similar predator-prey coupled differential equations can be used to determine the equilibrium state of vampires and humans in the Buffy the Vampire Slayer universe. The equilibrium population size for the city where Buffy lives is about 36,000 humans and 18 vampires. As it turns out, the population of Sunnydale is actually very close to the equilibrium population size computed with the differential equations! (h/t Pharyngula)

Other fun vampire population ecology links:
Punk Rock Operations Research: On Vampires and Stochastic Processes
The Oyster's Garter: Vampire Ecology: Twilight vs Buffy

Supercomputer Supermodel

Earlier this week, I spent nearly two hours in photo shoots at work. Pictures were being taken for our annual report and publicity materials.

Of course, since they wanted to make everything as realistic as possible, they chose two women and one man to pose between the rows of supercomputer cabinets. (After all, that is the gender ratio at my workplace.) In addition, we held a laptop while we examined the cabinets carefully. (Another thing that I'm always seeing people do.) We opened and closed cabinets, pointed out things to one another, and tried to be conversational despite the fact that we were wearing earplugs (it's loud enough in the machine room to damage your unprotected ears) and couldn't hear a thing. (Thanks to the wonders of Photoshop, those earplugs will disappear from the pictures.)

After the grueling hours in the machine room (hey, I was squatting for something like ten minutes, which gets really painful!), I told my boss that I really needed a personal upkeep allowance to buy clothing and have beauty treatments now that I'm a supercomputer supermodel. For whatever reason he didn't agree, claiming that he paid me enough for me to buy my own (damn) clothes and beauty treatments, with plenty left over for feeding my starving child. Personally, I think he refused because he's afraid he'd have to share the money they give him for that purpose. (Money he probably spends on conferences, just to obtain the conference shirts that are a staple of his wardrobe.)

Mother-Son Evening

This evening Jeff was taking a watercolor course so Vinny and I had an evening out on the town together.

We started by going to the "Pizza House" (as Vinny calls our local pizza buffet restaurant) for dinner, where we saw an older woman whom we recognized, sitting alone. I invited her to sit with us, and she did. I asked her about her past, and she told me she had a masters degree in mathematics, and that she'd worked as a programmer on my workplace's first supercomputer. I thought this was just about the coolest thing ever, and I asked her quite a few additional questions about her computing experience, and then told her a little about what things are like now.

After dinner, we went to play on the playground, but we didn't stay long because the sun was setting. We came home and it was soon time for bed. I tucked Vinny in just before Jeff came home.

Exploration Day

Yesterday was a really nice day. It was beautiful: sunny, but not too warm. Perfect for a family outing!

First, we went to the Aquarium of the Smokies. They have an exhibit where you walk through a glass tunnel and see sharks and other fish. At first Vinny was restless and didn't really like that exhibit but soon he got interested in looking at the sharks.

Then we had an early dinner before going into the park and seeing the Elkmont area. Elkmont was once a retreat for rich people to escape the oppressive summer heat in the city. When the national park was formed, instead of giving up their land they were paid a reduced amount of money and given long-term leases on their property, the last of which expired in 2001. We saw many of the former vacation homes, a number of which were in ruin. The area was placed on the National Register of Historic Places, though, so the ones that are salvageable will be preserved. I don't know what their plans are -- perhaps it will be something like Cade's Cove.

Yesterday was a fun day out with my boys. Today, by contrast, was cold, rainy, and overcast. We spent the day indoors.

Bedtime Routine

I put Vinny to bed just about every night (the exceptions being when I'm on travel or so exhausted that I crash early). We have a bedtime routine, in which we brush teeth, pee-pee in the potty, put on a diaper and a sleeper for the night, and then go in his room, read three books of his choosing while sitting in the rocking chair together, and then sing two songs of his choosing while he's lying in bed with the lights out, before I finally kiss him goodnight and leave.

For some reason, he feels obligated to tell Daddy that he brushed his teeth, so there's always that interlude in the routine where he has to shout to Daddy about brushing his teeth.

Sometimes, we read the same book three times. He goes through phases of liking some books above the others, but some of his favorites include Goodnight Moon, On the Day You Were Born, Ten Minutes to Bedtime, and The Little Engine that Could. We get books every month courtesy of Granny, and also one book a month from Dolly Parton's Imagination Library. The Little Engine that Could was the first book we got from that program.

I used to sing him actual songs, but nowadays he requests songs about various topics, such as sirens, the letter X, and Grandma Marvis. So unless I know a song that has that word in it (which is highly unlikely, since I know very few songs), I just make something up.

Finally, I give him a kiss and leave the room. Lately, we've started doing a funny little ritual where upon leaving, when I get to the foot of his bed, near the door, he says, "One more kiss!" and I go back and give him another kiss. It is the funniest thing ever, at least in the mind of a two-and-a-half-year-old.

He falls asleep pretty well, provided that I go downstairs immediately after putting him to bed, and wait for about an hour. Otherwise, he knows I'm still there and I hear shouts of "Hey, Mama!"

Hi, Cutie!

A funny Vinny story, to lighten the mood around here:

Jeff and Vinny were grocery shopping. They were waiting in one aisle for a woman to finish getting stuff off the shelf so that Jeff could pick up some stuff from that same shelf. Vinny looked over at the woman and said, "Hi, cutie!"

She didn't seem to hear him, so he tried again, louder. "Hi, cutie!"

Eventually Jeff told him that she was busy and not listening to him. At this, the woman noticed something was going on and Jeff explained that Vinny had been trying to get her attention. She was charmed by Vinny's greeting and laughed.

"Hi, cutie!" may work when you're two, but as he gets older, he's going to have to come up with something a little more sophisticated.

Same Thing, Different Grandmother

My one-hundred-year-old grandmother passed away on Friday night at about 8:30 pm. She had double pneumonia and went pretty quickly, from what I understand. She spent her last moments in the place she'd called home for more than a decade, an assisted living home in my hometown.

I am saddened by her death but it did not come as a surprise to me -- I'd expected her to go a year and a half ago. I'm glad that it was short and probably painless.

I'm more saddened by the implications of her death. As I've indicated before, she was the last link I really had to the maternal side of my family. My mother and I are estranged -- which hurts, but hurts a whole lot less than not being estranged. I won't go into the details, but it's a matter of dysfunctional family dynamics, inherited from previous generations, that have rendered us incapable of relating in a constructive manner.

I should probably be angry at my grandmother for her responsibility in this, but I cannot. While my mother's experience was very different, to me, she was always kind, always loving. She loved me and would not budge from it.

At the time of my parents' divorce, when the rift between my mother and me first appeared, Grandma remained stalwartly neutral, proud of both of us. At the time, it infuriated me, but in my advanced age, I appreciate it now. I strive to emulate this unconditional love with my son, to separate his actions from his person, and to love him forever. There is no better legacy than this.

She'll be cremated and a small funeral will be held next month in Nebraska, to which I am invited. I will be there, to show my respect for her and the last of that chapter of family history.

Still Kicking

Just a quick note to let my vast audience know that I am still alive. I made it home safely on Sunday, but it was really hard to adjust back to Eastern time. Yesterday's 8 am appointment was a real shock to the system!

I am working on some nefarious plans at work, which has me busy along with exhausted. I am considered an OpenMP expert (see the latest installments of the supercomputing course) and as such I am giving a one-hour presentation all about OpenMP at our users' workshop next week. In addition, I have a paper that I am writing that is due on May 1, a proposal due May 13 (but essentially, thanks to internal deadlines, due May 1), another paper I am determined to get out the door by May 1, an idea that I'm pitching to some higher ups next week, plus all my regular job responsibilities on top of that, including software policy stuff. So you'll have to pardon me if posting gets a little light for a while.

I'm Ready to Be Home

I enjoyed the conference, and meeting all the new people, and talking and being a role model, but I miss home.

I miss my boys. I miss Vinny's smile, and his infectious laugh. I miss Jeff.

I miss my own bed and my own house.

I'm ready to be home.

Progress (Yeah!!!)

I was overjoyed to learn today of the Iowa Supreme Court's unanimous ruling striking down the state's ban on same-sex marriages!

The justices cited equal protection in their decision, and also noted that objections to same-sex marriage are purely religious in nature:

In one part of the decision that focuses on religious opposition to same-sex marriage, the justices seemed to anticipate negative reactions, saying they considered the unspoken reason for the ban on same-sex marriages to be religiously motivated. The justices said marriage was a “civil contract” and should not affect religious doctrine or views.

Thank you, Iowa Supreme Court, for saying exactly what I've said for years: marriage as regulated by the government is a secular institution. If two heterosexual atheists are allowed to get married, then the civil marriage contract cannot be a religious contract. Therefore, religious arguments against any type of marriage -- mixed-race, same-sex, ugly people, you name it -- are irrelevant to the practice of marriage contracts as regulated by the government.

If your church doesn't want to marry two people of the same sex, that's fine -- don't do it. Nobody can force you to, just like they can't force you to sanctify the marriage of atheists in the church, or people of two different races, or whatever other couples who break your religious tenets. But your religion does not get to inform the government of the fitness of couples to be joined in civil marriage. No way.

Thank you, Iowa Supreme Court, for getting it. You are made of awesome!

A Good Time Is Being Had

I am having a great time at this conference. For one thing, I am realizing for the first time that I am a role model! I knew, intellectually, that I am a role model for young people who are interested in the computing field, but it never really sank in until now.

This conference is overwhelmingly attended by students, and they all want to be like me! Weird! Wacky! Incredibly flattering!

Which is not to say that they all want to go into my field, exactly, or work where I work. But there are an awful lot of them who plan to get a Ph.D. and enter the computing field, some at national labs, others in industry or at universities. And they want to hear my story, and get some advice. They are attentive and ask thoughtful questions.

And they are all so bright and so ambitious! (I mean that in a good way.) I was talking to some young women and in doing so recruited myself a summer intern to work with me on software. I've given away more business cards than I can count.

I'm also loving the diversity. The faces I see at this conference are very different from what I see every day at work. A white male friend of mine, in attendance at this conference, remarked upon his new-found minority status. "Welcome to my world," I retorted, with my African-American colleague in concurrence. We felt little sympathy for his discomfort.

Our presentation yesterday went well. It was well received and we got a lot of good feedback. I've networked a lot and made connections for my newest proposal, which involves broadening participation in the computing area. I'm really excited about outreach and getting a broader segment of society involved in computing!