Just flip a coin

I received some feedback on the fact that I have not written anything for a while. You mean those pictures on the left don't make enough 1000 words to make up for it? There are a lot of pictures over on the sidebar.

Fine. Here, consider this.

Your friend holds up a coin and asks you, "if I flip this coin, what's the chance it will come up heads?"

Being a rational human being, you reply "50 percent." If your middle school fractions teacher was a stickler for this kind of thing, you might add, "which can also be expressed as one-half, or zero-point-five." But essentially, it's a 50-50 chance. All right. Got it. Okay.

Now your friend flips a coin, catches it, puts it on her palm and covers it with her hand before you can see what the outcome was. Now she asks you, "what's the chance this coin is heads?"

What do you say?

No, really, what would you say? What are the chances?

I could just wait for people to comment, but that would be boring because who would bother? I just gave the answer, right?

WRONG!

The chance that the coin that has already been flipped is heads is either 1 or 0. It cannot be 0.5, because it is either heads, or it is not.

How is this different from asking before you flip the coin? It's either heads or it's not then, too, isn't it?

No, because then it hasn't happened yet. At that time, it could still be either one. You don't know, and the coin doesn't know, either. After you flip the coin, though, even though you don't know, the flip is already determined. It has happened. So the probability is either 1 or 0, and nothing in between.

Interesting, is it not?

I argue that this same reasoning is applicable to Newcomb's paradox. Some people disagree with me, but then again I bet many people would disagree with the argument above. That is why we have such controversies as the Monty Hall problem.

Other than the obvious perk of having all of my classes and professors in the same building, this is one of the best parts of being a math and psychology double major, because all these problems that are so hard in psychology are so simple if you blind yourself to everything but the math.

Engagement photos

Yesterday I took engagement photos for some people at Williams, a current student and her fiancé. I had never had to take high-stakes pictures like that before, but it was fun. The two of them were happy with them, at least happy with what they saw on the little LCD screen on the camera, and hopefully they'll be happy with the six-megapixel version, which is what matters.



We took six different sets, and the best one (in my opinion) of each is above. You can see them all here. They are getting married in August, and I might just be the wedding photographer. That would be interesting. And apparently they'd pay me. They paid me for this, too, which was kind of weird, because I was just taking pictures. It's not like I was painting pictures; I was just pressing the button. But I guess that takes skill, and you can judge for yourself whether I have that skill.

Sudoku

Someone found my blog searching Google blog search for combinatorics, so I looked at the results and found someone discussing the number of sudoku puzzles. It doesn't appear on the results anymore, but what I saw was this post which a female math teacher named Suzie apparently wrote yesterday, which said, "Without figuring out the exact number of Sudoku puzzles, I know for sure that there are more than (9!)^3 of them. Rounding down, that’s over 4.778 x 10^16 puzzles." She goes on to calculate how long it would take you to do all of them if you did a hundred per second and compares this to the length of time humans have existed.

This all seems like a bit of a daft misadventure to me, because although I am not sure how she came up with her number, I'm sure that the real number is indeed larger than that -- much, much larger than that. One thing you will never be able to say about my writing is that you don't know how I came up with my answer, so now I'm going to tell you.

Sudoku is a 3x3 grid of squares wherein each square contains a smaller 3x3 grid of squares, each of which contains each number from 1 through 9 exactly once. In each of the nine large squares, there are nine small squares in which the number of possible arrangements is 9! (9x8x...x2x1. So for each of nine big squares, there are 9! ways to arrange the numbers in the small squares, i.e. (9!)⁹.

Of course we have to factor in all of the symmetries; there are horizontal, vertical, and two diagonal directions of reflection, so we divide by 2⁴=16. Furthermore you can rotate four ways, so we divide by four. These are all essentially the same sudoku puzzle, except rotated or reflected, so we'll eliminate the copies.

Now we have (9!)⁹/(2^4x4), which is 1.705x10⁴⁸. So yes, much bigger than something on the order of 10¹².

Is this reasoning sound? Am I missing something?

Yes, of course I'm missing something. As stated, I'm right. But the crucial thing about sudoku is that each row and column in the global grid also has to contain the numbers 1 through 9 each exactly once. So this eliminates a lot -- really, a lot -- of the possibilities.

In fact, the problem is significantly more complicated than at first meets the eye. Wikipedia has this to say about it:

the number of valid Sudoku solution grids for the standard 9x9 grid was calculated by Bertram Felgenhauer in 2005 to be 6,670,903,752,021,072,936,960. ... This number is equal to 9! × 722 × 27 × 27,704,267,971, the last factor of which is prime. The result was derived through logic and brute force computation. The derivation of this result was considerably simplified by analysis provided by Frazer Jarvis and the figure has been confirmed independently by Ed Russell. Russell and Jarvis also showed that when symmetries were taken into account, there were 5,472,730,538 solutions

So somehow I don't think I would have figured it out tonight on my piece of paper, and neither do I think that (9!)³ is a helpful number in coming to this conclusion.

By the way, that number is 6.67x10¹⁸, which is more than Suzie's number (as she said) and less than mine (as I said).

Spring 2006 courses

The semester is in its full swing now. I have dropped the class in which I considered two pitchers of Gatorade, and I am now taking two math classes and two psych classes. Gah. I'm such a typical junior double-major. Anyway, I shall now discuss the four courses in which I am enrolled.

Decision-Making
This title makes the class sound like something Betty Friedan would have complained about, where women go to college merely to major in courses on how to manage a family budget, conflict resolution for spouses, and how to raise children properly. "Here's a course on how to make good decisions for your family, like how to decide whether to buy the name brand which may have more vitamins, or the store brand which is cheaper."

But that is not what the class is about, so when I tell people I'm taking it, I call it Decision Theory. That's what it is, really, so there you have it. Professor Kirby's research is all about decisions, so it's pretty cool to be taking a course with him on the subject. We've been talking a lot about economics, in terms of maximizing utility and using utility curves to understand why people make various decisions, and I have found the examples given in the readings to be quite interesting. It turns out that a lot of Nobel Prize-winners have worked on this sort of thing.

The only problem with psych classes is when they involve too much math. This is not because the math is too challenging for me; it is because I find it difficult to keep my eyes open. I had this trouble in psych stats when we went over for the twentieth time how to add, subtract, multiply and divide numbers. Now I have that trouble when we learn how it is, exactly, that the probability of A and B is the product of their individual probabilities. And we didn't even mention that the events were disjoint. Pity.

Psychotherapy: Theory and Research
This course makes me glad I didn't go to Wellesley. I was actually considering it for a time, and gosh, that would have been the most horrible decision ever. This class is composed of 12 females, and Professor Heatherington is also female. There is nothing particular about it that is bad, but the whole dynamic is just weird. Girls. Girls are weird all together with no boys around. It makes it feel like it's a special class for special people. And it's not.

Anyway, the class is all about psychotherapy, including psychoanalysis (Freud), behavior therapy, and anything else of that sort. We do the readings, and we come to class to discuss them. That is really all there is to it. The readings are long, and the class is all females. I am learning more about behavioral therapy, and the more I read, the more I believe it. I thought I didn't want to have kids, but now I'll probably have to have some just so that I can try out techniques of behavioral therapy on them. You know, to see if I can make them afraid of oranges and love apples, to see if a precisely planned-out schedule of reinforcement and punishment makes them achieve higher and higher until they are accepted to Harvard Graduate School at the age of 12. I am going to live vicariously through my children.

Tiling Theory tutorial
This is my second math tutorial, and an excellent second math tutorial it is. Tiling theory is about how you can tile the plane with shapes. For instance, you can tile the plane (i.e., the floor) with squares, triangles, hexagons, parallelograms, rectangles, and plus signs, among many other shapes. However, given an arbitrary planar shape, there is no finite algorithm for telling whether it can tile the plane. So we are investigating what is known and drawing lots and lots of pretty pictures.

The way the tutorial works is that we do some reading and a problem set over the weekend, and then my partner and I go to Professor Adams' office and one of us presents the material, and we all talk about it for an hour or so. Sometimes we ask questions and then try to prove the answers on the spot on the board. We always draw lots of pretty pictures.

Combinatorics
Combinatorics is about arranging things, like how many ways there are to arrange the letters in Williams (1260). It's also about all the nifty little relationships you can get out of Pascal's Triangle.

Combinatorics involves some cleverness and a lot of multiplying. I haven't come to accept the fact that I am now taking a math class in which a calculator might be useful, so I haven't yet remembered to bring along a calculator when I do my math homework. Therefore, I have done all of the multiplication by hand. The largest numbers I have had to find so far have been 26⁴ and 32x27x56, unless you count such things as 2¹² and 10¹² which have more terms to multiply and come out as larger numbers, respectively, but are not very hard. I also multiplied .9⁷ in decision theory class, but that was just to make sure that the author of the paper wasn't lying. The thing is, in combinatorics, most of the numbers cancel out. It would take me longer to type all of the exclamation points into my calculator than it does for me to write the expression on a piece of paper, cancel out everything, and multiply the very few numbers that remain.

I believe that calculators are useful mostly for the purpose of preventing this kind of needless work. When kids use calculators to add two-digit numbers "just to make sure it's right," that's useless. When kids have added numbers many times and are confident in their ability to do so, I think it's okay for them to use a calculator to add up three five-digit numbers. When they've plugged numbers into the quadratic equation a hundred times, they can use a calculator to find the solutions after that.

But for instance, once I loaned Ronit my calculator for an exam. The exam involved some sort of combinatorics problem, and Ronit didn't know where the factorial symbol was on the calculator, so he spent a long time typing out something like all the digits of 35!/(33!2!). When he got back from the exam, he complained that he had had to waste a lot of time typing out 35x34x33x... because I hadn't told him where the factorial button was. I got a piece of paper, multiplied 35x17, and told him he was a stupidhead. Which he was. This is why I say that students are too reliant on calculators and do not use their brains enough.

It's hard to live strong

A little over a year ago, during winter study, I put on a Livestrong wristband. Rebecca sent it to me, and I put it on. That was great. I wore it for about two weeks. Then it disappeared. I searched everywhere for it, and then I gave up and asked Rebecca to send me a new one. I tied that one to my wrist with dental floss, which succeeded in getting it to stay on, but looked stupid and induced me to fiddle with it all the time.

So I bought a child size wristband, and put it on, and didn't take it off for a year. Actually, I never took it off. It just disappeared one day during winter study. Poof! It was there one time when I checked, and the next time, it was gone.

No matter, I thought, it was nice to wear the same one for a year without taking it off, but now that it's gone I'll just put on another one. I had two, so I put one of them on. That one only lasted a week. It too disappeared without a trace.

So at that point, I only had one child size wristband left, so I didn't put it on. I didn't wear any wristband for about two weeks. I felt bad. I didn't know what to do. I didn't want to use up my last child size wristband, which would certainly disappear in this season of switching clothes often and gloves and multiple layers.

Eventually it occurred to me that I could wear an adult-size wristband, because I have a large surplus of those, so if one disappears, so much for that. So this is what I am doing now. It's annoying after all those months of one that fit, and it's sad that I lost the one that I had worn for a year, lost without a trace, but at least I am wearing one. Not that anyone cares other than me. But I care. And one day, I will take off the adult-size wristband and put on a child-size wristband, and then everything will be perfect, at least in the area of my wrist.

A very happy Valentine's Day

Today, on this wonderful Valentine's Day, I have an exciting announcement: I broke up with Ronit a month ago.

This is very exciting because it is something I should have done long, long ago, like a year or two ago, and finally I did it.

I am announcing this because a significant proportion of the Williams campus reads EphBlog, and a nonnegative, nonzero fraction of the EphBlog readership reads my blog, so this is a somewhat efficient way to alert the Williams campus to the fact that Ronit and I are no longer going out, that he is no longer my boyfriend, that I am no longer his girlfriend, that we no longer have a relationship, that we are both single, etc.

Why, you ask, would I care if the Williams campus knows this? Am I trying to seek attention?

No. See, I didn't even think that most people at Williams know who I am, and I persist in this belief. However, it has gradually become clear to me that those who do know who I am all apparently know that Ronit is my boyfriend. And he's not. So I'd like everyone to know that. Please, spread the word. Oh, and if you see me around with him at dinner or something, it's not because we've somehow decided to go out again -- because that will never happen, believe me.

So anyway, I am now free to do whatever I want with whomever I want. The first thing I did to take advantage of my newly liberated state was to go speed dating.

Speed dating was a college-wide thing held in the Log wherein all the guys were on one side of the tables, all the girls were on the other, and every three minutes the guys shifted to the left (their left, my right, but it doesn't matter). About half of the guys were freshmen, some hopelessly awkward, but many were very nice guys. Many, in fact, were guys I already knew and even liked. So it was nice to be able to talk to each of them for three minutes.

Here are a couple of interesting conversation snippets that occurred. I am protecting the identities of the clever.

Him: So what are you here for, dating?
Me: Well, yes, that or, you know, eternal love. Either one is okay. What, what are you here for?
Him: To meet people without having to dance with them.

Me: What is your idea of the perfect romantic date? (Someone else had already asked me this, and I said a picnic on the beach with the sun setting over the ocean.)
Him: One in which you really connect with the other person and feel like they understand you (he was more eloquent than this).

So anyway, now you know. And the rest of my matches who haven't yet should write to me. I added them as facebook friends; now it's their turn.

Ice on the windows

When I open my shades for the first time in the morning, there is the most beautiful ice on the storm window. Photographing it is a mad dash in which I turn on the camera before I even pull up the shade and slide up the inner window, because the ice melts and turns to droplets so quickly.



Since I am always thinking about math, I can't help but see the tiling, and maybe even the fractals, in the ice. Check it out.



Those are all from the same window, the one facing Route 2. That's usually the only one that gets ice on it, but then this morning the other window had very different ice, the frosty snowflake crystals you usually see on windows, and with Faye in the background and such a wide variety of shapes of ice, it makes for a nice wintry feathery collegiate view.



You can see the water droplets from the tiny ice crystals already melting -- and this was the first picture I took.

Now, don't you wish these beautiful patterns greeted you in the morning? Every morning they're there, and every morning they're different. Awesome.

Topologically equivalent

Question: Are males and females topologically equivalent?

If two objects are "topologically equivalent," this essentially means that if they were made out of rubber, they could be stretched into each other without tearing or pasting. The important question, then, is how many holes each item has.

For example, a tennis ball is topologically equivalent to a football, a pencil, an orange, a shoelace, and anything else that doesn't have any holes. These are all topologically equivalent to a sphere, a 0-holed torus, if you will (and please don't).

Question: Why do topologists have trouble eating breakfast?
Answer: Because they can't tell their donut from their coffee cup.

This common joke (common if you surround yourself with mathematicians) is based on the observation that a donut and a coffee cup both have one hole. These are also equivalent to an inner tube, a sock with a hole in the toe, and a severed pierced ear, all of which are topologically equivalent to a 1-holed torus (commonly known as a torus).

Here is my favorite example. Suppose you have a bottle of syrup, the Aunt Jemima kind of syrup where there is syrup in the handle. Then if the bottle is full of syrup and sealed, you have a 1-holed torus (the handle part where you put your fingers through). If you take off and discard the cap and pour out all the syrup (and wash the bottle so that you can recycle it), you now have one hole that starts at the opening where the syrup comes out and connects all the way around the handle and goes through the whole inside of the syrup bottle, and you also have that original hole where you put your finger through in the handle.

That is a sort of complicated example, and I still haven't been able (after almost a year) to mush the plastic around and end up with a pretty 2-holed torus. But one way you can visualize this better is that it's kind of like how many strings can you loop through holes of the torus if the person holding the ends of the string is very far away and each string can only go through one hole?

In the case of the donut, the string goes through the center of the donut (1).
In the coffee cup, it goes through the handle, just like your fingers (1).
In the full syrup bottle, it also goes through the handle (1).
In the empty uncapped syrup bottle, one goes through the inside of the handle, and the other goes around the handle like your fingers (2).

Now that you have some definitions, you can consider the problem of the topological equivalence, or not, of males and females.

Except that there is one problem, or omission, from these definitions and examples. What if instead of just drilling a hole through a ball and making it into a donut, you then drill a hole from the side that goes from the outside of the ball to the already-drilled tunnel? What then? To what is this new surface (since we really only care about the surfaces that remain) topologically equivalent? This is of major importance to the male/female problem, because, for instance, the hole that connects your mouth to your bum also has the holes from your nostrils going into it from the side. So stand by on that while you think about the rest of it.

But wait! We don't care what n-holed torus a male or female is topologically equivalent to; we only care if they are topologically equivalent to each other. So the nostril question, while interesting and important, has no real bearing on the question at hand, because females and males both have nostrils and mouths and the connection is the same. The only thing we have to wonder about is, let us say, the plumbing beneath.

I know from biology classes that there is a pathway, a "hole," if you will, connecting the mouth, the esophagus, the stomach, the intestines, and the bum. I am not so sure about the mechanism for urine. Is there a single pathway? I don't think so. I think the liver collects stuff out of the blood and there is a tube of sorts going from the liver to the orifice for ejecting urine.

This is the same for females and males, but we will consider it anyway: If there's a tube connecting an opening in the skin to the liver, and at the liver end, this tube ends: It doesn't connect, say, to your nose, so it doesn't add an extra hole to the object. Then this is just like if you had an orange and you poked it with a pencil but not all the way through. It would still be topologically equivalent to a sphere, the fact that you poked it would not affect its topology at all. Similarly, if you glued a raisin to the outside of the orange, or if your orange for some reason just had a strange protruding lump on the outside, it would still be topologically equivalent to a sphere. Simple enough.

So the urine-ejecting system does not add an extra hole to the torus. Recalling the raisin discussion above, the fact that males have an extra protrusion in that area also does not change the topology from what it would be if they did not.

Thus, we are ready to consider the most pressing question, which is: Females have an extra hole. Does that mean they are not topologically equivalent to males?

My answer is no, and my reasoning is the same as with the urine system above: That hole connects to the uterus and the ovaries, which don't connect to anything else. So it's like poking into, but not all the way through, an orange.

Do you agree?

Math is better

Yesterday I was having lunch with Brian and Kathryn, and Brian mentioned that he had recently sent out a list of 10 reasons why math is better than sex.

"For instance," I asked him, "what's one of them?"

Brian thought for a moment. Kathryn and I are female, and we were having lunch, so he had to censor. "Let's see. Nobody is upset if a man solves a math problem very quickly," he said.

"Um, that's not very funny," I said, "and plus, I do get mad at you if you solve a problem very quickly because maybe I don't understand it yet."

"Okay, okay," Brian said. I am not sure if he actually said "okay, okay," but he says it a lot and it seems like something he would say in this situation. "Okay, here's another one: you can do math in public without getting arrested."

"Come on!" I said. "That's not clever. That's not even funny! I could do better than that."

"Fine!" said Brian.

I thought for a moment. "In math, you can use a rubber more than once."

Brian's eyes exploded. I will have to assume this was because he was astounded at my cleverness.

Thus began my quest to think of 10 clever reasons why math is better than sex. This quest has occupied much of the past 32 hours, but it has been fruitful:

10 reasons why math is better than sex:

1. In math, you can use a rubber more than once.

2. You learn maximization strategies in school.

3. You can be past your prime for sex, but in math you have infinitely many primes.

4. Sometimes people won't have sex with you if you're the wrong gender, but in math, women and men are topologically equivalent.

5. In sex groups are usually just a fantasy, but in math all the geeks get group actions.

6. In sex when two x's come together, you get a baby. In math you just get a parabola.

7. You can usually only sleep with a finite number of people each night, but in math you can have an infinite series.

8. Mathematical satisfaction doesn't put you to sleep.

9: Just because you don't have an open relationship in math doesn't mean it has to be closed.

10. In math, a union of closed balls is sometimes complete. But in sex if your balls are closed, your union will never be complete.

If you don't understand all the terminology, that's okay. Brian added another one:

11. In math, even some of the oddest and most exotic things are still called normal. The same does not hold true for sex.

NMH

I got a job for the summer! I'm not going to be unemployed after all! Now they just have to send me the job offer letter and I really hope they do!

!!!

Consider two pitchers of Gatorade

Update: As I was eating breakfast this morning, I realized that there was one thing on this page that was wrong, and one that could be simplified. I have changed them below.

I was thinking about taking this Econ class that would fulfill my Peoples and Cultures requirement (argh, Peoples and Cultures requirement) so I went to the first class. It was very interesting and all, but I started thinking about this problem that was in my middle school math textbook, and so I was very excited when he handed out the syllabus so that I had a piece of paper to work it out. I didn't have the slightest idea how to solve it in eighth grade, but now I have more "mathematical maturity," so such problems are piddly and most of all FUN!

Here is the situation. You have two pitchers. The pitcher on the left contains two quarts of full-strength Gatorade. The pitcher on the right contains one quart of water.

Pour half of the contents of the pitcher on the left (one quart of full-strength Gatorade) into the pitcher on the right. Then pour half of the contents of the pitcher on the right (one quart of half-strength Gatorade) into the pitcher on the left. And so on.

Q. How many iterations does it take until the concentrations of Gatorade are the same in both pitchers?
A. Infinitely long. Don't ask stupid questions.

Q. How many iterations does it take until the concentrations of Gatorade are the same in both pitchers, to three decimal places of accuracy?
A. Surprisingly, 10.

This problem is not very hard if you leave everything as a fraction. And if you don't leave everything as a fraction, you really don't deserve to be doing math problems. Go sit in the corner with a calculator and punch the buttons like the rest of the stupid Americans who don't bother to use half of their brain cells.

But wait, you said to three decimal places of accuracy. Ha! That means you used a calculator! (Diana Davis is a strange person who likes to refer to herself in the first, second, and third person, all in one post. Deal with it.)

Don't be silly. After ten iterations, I had two fractions, 683/1024 on the left and 341/512 on the right. I did long division and calculated them to five decimal places. During economics class. And I participated in the class discussion. Take that.

After class, I went and waited outside the crew office for half an hour. I had nothing better to do than try to find an explicit formula for the concentrations after n iterations, so that is what I did. Unfortunately, I was only able to come up with a recursive formula, and a recursive formula is vastly inferior to an explicit equation, but a recursive formula is better than no formula at all.

Here it is, because I am just mathy like that.

Let L_n, R_n be the numerators of the concentrations of the pitchers on the left and right, respectively, after n pourings from left to right or right to left, respectively. Then:

L_n = 4 L_n-1 - 1
N_n = 4 N_n-1 - 1 4 N_n-1 + 1

where L₀ = 1 (full-strength Gatorade)
and R₀ = 0 (water).

The denominator of the concentration is 2²ⁿ 4ⁿ.

Now you know.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

A similar problem is to start with two pitchers of water, and pour half of the volume back and forth as above, without worrying about the concentrations. I think this was the original problem in the math book. As you might expect, you eventually get 2/3 in one and 1/3 in the other, with 1/3 of the total volume being passed back and forth each time. This is the stable solution, so you'd expect to get it eventually.

You can start with whatever volumes of water in the pitchers that you like, and eventually you will always reach the 1/3 2/3 situation. If the initial volumes are equal, it only takes about six pourings to get .33 and .67 to two decimal places. If the volumes are very different, it would take about the same amount of time, because if one is empty and the other has all the water, after one pouring the volumes are equal and you are back to the situation just described. I suppose it wouldn't take very long in any case. Is this surprising? Maybe.

I think the actual problem back in eighth grade -- it wasn't assigned; it was just there in the book -- was to say what the volumes would be after 1982 pourings back and forth. This is what textbook authors do to try to stay trendy, use the publication year to make the math seem interesting and current. But if you go to public school and the teachers realize that basic algebra hasn't really changed much in the past couple of millennia and that textbooks are very expensive, they don't buy new textbooks all that often, and a problem involving 1982 doesn't seem so current and trendy in 1998 or 1999.

So you see, I really am learning things in college. They're just all in my head.

Ridiculously anemic

Mr. Parris used to say that everyone should get their ferritin checked. Ferritin is very related to iron, and it's a key predictor of performance in endurance sports. For instance, Carolyn was working hard and not improving, so he had her get her ferritin tested and it was 14, which was very low, so she went on iron and got way better. So it's good to test for ferritin.

But getting your ferritin tested requires a blood test, and I only ever had one blood test in high school, and they were already testing for so many things that I felt bad asking them to test for another one. And then when I had that blood test I passed out, so I decided I didn't like blood tests. This is why I don't give blood, other than the fact that I am ALWAYS an in-season athlete, because if I have trouble with them taking 1 mL or 10 mL or however much they take, there's no way I could survive their taking a pint.

Anyway, they thought maybe I had mono so they took a blood test last week, and I didn't pass out, and I don't have mono, and they tested for ferritin! I was really excited when I heard they were going to test for ferritin. It was the most exciting thing that happened to me all week.

Today the results came back. My ferritin is at 8. Eight! And Mr. Parris was shocked when Carolyn's was 14! The normal range is between 20 and 60. Athletes should be in the high 20s. And mine is at 8. Other than the fact that I didn't train all fall, this explains why I am working hard and running really slow.

Ferritin, if you can't tell from the name, has to do with iron. Basically there is no iron in my body. So I am really anemic, and I have to take a lot of iron. Twice a day, unless it upsets my stomach, and it is not going to upset my stomach because nothing upsets my stomach. In the past six years I have had an upset stomach twice, which was the two times I ate lots of mushrooms. Iron is not going to be a problem.

So I went to the pharmacy to buy iron. They were sort of closed, so I was looking really fast to find a bottle of iron pills. I was looking all over for something that said iron. Alphabetical order? Vitamins separated from minerals? I couldn't figure out how it was organized, and I couldn't find the iron.

Finally I found it, labeled "Fe tabs." You know your pharmacy is catering to an educated audience when the supplements are labeled by their chemical abbreviations. "Excuse me, do you have any Ca? I need 200 mg of Ca. And how about some Fe?" So I got 100 Fe tabs. In a box. It was very strange.

Apparently this will help me with shortness of breath. At the health center they asked me if I had experienced shortness of breath. I said yes. Then they asked me about certain details about this alleged shortness of breath and I got all confused. "What's is the definition of shortness of breath?" I asked.

Apparently this is not a normal question. Apparently normal people don't ask for definitions. But I am one of those precise people who wants to know what, exactly, we are talking about, and they told me the definition, and I realized oh, I do have shortness of breath. I get way more tired when I sprint from my dorm to the math building than I used to. When I run up the stairs to my room I am tired. And the iron, we hope, will alleviate these issues. This is just what happens when you're ridiculously anemic.

I had a plan, and I followed it.

Yesterday I decided on a race plan for today's 3000, which was to run 100 seconds per 400. In my last race, someone for some unknown reason was kind enough to take my splits, and although I ran some laps in 100 seconds, the majority were between 104 and 107. 100 sort of sticks out in the mind as a nice number, and so I remembered that back in high school when I used to run the 3000, most of my laps were 95-98 seconds, with only a few up at 100. So I decided to run them all at 100.

100 seconds per 400, 50 seconds per lap for 15 laps means 12:30 for the race. This would be an 18-second improvement over my previous race, which sounds like a lot. But to put it in perspective, in tenth grade there was this meet at Bates where I ran the mile (5:55) and really didn't feel good, but my coaches said to run the 3000 anyway at tempo pace as a workout, so I did, and I finished in 12:31, no straining, tempo pace.

So the gun went off, and I settled happily into last place. Last place is a good place to be at the beginning of a race, because everyone goes out too fast. And indeed, I ran the first lap in 47. "FORTY-SEVEN, HEATHER," I heard a coach shout. "RELAX A LITTLE BIT." I knew I needed to lay off the pace a bit too, so I did, and the second lap was 51. "FIFTY-ONE, HEATHER," I heard this time, "PICK IT UP A LITTLE."

At this point I heard a strange slapping noise. I wondered what it was, and then I realized that it was the sound of the girl in front of me's thighs slapping each other. I decided I would not be beaten by someone whose thighs slapped together in a race. However, I decided to hang on behind her for one more lap and see if she picked it up from 51, because there would be nothing worse than passing someone only to have them get all antsy about your passing them and speed up and make a huge pain and totally ruin your race plan, all because the second lap of a 15-lap race was one second too slow.

The third lap was also 51, so I passed her. As we came around the end of the fourth lap, the coach shouted "FIFTY, HEATHER, PERFECT." So I decided to capitalize on the situation.

"HI, HEATHER," I shouted, because she was right on my shoulder. "I'm trying to punch out perfect 50s; what are you doing?"
"50s are the goal," she said.
"Awesome," I said.
"I'm not trying to pass you," she said, "I'm just pacing with you."

Here is a picture of Heather sitting on my shoulder:

Ryan Ford '09 took that picture. I was busy racing.

Anyway, it was good for her to pace off of me, because I proceeded to punch out perfect 50s. After seven or eight laps of "FIFTY, HEATHER, PERFECT," her coach stopped telling her to pass me. Then suddenly I no longer sensed her shadow just out of my field of view. I glanced back as we went around the turn and saw her two or three meters back. "YOU FOUND A GOOD ONE, HEATHER, STAY WITH HER," said the coach this time. That's right, if you're lucky enough to be able to pace off of Diana Davis, you stick with it, because you've found a good one.

To achieve this feat of metronomic pacing, I looked at my watch every 100 meters to ensure that they took exactly 25 seconds. Looking at your watch during a race is like looking over your shoulder: If you do it, people cringe. It's just not done. But I decided that I'd rather lose a fraction of a second over the course of the race and run perfectly even splits. So that is what I did.

Here is a picture of me looking at my watch:

Ryan Ford took that picture, too.

You'll notice that Heather is no longer on my shoulder in this picture. That's because eventually she was unable to keep up the perfect 50s, and she dropped back. But I kept going, and wouldn't you know, just running even splits I caught up to the next person on lap 10. Passed that one and moved up to the next pack, not straining, just running 50s. Passed them too. A few of these efforts resulted in 49s.

I had decided at the beginning of the race that if I was feeling strong with the 50s, I would go as fast as I could with three laps to go. So with three laps to go, I put in surges to pass the people in front of me, and punched out a 48. Then there were just a few more people left to catch -- even pacing, you'd think it was a new idea or something -- so I poured it on and went as fast as I could for the last two laps, sprinting it in without looking at my watch for the last 400 meters.

Here is a picture of me sprinting it in:


You'll notice that I am all alone. This is because that is how much I passed those other people by. No, really, not kidding. Looking at that picture, you wouldn't think it was possible, but a plan is a wonderful thing.

I finished in 12:15, which is 33 seconds faster than two weeks ago. Amazing what a few weeks and a couple of hard workouts can do. And amazing what you can do when you're sick if you take a little bit of medicine.

The Sweater

I have this brown sweater with a griffin on the lapel and leather pads on the shoulders and elbows. It's not a great sweater, because it's brown, and it's too big for me. But there is one really awesome thing about the sweater, and this one thing makes me bring the sweater to college every semester and even wear it from time to time. And that is: Professor Morgan has the same sweater.

It is a highly amusing game for me to try to wear the sweater on the same day that Professor Morgan wears his. I have several tricks that help me to do this, but let me not digress from the point, which is: today was the first day of Applied Real Analysis class, and we were both wearing the same sweater.

The class didn't notice it at first, really. Then Professor Morgan introduced me as "this is Diana Davis, wearing that nice brown sweater, and she'll be our TA." Then they looked at my sweater, and they looked at his sweater, and they were sort of confused, and I was laughing, because I basically think that trying to wear the same sweater as Professor Morgan is the most amusing game ever.

And then they asked why we were wearing the same sweater, and I had to explain that it was simply because I think it's the most amusing game ever, not because, you know, we got them at a math conference or something. That would be the lamest party favor, a brown sweater with leather shoulder and elbow patches. But I'm just lame for fun.

Summer jobs

I have now applied for two summer jobs. I started applying for the Exeter job last November, even though the deadline is February 15. I got all of my materials in my January 16, which was good because January 15 was my goal.

I wanted that job so bad that I dreamt about it. For four nights in a row, I dreamed that I had gotten the job. One night I dreamt that I had been assigned to Mrs. Parris's "Introduction to American Culture" class; two nights later, I dreamt that this guy was making a certificate in calligraphy with green ink for me that said I got the job and could choose between teaching with Mr. Parris and teaching with Mr. Wolfson. While I was weighing the options, I woke up. I was extremely disappointed to wake up.

I wanted that job so badly that I procrastinated on applying to other jobs until all but one of the deadlines had passed (that was the one that is rolling, with no deadline). But I sent in my application to that one today, with my transcript and recommendations to follow shortly, I hope. We shall see what happens with that.

I will find out about the Exeter job shortly after the deadline of February 15, and about the NMH job whenever my application is complete and they do their rolling review of applications.

If I don't get one of those, I guess I'll have to do something that will build my resume for grad school, like another REU or something. We'll see.