The One-to-Many Problem

I've been thinking about a class of related phenomena recently: those where a one-to-many relationship leads to inappropriate feelings or behaviors. I'll give a few examples.

Often, some shared cultural item (The Chronicles of Narnia, Amsterdam, Ernest Hemingway, chopsticks, etc.) comes up, and I feel as though I have a special relationship to it. I want to impress upon others my special relationship, to tell them the stories about myself and the item. And then I realize how extremely common it is for someone to have specific personal memories of reading a popular book series or using or watching others use chopsticks or whatever. Just because I visited Holland in the mid-90s doesn't really mean I have a special relationship with the country.

Professors commonly get a lot of annoying emails from their students. If you think about it, a student generally has at most five or six professors at a time, while a professor may have anywhere from 20 to several hundred students. Three or four emails per semester to each professor is easily manageable to the student, and overwhelming for professors. Students also feel that their own experiences are more unique than professors find them to be.

There are a few well-known blog authors whose blogs I have read for years. (John Scalzi and Andrew Sullivan, for instance.) I feel like I know these bloggers, have a sense of their personalities and experiences, etc. If I saw one of them, it would be easy for me to assume some kind of mutual familiarity that does not exist at all; they don't know me from Adam. I think people often have this feeling about celebrities.

Of course, it is always tempting to regard one's own experiences and situations as unique and special anyway, given that one's world revolves around oneself. But I do think these one-to-many situations, where something is more unique for you than you are for it, are especially prone to provoking such feelings. Perhaps this is why people like to have known indie bands before they became popular; it makes their special relationship to the band more plausible because it existed when the many wasn't so multitudinous.

Grad Apps In

As of today, I have done every single thing for my graduate school applications. One of my recommenders has submitted all of his letters, and the other two have shown signs of working on theirs, so everything seems to be well in hand.

I'm glad to be done with the process. I have applied to the following schools (in no particular order):

• Colorado State University
• New Mexico State University
• Texas A&M
• University of North Texas
• University of Florida
• University of Tennessee
• University of Kentucky
• University of Pittsburgh

I think I have a decent chance at some of these schools, but we'll see. If I don't get in this year, I will take some more classes (perhaps a graduate-level one in the fall, though I could also use a couple more undergrad classes to improve my background), take the GRE mathematics subject exam, and apply again next year.

Fake English

I really enjoy listening to people do "fake English" - I mean things like improv comedians in foreign countries doing gobbledegook that is supposed to represent someone speaking English. This guy did a whole song, and to me, the "English" is really so convincing that it's almost frustrating that I can't understand it. It's actually a pretty good song too, of a particular, easily recognizable American genre. I've seen this a few times, anyway, but ran across it again today, so here it is:

See more funny videos and Music Videos at Today's Big Thing.

Netflix to Blockbuster

I've had a Netflix subscription for several years now, but I've never gotten as much out of it as I could. It's very hard for me to mail movies away, since I can't get anything right away. And then when I do want a movie, I can't have it right now. I probably watch 4 or 6 movies a year from Netflix, which is ridiculous considering that I could buy a couple of DVDs every month for what I pay them.

Lately we rent a lot at Blockbuster. (By "a lot" I mean once or twice a month.) That's very convenient and nice, except that I never take the movies back, so I end up owning them. They are only $10 or $12 each, so it's not that expensive, but...still.

So, I have cancelled Netflix (and I give them major props for letting you do this on the website; so many services make you call them) and opened an account with Blockbuster online. What I got, for $12/month, is 1 DVD at a time by mail, and up to 5 in-store exchanges per month. This means that for less than the cost of one rental (when you figure in the high probability that I will never return the movie), we can just go to Blockbuster any time and switch out our movie. Or we can get one by mail if we want one that isn't available locally.

I'm pretty happy with this decision.

Attitudes

For weeks, two of my coworkers (let's call 'em James and Morgan) and I have been speculating over the situation with bonuses, which are typically given out in December at my company. James has been saying all along that he didn't think we'd get a bonus this year. We had been assured (since our president heard about these rumors) that a bonus with forthcoming, but James pointed out that any token amount could qualify as a "bonus" so the assurances were meaningless.

Last year, my first year here, I got quite a magnificent bonus. I was told that 1/3 of it came from the group that had recently purchased our company, and the rest was from our company. It was awesome. My offer letter says that the company typically pays bonuses of around 10%, depending on company profits and individual performance. I didn't have much hope of getting the same bonus as last year, but I was hoping for around 10%. That is still a really large bonus, in my book, despite what we may have seen last year.

Santa Claus finally came today, in the form of our president telling us our amounts. Mine was slightly less than last year, and well above any line at which I would have felt disappointed. I am pretty thrilled with it.

I made the mistake of going to lunch with James and Morgan. James is angry - he saved the company some large amount of money this year, was told this would be remembered at bonus time, and yet he didn't get a proportionately large bonus, he didn't feel. Morgan was not dissatisfied with her amount (she also reported getting slightly less than last year, but none of us shared our amounts or percentages), but was fretful over various things she's heard. She fears that because she is sort of mousy and doesn't often work directly with the people who decided the bonus amounts, it might be easier to "screw her" by not giving her as much as she should get. She had a lot of process worries over how these amounts were decided, and was also upset because of some conflicts over other people's bonuses. (Apparently one employee was upset that another employee got a larger bonus - something she was in a position to know about - and left for the day.)

It was basically non-stop negativity from those two. The president had apparently made a comment to James that, given that she didn't have as much total bonus money as she would like, she trimmed down the bonuses to some people who are highly paid in order to boost bonuses for people who make less. He was very angry and upset over this prospect, calling it "unprofessional" and commenting, "A company that knew what they were doing would pay people their market value," and then going on for at least 5 minutes explaining how this idea that some people make a "premium" could be applied to anyone and bitching how there are no standards and so on and so forth. Morgan mostly cavilled about this, that, and the other.

Morgan also pressed me about how I felt, and though I didn't want to be self-righteous about it, I did have to make it clear that I thought the amount was very satisfying and generous, and that I have chosen not to concern myself with the sausage-making aspects of how the company is run, both in general and with regard to bonuses. (I have found that worrying or becoming annoyed at the ways of corporations only leads to madness, especially since I'm never privy to the real details of what is going on. Best to just let them run the company, assume they know what they're doing, and look out for my own interests in more productive ways.)

I did not say any of this, but I find it really unproductive and, frankly, immoral to have the attitude (in life in general) that, while what you got might be OK, someone else might be unfairly getting more. Our whole economic system invariably leads to a lot of "unfair" things that people at my company, at least, are benefitting from. I have friends who are harder working, probably smarter, and definitely more educated than I am, and who make less money than I do even though their jobs are not in any sense easier. That is not "fair." It is not supposed to be fair. Fair did not come into it at any point.

Morgan was concerned that some people might get higher bonuses because they are more liked rather than because they are better employees. On what basis is an employee liked? How do we judge "better"? Why worry about the parts you can't control? Why choose to be dissatisfied when things are, actually, really good?

I don't think either of these people has had a serious job working for another company, or they would know that all companies are fucked up, to a lesser or greater extent, and that this one is particularly great to work for, and very generous in every way. And, you know, if you don't think you're being paid your "market value," there is an easy remedy for that. (That would be the, um, job market.)

If I do go to grad school, and if my cohort is large enough that there are subgroups to it, I really need to be part of a subgroup of people who work hard and have good attitudes. Because this stuff does influence me and I don't want to be around a bunch of whiners who think life is unfair all the time.

(NB: I don't think people are wrong for complaining about legitimate grievances. If you work at Walmart and can't afford to take your child to the doctor, rail all you want - I'm with you. But if all you have are upper middle class problems, then STFU with your BS about "unfair.")

Taking the Putnam

Yesterday morning, I went to school to participate in the Putnam Competition. This is a six-hour math exam (if you want to call it that), split into two 3-hour sections, with a lunch break in between. Each section has six questions that require college mathematics and a lot of creative thinking to solve. Each question is worth a maximum of 10 points, with partial credit given, and the median score is typically 1 or 2 points (out of 120).

I didn't really have time to go, but I didn't see how I could miss it. The competition is only for undergraduates, so this was my last chance, and I'd never done it before (nor had an opportunity to, that I was aware of, though you can take it four times overall and needn't be a senior nor a math major). I wanted to support our math department as well; I knew some people wouldn't show up, and I wanted to be able to say that, yes, we can at least field a Putnam team. (I wasn't on the actual team, which is three people from each school, in the end. But that's fine. You don't work together anyway - it's a purely individual endeavor.)

The morning session was fun. Of the six problems, one looked tractable, but I didn't get anywhere with it. I turned to another question that looked less tractable and ended up writing out an answer. (You have to write a full proof for the answer, not just solve the problem.) I am pretty sure a central assertion in my proof was wrong, though, but I haven't had a chance to check it yet. (It involved an 18x16 matrix, which I'm sure was not how the problem was meant to be solved.)

What was fun was that I was only trying to score any points at all. On a normal exam you're trying to get all of the points, or fall short as little as possible, but I was aiming to just get above 0, so it wasn't really stressful. I had three hours to work on as little as one problem.

The professor running the show bought us lunch - we all walked over to Old Chicago. It was actually pretty blissful. There were six of us students, of whom two are in my advanced calculus class, one is in my "senior seminar" next semester (but I hadn't met him yet), and the other two were unknown to me. (One I'm not so sure about - he argued on the way to lunch that irrational numbers can be accurately represented as fractions, using 22/7 - a classic approximation for pi - as an example.) We talked about the test, and other math topics, all through lunch. The professor kept quiet and just let us talk, which for all I know might have been out of peevishness at our annoying qualities, but felt gracious.

I found myself hoping that this is what grad school is like - that there are other people around and you can talk about math with them sometimes. I realize undergrad is like that for some people, but it hasn't been for me. I really enjoyed it. I also realized that I hope my graduate program does not have a competitive feel to it, because I wouldn't have enjoyed lunch nearly as much had we all been trying to one-up each other.

After lunch, we had six new problems. Several of them seemed tractable but I couldn't gain any traction for a long time. I was really tired from my week (I've been exhausted pretty much all week, and had to get up extra early for this thing), and that started to kick in, and I had had too much iced tea at lunch, so I had that nervous/sick kind of feeling, plus I kept having to pee. I finally did get an answer to one question. I now think that part of my answer was wrong, but I was really happy with the way that I approached it and the style of proof that I wrote for it. Still, I did not enjoy the afternoon session very much.

In the end, I am really glad that I went, and I'm hopeful that I might have scored 2 or 3 points on the exam. I'll post when scores come out.

Mathematics Genealogy

I was looking at The Mathematics Genealogy Project today. It's a project that kind of sounds like what it is - for (many) math professors, it lists their advisor and students, so you can trace up and down. And it's kind of astonishing.

I did a search on one of my professors, and this is what I found as I went up the chain of advisors (leaving out some initial steps for anonymity):

1. my Professor - no known students (makes sense; my school doesn't have graduate programs)
2. his advisor
3. the advisor's advisor, PhD from Indiana University, 1960.
4. Tracy Yerkes Thomas, Princeton, 1923. I knew I was getting into the past because the dissertation title was "The Geometry of Paths," which is just way too basic and short to be modern.
5. Oswald Veblen, U of Chicago, 1903.
6. E.H. Moore, Yale, 1885.
7. H.A. Newton, Yale, 1850.
8. Michel Chasles, École Polytechnique, 1814.
9. Simeon Denis Poisson, École Polytechnique, 1800.
10. Poisson had two advisors - Joseph Lagrange, and Pierre-Simon Laplace.
11. Lagrange's advisor was Euler, and Laplace's was d'Alembert.
12. Euler's advisor was Bernoulli.

Anyway...it's kind of amazing how few steps it takes to get from anyone to someone famous (even famous to me).

Another of my previous professors led me upward to Darboux (of Darboux sums fame, presumably) within a few clicks.

I got from one of Sally's professors to Isaac Newton! (It did take a few clicks, though.)

Pandora on xkcd

This is so true:

Grad School Applications

As of today, I have applied to four graduate schools. I've finished the online applications for all four, submitted my Statement of Purpose (except to one school, pending an email inquiry), sent my GRE scores, and emailed instructions to my professors on how they can send/submit their letters of recommendation for me.

I can't send my transcripts from Metro until the semester ends, because I need those grades on there, and that will be mid/late December, which is in time for all of the deadlines, but still makes me feel a little bit nervous. I don't want to send my other transcripts until then either, because I don't want them to be looking at all my crappy older grades without the better, newer grades. (That's probably just irrational, but whatever.)

I still have five more schools to finish my applications to, but I'm glad that I've made progress and have some apps in. I still have no idea how good or bad a candidate I am; I can't tell if I'll be lucky to even sneak into my lowest-rated programs or if I can expect several programs to invite me. But all I can do at this point is apply and wait.

Math Gaps

I read something recently where a person was talking about her approach to teaching math - that she reassures her class that they are not "bad" at math, but that somewhere along the way, they had a bad teacher, or they missed a day, and the lacking knowledge accumulated so that now they are confused by various things. And I was thinking of how many gaps I have in my own knowledge of math, and how crazy these gaps drive me when they show up.

It's hard to even recognize that something is caused by a gap. A certain topic will show up (infinite series, say, or rules of limits) and my mind will just go "that's too hard" or "I can't do those" without asking why. Are these topics somehow such that I alone cannot learn them? Do I have some tiny genetic flaw that has knocked out the part of my mind that would let me understand what a Taylor series is?

No. I just don't understand something because I have some gaps, and the thing to do, then, if I'm serious about math, is to figure out what the gaps are and fill them in. It's unlikely I'm missing anything that I can't learn, so I need to just get on that, as it comes up. And now that I'm finally more of a badass about reading and understanding math, I'm in a perfect position to do so.

Gendered Language

Sometimes my grandmother used to tell me, "Act like a little lady," and it always rankled me. Even when I was four years old I didn't like the word "lady" and didn't want to be one. But it strikes me that I have an unusual aversion to unnecessarily gendered language.

I noticed right away that my new therapist tended to say things like, "You're clearly a very [adjective] woman," and that it rubbed me completely the wrong way, even though the adjectives were positive things like "intelligent" or "passionate." (I mentioned it and he seems to have stopped.)

I never say things like "when I was a little girl" -- it's always "kid" or "child." I don't think I ever refer to myself as a woman unless there are situations that clearly call for it ("I'm not sure how other women manage their facial hair").

I found myself saying the other day that Ed would probably not be a good partner for the type of person who prefers not to know certain things. I don't think Ed will ever date a man, so I'm not sure why the language is gender-neutral except that "the type of woman who prefers not to know certain things" seems slightly offensive to me, like it invokes a stereotype, while "type of person" does not.

I don't think it's only female gender that I tend not to specify. I would never say, "What were you like as a little boy?" instead of "kid." I wouldn't call someone a sensitive, smart, fair, or caring "man" instead of "person." (I would only use "man" if I intended a constrast, e.g., "You're a really maternal man," and even then I'd probably say "person" most of the time.)

I don't do this gender-neutrality on purpose, I don't think. I use common words like "waitress" and "actress" and "handyman." I certainly use pronounce like "he" and "she" in the normal way (though I'm also a fan of the unfairly-maligned singular "they").

I wonder if this is a function of my feminism (using the word in a very basic sense to incorporate the feminism I already had when I was 4 years old), something that is more accepted in my social environment, or a result of some personality trait.

Idiot David Lane

So, Richard Heene pled guilty today to a felony. He's the guy who, along with his family, engineered the hoax that caused a big rescue operation to save his son who was supposed to have accidentally taken off in a helium balloon, but who was actually hiding in the garage as instructed by his parents. A lot of Americans watched this rescue effort anxiously, including some people in my office.

From the Denver Post article, we get this:

After the hearing, Richard Heene's attorney David Lane said that the seriousness of the charges reflects the anger Americans felt after learning they had been duped by the parents into fearing for Falcon's safety.

"Don't mess with America's emotions," Lane said. "America has the emotional instability of a hormonal teenager."

I can't believe the man's lawyer would say something so offensive and unprofessional. It is not "emotional instability" that causes people to become angry when they've been tricked into fearing for a young child's life, or to want restitution for a foolish crime that wasted public money on an unnecessary rescue operation.

Thomae's Function and Integrability

Thomae's Function is something we've discussed in advanced calc a few times - it's basically a sort of pathological function that is discontinuous at every rational number. I've drawn a picture here, along with the definition:

For irrational numbers, the value of f(x) is zero, and for rational numbers (other than 0), it's 1 over the denominator in reduced terms, so for instance f(1/5) = f(2/5) = f(3/5) = 1/5.

Between any two real numbers, there is a rational number, and between any two real numbers, there is an irrational number, so there are two things to notice here, to wit:

1. the x-axis is extra black because there are infinite irrational points on this interval [0, 1] that are irrational so that f(x) = 0
2. points below 0.1 on the y axis aren't shown, but would continue this sort of ever-thickening pyramid structure all the way down

Now let's talk about integration.

When Newton and Leibniz invented caculus, they conceived of integration solely as using antiderivatives. That is, if you have two functions, F and f, such that the slope of F at a point x is the value of f(x) -- i.e., F'(x) = f(x) -- then f is the derivative of F, and F is the antiderivative of f. By the Fundamental Theorem of Calculus, you can use an antiderivative to calculate a definite integral of f - that is, to find the area under the f(x) curve between two points (the area of S in this picture):

Now, obviously, you can't conceive of integration in quite the same way for something like Thomae's function. It can't possibly have an antiderivative - even if you can make a function with that kind of infinitely discontinuous slope, which I can't imagine you could, it wouldn't have a derivative.

So in the 19th century, a different way of conceiving of integrals was conceived. In calculus, you learn about Riemann sums. Basically, if you divide the area under the curve into vertical boxes, and then calculate the area of each box, that's an approximation of the area under the curve. The more boxes you have, the closer your approximation gets to the actual value, and the limit of those approximations is the area under the curve, as in this picture:
It turns out that using a method similar to this, Thomae's function can be integrated on the interval [0, 1]. The method is called "Darboux Sums."

One question when you use Riemann sums is how to calculate the height of each box. An easy way to do it is to use the leftmost or rightmost edge of the box as the height. As long as you use some method, it actually doesn't really matter what it is -- the approximations will still get better and better -- but Darboux does it a particular way.

Specifically, for Darboux sums you get an upper sum and a lower sum. For the upper sum, you use, as the height of each box, the highest value inside of that box, and for the lower sum, you use the lowest value inside of each box. You then add up the areas of all of the boxes, and that gives you an upper sum and a lower sum for the integral.

What next? Darboux's Criterion for Integrability is a theorem that says that if, given an error amount (epsilon), there is a way to divide up the function (i.e., a placement of the boxes - they don't all have to be the same width) such that the difference between the upper and lower sums is less than epsilon, the function is integrable.

If we apply this method to Thomae's function, no matter how we partition the function, the lower Darboux sum will always be 0, because every interval will contain irrational numbers. Since, if it's integrable, the upper sum has be able to be made arbitrarily close to the lower sum, it's clear that, if we can integrate Thomae's function on [0, 1], the result (the area under the "curve," if you will) must be 0.

And it turns out that we can indeed get the upper sum to be as close as we want to 0 (though never actually 0 - but that is never required in calculus, which deals in limits). I won't go through the proof of that, but it relies on the fact that, basically, if you draw a horizontal line somewhere above 0 in this function, there will only be a finite number of points above that line. Then you can just make the boxes that contain those points skinny enough that their overall area is arbitrarily low, and there you go.

Google Images as Visual Dictionary

One of my favorite ways to use Google lately is to look up things I'm unfamiliar with in Google Images. It doesn't work for straight-up words (like "mendacious"), but it works great for things like "hipster" or "umbros" or "engineer boots." You almost immediately find out what the thing is without the annoying mediation of words.

It's like the best visual dictionary of all time.

And Then What?

In a recent Since You Asked column, a woman asks, "How can I detach from my mother without feeling like a horrible person?" Cary counsels:

Cognitive therapy lets us ask, OK, so, What if, indeed, I were to feel like a horrible person? What does that really mean? What would be the end result of that? Would I die? Would I feel intense pain? Would others be harmed? Maybe we have had this voice in our heads, this little voice, saying, You can't do that or you'll feel like a horrible person! If we write these thoughts down, and see them, we see that they are not so accurate. We can ask ourselves, OK, how long would I feel like a horrible person? Would it be momentary? Would it last an hour, or days? And just how horrible a person would I feel like?

I have discovered lately that this general technique - going down the "what if" path rather than treating it as intolerable - works for a lot of fears. Sometimes it is the key to resolving insecurities.

For instance, if I am worried that Ed is mad at me, it can make me very upset. I might then expend mental energy trying to figure out if he is, indeed, angry. Maybe he says he's not, but I think he's lying, or he's angry and doesn't even know it. (A lot of this is hypothetical, but such concerns do come up around some of my other insecurities. For another person, the question might be, "What if he/she is cheating on me?") There's no way to be sure.

I have to stop and say, OK, so he might be angry. What then? Everyone gets angry sometimes. It's not a big deal to have someone angry at you. It's not like he's going to physically attack me. If he yells I'll just wait until he stops, or I can always leave. He probably won't yell anyway. And who is he to be angry? Why do I care? Fuck him if he's mad, I didn't do anything. Whatever.

Sometimes consequences really are pretty catastrophic. What if I have an incurable cancer? The best I can do there is perhaps to consider that I knew I would die of something someday in any case. It's not much comfort. But most fears don't have consequences that are actually that bad. What if I have a panic attack on the airplane? Well, then, I'll feel absolutely horrible for a while, but at some point it will end, and I'll still land on the other side and go on with my life. What if this woman cutting my hair accidentally nicks my ear? Well, it'll hurt a little and then heal.

So I think the key to a lot of those "Oh my god, what if...?" moments is to go ahead and answer the question.

Fenceless Confusion

Every Monday and Wednesday when I go to my class in the science building, I park in a corner lot, walk up to and then through the North Classroom building, and when I emerge, walk around the gigantic fence that has surrounded the Science building for probably about two years while they've been working on the new building.

Monday night I came out of North Classroom and...what? Was I in the wrong place? Everything looked different.

Oh. The fence was gone. Amazing! Now you can walk right up to the new science building:


Later, when I came out of class, I headed down the sidewalk, and automatically turned left where the fence has a corner, except...there was still no fence, and I was automatically dodging nothing.

So I walked over to the new building instead and looked through the windows. They're not quite done finishing the inside, and it's not open yet (to judge by all the signs direly warning you not to go in), but it looks pretty great. One thing I was happy to see was that at least the classrooms I could look in had tables with simple chairs rather than one-piece desks. I find that type of arrangement far more comfortable.

Hopefully at least one of my three classes next semester will be in there so I get to experience it before I graduate. It's the least I deserve for having to walk around that fence for years.

Severely Awesome Response

On this Ask MeFi thread, a woman asks

Sometimes my partner says silly things. I forgive him because, after all, we do all have our faults--and mine is leniency. However, sometimes he makes statements like,

"I'm glad I didn't go; if I had gone, and seen hipsters running amok, I would have cried severely."

He uses 'severely' in that fashion ALL THE TIME. I finally took issue with his grammar, & he said that it can mean "to a great degree, or requiring great effort," in which case I put up with him (severely), but that's hardly a good explanation.

I understand that 'severely' is an adverb modifying 'crying.' I still think he's ENTIRELY INCORRECT. MeFi, help a girl out?

When asked later whether she's objecting to the grammar (e.g., the word order or something) of the statement or the semantics, she clarifies that it's the semantics.

I loved this response by ROU_Xenophobe:

I feel that, semantically, one cannot cry severely.

If it's just a light slang usage of a perfectly cromulent word, sure you can.

I mean, say that he was using "thermonuclear" instead. As in, "I would have cried, thermonuclear" or "You hurt me thermonuclear bad." Clearly, he cannot actually cry thermonuclear because his body could not survive converting matter to energy inside his tear ducts.

Or say that he used "level 10" instead. I would have cried level 10. This also can't be, because crying does not involve discrete levels.

Or say he used "filthy." As in "I would have cried filthy" or "I kill you filthy, Vorga." Obviously you can't cry filthy, unless you consider tears to be filth, which is verging on the pathological.

But in all cases you know what he means. He sounds a bit like... dude... but in most circumstances that's not a big deal. If he can speak proper when he needs to, and if he'll stop if this is causing you actual no-shit consternation, all is well.

I love those examples so hard.

Wavelets

When I looked up my professor for next semester's "Senior Math Seminar" (the 1-hour class I have on Fridays), I saw that he had written a book about wavelets. And apparently that is going to be the topic for our class, and we'll be using his book.

I don't think I've had a textbook written by my actual professor since...well, Rice. And I only know I had one at Rice because of Jason's famous comment (on a course evaluation he happened to be present for) that the lectures were much better than the textbook (which had been written by the professor). And come to think of it, that may have been Sally's class, so I'm not sure I've ever had this particular experience.

Next Semester

I was only going to have two classes (one 3-hour and one 1-hour) next semester, but when I checked the schedule, I saw an opportunity to take Abstract Algebra, which, along with Differential Equations, is one of the most noticeable courses missing from my schooling so far. As of this moment, I am registered for the following classes next semester:

Advanced Calc II (Mon/Wed 7:00-8:15 PM)
This is the continuation of my current class, but unlike my current one, it is 3 hours instead of 4, which will be easier on the schedule.

Abstract Algebra I (Tue/Thu 5:30-6:45 PM)
Yes, once again I will be going to school every day of the week. But wait! There's more!

Senior Mathematics Seminar (Fri 10:00-10:50 AM)
This is a one-hour course required of all math majors. I've looked up past syllabi, and it looks like the professor just picks a topic of some kind and you do projects or something like that. It's convenient that this only meets once, for an hour, and I'm glad it's not on the same day as any of my other classes, but of course it's a bit inconvenient to go to campus in the middle of my morning at work.

Anyway, it should be a fun semester. It's technically 1 less credit hour than I have this semester, despite that I'm taking one more class. We'll see. And, of course, I am supposed to graduate at the end.

"Bayesian" Approach to Lie Detection

You may have heard about this guy, Richard Heene, who played a hoax in which he and his wife claimed that his young son Falcon had stowed aboard a balloon. It was quite the national news item, with TV stations playing footage of this saucer-shaped craft as it flew around, while various rescue crews tried to figure out what to do. It turned out that Falcon had been hiding in the garage, and the next day, Falcon spilled on TV that his dad had said they were "doing it for a show," and now it is generally known that it was a hoax.

Slate has an article today about why we couldn't tell that Heene was lying. It is an interesting look into how we try (and often fail) to detect emotional falsity, for instance judging the Heene family's fear for their son's life, versus how we detect lies. People are pretty bad at both, generally speaking, though of course some people are better liars than others.

My best way of guessing about lies is to take what I think of as a Bayesian approach to it.

What I think of as the default, non-Bayesian approach to lie detection is to watch and listen to the person making the statement and try to evaluate directly whether they are lying. Often we're not even listening for lies, so a ton of lies can pass completely unnoticed, but if the truth is important and you're not sure, you might be paying close attention to the teller.

I find it more useful to reason about the entire situation. For instance, say you are selling a car, and a man who lives in Kenya contacts you, wanting to buy it. He will send you a money order for the amount plus $600 and he needs you to pay the $600 in cash to his man stateside so that the car may be shipped. He sounds perfectly professional and nice and you have not heard of this particular scam before.

Still, you can ask yourself, "Is it likely that a person in Kenya wants to buy my specific car? Why would that be? Don't they have cars in Kenya?" and then proceed to this question: "Is it more likely that a perfectly nice gentleman in Kenya wants my car, and needs to handle the finances is this way, or is it more likely that someone is trying to scam me in some way?"

I was dating a guy once, and things weren't really going anywhere, but I was having a good time. He disappeared for a bit and then told me that he wasn't going to continue seeing me because he didn't want a commitment. I was kind of boggled because I hadn't said anything about a commitment, had shown no signs of wanting one, and was just having fun. Yet he seemed sincere about it, so it was kind of confusing.

Then I realized it was far, far more likely that he just didn't want to see me, for whatever reason ("just not that into me"), and he made up the commitment thing as a plausible and not hurtful thing to say about it.

I guess one way to go about this is to consider the alternative scenario and what it would look like. One time two friends of mine, a couple, were arguing. The woman had forgotten to get a (psychiatric, I think) prescription refilled and the man was insisting that she do so, and saying he would go do it for her, and she was being fairly belligerent in return. At some point, it crossed my mind that, had she refilled the prescription yet not wanted to take the pills, it would explain her behavior quite well. And indeed it turned out that she was lying and the pills were in her jacket pocket.

Since we understand the world, we can often imagine what scenarios might be in place around us, and starting there and moving down to people's behavior is, I think, a more accurate way to detect lies than starting from the behavior and trying to reason "up" to the scenario.