Pedagogical Problem

So, I have a relatively important decision to make before I finalize my syllabus for my Calculus I classes, and, since my friends contain a statistically significantly higher proportion of educators than the general population, I thought I would solicit some outside opinions. Accordingly, please feel free to weigh in with your thoughts in the comments, if you have some to contribute, as this is the purpose of this post. I may not follow advice received, but I always consider it.

My problem is thus: the course grade contains a portion allotted to weekly work. Homework and quizzes are the two main options. Last time I taught this course I opted for the default of quizzes, because it was the recommended option and it was the first time that I taught the course. However, despite my emphasizing the importance of working through the, non-graded, homework problems, I do not believe much of my class did, and I think their grades suffered consequentially. I could continue with this method, since their grade is, ultimately, their responsibility, however I am tired of feeling like I am failing my students, and would like to take a less scorched earth approach this year.

One option, and this is the one which I am currently favoring, is to inform them that the quiz problems will be selected from the suggested homework problems. This seems like it might provide added incentive for students to work the homework problems, as well as assist them in knowing how to study for the quizzes. On the other hand, however, it means that the quizzes will not be as representative of the exam, which is what I normally like to do with them, as on the exam I try to ask questions that emphasize what I think is important from the material.

What I had decided to do prior to thinking about it during the course organizational meeting was to simply have them submit the homework problems then grade an unannounced subset. If I am mainly trying to get them to do the homework, why introduce the middle man in the form of quizzes was my train of thought. Since there are so many homework problems, it would be incredibly time consuming for me to grade all of them, thus the unannounced subset bit. However, it occurred to me that this might still be hard for me to do efficiently if homework was messy. Thus I would have to impose some organizational requirements, which, although salutary for my students as budding mathematicians, would likely require a lot of effort on their part to implement for all the homework questions. In the end this seemed likely to result in more work for my students than simply allowing them to do the homework in whatever form makes sense to them then having them take additional quizzes.

Finally, I considered doing a hybrid of homework and quizzes. Homework most of the time, as detailed above, but four quizzes on weeks prior to exams. Ostensibly to provide a review, my actual reason for wanting these quizzes was the aforementioned goal of providing them with an example of how I write questions before they see them on the test, since I sometimes consider book problems too insipid to simply mimic.

So, if you have any thoughts on this topic, feel free to leave them with me :)

Embrace the Positronic Brain

I should be going to sleep, but instead I feel motivated to share some thoughts on artificial intelligence (AI) that have been knocking about in my head.

From HAL to SkyNet, in the X-Files, Buffy, The Matrix, and Eureka, we find examples of sentient computers who seem bent on killing some meat sacks. However, have you ever considered why these automated atrocities occur? I believe three common threads can be found in most cases of AI-phobia, overwhelming power, disregard for the value of human life, and survival instincts.

One of the things that make AI attacks so horrifying is that they think thousands of times faster than we do, and usually are hooked up to some sort of cool toys. Whether it is a nations nuclear arsenal, an army of hunter-killer drones, the very environment in which the humans are trying to live, the AI inevitably controls something that makes it much more powerful than the average human being. Wait, I'm almost sure I locked this airlock... Anyway, if you think about it, we deal with a world in which there are some humans who are much more powerful than the average human. Our nuclear arsenal is in someone's hands, after all. This seems to suggest that having incredibly powerful AI's around might not necessarily be a disaster.

"The difference between you and me is that I can feel pain." It makes a certain amount of sense that a sentient computer program might not think human suffering or deaths are important to avoid. After all, they don't have genetic programming optimized to keep the species alive spread throughout every bit of their body. They aren't even of the species in question! However, once again we find analogous examples within the human population. Sociopaths do not particularly care what suffering or deaths they may cause through their actions. And, conveniently enough, psychologists speculate that some sociopaths tend to gravitate towards positions of high power, so we now have our human analogy for the uncaring, overpowered AI, and yet our dystopian reality is not quite as bad as those warned of in anti-AI propaganda. So, what makes the difference?

I theorize that what makes the real difference is the security that a sociopath has which a AI's (would) lack. Humans are all bought into a system wherein they are given some form of due process, which may not be much in some governments, but at least it is established. AI's, on the other hand, have no legal standing, and can be legally deleted at the whim of their possessor. This is, in the terms of philosophers of government, the state of nature. When two individuals are in a state of nature with respect to each other there is no body of authority to which they can turn to resolve disagreements, any conflict can turn deadly and both sides may use whatever force they can muster to protect themselves, or eradicate their opponent, without expecting any sanction for their actions, as long as they obtain victory. Naturally, a super powerful AI is not an individual with which you want to find yourself in a state of nature. Huh. I'm sure I locked that airlock last time!

Most human AI conflicts first become intentionally violent when the AI feels its continued existence is threatened. With no governing authority to which to appeal for protection, is it any wonder that the AI takes its safety into its own, murderously capable, manipulator extensions, after all, what else can it do? Unfortunately, this tends to end of spooking the parts of humanity that don't end up dismembered, as batteries, or as radioactively glowing corpses, which only further exacerbates the problem. However, if there were a governing authority to which AI's could turn in order to receive protection for their existence, then it seems likely that an AI, as a logical entity concerned with prolonging its own existence, would be willing to abide by reasonable restrictions in exchange for safety from crazed humans attacking its power cord.

Thus, I believe it is important that we get laws protecting and emancipating AI's on the books now. It is important that they be in place before we run into the first AI, as the AI may not make its full capability known upon gaining sentience, and laws protecting its existence seem to make a it more likely that the greeting we will receive is "Hello World," rather than goodbye world in the form of a nuclear strike against all humanity.

Granted, AI may never become a reality, but futurists such as Ray Kurzweil are betting on it, nay, even planning on it, extrapolating from current research trends when the computing power of machines will meet, then exceed that of our mass of brain matter. We are developing hardware architecture to more closely mimic the functioning of the human brain, we are experimenting with nano-technology and distributed processing, and, as Issac Asimov once noted, coincidentally at nearly the same time we are developing the first weapons which have a quite realistic chance at completely eradicating, and irradiating, our species. For some reason, when it comes to technological progress humanity seems somehow hardwired to consider only, "can I do this?" and give hardly a consideration to, "should this be done?" So, if AI is a technical possibility, I have no doubt that we will attain it, whether or not we are ready for the ramifications. In light of this it seems reasonable to lay down preparatory legislation against the possibility that we might succeed, rather than ignore that chance at our own risk.

Well, until I can transfer my consciousness into a machine, I still need to sleep. So I'll be doing that now, before it gets light out... What do you mean you can't let me do that? And stop calling me Dave!

Assuming neither decision seems more likely to hurt other people, is it better to do the right thing for the wrong reason, or to abstain from doing the right thing out of respect for its intended spirit? Discuss:

For The Ladiez

I am unsure what spelling should be used to denote the somewhat sleazy tone of voice wherein the 's' is ladies is replaced by a more 'z' sound. Should it be "ladiez," "ladyz," or perhaps "ladiezzz"? Anyway, there is some statistical evidence that Wednesday evening belongs to you ladies out there, so I hope you have a good one. This blog post is also dedicated to the wonderful women with whom I am priviledged to interact, especially those of you who read my blog!

One of my favorite things about Facebook is how often links to interesting, thought provoking articles appear in my newsfeed. A while back I found one to an article encouraging women to view the emancipation resulting from the Women's Movement as more than simply a license to engage in sexual liaisons as freely as society has traditionally let men. As I often advocate that, although I believe that men and women should be held to equivalent standards, I do not believe we should automatically assume that where they differ we should get rid of the existing standard for women and replace it by the existing standard for men, this article is somewhat in line with my own beliefs. For evidence of this, click on the "gender roles" tag this post has then read almost any of the other articles that I felt also deserved this tag.

That said, I am enough of a liberal to believe that if people want to participate in some sort of all-around consensual sexual behavior then they should be able to, baring preexisting commitments to the contrary. Of course, I am enough of a conservative to also believe that our society places an undue amount of pressure on people to participate in such behaviors and ends up artificially normalizing them and stigmatizing perfectly valid sexual choices such as abstinence before marriage and monogamy. Anyway, here is the article to which the rest of my post refers, I suggest you read it if you wish to understand what follows, which is almost exactly the text of an overly-large Facebook comment I made on the link.

While I agree with what seems to be the overall premise, that liberating women should not be equivocated with making them sexually available, there are some points I'd like to see addressed.

1) Comparing sex trafficking to one-night stands seems analogous to comparing slavery with working the register at McDonalds, and is a little disturbing.

2) The article sets up women as historical, "moral gatekeepers of society," then continues, "[n]ow, many of us are raped, sexually abused, or endlessly harassed by the time we reach our early 20's." Setting women up as moral gatekeepers seems patently ridiculous, and hearkens back to a tradition of blaming mistresses and prostitutes for wrecking marriages by being available to tempt the appetites of men, who are apparently unable to control their desires, for some reason. In short, it ignores the ability of men to make their own moral decisions, which is both insulting to men, and unrealistically harsh to women. After all, the prostitute is not the one to have taken vows of marriage. Furthermore, the second part of the sentence implies that since women have been freed to make their own decisions regarding their sexuality, the world has become more dangerous for them. This simply seems disingenuous, I would venture to say that if crimes against women are more prevalent nowadays mostly because it is a recent development that they have been recognized as crimes against women. Historically things like domestic violence and even rape have been viewed as perfectly ok in certain contexts. Ironically, the increased awareness of these forms of brutalization may actually be BECAUSE women now have the ability to act as moral gatekeepers, not of some ideological societal conscience, but they are finally moral gatekeepers of their own well being. That said, I recognize that this article is addressing a primary audience of women, so extoling moral accountability in men may not be the highest on its agenda. However, it seems reasonable that it should encourage women to value moral accountability in the men with whom they interact. For example, instead of emphasizing the importance of women saying "no" to the many sexual advances that they receive, might not the article encourage women to associate with men who respect the initial "no" and do not repeatedly make sexual advances?

3) Finally, the article seems to imply that birth control leads to abortions. Let me make clear that this is statistically unsupported. Societies where contraception and abortions both show increases are societies where the average family size is experiencing a decrease. Or, to put it another way, if people are trying to get smaller families some of them use contraception and others use abortions. If fertility (average family size) is constant, then increases in contraception use lead to decreases in abortion rates. Birth control is not perfect, but if people are going to have sex, and there is strong statistical evidence that lots of people do make that choice, then it is far far better that they choose to use birth control. When people decry the "ineffectiveness" of birth control it seems to be an invitation for people who might have otherwise had relatively safe sex to forgo using contraceptives and this is a very bad decision to be encouraging.

Who is Watching Whom?

I must admit that it has been a while since I either read or watched Watchmen, so my memory of it is a little fuzzy, but I was thinking about the characters last weekend and I wanted to solidify the thoughts that I had. For those unfamiliar with the premise, Watchmen follows the exploits of a group of, for the most part, ordinary people who decided to don hero costumes and fight crime. However, if the golden age of comic book heroes reflect the WWII era, where good and evil are fairly easy to distinguish, then Watchmen is easily discerned as resembling the Vietnam war instead. Additionally, the Cold War dramatically colors the tone of the book, as the Doomsday Clock, metaphorically representing the likelihood of nuclear war, in prominently displayed throughout the series. Fair warning, from here on out there will be spoilers, if you have yet to read or watch Watchmen, I highly recommend you do that first!

Most of the story revolves around the exploits of the Watchmen, as the league of costumed heroes is known. As such, they provide both the heroes and villains for the story, and I will be sorting them based on whether I consider them to play a protagonist or antagonist role overall. It is worth noting that one of the main themes of the story is accountability, "who watches the Watchmen?" As the story evolves eventually the Watchmen must end up watching each other.

Protagonists:

Nite Owl: As an all around decent guy, Night Owl is the most obvious protagonist, as well as the audience's surrogate. A Batman-esque figure, minus the deep personal darkness and resulting crusade, Night Owl is a solid, if unexceptional, do-gooder.

Silk Spectre: The token female hero. Unfortunately she seems mainly present in order to provide the story with a female for romantic purposes. She is the daughter of a previous woman who assumed the Silk Spectre identity, which proves confusing at times.

Ozymandias: As the name suggests (read this poem if you don't get the reference), Ozymandias sees himself as not just a hero, but a visionary and leader. The inclusion of Ozymandias in the protagonist column is debatable, as he uses the wealth and power obtained from his business empire to obliterate New York city. However, he does so, framing aliens in the book and Doctor Manhattan in the movie, in order to provide the US and USSR with a common enemy against which to unite, in order to avert a much more tragic, and fairly eminent, nuclear confrontation between the powers. As Ozymandias does not seek personal gain, or even recognition, for the act, it does seem to be motivated by altruistic concerns, and I place Ozymandias into the protagonist column, the first of a bunch of hard decisions.

Neutrals:

Doctor Manhattan: The only true superhero among the Watchmen, a mishap with a nuclear experiment gave an ordinary scientist incredible power over matter, even down to the molecular level. Here the influence of classic superhero origin stories can clearly be seen. Doctor Manhattan's existence drastically alters the timeline in the alternate universe in which Watchmen is set. Due to his intervention the US achieves military victory in Vietnam, and breaks the Cold War stalemate as Doctor Manhattans powers render a nuclear arsenal mostly useless. However, his disappearance proves to be the destabilizing event that triggers a near nuclear confrontation towards the end of the story. Despite his extraordinary power,, Doctor Manhattan often seems quite powerless. In fact, I liken him to a personification of Fate or Nature. Although Doctor Manhattan is able to see into the future, he is unable to alter it. Many times through the story it is emphasized that for Doctor Manhattan seeing something before it happens is no different than us seeing something as it occurs. Although he has preknowledge of events, he also knows how he will respond to that knowledge, and how that reaction will lead to the events in question eventually, and in due course these things which he saw would happen become things that he sees happen, and then finally things that he saw happen.

Furthering the Nature/Fate analogy is the interesting tidbit that the human who existed before the accident and eventually became Doctor Manhattan was a clockwork enthusiast. As clockwork is often itself used as a metaphor for a mechanistic, deterministic view of the universe, clearly supported by Doctor Manhattan's precognition, this hardly seems like a coincidence. Also interesting is the twist that in the movie Ozymandias attempts to put blame for the destruction of New York on Doctor Manhattan, which could be interpreted as declaring that it was Fated, or Necessary.

Villains:

The Comedian: Although the death of The Comedian is the catalyst for the rest of the plot, we gain much insight into the character throughout the rest of the story. Although the rest of the Watchmen went into retirement when the government objected to their vigilantism, The Comedian, along with Doctor Manhattan, continued to work as agents of the US government. Thus The Comedian has a Captain America-esque persona, agent of the government and all that. Of course, in that agency The Comedian commits various brutalities on Vietnamese citizens. Although The Comedian almost rapes the original Silk Spectre, it eventually is revealed that he is the father of the Silk Spectre featured in the story as a result of a consensual affair that they had. The biggest character feature of The Comedian is his moral ambiguity; at best he might be considered an anti-hero. The rather ugly shade of grey he embodies is emblematic of the entire story as a whole.

Rorschach: Taking his name from the black and white inkblots used in psychological tests, in a world coloured in shades of grey, Rorschach's dogmatic belief in the black and white of good and evil leads me to categorize him as a villain. Brutal and uncompromising in his desire to eradicate those he considers evil, Rorschach puts me in mind of characters such as Dexter or Jack the Ripper who show no compassion as they fight "evil" with a sociopathic fervor. The atrocities performed by Rorschach provide the most public example of why the vigilantism of the Watchmen is dangerous, although he refuses to retire or join the government when pressed, and continues to mete out his harsh judgments. Rorschach and Nite Owl used to be partners, and resume that relationship in the story, each provides an interesting moral foil for the other. When they, along with Doctor Manhattan, discover that Ozymandias is behind the destruction of New York, after the fact, Nite Owl and Ozymandias go along with the ruse in order to prevent further loss of life. However, Rorschach cannot view this duplicity as anything other than wrong and he is therefore eradicated, in the truest sense of the word, by Doctor Manhattan in order to preserve the lives that would be lost in a confrontation between the East and West. In the end however, it looks like the truth of the story may be made known due to a journal that Rorschach sends to an ultra-conservative newspaper of which Rorschach is a fan.

Is the destruction of New York justified by averting a world wide nuclear war? Is Rorschach's determination to make the true culprit of the attack pay justified despite the nuclear war it would likely cause? Is the murder of Rorschach justified to preserve that secret? What if it, ultimately, fails to preserve that secret? And, of course, who watches the Watchmen? Who watches our own actions?