3.28.2005

You Know What They Should Have...

How many times have you been typing a paper or sending an email or whatever and had to stop because the right word, the one you know expresses your idea perfectly, is stuck on the tip of your tongue? I'm not a psychologist but isn't it true that people think of words in terms of concepts. How often do you forget a word but know what you want as a cross of two or more other words? Wouldn't it be useful if someone created a thesaurus that gave answers based on cross-referencing multiple word inputs? Like if I'm looking for the word that's a cross between "confusing" and "secret" I'll quickly find "cryptic." The way it is now, you'd have to wade through up 10 definitions for each word, with huge lists of synonyms corresponding to each definition; in total you could easily have to look through hundreds of words before you found the one you were looking for. These days, given the widespread use of computers and the wonders of the internets, it should not be hard at all to write a program with this function.

Abstinence Now! - for $15

My friend Noah has brought to our attention an organization relevant to every young adult, be he male or female, gay or straight, muslim or buddhist, black or white. It's called the Abstinence Clearinghouse, and its purpose is to "serve as an association for the abstinence community." Absurdity abounds here. I'll list some of it.
  • The premise that the cause of abstinence is faciliated by a social network.
  • The "Abstinence Online Store," i.e. the assumption that abstinence propoganda is something that people will pay money for rather than something you will have to force down their throats
  • The very idea of "faith-based information" used in product blurbs
Peruse the site for the products. Here are some good ones
The Casualties of Kinsey booklet: "the truth about the founder of spiritual decay in America." Special introductory price timed for the release of the movie whose release it deeply regrets!
God's Gift to Women: "...Eric Ludy challenges you to forsake modern male mediocrity for Christ-built, warrior-poet manhood-manhood that will capture the heart of a woman and change the course of history." In other words, Eric Ludy challenges you to come up with four words that are more mutually contradictory than "Christ-built warrior-poet manhood."
'Keep It' Underwear: "Keep It Underwear aims to approach the serious subject of abstinence in a light-hearted way by letting teens show their statement of choice - even if it's just to themselves." Features cool and tactful "STOP!" signs right on the front.
The Princess And The Kiss: "Contains faith-based content. The Princess and the Kiss is a wonderful fairytale with beautiful illustrations that convey the message of purity with beautiful symbolism. Kit comes with the book, coloring book, crayon and tiara. " I guess everything people teach kids is basically indoctrination right, so why do we have to be so careful anymore? On the plus side, it claims to have faith-based "content" not "information."

3.11.2005

I met with a psychologist and professor I knew in high school the other day, and one of the topics that came up in conversation was the issue of trying to gender-neutralize standardized psychological tests. This is particularly an issue with politically-charged tests like the IQ test. I hadn't been aware this was done, but apparently standard IQ tests are constructed so that in no question does one gender show substantial better performance (although I'm not sure if it's anything of statistical significance or what). I forgot exactly what this procedure is called, something like "item-pairing." The thinking is that if you start with a large pool of questions which are purported to test for general intelligence, and some of these questions are answered correctly much more frequently by people of one gender, then those questions must be biased in some way so you reject them.

There are a lot of issues here. One preliminary question you might ask is who does this procedure help? I don't know the data, but my suspicion is that men probably score better on some types of questions, and women score better on other types of questions. Overall, men score slightly better on SAT tests, for instance, so one might infer that more of the questions showing a gender disparity favor men. This is obviously not necesarily true though, since men may just be showing stronger performance in general, but women may be the ones showing superior performance on certain types of questions. Therefore this protocol doesn't necesarilly serve a moderating function; it seems it could potentially exagerate already existing performance gaps.

The real question comes down to not what is the statistical basis for carrying out such a protocol, but what is the conceptual basis for doing so. Since you could always form arbitrary groups of people who perform differently on any given question, and argue that therefore the tests must be biased against them in some way. If you carried this scenario out to its logical conclusion, you would end in a situation where all individual variability in performance is banished - and this is obviously absurd. Of course, the argument will be made that genders are not an arbitrarily drawn group. But a group is only significant to the extent that it is correlated with other, confounding factors. The fact that members of a group perform worse on a certain question is not definite evidence that bias exists; it may just as well indicate that the question tests for something that members of that group are less able in.

The permissibility of this analysis depends on your fundamental philosophical view of what the test is testing. If you thought that there was a single quantity that all test questions were designed to measure, then it would be logical to only accept a test that has no significant variation across questions in the gender answering patterns, because presumably all questions are testing for the same quantity whose relationship with the genders should be static. Note that this doesn't necessarilly mean that the set point of correct responses should be 50-50; what if one gender really does have slightly more of the quantity that the tests measure? A "fair" test would take into account that that gender will invariantly score a given amount better on any question that validly measures that quantity. But in reality it's hard to know what this set point is without the input of a test, so you're back to square one. On the other hand, if you thought the test was measuring multiple discrete skills, you'd expect these would vary between genders. Hopefully, when it comes to IQ tests, political correctness isn't intervening and saying, "well let's just assume that men and women are absolutely the same cognitively, and therefore we'll reject any questions (or groups of questions) that show one gender performing better than the other as either ineffective or flawed" or holding some presumptuous, anti-scientific "intelligence is gender-neutral" dictum. This would be a good way to create a gender-equalized test in terms of scores, if that was your goal for some reason, but wouldn't necessarilly create gender impartial questions. Interestingly, the people who would would probably want to make each question as gender-neutral as possible would probably also tend to be the same people who adhere to the multiple intelligence theory of intelligence - which is logically inconsistent.

My general conclusion is that it seems really stupid to gender-neutralize a test based on rejecting individual questions that show a gender disparity. Probably a smarter way to do it would be to do a kind of latent variable analysis: that is consider GROUPS of questions that show a pattern of one gender answering more correctly, infer some kind of latent common cause, and try to identify (through non-statistical analysis) if it's due to something that the questions are TESTING or something about the way the questions are worded, expressed, or presented. You can't just summarilly reject any group of questions because they are answered more correctly by one gender before determining what the probable cause is, since it very well may indicate a difference in whatever the test is supposed to measure, rather than an unfair bias in the question.

3.02.2005

Here's an intereting little optimization problem that occured to me while working on a side job I have of labeling the contents of audio tapes. Basically, the job involves archiving cassette tapes that have multiple concerts or sets recorded on them. I have to record the time into the tape at which the next recorded set starts. The only way to accomplish this is to manually rewind / ff, and hit play. Most of the time there's at most one additional recording per 45 minute side. To simplify the problem, I assumed that this is the case.

If you are getting paid on a task basis, maximal efficiency is of utmost importance, especially if you are busy. In reality, I'm getting paid on an hourly basis, so I want to do the opposite, but I just as easily could get paid that way. The problem is then, how do you get the most tapes done in the least amount of time? In other words if the location of the beginning of the second set on the tape is completely unknown and random for all intents and purposes, what is the best method of hitting fast forward, play and rewind to use that will ensure you find the location of the beginning of the second set quickest?

It simplifies the problem somewhat to assume that the second set continues to play until the end of the tape, so that you're guaranteed to reach some point in the second set if you fast forward all the way to the end of the tape. Also, there may be different answers depending upon whether efficiency is gauged in terms of # of stops on the tape (or times you hit play) versus amount of time spent on the search. It also depends on how realistically you are going to model the actual time it takes to press buttons, reverse direction etc. I'm not absolutely sure there's an optimal strategy if the set placement on the tape is completely random. But I have some preliminary thoughts on at least creating a model that might lead to an answer:

  • It's good to fast forward not too far into the tape and hit a point where there is music recorded. This means the beginning of the set is between where you are (which is not too far), and where you started. It's equally good to fast forward far into the tape and hit a point where there isn't music recorded. This means the beginning of the tape is between where you are, and the end of the tape (which is not too far away). But, you're just as likely to find music recorded far into the tape than to not find music recorded not too far into the tape, so neither choice is more likely to pay off.
  • However, all other things being equal, if you choose to fast forward not too far into the tape, you have wasted less time. So the general algorithm is something like always choose to fast forward to the point not too far into the tape.
  • I can't prove that it's best, but it simplifies the problem a lot if you just assume that the initial move is to fast forward exactly half-way through the tape. If you do this, when you push play, then you are faced with two equally likely options:
1) You hear music
2) You do not hear music
As I said, I can't prove that this is the best fast forwarding / rewinding regime, but it seems equivalent to any other. Since if you initially fast-forward less than half-way into the tape, say 30% of the way, then if you happen to hear music, then you have effectively diminished the length on the tape you have to explore to 30% of the original length of the tape; however, assuming that the placement of the set on the tape is random, you have only a 30% chance of attaining this outcome, so the advantage seems to be nullified. After you fast-forward to where you are going to stop, you push play and listen for a period of time. To simplify the problem, I assumed you always listen for the same amount of time.
As suggested before, if you are to choose as your first move fast forwarding to exactly the half-way mark, then it logically follows that you would choose the same protocol as your second move. This follows from the fact that after your first move, you are logically faced with the same problem you are faced with on the first move: you are given a length of tape over which the beginning of a set of music is equally likely to appear. The only difference is that the movement can now take place in two directions: either backward or forward depending on whether you hear music or not. However this doesn't affect the amount of time you spend, so you don't need to take it into account. The pattern equally applies to the next step, and the next step, and so on. Therefore you can express the total time, which you want to optimize, in terms of time spent fast-forwarding/rewinding and spent listening to the tape. If "f" is the speed of fast-forwarding/rewinding, "w" is the length of the whole tape, and "d" is the standard displacement due to listening to the tape - which is also equal to the time spent listening to the tape, since the play function operates in real time...
T = (1/2(w/f) + d) + (1/4(w/f) + d) + (1/8(w/f) + d) + ...
The first parentheses indicates the time you spend searching and listening on the first attempt, the second parentheses expresses this for the second time, etc. I assume that the displacement on the tape, d, is negligible compared to the displacement traversed in fast-forwarding/rewinding. Of course, this is a worse and worse approximation with each round of fast-forwarding.
The total time T is just the sum from n=1 to n=N of [1/2^n(w/f)] + Nd, where N is the number of times you apply the protocol. However the sum doesn't continue infinitely. There comes a point where the displacement you fast-forward into the tape is less than the displacement into the tape that you pass by from listening to it, and at this point it will be useless to continue the cycle further, since you will have accounted for all the space on the tape. This occurs when d > 1/2^n(w/f) . If you solve for n you get n > log2(w/fd). Therefore, this is your upper limit to the sum, N. Stating the sum again
T = sum from n=1 to log2(w/fd) of [1/2^n(w/f)] + log2(w/fd)d
You can actually figure out that sum based on a simple formula. To spare you the tedium, unless I've made a mistake, the sum comes out to
T = w/f - d + log2(w/fd)d
At this point you can find the listening time, d, at which the total time, T, is lowest by solving a simple max/min problem. Once you take the derivative of T with respect to d and set it equal to 0, you can solve for d... You get
d = (w/f)/2^(1/ln2 + 1), which is somehow a pleasing answer. Unfortunately, this is a maximum, not a minimum. So this tells the optimal amount of time you would want to be listening if you wanted it to take as long as possible to find the spot in the tape. Basically it says if you reduce the total time it takes you to fast-forward through the entire side by a factor of 1/2^(ln2 + 1) you get the optimal time you should spend listening. The speed of the fast-forward mechanism will vary by tape recorder, but mine has a speed of 16 1/2 minutes tape displacement per minute. Therefore, working with my tape recorder, with a 45 minute-sided tape, I will optimally want to spend 3o seconds listening to the tape per round before I choose fast-forward or rewind. This is the protocol you would want to use if you were getting paid by the hour, as I am, and if you for some reason had to appear as if you were trying to complete the task as quickly as possible. However, it should be noted that in the real situation, this is only a local maximum, as one easy way to spend much more time is to just set d so that it exceeds w/f.
There is a minimum of the function for T, and it occurs when the time spent listening to the tape approaches 0. It's interesting that the value of the equation T = w/f - d + log2(w/fd)d in the limit where d --> 0 is T= w/f, which is the original time it takes to fast-forward through the entire tape. This constitues the maximum time you would spend searching for the spot in the tape if you were using the minimizing protocol. On my tape recorder, it takes 2 minutes and 45 seconds to fast-forward through an entire tape. This is probably the one actually useful result to come out of all this, since it seems intuitively obvious that you would want to minimize the time spent listening to the tape as much as possible if your goal was to find a spot on the tape the fastest. This is the protocol you would want to use if you are getting paid by the amount of work you get done.
Looking back, you can judge whether the "d is much less than w/2^n" approximation is a good one. Using the maximize protocol, you can go about 5 rounds before the distance you displace on the next fast-forward/rewind is comparable to the distance you displace listening to the tape. You can calculate that probability that 5 rounds will be sufficient to locate the spot on the tape. Since you always spend 30 seconds, the chance of finding it on the first blind attempt is 30/(45*60), on the second attempt, 30/1350...and the total sum of all these is somewhere around 30%. This is obviously not a very good approximation. A new model is clearly needed. Of course when d=0 the approximation is still good, so the minimize protocol is definitely good.
Pretty much the only valuable thing to come out of all this inquiry is the realization that your optimum minimize strategy is to listen for as little as possible. In fact I'm not sure if any of these results are even meanginful with all the approximations I made. Perhaps someone will come to another answer, or one that's based on fewer approximations?
I am basically ignorant when it comes to analyzing politics. However, this gives me the right to toot my own horn when it looks like I do get something right. A while back I spewed my thoughts on the Iraq War, its motivations, and its implications. Briefly, the conclusion I came to was that the provided rationale for going to war (support of terrorism, WMD's, nuclear program, humanitarian concerns) was contrived and probably totally specious, and that the war would accomplish none of the stated primary goals of operation except remove Saddam Hussein from power. In fact, this is pretty much how it has worked out: there was no weapons programs, consequently there was no potential for the former regime to aid terrorists, and there has been little immediate progress against "the forces of terrorism" - in fact, it seems you would have to be deceiving yourself to say the current environment in Iraq hasn't attracted new jihadists to the area. I also said that I thought the main motivating reason behind the war was democratization. Democratization has two aspects:

1) Democratization of Iraq prope. This is desirable because a democratic Iraq is inevitably much friendlier to its neighbors and to U.S. interests than a dictatorship, especially one that is run by a sworn enemy. Accomplishing this objective at minimum is important because at the very least, it means that the U.S. has one less enemy and a sphere of influence in the middle east.

2) Democratization as an example for the greater Middle East. This is desirable for many reasons. One, the huge antagonistic force we are fighting at this point in time is Islamic totalitarianism, exemplified by bin Laden and his associates. Reasonable people may disagree about the extent two which these forces currently pose a threat to the United States, but it is undeniable that the ideology is extremely dangerous and antagonistic. Democracy necessarilly excludes Islamic totaliaranism and its success in the middle ease will be a huge blow to it. Second, an implicit belief of the Bush people seems to be that turning Arab countries into democracies will significantly lower the tension that characteristically plagues the area. Third, as before, other democracies are more likely to turn out regimes friendly to the U.S. and U.S. interests. This means more U.S. influence in a region that is vital to our economy.

Back in October I predicted that the democratization objectives of the war would turn out decidedly more positively than any other causes. With what's going on in Lebanon, Egypt, Saudi Arabia, the Palestinian Authority, and to some extent Syria, it appears that my prediction was right. Of course the by all counts successful election in Iraq goes to this credit as well.

On the other hand, I said before that I am totally against the way all of this was carried out. One can say without cynicism that Administration cronies exploited the fear environment created by 9/11 to sell a distorted case for a war, and that is not acceptable. Presenting false intelligence and rationales to the American public, probably with the knowledgeable intent to deceive, is a terrible precedent to be setting - especially when the issue in question is something on the magnitude of a war. Further, word has it that the war itself was not particularly carefully or well-executed. I can't comment on this aspect; I'll let the reality speak for itself, and leave commenting on it to those with greater knowledge of miltary policy, or greater pretense to know about such things.

The dillemma I face is was any of this possible without the mendaciousness, deception, and strong-arm tactics with which this administration carried out this war? Is it really possible to say, "I like what is going on now, but I would have gone about it better"? The central question there is whether the country ever would have bought into a war based exclusively on subtle and long-term structural goals like democracy reform in the middle east. It's possible that the country would have bought into that rationale alone, but it would have required a much longer period of selling the war, which the administration just didn't have time for. Or it's possible that all the best political analysis said that the democracy pitch was a big loser. Ultimately, this war forces us to ask fundamental questions about the nature of the foreign policy process in our country. In theory, war is supposed to only be declared by Congress representative of the wishes of its constituents, whereas the President is only supposed to be able to suggest war to a critical Congress, and then choose when to carry it through once it has been passed. In reality there are all kinds of vaguely worded loopholes that allow for the use of force in "extenuating circumstances" and "matters of urgent national interest" and the like, and the War Powers Resolution which allows for the unmediated use of force for 60 days. In fact, a formal declaration of war has been resorted to on only 5 occassions in U.S. history. De facto, we have a situation where the president who is elected has unlimited control of military force, within reasonable constraints. We should be asking what role the public should play in foreign policy decisions, and how much accountability Congress should have to the public on these matters, which is currently very little. We should also be asking whether in matters of national interest in which the public is not informed is it OK for authorities to present a distorted case for a benign foreign policy action. Basically we have to clarify the precise role that the public, and presumably Congress which is supposed to represent them, is going to play in the formation of foreign policy decisions in the future.

3.01.2005

Interesting Searches

People are continuing to reach my blog through searches even though I haven't been updating. The first one involves, as unlikely as this may be, someone at Bank Of America musing about quote "Could the disparity eventually lead to the class conflict that Karl Marx and Max Weber predicted? " Apparently this person is quite conflicted. Way to go continuing to perpetuate disparities in wealth through your facilitation of the capitalist system and then agonizing over its philosophical consequences.

The second noteworthy search came someone wondering about "Immanuel Kant's views on gay marriage." I wasn't aware that the gay marriage debate extended back to the 18th century. Kind of reminds me of the title of one of Oren Cass's blog posts, "Shakespeare opposed the war in Iraq," but that one was supposed to be a joke.