Monday, December 26, 2011

this week's MGRE Math Beast Challenge problem

From here:

This Week's Problem: "Honeycomb"

The honeycomb figure above consists of six identical regular hexagons, each with side length 2√3.

Quantity A
The total area of the honeycomb

Quantity B

(A) Quantity A is greater.
(B) Quantity B is greater.
(C) The two quantities are equal.
(D) The relationship cannot be determined from the information given.

Good luck! My own answer will appear in the comments. (Please show your work if you decide to submit your own answer!)



I got last week's MGRE Math Beast Challenge problem right. MGRE's reasoning:

The chemical division’s legal expenses are between 1/3 and 1/2 of the $720,000 spent by the pharmaceutical division on legal expenses. Thus, the chemical division spends between $240,000 and $360,000 on legal expenses.

The chemical division’s legal expenses are also given to us as 15 percent of the division’s total expenses.
$240,000 < 0.15c < $360,000, where c represents the total expenses of the chemical division. Solve for c by dividing by 0.15 (remember to do so on ALL sides of the inequality): $240,000/0.15 < c < $360,000/0.15 $1,600,000 < c < $2,400,000 The only answer choice between $1.6 million and $2.4 million is $1,855,100. The correct answer is D.

Pretty close to what I said in the comments.


lazy blogging

I may be blogging very irregularly this week, given that we're between Christmas and New Year's. Just thought I'd let you know. Enjoy the holidays!


Friday, December 23, 2011

"The Christmas tree is a pagan symbol!"

[This is a repost of an entry that originally appeared here.]

Very often you'll hear some wiseacre deconstruct Christmas. He'll talk about its components-- the date of Jesus' birth, the elements involved in Christmas celebration, etc.-- then claim that Christmas is a sham in both form and content: no element of Christmas is originally Christian, after all. What usually follows, after this scholarly lecture, is the non sequitur that "the Christmas tree therefore isn't a Christian symbol."

Well, no: the tree is a Christian symbol, because Christians have made it so. Christians who use Christmas trees aren't focusing on the tree's pre-Christian origins when they set such trees up. Such people belong to a tradition that has appropriated the tree, i.e., made the tree its own.

Some people have a hard time wrapping their minds around the concept of appropriation, which isn't the same as the concept of theft (another idea associated, often rightly, with Christianity's frequently unhappy history). Here's a general example of how appropriation works: as Buddhism moved out of India and into other Asian countries, it took on the trappings of those countries. In Korean Buddhist temples, you might see imagery that's not originally Buddhist: mountain spirits, deities of magico-religious Taoism, etc., might all make their appearances somewhere on Buddhist ground. Buddhism appropriated the local colors and flavors, and was changed thereby. This is a natural sociological process, and it's not limited to religion: it happens in other human spheres as well-- culture, politics, art, and all the other human endeavors you can think of. Ideas are memes; they cross-pollinate.

A more specific example: the bodhisattva Avalokiteshvara represents the sort of change that occurs as religions move from place to place. As the Indian name implies with the ending "-ishvara," this entity was a "lord," i.e., male. As the concept of Avalokiteshvara moved northward into China, however, it became associated with the Chinese deity Kwan Shih Yin (or just Kwan Yin)-- a deity that was arguably native to China, and usually portrayed as female. Whatever Avalokiteshvara was, the Bodhisattva of Compassion is now thought of as female in all of East Asia. More philosophically minded Buddhists, aware of the bodhisattva's Indian origins, will say the bodhisattva transcends gender, but folkloric Buddhists in East Asia will be comfortable with Kwan Yin's femininity. East Asians appropriated Avalokiteshvara.

People who claim "X is not really X because it was originally Y" are demonstrating a lack of understanding about how symbols work. Culturally speaking, symbols derive their power and significance from a widespread agreement as to their general meaning. This agreement is often induced and enforced diachronically, when the older generation teaches the symbol's meaning to the younger generation.

It may sound strange to give so much legitimacy to the "because we said so" crowd, but the saying-so is integral to what symbols are. The implication, then, is that the critic of Christianity can't afford to be too smug about the "original" significance of the Christmas tree. Those pagans came to an agreement about what their tree meant, after all, and they may have done it in consonance with-- or in defiance of-- some even earlier, pre-pagan tradition.

If religious symbols are too abstract for you, let's think about this problem in terms of language. The sound "ah" occurs in American English, but it's also an ancient sound-- one of three sounds common to all languages (the other two being "ee" and "ooh"). Does the ancient pedigree of "ah" make it somehow un-English? To put matters another way: "ah" might have come from our distant past, and might currently be found in other languages, but does that make it any less a part of English phonetics? Conclusion: "ah" is English-- not originally English, nor exclusively English, but legitimately English all the same. And why? Because users of English have, through a massive and self-perpetuating agreement, chosen to include the sound as part of their language.*

By the same token, then, the tree known by Christians as "the Christmas tree" is certainly not exclusively Christian, nor is it originally Christian, but it is nonethless legitimately Christian. Why? Because Christians have made it so.

There's another side to this issue, though: we should take a moment to consider the Christians who get upset upon hearing that their precious symbol doesn't originate with their tradition. My question to them would be: why are you upset? Did you really think Christianity wasn't composed of non-Christian elements? As Thich Nhat Hanh notes in his Living Buddha, Living Christ, all religious traditions are composed of elements not of that tradition. Viewed in terms of Buddhist metaphysics, religious traditions are dependently co-arisen: they form out of a matrix of intercausality. The late Father Cenkner, one of my mentors at Catholic University, used to say: "It's all syncretism!"**

I personally have no trouble with the claim that the Christmas tree isn't originally Christian, or that prayer pre-dates Christianity, or that Madonna-and-Child imagery is very likely derived from Isis-and-Horus iconography, or that sacred birth narratives and the concept of resurrection are pre-Christian. None of this changes the fact that almost all Christians pray, that many Christians set up Christmas trees for Christian purposes at Christmas, or that the Madonna and Child are wholly integral to the Christian tradition. A healthy Christian attitude would be to realize that one is part of a constantly evolving and interwoven global network of tradition-streams. In the meantime, the non-Christian who attempts to claim that "aspect X of Christianity isn't originally Christian" needs to realize that this in no way implies that "aspect X isn't Christian"-- a claim that is demonstrably false.

*Some scholars have proposed a "language model" of religious pluralism that makes religious traditions analogous to languages. The model is helpful in elucidating certain aspects of how religions may have evolved over time, but I question the model's effectiveness in resolving what many pluralists see as the basic problem of religious diversity-- namely, the fact that the various traditions, in their doctrines and metaphysics, often make conflicting or even contradictory truth claims. If the language model is meant to be used normatively, it implies that no one religion is any more legitimate than another-- an implication rejected not only by divergent pluralists but also by inclusivists and exclusivists. Even convergent pluralists exclude certain traditions from the sphere of legitimacy; Satanism immediately comes to mind.

**You're allowed to make sweeping generalizations about the universe when you're over 70, even if you're an academic. In his defense, I'll note that Father Cenkner said this outside of the class context. While the sentiment lacks the usual pile of scholarly hedges and qualifications, I still think it's basically correct when applied to religion. Can you name a causa sui religious tradition?


Thursday, December 22, 2011

Sting lyrics: "La belle dame sans regrets"

From Sting's album Mercury Falling, we have "La belle dame sans regrets." Lyrics:

Dansons tu dis
Et moi, je suis
Mes pas sont gauches
Mes pieds tu fauches
Je crains les sots
Je cherche en vain les mots
Pour m'expliquer ta vie, alors
Tu mens, ma soeur
Tu brises mon coeur
Je pense, tu sais
Erreurs, jamais
J'écoute, tu parles
Je ne comprends pas bien
La belle dame sans regrets

Je pleure, tu ris
Je chante, tu cries
Tu sèmes les graines
D'un mauvais chêne
Mon blé s'envole
Tu en a ras-le-bol
J'attends, toujours
Mes cris sont sourds
Tu mens, ma soeur
Tu brises mon coeur
Je pense, tu sais
Erreurs, jamais
J'ecoute, tu parles
Je ne comprends pas bien
La belle dame sans regrets...

The French strikes me as a bit awkward in this song, but it's not a bad song for beginning students to try and figure out. By my estimation, a French 2 student should be able to translate most, if not all, of the lyrics.

Be careful, though, O Student, because some of the words might not mean what you think they mean! For example: the phrase "je suis" doesn't mean "I am." The suis comes from a different verb! Can you guess which one? Also: the masculine plural adjective sourds doesn't mean "deaf." Can you guess what Sting means by "mes cris sont sourds"?

Have fun decoding! And if you want to hear the song itself, YouTube has several vids. Here's one. It's interesting to hear Sting's accent: he tends to roll his "r" sounds, as if he were singing in Spanish. This might simply be because he can't speak French all that well, or it might be that the French he's learned is more southern in character. When I lived in Nice, I heard plenty of trilled and rolled "r"s.


Wednesday, December 21, 2011

finding connections

One thing we like to do in American education is encourage students to think. Higher-level thinking involves synthesis, the act of finding previously-unseen connections and/or engaging in creative rearrangements.

Try this on for size: see what sorts of connections you can find between these apparently unconnected things:

1. diet/nutrition and gun violence

2. hairstyle and presidential elections

3. Governor Rick Perry and Mahatma Gandhi

And see what people have written about the connections between these things:

1. religion and life expectancy

2. heart attack and cancer

3. texting and car accidents

4. the speed of light and GPS systems

5. parking lots and national defense

6. solar activity and terrestrial climate

7. manufacturing and frogs

8. invasive foreign species and restaurant menus

9. Marriott and the moon

Have fun! Leave your insights in the comments thread.


Tuesday, December 20, 2011

Monday, December 19, 2011


Whether you're taking the SAT, the GRE, or the TOEFL, the harsh fact of the matter is that you'll be undergoing an endurance test. Such standardized exams aren't merely a measure of your verbal and mathematical ability; they're also a test of your stamina and willpower.

All of these tests are somewhere in the neighborhood of four hours long. If you're tired during the first hour, it's hard to imagine how well you'll do during the final three. If you're pumped up with nervous energy at the beginning, but feel yourself crashing by the halfway point, you're toast.

Takers of the computer-based GRE are allowed a ten-minute break after the first couple hours; it's the only official break (other breaks may be possible by special request, but I don't think they stop the clock for you). High schoolers taking the SAT I will normally get several short breaks (about five minutes) and one long break (about 30 minutes). For TOEFL takers, ETS gives one sanctioned break and allows testers to take additional breaks without stopping the clock.

Obviously, most testers will prefer to tough it out and stay at their desk except during the mandatory breaks. This means that, before the test, testers should get themselves mentally and physically ready for the ordeal ahead.

The most common and long-standing piece of advice is to sleep well the night before the test. Another bit of practical wisdom is to work on practice problems just before going to sleep so as to be in the proper frame of mind on test day. Manhattan Prep's GRE blog also recommends watching one's nutrition: a tester should eat well and go for complex carbs and natural sugars on the morning of the test: oatmeal, wheat bread, fruit, etc. will break down slowly, releasing energy in a steady stream, thus reducing the chance of a high-and-crash, such as when one eats processed sweets (think: candy, Pop Tarts, etc.).

What you do before the day of the test will affect your performance on the test. If you cram the day before, sleep fitfully the night before, wake up tired and anxious the morning of the test, and feel yourself drowsing (or becoming generally unfocused) during the test, you aren't doing yourself any favors, and you shouldn't be surprised at your low score when test results are sent out.

Keep in mind that knowledge isn't enough for these standardized tests: endurance matters.


Friday, December 16, 2011

my talk with a Zen master

NB: This is a repost from my blog Kevin's Walk. The original post can be found here.

The following is a transcript of a talk I had with Genjo Marinello, who heads up Choboji, a Rinzai Zen temple in Seattle, Washington. I was at Choboji in mid-June [2008], and felt very welcome at the temple, even though I was a mess during meditation the following morning (as I've written before, the Japanese way of handling zazen is markedly different from the Korean way of approaching ch'am-seon). The transcript has been edited for style and content. The original recording is not currently available online.

KEVIN: I think we're go.

GENJO: All right!

KEVIN: OK. Well, first off, I'm acquainted with the Korean pronunciation of a lot of Chinese characters, but "Genjo" means what?

GENJO: It could mean several things. The two characters in my name, given to me by my ordination teacher quite some time ago now, back in 1979, are the characters gen and jo. Gen, in this case, is the character sometimes translated as "heavenly silence"; it could be translated as "essential mystery"; the most literal translation is "the black before black before black."

KEVIN: Huh. Interesting.

GENJO: And gen-cha, in Japanese, is very black tea. And jo is the character for "realize." So: "realizing the black before black before black" is my name.

KEVIN: So then, having put those two characters together, "realizing the black before black before black," what does that mean?

GENJO: A dharma name is something you aspire to, and in this case, I aspire to the realization of what is the mystery of the universe, and he [i.e., the ordination teacher] saw some potential in me back then, that I would be able to experience in an intuitive way and relate with the mystery of the universe. So that was his dharma name for me-- that I would be someone who not only could intuit what the black before black before black was, but share it with others.

KEVIN: OK. How does one share something like that?

GENJO: We're doing it right now. You know, it doesn't have to be through words; just through the presence of one's ordinary activity would be best. But certainly, and also in dharma talks, trying to explain the ancient dialogues between masters and disciples, and making, say, ancient Chinese poetry accessible to modern American idiom.

KEVIN: Is that part of what happens here at your community?

GENJO: [nods]

KEVIN: I notice you're wearing an aikido shirt. [NB: I don't want to give the impression that Genjo was sitting on his front porch while wearing a full-dress aikido uniform, which might be a breach of aikidoka etiquette; he was, instead, wearing a shirt with some sort of aikido logo on it, and this had caught my eye.] When I was walking up here, I saw there was an aikido--

GENJO: Dojo.

KEVIN: Dojo. And when I was in Bellingham, there was an aikido dojo very close to the Red Cedar Zen Center. It's just a random connection, but it makes me wonder: do you have any connections with those communities?

GENJO: I do. Morihei Ueshiba O Sensei was the founder of aikido in Japan, of that particular martial art form, which [essentially] blends judo and kendo, which is sword. And he very much was taken with Zen, and didn't insist, but invited his senior students to also practice Zen. And most of the major art forms in Japan, anyway, turned to Zen as an augmentation of that art form, so whether it's martial arts or the high arts of calligraphy or painting or pottery-making or flower-arranging or whisking tea, they all turned to Zen as a way to augment or nurture their art form, and this was no exception when it came to O-Sensei [and] aikido; some of his senior students in the West have followed that, and I'm sort of the aikido-- I'm the Zen master that the aikidoists use, at least with a particular branch. There are many branches of aikido, in the same way that there are many branches of Zen. But there's something called the Birankai International branch of aikido, and I'm their Zen teacher.

KEVIN: Oh, OK. So does that mean that you visit the dojo and do your teaching there, or do they come here?

GENJO: Both. Our most intensive retreat is in the winter, and at our winter retreat, very often, senior students and instructors from Birinkai International will travel from all over the world to come to our retreat here in Seattle. It's also true that I go to Michigan, Pennsylvania, San Diego, Birmingham, England, and Strasbourg, France, and teach Zen to aikidoists in those locations.

KEVIN: Oh, wow! Fantastic! In France... you speak French?

GENJO: No, but I have good translators.

KEVIN: Oh, that's good. I was reading a book that came out in [French] first, and then it came out in English maybe a year or so later. It's called The Monk and the Philosopher. It was a dialogue between father and son: Jean-François Revel, the French humanist philosopher, and Mathieu Ricard, his son, who became a monk in the Tibetan tradition, and is the Dalai Lama's French interpreter whenever the Dalai Lama goes to France.

GENJO: Oh, how interesting!

KEVIN: I think the dialogue was mainly about how the father couldn't really understand why his son, who had been on a path toward science, suddenly switched gears and went into Buddhism. For you, what-- are you a cradle Buddhist, or--

GENJO: I'm a cradle nothing. My parents were both fallen-away Catholics, as they were married to other people when I was born, so that didn't sit too well with the Catholic Church on either side of that family, and my mother was afraid that if she let me too close to the Church, I would've been a priest, so the standard joke in my family, from my mother, is: "I shoulda' let you become a priest. At least then, you'd have hair!" And--

KEVIN: So in your strain of Zen here, you can't have hair.

GENJO: We shave our heads.

KEVIN: You do that, like, every two weeks or so, or--

GENJO: Oh, no; every few days.

KEVIN: Every few days. [At] many Korean temples, they do it every two weeks, like a big shaving event.

GENJO: Yeah, in Japan, it's on any day that has a 4 or a 7. I don't know why, but any day-- so the 4th, the 7th--

KEVIN: The 24th--

GENJO: Right. The 14th, the 17th...

KEVIN: Interesting. So, here, what-- would I call this building that we're sitting at now... would you consider this a temple, or what should I call this?

GENJO: We call it a temple. It's really more like a city center. It's not formally a temple, it doesn't look like a temple, it doesn't act formally like a temple would in Japan or Korea or Vietnam, but it's a little bit more on the temple side than it is on the center side. Basically, this is the Zen house, where my wife and I and the two dogs live, and there's one student who lives here, too, and then the group comes every day to sit, and four times a year, we do a week-long retreat.

KEVIN: This group is the one I'll be meeting tomorrow?

GENJO: Correct.

KEVIN: OK. How big is the group?

GENJO: Our mailing list is a hundred; our active paying membership is about forty; the number of people who will be here tomorrow morning, on any given morning-- about a dozen.

KEVIN: You told me about your aikido affiliation, but your strain, uh... how would you describe that affiliation?

GENJO: My sect of Buddhism?

KEVIN: Well, yeah, I guess that, and any specific organizations you belong to.

GENJO: Well, this temple, as I am, [is] in the Rinzai form, which would be Lin Chi in Chinese--

KEVIN: Im-jae in Korean.

GENJO: Right. So we're in that sect of Buddhism. And then within the Japanese stream, we're subsection Hakuin, so we're a Rinzai-Hakuin line. We're loosely affiliated-- we're definitely associated and loosely affiliated, though there isn't a direct financial link or directorial link, but we're associated with one of two Hakuin-Rinzai monasteries in the United States. There's an active one in Los Angeles and another active one in New York. And there is one on Whidbey Island that's also Rinzai Zen, but the teacher comes only twice a year. There are residential teachers in New York and Los Angeles: Joshu Sasaki-roshi in Los Angeles and Eido Shimano-roshi in New York. And of those two mother temples here in the United States of the Japanese Hakuin-Rinzai line, I'm most closely associated with the New York Zendo.

KEVIN: OK. So "Genjo" is how I should address you? You say it's your dharma name--

GENJO: The complete title would be "Genjo Osho"; "Genjo Osho-san" would be the most formal.

KEVIN: (repeating) Genjo Osho-san.


KEVIN: You speak Japanese? You trained in Japan?

GENJO: I was trained in Japan, briefly, and I speak a little Japanese. (speaks in Japanese)-- which means, "I humbly beseech you, I really don't speak much Japanese at all."

KEVIN: I caught the "ma-sen"-- "don't," "not," negation.

GENJO: That's right.

KEVIN: And "nihongo"-- I caught that part, too. I don't speak any Japanese at all. When I went to Japan [once], I had to stay for a day. I was in Fukuoka because I was changing my visa status. I don't know very many kanji, and I don't speak a lick of Japanese, so it was the first time I'd ever felt totally lost. I'd been in Korea, and so, going to Japan, I saw a lot of things that looked similar, but it was really a cool feeling to just kind of realize: "I can't say anything to anybody!"

GENJO: Of course, they looked at you and probably thought that you might be able to say something.

KEVIN: That's-- that's possible. Well, actually, in Korea, though, they don't look at me and see a Korean. They usually just see an American.* Whereas when I was in France, they saw: "Vous avez l'air asiatique," you know-- "You look Asian." That was the first thing they caught on [to].

GENJO: Clearly, you speak French.

KEVIN: Yeah, I was a French teacher.


KEVIN: So, all right, let's turn a little bit to interreligious issues, because I have a feeling tomorrow, in a half-hour, I'm not gonna be able to get much substance in that [time]. Your background is very interesting.

GENJO: Pretty unchurched.

KEVIN: "A cradle nothing," as you said. "Pretty unchurched"... oh, so you're familiar with that term! I thought that only Christians tossed that around.

GENJO: Well, I still grew up in the Judeo-Christian tradition, so I understand the things, and about the same time I found Zen, or a few years after, I found Quakers. So I'm also a Quaker.


GENJO: And I'm a member of the University Friends Meeting here in town.

KEVIN: You do self-identify as a Quaker--

GENJO: Correct--

KEVIN: As well as a Zen master?

GENJO: Correct. And there are a number of Quakers from the University Friends Meeting who sit here at the temple. So there's definitely a crosscurrent there. There's also a UCC minister, who'll probably be here tomorrow morning; an Episcopal priest, a woman, who comes here to sit; there's people who have a Jewish background who come here to sit...

KEVIN: What do you think these people are doing this for? These people coming from very specific traditions, they sit zazen here. Why are they doing that?

GENJO: You know, meditation, whether it's called "centering prayer," or it's called "contemplation," or it's called "meditation"... my attitude is that it all gets to the same place.

In many Christian traditions, prayer or contemplation or centering prayer is not terribly strong-- not nearly as strong as it's been handed off in the Buddhist tradition. And even Quakers, who are used to having an hour in silence, sort of once or twice a week... you know, we do an hour of silence every single day. So even for Quakers, who are a contemplative branch of Christianity, it's not as sharply honed.

So I think a number of people who want a contemplative part of their religious spiritual life can turn to Zen, and either identify as Buddhists or not, but use the tools that have been handed off from the Zen tradition as a way to deepen their spirituality, period. And whether that spirituality is Christian-based or Buddhist-based doesn't much matter to the people who come. It's deepening their sense of touching the divine, however they define it-- spirit, Ground of Being, however they define it.

And we're not so tightly wound up in words or definitions, especially in the Zen tradition; we're much more interested in the experience, and the commonality of the experience, at least from my reading and my cross-religious endeavors. The genuineness and universality of the experience seems to be anywhere and everywhere. Zen just happens to have the tools that appeal most to me, that help me, speaking for myself, go the deepest quickest, or more solidly, in a rooted way. I obviously am a Buddhist in the sense that I'm a Zen Buddhist priest, but I don't really cling to definitions of what "-ist" I am-- Christian or Buddhist or... that seems so, to me, superficial, and I think [that's true for] many others who come here.

I think the point, at least for the people who come to this temple, is that it [i.e., Zen practice] provides a kind of-- for them-- a direct route to their own sense of the divine and spirituality, and they take that and put it into their ordinary lives, hopefully, and it augments, hopefully, whatever religious tradition they're from, if they're from any. There are many who aren't from any.

KEVIN: I've been talking with other people about that. In Korean, the label for such people is mu-gyo, mu meaning, you know, "not" or "no"--


KEVIN: --and gyo meaning "-ism," tradition, or whatever. You don't belong in any particular... you don't fit into one of those squares.

GENJO: So even though we do very definitely fit into a certain square in terms of tradition, we understand that the tradition is handing off tools, and the tools bring us to a place of no-religion or non-religion. So I like that character mu a lot, of course. In Zen, we use that quite a lot--

KEVIN: The very first koan, right?

GENJO: Yes, indeed. One of your questions on your essay was "What metaphor do you use for the differences between religions?", and I want to give you mine.

KEVIN: Oh, good! Yes! Please! That's a religious pluralism question. I'd love to talk about that all day.

GENJO: To me, the great religious traditions are like trees. They may be entirely different species of trees, but they've all got great trunks, great roots, and beautiful canopies. They may be very different species of tree, but they're still trees. They reach towards the same source, in terms of the water table, and they reach towards the same light. So they stretch in both directions, and they're both trees; they've got a lot more in common than what separates them, and yet they're distinctly and uniquely different. You wouldn't want to say, "Well, because I've got this tree, I don't wanna have that tree." Why can't we have an olive tree and a pine tree and a eucalyptus tree, all right here in the yard? Yeah, that makes better variety! But they do still reach toward the same water table, exactly the same water table, and exactly the same light, and to me, that's how I see different religions.

In terms of Zen and Quakerism, for me again, just speaking for myself, if you thought of two trees of different species, great trees, reaching down to the same water table and the same light, and they're on different banks of the same river-- pretty different, and yet, where their branches intermingle and just gently blend-- for me, [that's] Quakerism and Zen.

Also, people have asked me, "Well, how can you do two traditions at once?" And I say, "Well, I have two legs! I get by just fine with two legs. In fact, I walk better with two legs. You don't have to have one leg; it's perfectly fine to have two legs."

KEVIN: Um... where did I wanna go with that... The question of the same source and the same light: would you apply that to just the major religious traditions that are out there, or would you apply [that] to even some of the wackier stuff that's around? I'm being a little bit difficult on purpose, here.

GENJO: I really can't say and I don't want to venture, because there's only two traditions that I've explored. I mean, I've done reading in Taoism and Islam and Judaism, and from what I can see-- very superficially, because I haven't delved into them greatly-- the great religious traditions do all do that [i.e., reach toward the same water and light], but I haven't explored sufficiently the others to say. I have no right to say. The only ones I have experience with to some degree are Zen and Quakerism. On those two fronts, I can say, because I'm practicing both traditions.

KEVIN: So there are at least two trees in this forest.

GENJO: There are at least two; I think I see many more. And whether it's a relatively new tree, or trunk of a tree, time will tell. But unless I investigated more directly, how could I say?

KEVIN: Right. I think one of my questions, probably not a very good question for you and for this community, was about marrying outside of the community and so on...

GENJO: (chuckling) Uh, yeah; probably moot. People want me to marry them, and they're from two different traditions, I'm happy-- I've done several ceremonies where we've had a priest from both traditions, or as the priest, I've mixed in elements from two traditions. I've had many people who would normally identify as agnostic, but have some sense that there's some unifying reality, turn to Zen and to Zen priests because they want something more than just a secular union, but they don't want something with too many trappings of the religions that they grew up in, and yet they do sense some kind of unifying reality that they want to speak to in the course of this ceremony. And I'm happy to do [it] that way, too. I say, "You can have anything on the altar you want." It can be a rock, it can be a tree... I ask that there be flowers, representing compassion, and a candle, representing wisdom. But anything else they want to put on there is fine.

KEVIN: Do you do some counseling for people, whether it's couples or one-on-one?

GENJO: Mm-hm. I do.

KEVIN: How does that work, usually, I mean, you don't have to go into specific cases, but just in general...

GENJO: Well, first of all, since I am a Zen Buddhist priest, I'm not gonna marry somebody that wants an entirely secular ceremony. I say, "Hey, look: here are some kinds of ceremonies that I've done, and can you pick and choose with what I've done to make something that works for you?" And if it doesn't [work out], then it's not a good fit, and, you know, you may need to go someplace else to find someone to help you celebrate a "spiritual" ceremony. I don't care if they call it "religious." There's a place on the marriage license that says, "Is it secular or religious?" and I always check "religious" if I'm doing the marriage. But in terms of counseling, mainly I'm looking at whether or not-- I don't care what traditions they're coming from, or whether they promise to bring up their kids in the Buddhist tradition or some other tradition. I'm trying to find out whether or not, as a couple, they have some common ground when it comes to their ideas of spirituality. And also, whether or not they have common ground as a couple: are they missing something that I might be able to help them see? And is this gonna be a couple that I feel [has a] sufficient bond to celebrate? If I don't feel like there's a sufficient bond, then I wanna work with them a bit to discover whether or not there is, then [if there's no such bond] I don't wanna get involved, either.

KEVIN: You're talking mainly about up to the marriage, right? I think my question was more along the lines of, uh, afterward-- you know: conflict arises or something... have you engaged in that--

GENJO: I've done that, too, from the Buddhist perspective, but I'm also certified as a spiritual director, and I'm also a licensed mental health counselor, so I've got quite a bit of background in that way. I have a private[?]** practice, but I also see people wearing either my Zen Buddhist hat or my therapist hat or my spiritual director hat. So yes, I do do that kind of counseling.

KEVIN: I'm curious as to how that works in Korea. I know it [i.e., counseling by Buddhist clergy] happens. I've seen ads for that sort of thing-- some smiling monk, a little phone number, but I don't know how that differs or how it's similar to psychotherapy as traditionally imagined in the West...

GENJO: I suspect it's very different, but I don't know, because I haven't been to Korea, or recently to Japan, even, to know. Here's another thing: I think Buddhism-- as it's moved from its original source, India, and has moved across the Asian continent to the US-- has picked up things, especially the branch of Zen Buddhism. When it moved to China, it picked up a lot of Taoism, and when it moved to Japan, it also picked up quite a bit of the Shinto sort of animistic ancestral component. I don't know whether it [i.e., Buddhism] did that in Korea, too. And as it moves here to the West, I think it's picking up a lot of psychology. And I think that's a wonderful blending, and it says a lot for the tradition that it's kind of, "Oh! That can be added to this! We can see how that can blend." It's a big jump to blend with whatever is indigenous to that location. I really like that about Buddhism.

KEVIN: I think a lot of religions, when they move from place to place, culture to culture, whatever, they do begin to pick up some trappings from the local--

GENJO: Sure.

KEVIN: I mean, if you go to Tibet, you see a lot of shamanism inside Tibetan Buddhism--

[Editor's note: I said the above so glibly that you might get the impression I've been to Tibet. Full disclosure: the only Asian country I've visited or lived in is South Korea. I've spent a day in Fukuoka, Japan, and several hours in Osaka and the Namba shopping district, but none of that really counts; in all cases, I was merely waiting for a new visa from the Korean Consulate or on layover as I waited for a connecting flight to Seoul/Incheon. So, no: I've never been to Tibet, or to any Asian country other than South Korea.]

GENJO: Exactly. And even Christianity, when it moved to South America or Central America, picked up a lot of indigenous components--

KEVIN: Right, right. Absolutely. The question of conflict spurred by religion: what's your diagnosis? I mean, if I take something like, say, Nigeria-- Christian-Muslim [conflict]-- how would you analyze that situation?

GENJO: As Buddhism in general would: that it's ego. Ego can corrupt anything. Whether it's individualistic ego or nationalistic ego or cultural ego, ego corrupts everything. Ego's all about having enough or having more, or being better, or being best. It can take the highest teaching and easily corrupt it to its cause of being better or best or more. And whether it appears in an individualistic way, or a more sophisticated or complex social, cultural, or nationalistic way, it's still ego. From the Buddhist perspective, it is the root of all so-called evil. It's where we get most corrupted. In Zen we would also say ego is nothing but no-ego; it's just one end of a continuum, but we so often get isolated in just that end of the continuum that we become quite corrupted and can do quite a lot of harm, nationalistically or even environmentally: raping the planet, our own mother. So whether it's conflict between natural resources, or conflict between nations, or conflict between cultures, or conflict between religions, from a Buddhist perspective, it all comes back to ego.

KEVIN: That sounds a little bit similar to a dharma talk I heard in Korea. There's an American monk there named Hyeon Gak [NB: romanized spellings vary: Hyun Gak, Hyon Gak, Hyungak, Hyeongak, etc.; credit to The Marmot's Hole, where I first saw this video]-- I don't know if you've heard of him. He's got some videos on-- some people put them up on YouTube and so on. He speaks fluent Korean; he's been living there for years and years now. He was talking about flipping channels-- watching the news on one channel, and he saw the people [on TV] were really angry and holding up their holy book and-- [mimics a demonstrator screaming in anger while holding up a holy book]-- like that, neck cords out and everything... and then he flipped the channel over to a conflict in America, and it was about the Ten Commandments being put into a courtroom, and the people were standing outside, demonstrating, and they had their holy book, and they were doing this [mimics angry demonstrator again] and he was like, "You know... it's the same thing." Pretty much the same thing. So I see where you're coming from.

OK, so, uh, I don't wanna hold you much longer, but one more question: What is God?

GENJO: The lovely thing about Zen is that we can say, "No-knowing." Beyond any kind of packaging. Even to use the word "God" or "Buddha-nature" or "Tao" or "dharma" or "sunyata" or "Ground of Being"-- anytime you put a name on something, you're already conceptualizing something that can't be conceptualized, that is inconceivable. And if it's not inconceivable, you've missed it, and if it's inconceivable, it cannot be grasped. So we're quite comfortable saying, "No-knowing," and there's actually a great relief in being able to say, "Can't be known. Cannot be said." But that doesn't mean it can't be experienced. It can definitely be experienced.

KEVIN: It should be, probably, the most ordinary thing, right?

GENJO: It is the most ordinary thing, if we have the eyes to see it or ears to hear it.*** It's the most ordinary thing, clanging at us in the wind chime or the motion of the leaves or the falling rain. It's shouting at us all the time, but usually we don't see it. However, the good news is there are ways to nurture our capacity to see what we think of as the divine in the ordinary, and that's exactly what Zen is all about. And when you have that experience, that realization of the divine in the ordinary, it's not only a relief, it's a blessing. It certainly generates a great deal of compassionate open-heartedness and peace of mind at the same time. If you're feeling that, you don't need to know.

KEVIN: Again, that's very similar to what I heard from Zen Master Seung Sahn, who was the teacher of the American monk I talked about before. He [Seung Sahn] wrote a book called Only Don't Know. "You have to keep that don't-know mind!" That's how he put it.

Well, I have a thousand more questions I could ask you, but I think I'll stop here and let you go.

GENJO: I'll let you get a good rest. I think your quest and your trek are really quite admirable. Happy to host you. See you tomorrow morning.

That marks the end of the recorded exchange between Genjo and me. I hope you've enjoyed reading it. I wish I had recorded the subsequent conversation with Genjo's meditation group; I didn't take notes and can no longer rely upon my shaky memory to relay who said what during that fascinating exchange (which, unlike my prediction, did turn out to be substantive).

I'll be writing some commentaries about this exchange as time goes on; in the meantime, I'll continue to prep the transcript of the hour-long dialogue between Brother Luke and me at St. Martin's University. Can't say when that will appear, but it'll appear. Sit tight.

Oh, by the way... this post is Number 500! We're at the half-millennium mark.

*This was one of those regrettable racial slips that comes from hanging around Koreans, especially older-generation Korean-Americans or Koreans in Korea (i.e., Koreans who haven't been fully assimilated into American culture). The word "American" is often a substitute for "Caucasian" or "white" in the Korean mind. All other races are swept under the rug. If you find yourself hanging around Koreans, you might find yourself sucked into this same linguistic vortex... unless, of course, you're a non-white American! If you hear a 50-year-old ajumma in Annandale, Virginia say, "Yeah, my daughter's dating an American guy," that probably means, "My daughter's dating a white guy."

**I wasn't clear, in listening to the audio, on whether the word was "private" or "prior." I think "private" makes more sense in this context. Genjo...?

***Compare what Genjo says here with Hyeon Gak's Jesus quotation (I'll need to dig up a scriptural reference, but quick online research reveals one possibility to be Mark 8:18, in which Jesus seems to phrase the eyes/ears matter as a question, not a declaration) from the above-linked video of the Hyeon Gak interview.


Thursday, December 15, 2011

French twins, triplets, etc.

Many French words that modify nouns will vary according to gender and number, and can often be written in clusters, like so:

le, la, les (the)

mon, ma, mes (my)
ton, ta, tes (your)
son, sa, ses (his/her/its)
notre, nos (our)
votre, vos (your)
leur, leurs (their)

du, de l', de la, des (some)

ce, cet, cette, ces (this/that)

A: C'est votre chien, monsieur?
B: Oui, c'est mon chien.

A: Je vous présente ma soeur.
B: Enchanté.

A: Ah! J'ai enfin trouvé ton livre!
B: Merci!

A: Où sont mes chaussures?
B: Tes chaussures sont sous ton lit.

A: Où est note voiture?
B: Aucune idée.

A: Leur fils a beaucoup grandi!
B: Et notre fils a beaucoup rétréci.


Wednesday, December 14, 2011

being American and writing in UK English

Some Americans like writing certain words in UK English. I find this pretentious, and if I were British, I'd probably find it laughable, too, because unless you're willing to "go all the way" and write in consistently British English, it seems silly to write only certain words that way. About the only people who can get away with UK-style spellings, while writing in a distinctly North American voice, are Canadians. Remember that, awkward American Anglophiles: if you're not Canadian, and you're writing in inconsistently British English, you're just making yourself look ridiculous.


Tuesday, December 13, 2011

this week's MGRE Math Beast Challenge problem

From here:

"Walter's Exercise"

Every day, Walter burns 500 calories from cardio exercise. On some days, he also burns an additional 600 calories from weight training. If, over a 240-day period, Walter burns an average of 850 calories per day from cardio exercise and weight training combined, then on how many more days did Walter engage in both cardio exercise and weight training than in cardio exercise only?

(A) 40
(B) 60
(C) 80
(D) 100
(E) 140

My answer will appear in the comments.


MGRE problem: wrong!

Even a teacher can get things wrong, and this time around, I did.

My answer to last week's Math Beast Challenge problem turns out to be incorrect. You'll recall that my answer was (D); MGRE's answer is (C): the quantities are equal. And they're right. But why? Because of one little fact about right triangles that I had missed: the triangle's altitude, drawn from the vertex of the two legs to a point on the hypotenuse, creates two right triangles that are geometrically similar to the large triangle. I should have realized this. Anyway, without further ado, here's part of MGRE's explanation for why (C) is correct:

This could be solved with the Pythagorean Theorem, as there are three right triangles in the figure: the small one on the left, the bigger one on the right, and the largest right triangle comprised of the other two. It should also be noted that these three triangles are similar triangles; that is, the three triangles have the same three angle measures.

For the largest triangle, a2 + b2 = c2 so by substitution, Quantity B = hc2. Now that Quantity B is more similar in form to Quantity A, we will compare.

Quantity A: abc
Quantity B: hc2

Divide both quantities by c. Dividing both quantities by the same positive number will not change the relative values; the larger quantity will still be larger. This comparison becomes

Quantity A: ab
Quantity B: hc

For similar triangles, the ratios of side lengths will be equal. For example, the ratio of the short leg to the hypotenuse will be the same in each triangle.

(short leg)/(hypotenuse) = a/c (from the largest triangle) = h/b (from the triangle on the right)

a/c = h/b

By cross-multiplying, we conclude that ab = hc and thus the two quantities are equal.

MGRE's explanation continues, but it's basically a plug-in-the-numbers approach. What bugs me is that I was obviously on the right track, but I stopped in my ruminations before I'd figured out the "similar right triangles" part. Had I done that, I'd have seen that the equality I had discovered for one case (45-45-90 triangles) must also obtain for all cases.

Live and learn, eh?


Monday, December 12, 2011

"Will reading old books help my vocabulary on the SAT?"

So you're stuck reading Twain's The Adventures of Tom Sawyer and Melville's Moby-Dick. You find yourself wondering whether the effort will be worth it: will any of this reading pay off when it's time to take those dreaded SATs? Can reading old books help me develop my SAT vocabulary?

The short answer to this question is: probably. Why? Because many of the words used in those old books are still very much in circulation.

You have two types of lexical libraries in your head. In linguistics, these libraries are called "passive vocabulary" and "active vocabulary." Passive vocabulary is associated with listening and reading; active vocabulary, which is usually smaller, is associated with speaking and writing. Passive vocabulary develops first: as a baby, you spend about a year producing no understandable words, and during that time, your rapidly self-wiring brain is greedily absorbing all the language it hears. Even when you finally start speaking, your passive vocabulary continues to grow. Trying to get your active and passive vocabularies to be about the same level is one of the Great Quests of your life. Many people are voracious readers; this by no means guarantees they'll be competent writers.

This biological reality obtains all throughout high school: your brain is still self-wiring, believe it or not, so everything you cram into it will have some sort of influence. The authors you're reading in English class are master word-slingers; they don't write a lot of "Duhhhh..." and "Uhhhh..." dialogue. Instead, they tend to lace their prose with phrases like "a vexatious situation" and "her surreptitious glance"-- almost as if they knew that, over 150 years later, someone would be needing such vocabulary to score well on the SAT.

The best thing you can do for yourself is to be curious about the words you encounter in your reading. Look up every single word you don't know; don't simply rely on context, because context can be misleading. Make flashcards, write sentences, look the words up on Google to see how they're used by others. Do everything you can to help yourself! Don't act as if your test results are a matter of fate. They aren't. You control your destiny, which means you're responsible for how well you perform on those crucial exams.


Friday, December 9, 2011

a mindful pilgrimage

I've been following the blog In the Footsteps of Wonhyo since I'd learned about it. The blog is about a group of fellows who are attempting to follow the route taken by Wonhyo, he of "water from a skull" fame. The pilgrimage serves several purposes, one of which is the promotion of spiritual tourism in Korea.

The blog has already taught me a great deal about both the route Wonhyo took and some of the stories associated with the monk. If you haven't done so already, please consider adding In the Footsteps of Wonhyo to your daily blogging reads.

(Wonhyo even has a martial arts routine named after him!)


Thursday, December 8, 2011

les verbes CONNAÎTRE et SAVOIR

The French have two principal verbs meaning "to know." The verb connaître means "to know" in the sense of "to be familiar with." An example might be the sentence Romeo connaît Juliet. The verb savoir, by contrast, is more about knowing facts. Jacques sait que deux et deux font quatre.

Here are these irregular verbs' respective present-tense conjugations.

Je connais
Tu connais
Il connaît

Nous connaissons
Vous connaissez
Ils connaissent

Je sais
Tu sais
Elle sait

Nous savons
Vous savez
Elles savent

See if you can fill in the blanks with the proper verb, correctly conjugated.

1. _____-tu Michèle?

2. Vous _____ bien que votre frère n'est toujours pas arrivé.

3. _____-vous le Président des Etats-Unis?

4. Qui va gagner? Dieu _____ .

5. Nous ne _____ pas ce qui va se passer.

6. Je _____ que la France se trouve en Europe.

7. Elles ne _____ pas le patron.

8. _____-tu qui je suis? (Be careful! Something of a trick question. This is also the first line of "The Bourne Identity.")

ANSWERS (highlight to see):

1. Connais
2. savez
3. Connaissez
4. sait
5. savons
6. sais
7. connaissent
8. Sais ("savoir" is used because this question is about knowing a fact)


Wednesday, December 7, 2011

the Latin word capita

The Latin word capita means "head." If you're a Spanish learner, you may know the word cabeza, "head," which comes from the Latin. Several English words and expressions come from this Latin root. Here are a few examples.

per capita: This is an expression that means "per person." How do we count people? We do a head count, right?

capital: A capital city is the head city of a country.

decapitate: Literally, to "de-head," though we might more naturally say "behead."

capitulate: This means "surrender"; I tend to think of the notion of bowing one's head in defeat, but the actual etymology refers to putting things in sections (i.e., under headings). See here.

recapitulate: We use this word when we're talking about re-covering, perhaps in summary form, the topics we've just covered in a discussion. When we recapitulate, we're "taking it again from the top," i.e., from the head.


Monday, December 5, 2011

GRE advice: Kaplan and Manhattan Prep

For those looking for GRE-related tips, I can point you to two blogs other than mine:

Kaplan Grad Prep: From the GRE to Your Degree

Manhattan Prep GRE Blog

You can also follow these test prep services on Twitter.


Friday, December 2, 2011

two of my favorite Taoist passages

If someone were to ask me who my favorite philosopher was, I'd say it was Chuang-tzu (known as Jang-ja in Korean). Lao-tzu's Tao Te Ching may be more well-known than the Chuang-tzu, but both works should be taken together as complementary: the dead-seriousness of Lao-tzu needs the lively playfulness of Chuang-tzu.

From each work I have a favorite quote. Let's start with the Tao Te Ching, which contains one of the most powerful summations of the religious outlook I've ever encountered. From Chapter 29:

Try to make this sacred world
into more than what it is,
and you ruin it.

Try to grasp it,
and you lose it.

It's a concise statement of reality's dynamism, and of how useless it is to hold on to things or people. Like trying to grasp water by tightening one's fist, such an attempt is doomed to fail. You can't grasp reality and force it to stop: you're part of reality, and you're moving, too!

The Chuang-tzu, though, it more humorous in its approach to the question of how we relate to ultimate reality. Through words and concepts, the classic demonstrates the uselessness of words and concepts when you're attempting to integrate yourself with the Absolute. In that spirit, then, my favorite passage from the Chuang-tzu:

Now I am going to tell you something...

There is a beginning. There is no beginning of that beginning. There is no beginning of that no beginning of beginning. There is something before the beginning of something and nothing, and something before that. Suddenly there is something and nothing. But between something and nothing, I still don't really know which is something and which is nothing. Now, I've just said something, but I don't really know whether I've said anything or not.

--Chuang Tsu: Inner Chapters, translated by Gia-fu Feng and Jane English, 1974, p. 35

Zen Buddhism, which often takes its cue from philosophical Taoism, speaks of the nondualistic, nondiscursive "don't-know mind," or "beginner's mind," that makes life worth living. In the Christian Bible, the Sermon on the Mount alludes to this non-discriminatory state when Jesus says, "Suffer the little children to come unto me, and forbid them not: for of such is the kingdom of God." (Mark 10:14, Matthew 19:14) Jesus isn't speaking of the childish mindset, but of the childlike mindset-- one that doesn't waste time and energy drawing boundaries and creating separation.

A recent Korean Seon (Zen) proverb that can be seen on the wall of Hwagye-sa, a temple in Seoul, says, "All 24 hours of the day, don't make anything." The making, in this case, means the manufacturing of dualistic boundaries: this and that, yes and no, you and me, etc. Such boundaries may have their uses on a practical level, but they obscure the fundamental nonduality of reality.

We're all part of Something Bigger. Whatever that Something is, it's moving. We can't hold on to it, and it's folly to try to explain it. Sure, we can try-- but that Something will elude our grasping minds every time. Better to go with the flow, no?


Thursday, December 1, 2011

les verbes réguliers

You might want to refresh your memory by visiting my old post on conjugation here.

Regular verbs in French come in three flavors: the "-er" verbs, the "-ir" verbs, and the "-re" verbs. If you've revisited the above-linked post, you'll be familiar with the terms infinitive and infinitive stem. Let's look at three typical regular verbs:

INFINITIVE: parler (to speak)
STEM: parl-

INFINITIVE: choisir (to choose)
STEM: chois-

INFINITIVE: vendre (to sell)
STEM: vend-

Conjugation for "-er" verbs involves tacking the following endings onto the stem:

1st person sing. = -e
2nd person sing. = -es
3rd person sing. = -e

1st person pl. = -ons
2nd person pl. = -ez
3rd person pl. = -ent

For parler (to speak/talk), this means a conjugation that looks like this:

je parle
tu parles
il parle

nous parlons
vous parlez
ils parlent

Conjugation for "-ir" verbs involves tacking the following endings onto the stem:

1st person sing. = -is
2nd person sing. = -is
3rd person sing. = -it

1st person pl. = -issons
2nd person pl. = -issez
3rd person pl. = -issent

For choisir (to choose), this means a conjugation that looks like this:

je choisis
tu choisis
elle choisit

nous choisissons
vous choisissez
elles choisissent

Conjugation for "-re" verbs involves tacking the following endings onto the stem:

1st person sing. = -s
2nd person sing. = -s
3rd person sing. = [no ending]

1st person pl. = -ons
2nd person pl. = -ez
3rd person pl. = -ent

For vendre (to sell), this means a conjugation that looks like this:

je vends
tu vends
on vend

nous vendons
vous vendez
ils vendent

Try your hand at conjugating some verbs. Fill in each blank with the appropriate for of the verb or, if the verb form is given, with the appropriate subject pronoun.

1. Max _____ la pelouse. (tondre = to mow)

2. _____ attendons le train. (attendre = to wait for, to await)

3. _____-tu russe? (parler)

4. Elle _____ sur mes chaussures. (vomir = to vomit)

5. _____ restes ici? (rester = to stay)

6. Nous _____ tout ce qu'il faut. (fournir = to furnish/supply)

7. Pierre et Madeline _____ dans la même banque. (travailler = to work)

8. Jacqueline _____ son chat. (nourrir = to feed)

9. Vous _____ souvent? (skier = to ski)

10. Les poules _____ des oeufs. (pondre = to lay [eggs])


Wednesday, November 30, 2011

get unstuck: write the way you talk

In my regular job, I teach a wide range of students who run the gamut from fourth grade to adulthood. Much of what I do involves teaching writing, and it's common to hear some form of the complaint that I can't think of anything to write. While it's tempting to say that there's a single magic formula to cure all writing problems, the sad fact is that no universal solution to the problem of stuckness exists.

My own in-class approach is to get students talking about topics that interest them, or to get them thinking along lines they might not have explored. But one of the most frequent pieces of advice I give is to write the way you talk. I don't give this advice because I think my students' prose should sound as ungrammatical as their everyday speech ("I think I did good on my test yesterday" often makes me cringe), but because it's a way of becoming unstuck. Talking something out is often a great strategy for idea-generation, or for fleshing out previously-generated ideas. I've told some students that, if they have voice recorders, they should try talking to themselves and listening to the recitation of their own ideas. A lot of it will be lame, but buried among the bad ideas will be several good ones, and that's all a person needs, really, to start writing.

As Robert Pirsig notes in his classic Zen and the Art of Motorcycle Maintenance, no one can remain stuck forever. Stuckness is best thought of as a starting point, a blank slate, a field of potential. Stare at the empty page long enough, and your mind will begin to move of its own accord. Just let it happen peristaltically. And try talking-- to yourself or to others-- as a way to generate ideas.


Tuesday, November 29, 2011

exponents: multiplicative property

It's inconvenient to write exponents in HTML; you have to use the "superscript" command. What's easier is using the circumflex (^) to indicate "raised to the power of." That's what I'll be doing in this post as we cover one interesting property of exponents.

First, some vocab.

The term exponent refers to the tiny number that sits above and to the right of another number or variable. It denotes the number of times that the big number next to it-- called the base-- should be multiplied by itself. If, for example, we have something like this:

x3 (hereafter written as x^3)

--this means we multiply x times x times x (written as x*x*x). The variable x is the base; 3 is the exponent.

What would 34 be? (hereafter 3^4)?

Multiply: 3*3*3*3 = 81.

If two exponential expressions have the same base, you can do interesting things with them.

(x^2)*(x^3) = (x^5) Notice that, when you multiply these two quantities, the powers add! The general rule, then, is

(x^a)*(x^b) = x^(a+b)


(2^2)*(2^4) = (2^6) = 64

CAUTION: Be careful not to confuse an expression like 2^3 with 2*3!! Students often make this mistake. 2 cubed is 8, but 2 times 3 is 6.

How do we know that multiplying exponential expressions with the same bases means adding exponents? We can work it out the long way.

This equation

(x^2)*(x^3) = (x^5)

can be rewritten as

(x*x)*(x*x*x) = x*x*x*x*x (associative property of multiplication)

...which is x^5!

Remember, though, that if the bases are different, you can't multiply two exponential quantities together and expect to add the exponents. Doesn't work.

OK... more later!


Sunday, November 27, 2011

the GRE Analytical Writing section

I've taken the GRE twice this year and have scored a 5.5 out of 6 on the Analytical Writing section both times. That puts me in the 96th percentile, i.e., I've consistently done better than 96% of people who've taken the GRE.

And yet... I wonder how much it matters. Many universities don't even look at the AW score when evaluating you as a candidate for graduate school. I think that's too bad. But for the purposes of this post, I'm assuming my audience is people who are hoping to score a 5.5 or 6 on the AW section because they know they're applying to a school that views AW as important.

If you're taking the GRE, I can safely assume you're an adult, so the advice I'm going to give you here is adult advice: work your ass off. What that means, in practical terms, is that you need to be writing, writing, and writing some more, and you need to be doing what you can to get better at it. Specifically, you need to sharpen your essay-writing skills, because Analytical Writing isn't creative writing: it's about engaging in logical argument and identifying flaws in other people's reasoning.

In a previous post aimed at high schoolers, I wrote on writing logically and clearly. You might want to give that post a visit, because it applies to at least one of the two AW tasks that await you on the GRE: the Analyze an Issue subsection. (The Analytical Writing section is composed of two subsections: Analyze an Issue and Analyze an Argument.)

Let's focus, then, on the second subsection: Analyze an Argument. In this section, you'll be given an argument that contains flaws, and you'll have 30 minutes to note as many flaws as possible while also suggesting ways in which to repair them. Here's an example from my Kaplan manual (Kaplan New GRE Verbal Workbook, 7th Edition; New York: Kaplan, Inc., 2011), and I can vouch that this example conforms to what you'd see on the actual GRE:

The following is a letter to the editor of a psychology journal:

The data collected from a variety of studies now suggest a relationship between the medicine Hypathia and the heightened risk of anxiety in patients afflicted with bipolar disorder. In 1950, before Hypathia was widely used to treat bipolar disorder, relatively few patients were diagnosed as anxious or had symptoms that suggested anxiety. However, in five studies published between 2005 and 2010, more than 60 percent of the subjects with bipolar disorder who took Hypathia demonstrated symptoms of anxiety or reported having episodes of heightened anxiety.

Write a response in which you discuss one or more viable alternatives to the proposed explanation. Justify, with support, why your explanation could rival the proposed explanation and explain how your explanation(s) can plausibly account for the facts presented in the argument.

The nice thing about Analytical Writing is that you're not required to name or classify the fallacies you detect. You won't have to talk about post hoc, ergo propter hoc or tu quoque or argumentum ad ignorantiam (and so on ad nauseam). It'll be enough to spot the flaws and identify them in plain language. Let's try spotting a few of them now, shall we?

1. As a general comment: I notice the entire argument falls prey to a massive "correlation is not causation" flaw (this is, by the way, the post hoc ergo propter hoc fallacy: event B happened after event A, so A must have caused B!).

2. There's a faulty diachronic comparison between "relatively few patients" before 1950 and "more than 60 percent of subjects" between 2005 and 2010.

3. Sticking with the faulty comparison for a moment, I'll also note that the time periods aren't being rigorously compared: we seem to be matching up (a) a vague, pre-1950 era with (b) a more clearly-defined period. If "pre-1950" means something like "1900-1949," then wouldn't it make sense to compare that era with, say, 1960-2009? And what if the data from 1950 to 2009 undermine the writer's argument?

4. The relationship between "more than 60 percent of the subjects" and "five studies published between 2005 and 2010" is unclear. One gets the impression that the writer is saying that 60 percent of all the subjects in the five studies, taken together as a single group, experienced some form of anxiety after/while taking Hypathia. But what if some of the subjects in one study were also involved in one or more of the other studies? Or: what if the percent figure is hiding a real disparity in raw numbers (e.g., if the five studies all had very different numbers of patients, with Study A having 20 patients and Study E having 10,000)? Or again: what if four of the five studies showed only 20% of patients suffering anxiety, while the fifth study had radically skewed results, thus leading to the 60% figure? If one study is an outlier, then we need to take it with a grain of salt, don't we? At the very least, that study makes it dangerous to lump the five studies together in the service of some general claim.

5. Doesn't a distinction need to be made between patients who begin suffering anxiety and those that suffer increased anxiety? Is the writer conflating causation with exacerbation?

Can you find any other flaws in the writer's argument? Think about it for a bit, but now let's turn to the question of offering solutions, because you need to do more than pick out argumentative flaws in this subsection of the GRE.

1. How can we fix the correlation/causation problem? If you're a David Hume partisan, then you know that the best you can come up with is a "regularity theory" of causation (event B regularly occurs after event A). Because this flaw permeates the writer's entire argument, we really need to focus on how to fix problems (2) through (5).

2. For (2) above, it would have been good to see less ambiguity about the number or proportion of patients being compared. A raw-number comparison might have made for a stronger case.

3. For (3) above, it would have been nice for the writer to have been clearer about the time periods being compared. Why is "pre-1950" being compared with "between 2005 and 2010"? A more rigorous comparison would have noted (and related) trends between corresponding time periods.

4. For (4) above, well... a lot needs to be done. It would have been nice had the writer both spelled out the number of patients involved in each 2005-2010 study and offered similar figures for a corresponding pre-1950 period (say, 1945-1950). The writer would also have strengthened his/her case by noting whether there had been any patient overlap between/among studies.

5. For (5) above, the writer should have been at pains to discuss what s/he feels Hypathia does. Does it cause anxiety? Does it increase anxiety? Is there some sort of equivalence between causation and exacerbation?

It occurs to me that I've missed one rather obvious flaw in the writer's argument. Can you guess what it is? I'll write it below in white font between [brackets]; just highlight the space to see my thoughts on the matter. This flaw may, in fact, be one of the very first ones that you thought of.

[The writer never considers the possibility that something other than Hypathia might be causing the anxiety. Even if only to dismiss the possibility, the writer should have at least raised the possibility that the anxiety's etiology might stem from a different source.]

There are doubtless other flaws to be found, but if you were able to pick out the ones that I picked out, you'd be on your way to getting a 5 or a 6 for this essay.

Remember that this is an essay you're writing. You might be asked to write it as if it were a letter to the editor, but it's an essay all the same. The quality of your organization counts, as does the quality of your writing ability in general. Avoid typos, poor grammar and mechanics, misspellings, and all the other pitfalls that come with writing under pressure on an unfamiliar computer keyboard.

Based on my own experience with the AW section, I'd recommend going for at least five paragraphs-- more if you're a fast and competent typist. Organize your paragraphs this way:

1. quick intro
2. flaw #1 & #2 detected; solutions to patch them
3. flaw #3 & #4; solutions
4. flaw #5 & #6; solutions
5. quick conclusion

[NB: the Kaplan instructions call for a bit more than just finding problems and proposing solutions, but the question as written will still allow you, more or less, to craft an essay along the lines of the above-suggested template.]

For both of the AW subsections, leave yourself time to proofread your essays. You'll be embarrassed at how many mistakes you can make when typing in furious desperation.

Apologies for concentrating so heavily on the Analyze an Argument subsection, but I feel that the skills needed for the Analyze an Issue subsection have already been adequately covered elsewhere (and here as well).

In the meantime, get writing! Start up a blog; write letters to the editor; append detailed, well-argued comments to blog posts and news articles, and watch how your arguments get picked apart by the ensuing commenters. Learn from these experiences; strive constantly to improve your writing until you feel confident that you can "argue on command." Grad school involves plenty of discussion and debate: you'll often be required to think on your feet, so the GRE isn't a completely unrealistic simulation of that sort of pressure.

Good luck!


I'm available via Skype!

If you're new to this blog and haven't had a chance to explore the tabs underneath the banner image, you should know that I'm available via Skype if you want to talk face-to-face. My contact information for email, Skype, and Twitter is located at the bottom of the "About" page (see "About" tab!). Email me a note saying you want to talk via Skype and we'll arrange a day and time. I'll wait no more than 10 minutes, however; time is precious, so please be punctual.

I mention the Skype thing because you might be hesitant about signing up to be tutored by someone you haven't vetted. That's perfectly understandable, so if you want to chat via Skype for a bit to sound me out, I'm game.

Skype allows for long-distance tutoring, by the way: we might be thousands of miles apart, and separated by two or three time zones, but that doesn't mean I can't be your tutor. Multimedia distance learning is all the rage these days; educational paradigms are changing rapidly, and many students now prefer to learn from the comfort of their own home. Skype plays right into that scenario... and it saves you the extra cost of paying my gasoline bill! (If you've visited my rate chart, you're aware I charge extra for long drives. Sorry, but that's the economy we live in.)

So hit me with some Skype action!


Thursday, November 24, 2011

Happy Thanksgiving, all!

There might not be any updates until the weekend. Have a great Thanksgiving, and be sure to hug someone.


Tuesday, November 22, 2011

reading and taking notes

When you have to write an essay, the recommended SOP (standard operating procedure) is that you brainstorm first, outline next, then write a series of drafts. My feeling is that, if you're reading and you need to understand the material, you can work the process backward and try reverse-engineering an outline. This technique is especially good if you're reading something completely uninteresting: the creation of an outline is an analytical process; by creating an outline based on the reading material, you're forcing yourself to break the material down into parts and organize those parts correctly.

Let me show you two examples of this technique. The first example will be the more straightforward one: we'll be outlining text of an obviously academic nature. The second example, however, will come from a work of fiction, and will demonstrate that narratives, too, can be rendered in outline form.

FIRST PASSAGE (from SparkNotes, here):

The Italian Renaissance followed on the heels of the Middle Ages, and was spawned by the birth of the philosophy of humanism, which emphasized the importance of individual achievement in a wide range of fields. The early humanists, such as writer Francesco Petrarch, studied the works of the ancient Greeks and Romans for inspiration and ideology, mixing the philosophies of Plato and other ancient thinkers with the teachings of the Roman Catholic Church. Under the influence of the humanists, literature and the arts climbed to new levels of importance.

Though it eventually spread through Europe, the Renaissance began in the great city-states of Italy. Italian merchants and political officials supported and commissioned the great artists of the day, thus the products of the Renaissance grew up inside their walls. The most powerful city-states were Florence, The Papal States (centered in Rome), Venice, and Milan. Each of these states grew up with its own distinctive character, very much due to the different forms of government that presided over each. Florence, considered the birthplace of the Renaissance, grew powerful as a wool-trading post, and remained powerful throughout the Renaissance due to the leadership of the Medici family, who maintained the city's financial strength and were intelligent and generous patrons of the arts. The Pope, who had the responsibility of running the Catholic Church as well, ruled Rome. As the power of the northern city-states grew, the Papacy increasingly became the seat of an international politician rather than a spiritual leader, and many pontiffs fell prey to the vices of corruption and nepotism that often accompanied a position of such power. Nevertheless, Rome, the victim of a decline that had destroyed the ancient city during the Middle Ages, flourished once again under papal leadership during the Renaissance. Venice and Milan also grew wealthy and powerful, playing large roles in Italian politics and attracting many artists and writers to their gilded streets. Venice was ruled by oligarchy in the hands of its Great Council of noble families, and Milan by a strong monarchy that produced a line of powerful dukes.

Perhaps the most prominent feature of the Renaissance was the furthering of the arts, and the advancement of new techniques and styles. During the early Renaissance, painters such as Giotto, and sculptors such as Ghiberti experimented with techniques to better portray perspective. Their methods were rapidly perfected and built upon by other artists of the early Renaissance such as Botticelli and Donatello. However, the apex of artistic talent and production came later, during what is known as the High Renaissance, in the form of Leonardo da Vinci, Raphael, and Michaelangelo, who remain the best known artists of the Renaissance. The Renaissance also saw the invention of printing in Europe and the rise of literature as an important aspect in everyday life. The Italian writers Boccaccio, Pico, and Niccolo Machiavelli were able to distribute their works much more easily and cheaply because of the rise of the printed book.

Alas, the Italian Renaissance could not last forever, and beginning in 1494 with the French invasion of Italian land Italy was plagued by the presence of foreign powers vying for pieces of the Italian peninsula. Finally, in 1527, foreign occupation climaxed with the sack of Rome and the Renaissance collapsed under the domination of the Holy Roman Emperor, Charles V. The economic restrictions placed on the Italian states by Charles V, combined with the censorship the Catholic Church undertook in response to the rising Reformation movement ensured that the spirit of the Renaissance was crushed, and Italy ceased to be the cradle of artistic, intellectual, and economic prosperity.

The Italian Renaissance isn't the most exciting topic for most American high schoolers (and at a guess, it's probably not that exciting for Italian high schoolers, either), so let's do this as quickly and as systematically as possible.

First, I see there are four paragraphs, so these will be our I, II, III, and IV. Outlines shouldn't be essays: every part of the outline should be succinct, containing only the very essence of the information that's relevant for study. Students will be delighted to know that they should avoid complete sentences when taking notes or outlining. Personally, I encourage students to rely on whatever shorthand works best for them to get the job done... even if that means relying on (gack! barf!) online-style English.

Here's the skeleton:

Italian Renaissance = IR

I. IR's origins

II. IR's spread: where & how

III. IR's prominent features

IV. IR's decline

Textbook-style prose makes it easy to figure out how to write your outline: the people who wrote the information were probably using outlines to begin with!

With the skeleton in place, it's time to flesh out the outline by hunting down and listing main ideas.

I. IR's origins
    A. followed Middle Ages
    B. arose from humanism
    C. ascension of lit and arts

II. IR's spread: where & how
    A. began in Ital. city-states
    B. cities that were major centers
    C. papacy's role

III. IR's prominent features
    A. furthering of arts
    B. advancement of new techniques & styles

IV. IR's decline
    A. French invasion (1494)
    B. sack of Rome (1527-- foreign powers?)
    C. Charles V's final nails in coffin of IR

The final bit of fleshing-out means the addition of meaningful, relevant details:

I. IR's origins
    A. followed Middle Ages
    B. arose from humanism
        1. humanism emphasized indiv. achievmt.
        2. early humanists (e.g. Petrarch) studied Gk.& Rom. classics
            for inspiratn. & ideology
        3. classical ideas were mixed w/Catholic thought
    C. ascension of lit and arts

II. IR's spread: where & how
    A. began in Ital. city-states
        1. merchants & politicians supported & commissioned great artists
        2. "products" of IR "grew up" inside city-states
    B. cities that were major centers
        1. Florence
            a. birthplace of IR
            b. was wool-trading post
            c. remained powerful thanks to Medici family (big art patrons)
        2. Papal States
            a. centered in Rome; Pope ruled
            b. papacy gained power, became seat of intl. politics; corruption, nepotism
            c. Rome flourished under papal leadership
        3. Venice & Milan
            a. grew wealthy & powerful
            b. attracted many artists & writers
            c. wielded great political influence
            d. Venice = oligarchy, noble families
            e. Milan = monarchy, powerful dukes

NB: For Section II above, did you see that I changed the outline slightly to reflect the information I had gleaned upon rereading?

III. IR's prominent features
    A. furthering of arts
        1. refinement of technique of perspective (painter Giotto, sculptor Ghiberti)
        2. followed by those who built upon their work
            a. Botticelli
            b. Donatello
        3. High Renaissance = apex of talent & production
            a. Leonardo da Vinci
            b. Raphael
            c. Michelangelo
    B. advancement of new techniques & styles
        1. invention of printing in Europe
        2. rise of lit's importance in everyday life
        3. easy distrib. of works of Boccaccio, Pico, Machiavelli

IV. IR's decline
    A. French invasion (1494)
    B. sack of Rome (1527-- foreign powers?)
    C. Charles V's final nails in coffin of IR
        1. econ. restrictions of Charles V
        2. censorship by Catholic Church in response to Protestant Reformation

The above outline takes a bit of work to make properly, and it requires you to sweep through the text several times in order to put everything in its proper place. But the effort is worth it, because you'll have looked over the text several times, and will have had to decide where, exactly, the various details should be tucked into your outline. The outline itself, once made, can now serve as a useful tool for review when it's quiz or test time.

Let's try the above technique with a bit of fiction, now, shall we? Below, I quote from an online classic: Terry Bisson's science fiction short story titled "They're Made Out of Meat." Enjoy the story, then look at the outline that follows it.

SECOND PASSAGE (from here)


"They're made out of meat."


"Meat. They're made out of meat."


"There's no doubt about it. We picked up several from different parts of the planet, took them aboard our recon vessels, and probed them all the way through. They're completely meat."

"That's impossible. What about the radio signals? The messages to the stars?"

"They use the radio waves to talk, but the signals don't come from them. The signals come from machines."

"So who made the machines? That's who we want to contact."

"They made the machines. That's what I'm trying to tell you. Meat made the machines."

"That's ridiculous. How can meat make a machine? You're asking me to believe in sentient meat."

"I'm not asking you, I'm telling you. These creatures are the only sentient race in that sector and they're made out of meat."

"Maybe they're like the orfolei. You know, a carbon-based intelligence that goes through a meat stage."

"Nope. They're born meat and they die meat. We studied them for several of their life spans, which didn't take long. Do you have any idea what's the life span of meat?"

"Spare me. Okay, maybe they're only part meat. You know, like the weddilei. A meat head with an electron plasma brain inside."

"Nope. We thought of that, since they do have meat heads, like the weddilei. But I told you, we probed them. They're meat all the way through."

"No brain?"

"Oh, there's a brain all right. It's just that the brain is made out of meat! That's what I've been trying to tell you."

"So ... what does the thinking?"

"You're not understanding, are you? You're refusing to deal with what I'm telling you. The brain does the thinking. The meat."

"Thinking meat! You're asking me to believe in thinking meat!"

"Yes, thinking meat! Conscious meat! Loving meat. Dreaming meat. The meat is the whole deal! Are you beginning to get the picture or do I have to start all over?"

"Omigod. You're serious then. They're made out of meat."

"Thank you. Finally. Yes. They are indeed made out of meat. And they've been trying to get in touch with us for almost a hundred of their years."

"Omigod. So what does this meat have in mind?"

"First it wants to talk to us. Then I imagine it wants to explore the Universe, contact other sentiences, swap ideas and information. The usual."

"We're supposed to talk to meat."

"That's the idea. That's the message they're sending out by radio. 'Hello. Anyone out there. Anybody home.' That sort of thing."

"They actually do talk, then. They use words, ideas, concepts?"

"Oh, yes. Except they do it with meat."

"I thought you just told me they used radio."

"They do, but what do you think is on the radio? Meat sounds. You know how when you slap or flap meat, it makes a noise? They talk by flapping their meat at each other. They can even sing by squirting air through their meat."

"Omigod. Singing meat. This is altogether too much. So what do you advise?"

"Officially or unofficially?"


"Officially, we are required to contact, welcome and log in any and all sentient races or multibeings in this quadrant of the Universe, without prejudice, fear or favor. Unofficially, I advise that we erase the records and forget the whole thing."

"I was hoping you would say that."

"It seems harsh, but there is a limit. Do we really want to make contact with meat?"

"I agree one hundred percent. What's there to say? 'Hello, meat. How's it going?' But will this work? How many planets are we dealing with here?"

"Just one. They can travel to other planets in special meat containers, but they can't live on them. And being meat, they can only travel through C space. Which limits them to the speed of light and makes the possibility of their ever making contact pretty slim. Infinitesimal, in fact."

"So we just pretend there's no one home in the Universe."

"That's it."

"Cruel. But you said it yourself, who wants to meet meat? And the ones who have been aboard our vessels, the ones you probed? You're sure they won't remember?"

"They'll be considered crackpots if they do. We went into their heads and smoothed out their meat so that we're just a dream to them."

"A dream to meat! How strangely appropriate, that we should be meat's dream."

"And we marked the entire sector unoccupied."

"Good. Agreed, officially and unofficially. Case closed. Any others? Anyone interesting on that side of the galaxy?"

"Yes, a rather shy but sweet hydrogen core cluster intelligence in a class nine star in G445 zone. Was in contact two galactic rotations ago, wants to be friendly again."

"They always come around."

"And why not? Imagine how unbearably, how unutterably cold the Universe would be if one were all alone ..."

Reverse-engineering an outline from a piece of narrative fiction is, in some ways, harder than pulling the same stunt with a more academically-toned text. But because stories normally move in phases (think about the distinct scenes in a typical stage play), outlining is possible. So-- what are the phases in Bisson's story? You might analyze it differently, but here's what I see:

I. They're meat beings!

II. They've got brains and thoughts? What do they want?

III. What should we do about this discovery?

Those are the three major phases of the story. By now, you realize that the two interlocutors are unbelievably ancient aliens (they measure time in galactic rotations; the Milky Way rotates once every 250 million years, making Earth only about 20 rotations old!), and the meat-beings in question are human beings. That's right: we're the thinking meat! We're the ones making squishy meat sounds by flapping and squeezing air through our meat, the ones projecting our meat-thoughts via radio, the ones looking for other life out in the void. It's enough to make you wonder what the alien scientists are made of. In Arthur C. Clarke's fictional universes, superior aliens are often like gods-- incorporeal after having shed their material bodies aeons ago. Are Bisson's aliens like that? Or are they made out of a much tougher form of matter-- something that isn't as susceptible to the ravages of time? Perhaps these aliens are a bit naive; they do seem capable of surprise, despite being so well-traveled.

Fleshing out the above skeletal outline will involve adding a bit of detail. With a story this short, it shouldn't be hard to fill in the gaps. Here's my attempt:

I. They're meat beings!
  A. really made of meat
  B. not made of something else?

II. They've got brains and thoughts? What do they want?
  A. talk to other life
  B. explore the universe
  C. contact other aliens
  D. swap ideas
  E. they use radio to transmit meat sounds which represent meat thoughts

III. What should we do about this discovery?
  A. officially? contact them
  B. unofficially: leave them alone and remove all evidence of our existence
  C. contact other intelligences in this region of the galaxy

That wasn't too hard, was it? Just follow the narrative flow, and you'll be able to outline any story more or less systematically.

The point of all this, though, isn't that you should embrace only one particular note-taking technique. The deeper point I'm trying to make is that it's necessary to spend time with a text if you truly hope to understand it. Outlining a given passage is simply one good method for making you stop and analyze the information at hand-- to see how all the parts relate both to each other and to the whole. And as I mentioned above, an outline, once made, is an indispensable study tool for quiz or test time: it's a quick summary of the essentials.

You may be tempted to think that you can simply pick up a text, read it, miraculously commit everything to memory, and somehow manage to ace your tests. If you've got a photographic memory and a highly analytical mind, you might just get away with such laziness. But for most of us normal folks, it makes more sense to buckle down and do the hard work of reading actively and intelligently, taking notes as a way to organize and retain information.

There are no magic solutions, I'm afraid. As has been true over the millennia, study has always been an exercise in time, effort, and focus.