Go to it! My answer will appear in the comments. The official answer will appear next week.
_
Tuesday, February 21, 2012
this week's MGRE Math Beast Challenge
From here:
Go to it! My answer will appear in the comments. The official answer will appear next week.
_
Go to it! My answer will appear in the comments. The official answer will appear next week.
_
last week's MGRE Math Beast Challenge problem: CORRECT!
MGRE's solution to last week's problem:
While I like this explanation, it seems to involve a dangerous risk: how do you know you're double-counting everything?
_
From each of the 4 corners, we can draw 5 line segments as described in the problem. Note that we can’t draw a segment from the corner to any of the remaining dots without passing through another dot. From each of the 4 middle edge dots, we can draw 7 such line segments. Note that we can’t draw a segment from this edge dot to the one remaining dot without passing through the middle dot. From the center dot, we can draw 8 such line segments.
From the 4 corner dots, there are 5 line segments each: (4)(5) = 20
From the 4 middle edge dots, there are 7 line segments each: (4)(7) = 28
From the 1 center dot, there are 8 segments: (1)(8) = 8
The sum 20 + 28 + 8 is 56. However, this double counts each of the possible segments. For example, the line between the left top corner and the middle dot was counted among the 5 segments drawn from the left top corner, but it is the same as the segment drawn from the middle dot to the left top corner, which was counted among the 8 drawn from the center.
Thus, the number of unique line segments is 56/2 = 28.
The correct answer is D.
While I like this explanation, it seems to involve a dangerous risk: how do you know you're double-counting everything?
_
Monday, February 20, 2012
time budgeting and test prep
1. General Notes
It's one of the hardest life-skills for many of us to master: time-budgeting. In an ideal world, we would all go through the following train of thought:
Sounds simple, right? But this is a skill that escapes most of us because, as psychiatrist M. Scott Peck so famously noted decades ago, human beings are basically lazy. This is the fundamental sin of our species. We are, at bottom, unwilling to work to change ourselves, because it's so much easier just to remain where we are-- content, complacent, and unfulfilled. What's the remedy?
To be honest, I don't think there's any easy way around this problem. Laziness is a form of entropy, a downward-pushing, disorderly force that makes us resistant to the ordering processes of progress, evolution, and self-improvement. At the most basic level, there obviously needs to be a desire to improve yourself, but desire without direction leads nowhere.
It might help if you began your self-improvement with a clear vision of what you're trying to accomplish. For example, if your goal is to get into a non-Ivy League college, then it makes little sense to tell yourself that you need to score a perfect 2400 on the SAT I. You don't. In fact, many Ivy Leaguers didn't make perfect scores, either: they were admitted thanks to decent SAT scores plus other academic (and non-academic) merits-- their consistently good grades, their community-service extracurriculars, their student leadership, etc. Their SAT scores weren't bad, to be sure, but they didn't need to be perfect. Opposite case: what if your goal is to be an engineer (mechanical, electrical, civil, etc.)? In that case, I strongly recommend that you shoot for an 800 on the Math portion of the SAT I, because without that perfect score, you reduce your own competitiveness. If you're trying to get into Georgia Tech or Virginia Tech or MIT, you're not helping yourself by showing those schools' admissions committees a score of 700; many of the other applicants will have scored 800, and the schools want those applicants.
The upshot of all the above? Scale your goals to meet your ambitions. Figure out what your ambitions are, then strive for them, but do so realistically. Make a plan of attack. See where you are, grade-wise, in all your classes; figure out where you want to be in those classes; create a study schedule that will give you space to establish a routine. Cut out anything unnecessary to the achievement of your goals, and be wise with your free time. Be sure to include free time for yourself, but not too much. Now is not the time to be lazing around.
2. Specifically on Test Prep
Everything I've just written applies to how you should approach your test prep. Set realistic goals for yourself: "A 2400 would be nice, but for my purposes, I need to score at least a 2000, with Critical Reading being at least 700. That would get me where I want to go." Drill yourself by going to a test prep center (that's a good way of having a routine established for you), or take the cheaper route: buy the College Board's official guide to the SAT I, take the diagnostic test to figure out your weak points, then develop a plan of attack based on what you discover.
Achievement requires sacrifice. If you're not satisfied with your diagnostic score-- if, for example, you scored a 1500 overall-- then be sure to ratchet the level of your commitment upward so that you meet your goals. Be ready to turn aside opportunities to go see movies with friends, or to watch as much TV as you used to, or to surf the Net or text or tweet or use Facebook until all hours. Attack your goals with seriousness of mind. Remind yourself, again and again, of why you're going through all this trouble. The reward will be worth it.
Routines require stability. Your study should take place in the same location, at the same time of day, with a minimum of distractions. Stay away from TV, younger siblings, friends (unless they're actually studying with you!), and your smart phone. When studying the Math portion of the SAT, try to avoid calculators, even though calculators may be allowed. Don't vary your study time-- 6PM on Monday, 8PM on Tuesday, 7:30PM on Wednesday, etc. This is more harmful than helpful.
There's also nothing wrong with involving your parents or other adults in the study process, as long as they can offer competent help. Many parents will readily admit that they can't help you, and you should probably take them at their word. Seek help from a trusted neighbor, fellow church/temple member, or parents of a classmate. Ask these people to quiz you on your weak points.
In conclusion: there are no magic solutions. Time-budgeting is a matter of knowing where you want to go, taking those goals seriously, and establishing a routine that will get you there. Any strategy you adopt will require a certain level of desire, focus, self-discipline, and all the rest. If laziness is a form of entropy, then self-improvement means fighting against that natural tendency to be idle and complacent. Unfortunately, many adults take this lazy path, then spend their lives wondering why they didn't pursue their cherished desires when they were younger. Don't be one of those people. Make time, keep your goals in mind, and push yourself to achieve. When it comes to test prep, find your weak areas, establish your routine, and set about shoring those areas up. You can go it alone (in a distraction-free environment), or enlist the aid of friends, parents, or other trusted adult resources. Private tutoring (such as what I offer) or tutoring centers are also an option, if you feel you're not self-disciplined enough to fix your own schedule. Whatever you choose to do, keep at it!
_
It's one of the hardest life-skills for many of us to master: time-budgeting. In an ideal world, we would all go through the following train of thought:
1. To improve at anything, we need routine.
2. Routines take place in the same location, at consistent times. To establish a routine, we need to make time for ourselves.
3. To make time, we have to budget time.
Sounds simple, right? But this is a skill that escapes most of us because, as psychiatrist M. Scott Peck so famously noted decades ago, human beings are basically lazy. This is the fundamental sin of our species. We are, at bottom, unwilling to work to change ourselves, because it's so much easier just to remain where we are-- content, complacent, and unfulfilled. What's the remedy?
To be honest, I don't think there's any easy way around this problem. Laziness is a form of entropy, a downward-pushing, disorderly force that makes us resistant to the ordering processes of progress, evolution, and self-improvement. At the most basic level, there obviously needs to be a desire to improve yourself, but desire without direction leads nowhere.
It might help if you began your self-improvement with a clear vision of what you're trying to accomplish. For example, if your goal is to get into a non-Ivy League college, then it makes little sense to tell yourself that you need to score a perfect 2400 on the SAT I. You don't. In fact, many Ivy Leaguers didn't make perfect scores, either: they were admitted thanks to decent SAT scores plus other academic (and non-academic) merits-- their consistently good grades, their community-service extracurriculars, their student leadership, etc. Their SAT scores weren't bad, to be sure, but they didn't need to be perfect. Opposite case: what if your goal is to be an engineer (mechanical, electrical, civil, etc.)? In that case, I strongly recommend that you shoot for an 800 on the Math portion of the SAT I, because without that perfect score, you reduce your own competitiveness. If you're trying to get into Georgia Tech or Virginia Tech or MIT, you're not helping yourself by showing those schools' admissions committees a score of 700; many of the other applicants will have scored 800, and the schools want those applicants.
The upshot of all the above? Scale your goals to meet your ambitions. Figure out what your ambitions are, then strive for them, but do so realistically. Make a plan of attack. See where you are, grade-wise, in all your classes; figure out where you want to be in those classes; create a study schedule that will give you space to establish a routine. Cut out anything unnecessary to the achievement of your goals, and be wise with your free time. Be sure to include free time for yourself, but not too much. Now is not the time to be lazing around.
2. Specifically on Test Prep
Everything I've just written applies to how you should approach your test prep. Set realistic goals for yourself: "A 2400 would be nice, but for my purposes, I need to score at least a 2000, with Critical Reading being at least 700. That would get me where I want to go." Drill yourself by going to a test prep center (that's a good way of having a routine established for you), or take the cheaper route: buy the College Board's official guide to the SAT I, take the diagnostic test to figure out your weak points, then develop a plan of attack based on what you discover.
Achievement requires sacrifice. If you're not satisfied with your diagnostic score-- if, for example, you scored a 1500 overall-- then be sure to ratchet the level of your commitment upward so that you meet your goals. Be ready to turn aside opportunities to go see movies with friends, or to watch as much TV as you used to, or to surf the Net or text or tweet or use Facebook until all hours. Attack your goals with seriousness of mind. Remind yourself, again and again, of why you're going through all this trouble. The reward will be worth it.
Routines require stability. Your study should take place in the same location, at the same time of day, with a minimum of distractions. Stay away from TV, younger siblings, friends (unless they're actually studying with you!), and your smart phone. When studying the Math portion of the SAT, try to avoid calculators, even though calculators may be allowed. Don't vary your study time-- 6PM on Monday, 8PM on Tuesday, 7:30PM on Wednesday, etc. This is more harmful than helpful.
There's also nothing wrong with involving your parents or other adults in the study process, as long as they can offer competent help. Many parents will readily admit that they can't help you, and you should probably take them at their word. Seek help from a trusted neighbor, fellow church/temple member, or parents of a classmate. Ask these people to quiz you on your weak points.
In conclusion: there are no magic solutions. Time-budgeting is a matter of knowing where you want to go, taking those goals seriously, and establishing a routine that will get you there. Any strategy you adopt will require a certain level of desire, focus, self-discipline, and all the rest. If laziness is a form of entropy, then self-improvement means fighting against that natural tendency to be idle and complacent. Unfortunately, many adults take this lazy path, then spend their lives wondering why they didn't pursue their cherished desires when they were younger. Don't be one of those people. Make time, keep your goals in mind, and push yourself to achieve. When it comes to test prep, find your weak areas, establish your routine, and set about shoring those areas up. You can go it alone (in a distraction-free environment), or enlist the aid of friends, parents, or other trusted adult resources. Private tutoring (such as what I offer) or tutoring centers are also an option, if you feel you're not self-disciplined enough to fix your own schedule. Whatever you choose to do, keep at it!
_
Friday, February 17, 2012
a Philosophy of Religion course
In 2010, I created a syllabus for teaching my very own Philosophy of Religion course. Here it is, available through Google Docs. The original intent was to use the syllabus as a sample to apply for a full-time position at local community colleges, but the syllabus itself is solid enough for me to use it as the framework for an actual course in philosophy of religion.*
I had wanted to make this 16-week course available back in January for people wishing to learn on a face-to-face basis, but there didn't seem to be any interest (of course, my readership at the time was half of what it is now; the blog is growing!). If you're interested in learning about the philosophy of religion with me via Skype, however, I'm willing to teach you. The cost for the course is $286 (see here for an explanation of the rate), plus the cost of the two textbooks, both of which are available through various online sources.
As currently set up, the course assumes 3 hours per week for 16 weeks. Right now, my best available teaching day is Sunday; I'd recommend having the session between meals, from 2PM to 5PM, Eastern time. Skype will allow me to handle several callers at once, if I'm not mistaken, so we can have an actual class: me plus three or four students.
If you're in a different time zone, I hope you can rearrange your own schedule to fit this time frame. If not, we can see about arranging something privately, with the caveat that we stick to 3 hours a week, and that we keep strictly to whatever schedule we decide upon. For example: if we choose to have classes at 10AM every Monday, Wednesday, and Friday, we will not shift suddenly to 11AM during the third week of the course. I'm not a fan of wishy-washy behavior once a schedule has been established. Of course, there may be unforeseeable circumstances (e.g., my company occasionally schedules 11AM staff meetings)
General information about the Philosophy of Religion course has been available on this blog at this link. The syllabus itself provides more detail. If you're unclear on how to register, click the "Rates and Registration" tab under the banner, then click the "How to Register" link.
Just to put my price into perspective: $286 for 16 weeks' worth of education is extremely cheap. At 3 hours per week, that's 48 hours of class time. Divide $286 by 48 hours, and you get an hourly rate of $5.96. Who's insane enough to charge only $5.96 per hour for tutoring? Only someone who's more interested in cosmic questions than in money, that's who.
Get a few friends to sign up along with you, and let's get this thing rolling!
*A note on capitalization: whenever I refer generically to philosophy of religion, I leave the phrase uncapitalized. When I refer, however, to the name of the course I'd like to teach, I capitalize the phrase. No inconsistencies here.
_
I had wanted to make this 16-week course available back in January for people wishing to learn on a face-to-face basis, but there didn't seem to be any interest (of course, my readership at the time was half of what it is now; the blog is growing!). If you're interested in learning about the philosophy of religion with me via Skype, however, I'm willing to teach you. The cost for the course is $286 (see here for an explanation of the rate), plus the cost of the two textbooks, both of which are available through various online sources.
As currently set up, the course assumes 3 hours per week for 16 weeks. Right now, my best available teaching day is Sunday; I'd recommend having the session between meals, from 2PM to 5PM, Eastern time. Skype will allow me to handle several callers at once, if I'm not mistaken, so we can have an actual class: me plus three or four students.
If you're in a different time zone, I hope you can rearrange your own schedule to fit this time frame. If not, we can see about arranging something privately, with the caveat that we stick to 3 hours a week, and that we keep strictly to whatever schedule we decide upon. For example: if we choose to have classes at 10AM every Monday, Wednesday, and Friday, we will not shift suddenly to 11AM during the third week of the course. I'm not a fan of wishy-washy behavior once a schedule has been established. Of course, there may be unforeseeable circumstances (e.g., my company occasionally schedules 11AM staff meetings)
General information about the Philosophy of Religion course has been available on this blog at this link. The syllabus itself provides more detail. If you're unclear on how to register, click the "Rates and Registration" tab under the banner, then click the "How to Register" link.
Just to put my price into perspective: $286 for 16 weeks' worth of education is extremely cheap. At 3 hours per week, that's 48 hours of class time. Divide $286 by 48 hours, and you get an hourly rate of $5.96. Who's insane enough to charge only $5.96 per hour for tutoring? Only someone who's more interested in cosmic questions than in money, that's who.
Get a few friends to sign up along with you, and let's get this thing rolling!
*A note on capitalization: whenever I refer generically to philosophy of religion, I leave the phrase uncapitalized. When I refer, however, to the name of the course I'd like to teach, I capitalize the phrase. No inconsistencies here.
_
Thursday, February 16, 2012
French through cooking!
An excellent way to practice a foreign language is to find practical applications for it. It's hard to think of a better place to start than recipes, and in that spirit I offer you a link to an excellent foodblog called Jasmine Cuisine (i.e., "Jasmine cooks"). Jasmine herself is Québecoise, so her French contains some Canuckisms, but that's part of the fun for you French-language learners. No style of French is any more or any less legitimate than any other!
Think of this as a great opportunity to learn a ton of practical kitchen vocabulary: how to say "1 cup of..." or "simmer for 10 minutes" or "stir until thickened"-- not to mention the names of all sorts of fruits, vegetables, meats, seasonings, etc.
The recipes are all fantastic, and Jasmine is very frank about her successes and failures as she attempts each dish. The blog is written in a cheerful, intelligent style; I highly, highly recommend it.
_
Think of this as a great opportunity to learn a ton of practical kitchen vocabulary: how to say "1 cup of..." or "simmer for 10 minutes" or "stir until thickened"-- not to mention the names of all sorts of fruits, vegetables, meats, seasonings, etc.
The recipes are all fantastic, and Jasmine is very frank about her successes and failures as she attempts each dish. The blog is written in a cheerful, intelligent style; I highly, highly recommend it.
_
Wednesday, February 15, 2012
sonnet 109
In honor of yesterday, which was Valentine's Day, I give you Shakespeare's Sonnet 109:
Found here, with commentary.
_
O! never say that I was false of heart,
Though absence seemed my flame to qualify,
As easy might I from my self depart
As from my soul which in thy breast doth lie:
That is my home of love: if I have ranged,
Like him that travels, I return again;
Just to the time, not with the time exchanged,
So that myself bring water for my stain.
Never believe though in my nature reigned,
All frailties that besiege all kinds of blood,
That it could so preposterously be stained,
To leave for nothing all thy sum of good;
For nothing this wide universe I call,
Save thou, my rose, in it thou art my all.
Found here, with commentary.
_
Tuesday, February 14, 2012
this week's MGRE Math Beast Challenge Problem
From here:
Go to it!
Because of the nature of this problem (which I solved visually, with pen and paper), I'll be placing the solution right here on the main page, below this text.
[Scroll down a bit. No peeking if you're trying to figure this out for yourself!]
[Keep scrolling!]
[Oho!]
So it seems the answer is (D). Do you agree? Did you get a different count?
_
Go to it!
Because of the nature of this problem (which I solved visually, with pen and paper), I'll be placing the solution right here on the main page, below this text.
[Scroll down a bit. No peeking if you're trying to figure this out for yourself!]
[Keep scrolling!]
[Oho!]
So it seems the answer is (D). Do you agree? Did you get a different count?
_
solution to last week's MGRE Math Beast Challenge
MGRE has published its solution to last week's quantitative comparison problem. My answer of C was correct. Here's MGRE's discussion of the solution, which differs from mine:
_
Since x, y, and z are consecutive multiples of 3, let’s write all three integers in terms of x:
x = x
y = x + 3
z = x + 6
So, for Quantity A, the sum can be rewritten only in terms of x:
(x + 1) + (y – 2) + (z + 3)
(x + 1) + (x + 3 – 2) + (x + 6 + 3) {substituting for y and z}
3x + (1 + 3 – 2 + 6 + 3)
3x + 11
Now we find the remainder when this simplified sum is divided by 9.
(Remainder when (3x + 11) div 9) = (Remainder when 3x div 9) + (Remainder when 11 div 9)
Since x is a multiple of 3, 3x is a multiple of 9, and the remainder when 3x is divided by 9 is 0.
When 11 is divided by 9, 9 goes into 11 once, leaving 11 – 9 = 2 as the remainder.
Thus, Quantity A is 0 + 2 = 2.
The correct answer is C.
_
Monday, February 13, 2012
at what price victory?
The South Korean news (Chosun Ilbo) recently reported on a cheating scandal perpetrated by a Korean company called (appropriately enough) Hackers. The company teaches English conversation and test prep courses.
The article goes on to note that Hackers "vehemently denies the charges," but my own experience while living in South Korea tells me that the charges are probably true. TOEFL is, for example, key for those wishing to study in the US; Korean students comprise the bulk of TOEFL test-takers, and most US universities require a TOEFL score as part of the applicant's dossier. As a result, teaching mastery of TOEFL is big business in South Korea, and with so much money at stake, unsavory elements in the business world smell profits. This critique is not meant to discredit the sincere efforts of Korean students who only want to follow their dreams: I'm merely pointing out that certain cynical businessmen are willing to forgo ethics in their rush to capitalize on a trend.
So much of the Korean test-prep business is a racket based on poorly conceived pedagogy. Ideally, Korean students need to learn how to think through a test, not how to memorize "the 100 most likely TOEFL writing topics" or any of that nonsense. Many Koreans study English for years without achieving more than mediocre competence. This has less to do with student aptitude than with poor teaching methodology, I think. Of course, with something as nebulous as language teaching, there's no single method that works for everyone, which is why there will always be a plethora of "new" teaching methods-- most of which are ineffective-- promoted by people with no real notion of language curriculum design.
The problem with stealing actual test questions is that the stolen questions, when taught, prepare students only for those particular testing situations and do nothing to improve general fluency. Such teaching also hurts the students in the long run: they use the purloined questions to achieve artificially high scores, then come to the US (essentially on false pretenses) with an over-inflated sense of their own linguistic competence. Once it becomes obvious that they cannot keep up with other classmates in courses involving, say, rapidfire lecture or discussion-- not to mention lengthy research papers-- they realize they've been hoodwinked. Or hacked, in this instance.*
Personal note: I once applied to work for Hackers, way back in 2002 or 2003. I ended up teaching at Sookmyung Women's University instead, and I've never regretted that decision.
*Of course, some students realize what's going on and simply don't care: all they want is the Ivy League name on their résumé so, as the article notes, they're in it only for the high score. When prestige matters more than integrity, something is dreadfully wrong.
_
Staff of Hackers Group, one of the best-known English test preparation services in Korea, have been indicted on charges of illegally recording questions from official English language proficiency tests. Prosecutors said Hackers Group mobilized around 50 staff to record test questions over a four-year period.
"Through organized efforts to leak test questions, Hackers Group was able to achieve W100 billion (US$1=W1,122) in annual sales and W36 billion in net profit just eight years after its establishment," a prosecution spokesman said. Lax attitudes to copyrights that pervade Korean society and the belief that any means are justified to achieve high standardized test scores are the reasons such abuses continue, he added.
The Seoul Central Prosecutors Office on Monday said the 50-year-old chairman of Hackers Group identified only by his surname Cho instructed staff to sit 49 Test of English for International Communication (TOEIC) and 57 Test of English Proficiency (TEPS) tests in order to steal the copyright-protected questions between 2007 and early this year.
Prosecutors said staff memorized the test questions or used special devices to record the questions and then posted them on the company's website almost in real time and deleted them the following morning in order to avoid detection. The company then had its native English teachers review and touch them up for use as materials.
The article goes on to note that Hackers "vehemently denies the charges," but my own experience while living in South Korea tells me that the charges are probably true. TOEFL is, for example, key for those wishing to study in the US; Korean students comprise the bulk of TOEFL test-takers, and most US universities require a TOEFL score as part of the applicant's dossier. As a result, teaching mastery of TOEFL is big business in South Korea, and with so much money at stake, unsavory elements in the business world smell profits. This critique is not meant to discredit the sincere efforts of Korean students who only want to follow their dreams: I'm merely pointing out that certain cynical businessmen are willing to forgo ethics in their rush to capitalize on a trend.
So much of the Korean test-prep business is a racket based on poorly conceived pedagogy. Ideally, Korean students need to learn how to think through a test, not how to memorize "the 100 most likely TOEFL writing topics" or any of that nonsense. Many Koreans study English for years without achieving more than mediocre competence. This has less to do with student aptitude than with poor teaching methodology, I think. Of course, with something as nebulous as language teaching, there's no single method that works for everyone, which is why there will always be a plethora of "new" teaching methods-- most of which are ineffective-- promoted by people with no real notion of language curriculum design.
The problem with stealing actual test questions is that the stolen questions, when taught, prepare students only for those particular testing situations and do nothing to improve general fluency. Such teaching also hurts the students in the long run: they use the purloined questions to achieve artificially high scores, then come to the US (essentially on false pretenses) with an over-inflated sense of their own linguistic competence. Once it becomes obvious that they cannot keep up with other classmates in courses involving, say, rapidfire lecture or discussion-- not to mention lengthy research papers-- they realize they've been hoodwinked. Or hacked, in this instance.*
Personal note: I once applied to work for Hackers, way back in 2002 or 2003. I ended up teaching at Sookmyung Women's University instead, and I've never regretted that decision.
*Of course, some students realize what's going on and simply don't care: all they want is the Ivy League name on their résumé so, as the article notes, they're in it only for the high score. When prestige matters more than integrity, something is dreadfully wrong.
_
Friday, February 10, 2012
agree and disagree
I've been a faithful reader of the writings of Dr. William Vallicella for years. He and I have some fundamental disagreements, but I admire the clarity of his writing and can appreciate the reasonableness of his positions. His recent post on Daniel Dennett, anthropomorphism, and the "deformation" of the God-concept offers a good example of how I can read a "Vallicellian" essay and come away both agreeing and disagreeing with its various claims.
A bit of background: Vallicella is a theist, i.e., he believes that ultimate reality is personal. Regarding the status of human beings, he advocates a point of view that he styles ontotheological personalism. The onto- comes from the Greek on/ontos, which means "being/existence." (The terms ontology and ontological are central to most Western philosophy.) The personalism in question is, roughly, the idea that there is something about human beings that is irreducibly personal, i.e., people cannot be explained fully by scientific/empirical examination and analysis; their personhood can't be broken down into smaller parts. This personalism has its being (ontos) grounded in God (theos): hence ontotheological personalism.
This puts Vallicella in conflict with scientific atheists who believe, like philosopher Daniel Dennett, that the human mind can be explained in purely physical terms (i.e., brain activity). On his blog, Vallicella routinely critiques physicalism, the philosophy of mind that says The mind is what the brain does. Lately, he has also been writing on the spectrum of possible God-concepts, ranging from a God that is utterly physical and totally anthropomorphic to a God that is so depersonalized as to be no more than an abstract concept. Vallicella wishes to avoid these two extremes.
My own theological orientation is far different from Vallicella's. While I consider myself Christian, this is more of a sociological designation than a theological one: I've been too steeped in Asian philosophy to be a theological Christian. There's very little, in terms of Christian doctrine, that I literally believe; my own sympathies, at this point, are mostly with scientific skeptics and philosophically inclined Taoists and Buddhists; I haven't been a classical theist for a long time (I'd call myself a nontheist, i.e., someone for whom the question "Does God exist?" has no rational, discursive answer). I see reality as an intercausal being-in-process and take a very dim view of most shows of religious piety. My own philosophy of mind is probably much closer to Dennett's than it is to Vallicella's: I see the mind as something that arises from the brain; it is, in fact, utterly dependent on the brain for its existence. At the same time, I'm not so naïve as to think that the brain's activity is totally predictable: cogitation, being a supervenient phenomenon (i.e., something that arises from a lower stratum of being), follows its own rules. As author Robert Pirsig analogized it in his book Lila (I'm taking some liberties, here): it's like the difference between computer hardware and software-- each follows its own rules, but software depends on the hardware for its functioning.
With that background in place, let's turn to Vallicella's post on Dennett, anthropomorphism, and the "deformation" of the God-concept. He writes:
I think Vallicella has a point, here. Atheists, especially these days as the so-called New Atheism gains in popularity, seem unable to acknowledge that modern folk might actually conceptualize ultimate reality in ways that are philosophically and morally sophisticated. This is unfortunate, because it does indeed mean the atheists are furiously attacking straw men as opposed to real targets. There can't be any real dialogue when people insist on talking past each other. I'd add that this problem isn't confined to the atheists: religious folk too often attack science before they've made the effort to understand it. One example might be the Christian fundamentalist's dismissal of evolutionary theory because "the probability that development X or Y could have occurred is infinitesimally small." This sort of argument shows great ignorance about the massive timescales on which biologists have to think when pondering the phenomenon of evolution. No legitimate scientist believes evolution is a theory: there are theories of evolution, but evolution itself is a fact. (To his credit, Vallicella has no problem with the idea that humans evolved. He's a philosophical theist, not a religious fundamentalist.)
Later on, Vallicella writes:
Here, too, I agree with Vallicella's analysis of Dennett. This is indeed a popular form of attack on theism. Dennett might be accused, here, of committing the fallacy of the excluded middle: he's offering two stark alternatives on the (false) assumption that no middle-ground option is available.
Thus far, I've been in agreement with Vallicella, not because I'm a theist as he is, but because his accusations against Dennett strike me as reasonable. Dennett could have strengthened his own arguments by targeting a more philosophically sophisticated concept of God. Attacking the God of scriptural literalists is far too easy. (Dennett might shoot back that the world is full of scriptural literalists, which would be a fair point!) But Vallicella also makes some claims with which I disagree. To wit:
This is where Vallicella and I part ways. First, I find his dismissal of Tillich's theology to be overly hasty. Tillich was, in my opinion, saying something quite meaningful in defining God as "ultimate concern." The phrase was never intended to mean, the way his detractors argued, that "If golf is my ultimate concern, because I think about it all the time, then golf is effectively my God." The word "ultimate," as used by Tillich, still refers to that which lies at the utterest edge of reality. Golf, while entertaining, doesn't fit that criterion. The term "concern," too, was well chosen, for this is what human beings, at their best, are supposed to embody: concern for others, for the world, for all of existence. Concern involves an outward turn-- what theologian John Hick might call a shift from self-centeredness to Reality-centeredness. Ultimate concern, then, is concern about the ultimate. How is this so different from what other philosophers and mystics have said and written?
I also disagree completely with Vallicella's characterization of neuroscience. For him, neuroscience will never "teach us anything about consciousness." The reality, though, is that neuroscientific theories are paving the way for us to make machines-- robots-- whose behaviors are becoming increasingly complex. If one definition of "intelligence" is "problem-solving ability," then by that standard we have been building increasingly intelligent machines for years. Soon, intelligence will come to mean more than the ability to win at chess or participate in a Jeopardy! competition: it will mean the advent of machines that react without confusion in fluid social or physical situations. While true machine consciousness is probably a long way off, I don't see its realization as an impossible goal. Intelligence isn't consciousness, but it's a vital component of consciousness. One day, a machine is going to stare at us with the same speculative curiosity we train on it.
My point is that the increasing complexity of machine behaviors is the result of scientific theories that are grounded in a naturalistic (or, more precisely, physicalist) philosophy of mind. If mind is indeed utterly dependent on matter, as I believe it is, then we will one day be able to arrange matter in such a way as to form minds. This won't convince the diehard substance dualists,* of course; they'll go on believing that mind is somehow independent of matter without ever being able to explain how a particular mind is connected to a particular body. Unfortunately, their philosophy of mind can promise no progress: you can't strive to create artificial intelligence if you believe it's inherently unachievable.
As I wrote in Water from a Skull, the problem for people in Vallicella's camp is that they are participating in willful ignorance about the nature of mind. They spend their time critiquing the constructive efforts being made by scientists, while offering no new insights of their own. Their stance is little more than a case against physicalism; there's no real case for substance dualism. In fact, for their stance to hold water, they have to deny that mind, consciousness, has a knowable nature. The so-called "zombie" problem in philosophy of mind makes this clear.
Imagine a being that looks and acts perfectly human, yet has no actual consciousness-- no real feelings, no true sense of selfhood, nothing that comes with possessing an ego. It might cry, but that act is merely an observable behavior, indicating nothing about the being's inner reality. It might laugh at jokes, but that's also no indication that it's experiencing the humor behind the joke. That hypothetical being is called a zombie by philosophers, and there's a big debate over whether zombies can possibly exist. The TV series Battlestar Galactica (and, before it, the movie Blade Runner) dealt with the zombie problem. Are the Cylons, who were created by humans and who look and act just like them, actual persons? Or are they "toasters"-- lifeless robots that merely simulate humans? The TV show ends up promoting the idea that Cylons are people, too: they have thoughts, feelings, inner lives. They're capable of love and hate; they have dreams and ambitions.
Let's snap back to our own reality. Imagine an AI (artificial intelligence) expert talking with a substance dualist about the possibility of creating Cylon-like artificial life. "All you'll end up creating is a zombie!" declares the substance dualist. "It won't have sentience! No feelings, no real self-awareness, no interiority!" "And you know this how?" asks the AI expert. "Can we ever design a test to detect consciousness?" "No!" blusters the dualist. You see, the substance dualist is trying argue two things at once: (1) that we'll never know whether we've created a true machine consciousness, and (2) that whatever we create will be a zombie. Obviously, these two prongs are contradictory, but let's concentrate on the first prong.
Dualists can't argue that "we'll never know whether the being's really conscious" unless they're convinced that the nature of mind is essentially unknowable, i.e., that we'll always be ignorant about mind. If you want to make a test to determine whether someone has a disease, you have to know the markers for the disease in question: you have to know something about the disease's nature. The more you know, the more accurate the test. By the same token, if you want to know whether something has a mind, you have to know something about the nature of consciousness. It's a lame cop-out to argue that we can never know what mind is, but that's basically what substance dualists have been doing for years, and it's the only argument they've got. All the other arguments they make against physicalism are in support of this basic thesis.
Vallicella's positions are always well thought-out and reasonable, but there are some areas in which he and I are doomed, I think, to eternal disagreement. Philosophy of mind is one of those areas; theism is another. He thinks the physicalists are blinded by their scientistic ideology; physicalists see him (and substance dualists in general) as deliberately ignoring the evidence of science. I'm willing to grant that the mind remains a mystery, but I believe the mystery isn't indissoluble.
It's possible to respect people with whom one disagrees, and even to learn from them. To any students who might have taken the time to read this meditation: I hope you find yourselves challenged and invigorated by the different points of view that you'll run across in your high school and college readings. I hope you encounter thinkers who make you angry, who challenge your assumptions, who shock you into looking at the world from a different perspective. I hope you enrich your own lives by incorporating those perspectives into your own. Life is all about growth and constructive change, but sometimes the best change involves the tearing-down of old mental paradigms so that new, more robust paradigms can replace them. I hope your perspective matures as you wrestle with various authors, and that you never dismiss the entirety of a thinker's argument simply because you dislike parts of it. A mature viewpoint involves an appreciation of the world's complexity. Beware black-and-white solutions to complicated problems.
As process philosopher Alfred North Whitehead said: "Seek simplicity, and distrust it."
*Substance dualism, a perspective most famously laid out by philosopher René Descartes (he of cogito ergo sum fame), is the belief that mind and matter are substantially different from each other. Thoughts are mental phenomena, not physical. Substance dualists come in different shapes and sizes; many of them would argue that there is some sort of mind-brain connection, but even the dualists who acknowledge this connection would say that there remains a fundamental difference between, as Descartes called them, res cogitans (mental phenomena) and res extensa (physical phenomena). Vallicella has never overtly called himself a substance dualist, but he repeatedly expresses sympathy with their point of view.
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A bit of background: Vallicella is a theist, i.e., he believes that ultimate reality is personal. Regarding the status of human beings, he advocates a point of view that he styles ontotheological personalism. The onto- comes from the Greek on/ontos, which means "being/existence." (The terms ontology and ontological are central to most Western philosophy.) The personalism in question is, roughly, the idea that there is something about human beings that is irreducibly personal, i.e., people cannot be explained fully by scientific/empirical examination and analysis; their personhood can't be broken down into smaller parts. This personalism has its being (ontos) grounded in God (theos): hence ontotheological personalism.
This puts Vallicella in conflict with scientific atheists who believe, like philosopher Daniel Dennett, that the human mind can be explained in purely physical terms (i.e., brain activity). On his blog, Vallicella routinely critiques physicalism, the philosophy of mind that says The mind is what the brain does. Lately, he has also been writing on the spectrum of possible God-concepts, ranging from a God that is utterly physical and totally anthropomorphic to a God that is so depersonalized as to be no more than an abstract concept. Vallicella wishes to avoid these two extremes.
My own theological orientation is far different from Vallicella's. While I consider myself Christian, this is more of a sociological designation than a theological one: I've been too steeped in Asian philosophy to be a theological Christian. There's very little, in terms of Christian doctrine, that I literally believe; my own sympathies, at this point, are mostly with scientific skeptics and philosophically inclined Taoists and Buddhists; I haven't been a classical theist for a long time (I'd call myself a nontheist, i.e., someone for whom the question "Does God exist?" has no rational, discursive answer). I see reality as an intercausal being-in-process and take a very dim view of most shows of religious piety. My own philosophy of mind is probably much closer to Dennett's than it is to Vallicella's: I see the mind as something that arises from the brain; it is, in fact, utterly dependent on the brain for its existence. At the same time, I'm not so naïve as to think that the brain's activity is totally predictable: cogitation, being a supervenient phenomenon (i.e., something that arises from a lower stratum of being), follows its own rules. As author Robert Pirsig analogized it in his book Lila (I'm taking some liberties, here): it's like the difference between computer hardware and software-- each follows its own rules, but software depends on the hardware for its functioning.
With that background in place, let's turn to Vallicella's post on Dennett, anthropomorphism, and the "deformation" of the God-concept. He writes:
One of the striking features of Daniel C. Dennett's Breaking the Spell: Religion as a Natural Phenomenon (Viking 2006) is that Dennett seems bent on having a straw man to attack. This is illustrated by his talk of the "deformation" of the concept of God: "I can think of no other concept that has undergone so dramatic a deformation." (206) He speaks of "the migration of the concept of God in the Abrahamic religions (Judaism, Christianity, and Islam) away from concrete anthropomorphism to ever more abstract and depersonalized concepts." (205)
Why speak of deformation rather than of reformation, transformation, or refinement?
I think Vallicella has a point, here. Atheists, especially these days as the so-called New Atheism gains in popularity, seem unable to acknowledge that modern folk might actually conceptualize ultimate reality in ways that are philosophically and morally sophisticated. This is unfortunate, because it does indeed mean the atheists are furiously attacking straw men as opposed to real targets. There can't be any real dialogue when people insist on talking past each other. I'd add that this problem isn't confined to the atheists: religious folk too often attack science before they've made the effort to understand it. One example might be the Christian fundamentalist's dismissal of evolutionary theory because "the probability that development X or Y could have occurred is infinitesimally small." This sort of argument shows great ignorance about the massive timescales on which biologists have to think when pondering the phenomenon of evolution. No legitimate scientist believes evolution is a theory: there are theories of evolution, but evolution itself is a fact. (To his credit, Vallicella has no problem with the idea that humans evolved. He's a philosophical theist, not a religious fundamentalist.)
Later on, Vallicella writes:
Dennett's view is that the "original monotheists" thought of God as a being one could literally listen to, and literally sit beside. (206) If so, the "original monotheists" thought of God as a physical being: "The Old Testament Jehovah, or Yahweh, was quite definitely a super-man (a He, not a She) who could take sides in battles, and be both jealous and wrathful." (206, emphasis in original). The suggestion here is that monotheism in its original form, prior to deformation, posited a Big Guy in the Sky, a human being Writ Large, something most definitely made in the image of man, and to that extent an anthropomorphic projection.
What Dennett is implying is that the original monotheistic conception of God had a definite content, but that this conception was deformed and rendered abstract to the point of being emptied of all content. Dennett is of course assuming that the only way the concept of God could have content is for it to have a materialistic, anthropomorphic content. Thus it is not possible on Dennett's scheme to interpret the anthropomorphic language of the Old Testament in a figurative way as pointing to a purely spiritual reality which, as purely spiritual, is neither physical nor human. Dennett thereby simply begs the question against every sophisticated version of theism.
Dennett seems in effect to be confronting the theist with a dilemma. Either your God is nothing but an anthropomorphic projection or it is is so devoid of recognizable attributes as to be meaningless. Either way, your God does not exist. Surely there is no Big Guy in the Sky, and if your God is just some Higher Power, some unknowable X, about which nothing can be said, then what exactly are you affirming when you affirm that this X exists? Theism is either the crude positing of something as unbelievable as Santa Claus or Wonder Woman, or else it says nothing at all.
Either crude anthropomorphism or utter vacuity. Compare the extremes of the spectrum of positions I set forth in Anthropomorphism in Religion.
Here, too, I agree with Vallicella's analysis of Dennett. This is indeed a popular form of attack on theism. Dennett might be accused, here, of committing the fallacy of the excluded middle: he's offering two stark alternatives on the (false) assumption that no middle-ground option is available.
Thus far, I've been in agreement with Vallicella, not because I'm a theist as he is, but because his accusations against Dennett strike me as reasonable. Dennett could have strengthened his own arguments by targeting a more philosophically sophisticated concept of God. Attacking the God of scriptural literalists is far too easy. (Dennett might shoot back that the world is full of scriptural literalists, which would be a fair point!) But Vallicella also makes some claims with which I disagree. To wit:
Dennett's Dilemma -- to give it a name -- is quite reasonable if you grant him his underlying naturalistic and scientistic (not scientific) assumptions, namely, that there is exactly one world, the physical world, and that (future if not contemporary) natural science provides the only knowledge of it. On these assumptions, there simply is nothing that is not physical in nature. Therefore, if God exists, then God is physical in nature. But since no enlightened person can believe that a physical God exists, the only option a sophisticated theist can have is to so sophisticate and refine his conception of God as to drain it of all meaning. And thus, to fill out Dennett's line of thought in my own way, one ends up with pablum such as Tillich's talk of God as one "ultimate concern." If God is identified as the object of one's ultimate concern, then of course God, strictly speaking, does not exist. Dennett and I will surely agree on this point.
But why should we accept naturalism and scientism? It is unfortunately necessary to repeat that naturalism and scientism are not scientific but philosophical doctrines with all the rights, privileges, and liabilities pertaining thereunto. Among these liabilities, of course, is a lack of empirical verifiability. Naturalism and scientism cannot be supported scientifically. For example, we know vastly more than Descartes (1596-1650) did about the brain, but we are no closer than he was to a solution of the mind-body problem. Neuroscience will undoubtedly teach us more and more about the brain, but it takes a breathtaking lack of philosophical sophistication — or else ideologically induced blindness — to think that knowing more and more about the physical properties of a lump of matter will teach us anything about consciousness, the unity of consciousness, self-consciousness, intentionality, and the rest.
This is where Vallicella and I part ways. First, I find his dismissal of Tillich's theology to be overly hasty. Tillich was, in my opinion, saying something quite meaningful in defining God as "ultimate concern." The phrase was never intended to mean, the way his detractors argued, that "If golf is my ultimate concern, because I think about it all the time, then golf is effectively my God." The word "ultimate," as used by Tillich, still refers to that which lies at the utterest edge of reality. Golf, while entertaining, doesn't fit that criterion. The term "concern," too, was well chosen, for this is what human beings, at their best, are supposed to embody: concern for others, for the world, for all of existence. Concern involves an outward turn-- what theologian John Hick might call a shift from self-centeredness to Reality-centeredness. Ultimate concern, then, is concern about the ultimate. How is this so different from what other philosophers and mystics have said and written?
I also disagree completely with Vallicella's characterization of neuroscience. For him, neuroscience will never "teach us anything about consciousness." The reality, though, is that neuroscientific theories are paving the way for us to make machines-- robots-- whose behaviors are becoming increasingly complex. If one definition of "intelligence" is "problem-solving ability," then by that standard we have been building increasingly intelligent machines for years. Soon, intelligence will come to mean more than the ability to win at chess or participate in a Jeopardy! competition: it will mean the advent of machines that react without confusion in fluid social or physical situations. While true machine consciousness is probably a long way off, I don't see its realization as an impossible goal. Intelligence isn't consciousness, but it's a vital component of consciousness. One day, a machine is going to stare at us with the same speculative curiosity we train on it.
My point is that the increasing complexity of machine behaviors is the result of scientific theories that are grounded in a naturalistic (or, more precisely, physicalist) philosophy of mind. If mind is indeed utterly dependent on matter, as I believe it is, then we will one day be able to arrange matter in such a way as to form minds. This won't convince the diehard substance dualists,* of course; they'll go on believing that mind is somehow independent of matter without ever being able to explain how a particular mind is connected to a particular body. Unfortunately, their philosophy of mind can promise no progress: you can't strive to create artificial intelligence if you believe it's inherently unachievable.
As I wrote in Water from a Skull, the problem for people in Vallicella's camp is that they are participating in willful ignorance about the nature of mind. They spend their time critiquing the constructive efforts being made by scientists, while offering no new insights of their own. Their stance is little more than a case against physicalism; there's no real case for substance dualism. In fact, for their stance to hold water, they have to deny that mind, consciousness, has a knowable nature. The so-called "zombie" problem in philosophy of mind makes this clear.
Imagine a being that looks and acts perfectly human, yet has no actual consciousness-- no real feelings, no true sense of selfhood, nothing that comes with possessing an ego. It might cry, but that act is merely an observable behavior, indicating nothing about the being's inner reality. It might laugh at jokes, but that's also no indication that it's experiencing the humor behind the joke. That hypothetical being is called a zombie by philosophers, and there's a big debate over whether zombies can possibly exist. The TV series Battlestar Galactica (and, before it, the movie Blade Runner) dealt with the zombie problem. Are the Cylons, who were created by humans and who look and act just like them, actual persons? Or are they "toasters"-- lifeless robots that merely simulate humans? The TV show ends up promoting the idea that Cylons are people, too: they have thoughts, feelings, inner lives. They're capable of love and hate; they have dreams and ambitions.
Let's snap back to our own reality. Imagine an AI (artificial intelligence) expert talking with a substance dualist about the possibility of creating Cylon-like artificial life. "All you'll end up creating is a zombie!" declares the substance dualist. "It won't have sentience! No feelings, no real self-awareness, no interiority!" "And you know this how?" asks the AI expert. "Can we ever design a test to detect consciousness?" "No!" blusters the dualist. You see, the substance dualist is trying argue two things at once: (1) that we'll never know whether we've created a true machine consciousness, and (2) that whatever we create will be a zombie. Obviously, these two prongs are contradictory, but let's concentrate on the first prong.
Dualists can't argue that "we'll never know whether the being's really conscious" unless they're convinced that the nature of mind is essentially unknowable, i.e., that we'll always be ignorant about mind. If you want to make a test to determine whether someone has a disease, you have to know the markers for the disease in question: you have to know something about the disease's nature. The more you know, the more accurate the test. By the same token, if you want to know whether something has a mind, you have to know something about the nature of consciousness. It's a lame cop-out to argue that we can never know what mind is, but that's basically what substance dualists have been doing for years, and it's the only argument they've got. All the other arguments they make against physicalism are in support of this basic thesis.
Vallicella's positions are always well thought-out and reasonable, but there are some areas in which he and I are doomed, I think, to eternal disagreement. Philosophy of mind is one of those areas; theism is another. He thinks the physicalists are blinded by their scientistic ideology; physicalists see him (and substance dualists in general) as deliberately ignoring the evidence of science. I'm willing to grant that the mind remains a mystery, but I believe the mystery isn't indissoluble.
It's possible to respect people with whom one disagrees, and even to learn from them. To any students who might have taken the time to read this meditation: I hope you find yourselves challenged and invigorated by the different points of view that you'll run across in your high school and college readings. I hope you encounter thinkers who make you angry, who challenge your assumptions, who shock you into looking at the world from a different perspective. I hope you enrich your own lives by incorporating those perspectives into your own. Life is all about growth and constructive change, but sometimes the best change involves the tearing-down of old mental paradigms so that new, more robust paradigms can replace them. I hope your perspective matures as you wrestle with various authors, and that you never dismiss the entirety of a thinker's argument simply because you dislike parts of it. A mature viewpoint involves an appreciation of the world's complexity. Beware black-and-white solutions to complicated problems.
As process philosopher Alfred North Whitehead said: "Seek simplicity, and distrust it."
*Substance dualism, a perspective most famously laid out by philosopher René Descartes (he of cogito ergo sum fame), is the belief that mind and matter are substantially different from each other. Thoughts are mental phenomena, not physical. Substance dualists come in different shapes and sizes; many of them would argue that there is some sort of mind-brain connection, but even the dualists who acknowledge this connection would say that there remains a fundamental difference between, as Descartes called them, res cogitans (mental phenomena) and res extensa (physical phenomena). Vallicella has never overtly called himself a substance dualist, but he repeatedly expresses sympathy with their point of view.
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Thursday, February 9, 2012
Johnny et Hollande: rencontre
Pouvez-vous lire et comprende cet article (lien)?
A DISCUTER: Pensez-vous que ce soit réaliste de croire qu'il existe un président qui puisse "[faire] du bien" dans le sens qu'entend Johnny Hallyday?
(NB: PS = le Parti Socialiste)
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Soutien et ami de Nicolas Sarkozy, le chanteur Johnny Hallyday a dîné avec François Hollande et sa compagne Valérie Trierweiler fin janvier.
C'est une rencontre discrète qui a eu lieu le 23 janvier, au lendemain du meeting du Bourget. François Hollande et Johnny Hallyday ont dîné ensemble chez une connaissance, à Paris.
Le candidat du PS était venu avec sa compagne, Valérie Trierweiler. Une petite dizaine de personnes participaient aux agapes. Le socialiste a promis qu'il irait écouter le rockeur lors de sa tournée française, qui commence en mai. "Un feeling est passé entre eux", assure un convive.
Mais il n'a pas été question que de musique - présidentielle oblige. La star est un ami de toujours du chef de l'Etat. Mais le soutiendra-t-il comme en 2007? En décembre, Johnny Hallyday confiait: "Sarkozy nous a mariés (ndlr: avec Laeticia). C'est un ami. Je soutiens toujours mes amis."
Avant d'ajouter : "Pour moi, un bon président est celui qui fait du bien, qu'il soit de droite ou de gauche."
A DISCUTER: Pensez-vous que ce soit réaliste de croire qu'il existe un président qui puisse "[faire] du bien" dans le sens qu'entend Johnny Hallyday?
(NB: PS = le Parti Socialiste)
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Wednesday, February 8, 2012
what's wrong with this sentence?
Found this sentence here:
Imagine you're trying to make red pepper flakes, like the kind you sprinkle on pizza. See any problems with the above instructions?
Avoid ambiguity. The above sentence is exactly the sort that might appear in the "find the error" portion of the SAT Writing section.
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Remove the stems from the dried peppers and place them in a food processor, spice grinder or coffee grinder.
Imagine you're trying to make red pepper flakes, like the kind you sprinkle on pizza. See any problems with the above instructions?
Avoid ambiguity. The above sentence is exactly the sort that might appear in the "find the error" portion of the SAT Writing section.
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Tuesday, February 7, 2012
this week's MGRE Math Beast Challenge problem
This one doesn't look too hard:
Go to it! My answer will appear in the comments. If you want to work on the problem yourself, be sure not to peek.
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x, y, and z are three consecutive multiples of 3 such that x < y < z.
Quantity A
The remainder when the sum of x + 1, y – 2, and z + 3 is divided by 9
Quantity B
2
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.
Go to it! My answer will appear in the comments. If you want to work on the problem yourself, be sure not to peek.
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the answer to last week's MGRE Math Beast Challenge
You may recall that I wasn't particularly happy about the way MGRE designed last week's problem. As it turned out, I was right to think that they would pick (D) as the correct answer, even though I contend that (E) ("cannot be determined") is correct because of the lack of proper labeling.
For what it's worth, here's how MGRE arrived at (D):
Take it or leave it, I guess. I got (D) as well, once I'd "cleaned up" the problem.
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For what it's worth, here's how MGRE arrived at (D):
It may help to first redraw the figure by simply rotating triangle ACD about the center of the circle so that AD will be vertical. This is acceptable, because we aren’t changing any lengths or angles except to create a right triangle ADG, as shown:
Now, let’s start with the one length we were given. Since AC = CD, triangle ACD is an equilateral right triangle, or a 45–45–90 triangle (referring to the angle measures). In an equilateral right triangle, the hypotenuse is √2 times the length of either other side, so AD = ((√2)/2).
In the figure, AD is the diameter of the circle, and AE is a radius of the circle. Thus, AE is half AD, or AE = (√2)/4. Also, the square side length equals the diameter, and DF is half a side of the square, so DF = (√2)/4, too.
The problem states that BG = 4AE, so BG = √2.
We now have two of the side lengths for the right triangle we created:
By Pythagorean Theorem,
.
We are looking for GF, which is simply GD – DF. Since DF = (√2)/4,
.
The correct answer is D.
Take it or leave it, I guess. I got (D) as well, once I'd "cleaned up" the problem.
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Monday, February 6, 2012
scan first? read the whole thing first? look at the questions first? aaaaaggghhh!!
Students sometimes ask me how best to approach long passages in the SAT's Critical Reading section. They're usually wondering which of the following options to take:
The answer is: it depends. Students have different cognitive styles, which makes it impossible for me to recommend one specific approach. There's also the issue of time pressure: if you're pressed for time, then certain options, like reading through the entire long passage first, may not be available to you as the clock runs down. This will affect your strategy.
A lot of test prep companies recommend simply reading the passage first, be it long or short. There are obvious advantages to doing this. First, you now have the entire passage in your head, making it easier for you to scan more quickly for whatever you need to know. Second, because you've internalized the passage, you can figure out context-based relationships better. Third, you probably have a clear notion of what the passage's main idea is. All of this means that, if you've read well, you should be able to march relentlessly through the ensuing questions as easily as Einstein doing basic algebra.
But what if you're not the type who can get through a long reading passage without falling asleep? My first reaction to this question is: I feel sorry for you and your future college career. The fact of the matter is that you're going to be doing a lot of reading while in college, and much of it will involve literature that you just won't want to study. So toughen up! The only way around this obstacle is through it. My second reaction is a little more moderate: true, many passages will be boring, so find a method that works for you. If Method (1), above, doesn't work, then try Method (2). This strategy has also been recommended by test prep companies before. Especially if you're pressed for time, you need to read for information in a targeted way as opposed to trying to swallow the entire passage in a single mental gulp.
Method (3) has its uses, too. I find it especially helpful if I see questions about vocab-in-context: "In the context of the passage, the word mortal on line 36 most likely means..." That sort of question can be answered quickly, and without reference to the entire passage: just scan the lines above and below it.
Don't get trapped into thinking that there's only one magical method to beat the SAT. There isn't. In the end, the so-called "tricks" that test prep tutors teach their students are nothing more or less than good old reading skills-- the selfsame skills that you'll be using (and hopefully honing) while you're in college. Every method has its merits and demerits. Figure out what you're comfortable doing, make sure you can do it efficiently, within the allotted time, and be ready to switch to a Plan B if your preferred method doesn't seem to be helping you.
As Bruce Lee said: Be like the nature of water, my friend. Be flexible; shape your technique to fit both yourself and the situation. What that really means is: master several different techniques so that you don't run out of options when it's crunch time. True freedom comes from having options. Having options comes from self-discipline, and that involves time, effort, and focus.
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1. Read the whole passage first, then answer the questions?
2. Read the questions first to get an idea of what to look for, then scan the passage to answer the questions?
3. Use a "scan as you go" approach to answer the questions, trusting that the first question relates to the first part of the passage, the second question relates to the second part, etc.?
The answer is: it depends. Students have different cognitive styles, which makes it impossible for me to recommend one specific approach. There's also the issue of time pressure: if you're pressed for time, then certain options, like reading through the entire long passage first, may not be available to you as the clock runs down. This will affect your strategy.
A lot of test prep companies recommend simply reading the passage first, be it long or short. There are obvious advantages to doing this. First, you now have the entire passage in your head, making it easier for you to scan more quickly for whatever you need to know. Second, because you've internalized the passage, you can figure out context-based relationships better. Third, you probably have a clear notion of what the passage's main idea is. All of this means that, if you've read well, you should be able to march relentlessly through the ensuing questions as easily as Einstein doing basic algebra.
But what if you're not the type who can get through a long reading passage without falling asleep? My first reaction to this question is: I feel sorry for you and your future college career. The fact of the matter is that you're going to be doing a lot of reading while in college, and much of it will involve literature that you just won't want to study. So toughen up! The only way around this obstacle is through it. My second reaction is a little more moderate: true, many passages will be boring, so find a method that works for you. If Method (1), above, doesn't work, then try Method (2). This strategy has also been recommended by test prep companies before. Especially if you're pressed for time, you need to read for information in a targeted way as opposed to trying to swallow the entire passage in a single mental gulp.
Method (3) has its uses, too. I find it especially helpful if I see questions about vocab-in-context: "In the context of the passage, the word mortal on line 36 most likely means..." That sort of question can be answered quickly, and without reference to the entire passage: just scan the lines above and below it.
Don't get trapped into thinking that there's only one magical method to beat the SAT. There isn't. In the end, the so-called "tricks" that test prep tutors teach their students are nothing more or less than good old reading skills-- the selfsame skills that you'll be using (and hopefully honing) while you're in college. Every method has its merits and demerits. Figure out what you're comfortable doing, make sure you can do it efficiently, within the allotted time, and be ready to switch to a Plan B if your preferred method doesn't seem to be helping you.
As Bruce Lee said: Be like the nature of water, my friend. Be flexible; shape your technique to fit both yourself and the situation. What that really means is: master several different techniques so that you don't run out of options when it's crunch time. True freedom comes from having options. Having options comes from self-discipline, and that involves time, effort, and focus.
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a post is forthcoming, but not right now
I normally slap up a post about test prep on Mondays, but I'm finishing up a massive proofreading project right now, so the post will have to wait. Apologies!
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Saturday, February 4, 2012
Sam Harris on "the fireplace delusion"
Atheist thinker Sam Harris tries to offer fellow atheists a taste of what it's like to have cherished beliefs challenged as he attacks the notion that sitting before a fireplace on a cold winter's evening is a wholesome experience.
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Thursday, February 2, 2012
for those looking to learn Korean on their own
Sogang University has been running a self-paced online Korean program for quite a few years. Take a look at it here. While it's no substitute for taking an actual language class, it's not a bad place to start if you're motivated and self-disciplined. I haven't had the chance to review the entire curriculum, but I do like how the site deals with the rudiments of Korean writing and phonology.
Learning to read Korean script (hangeul) is vital for anyone planning to stay in Korea for any extended length of time. Although many navigational signs (e.g., in subway stations) also have English on them, you can't rely on this being the case everywhere you go. Many restaurant menus are written exclusively in Korean, as are many bus route diagrams. The ability to figure out place names, culinary terms, and other important words is vital, not to mention educational. Click on the Sogang U. link and get learning!
Keep in mind, too, that I'm offering to teach Korean!
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Learning to read Korean script (hangeul) is vital for anyone planning to stay in Korea for any extended length of time. Although many navigational signs (e.g., in subway stations) also have English on them, you can't rely on this being the case everywhere you go. Many restaurant menus are written exclusively in Korean, as are many bus route diagrams. The ability to figure out place names, culinary terms, and other important words is vital, not to mention educational. Click on the Sogang U. link and get learning!
Keep in mind, too, that I'm offering to teach Korean!
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Wednesday, February 1, 2012
a famous soliloquy
One of the most famous of Shakespeare's soliloquies comes from the tragedy Macbeth. This particular meditation, on the futility of life given the crushing inevitability of death, has come to mind lately thanks to a friend's having posted some YouTube clips of Ian McKellen's, Patrick Stewart's, and Nicol Williamson's respective performances of these lines.
The play is nearing its end, and Macbeth has just learned of the death of his wife:
Is life meaningless? Is living a futile act, like a bad play in which we're all players who "strut and fret"? I occasionally ask my students this question: Why do anything? The question itself is vitally important, I think, because if you seriously believe that nothing is worth doing, then life becomes either a long wait for death or a preparation for suicide.
So I ask you: why do anything? What makes life worth living?
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The play is nearing its end, and Macbeth has just learned of the death of his wife:
To-morrow, and to-morrow, and to-morrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time;
And all our yesterdays have lighted fools
The way to dusty death. Out, out, brief candle!
Life's but a walking shadow, a poor player,
That struts and frets his hour upon the stage,
And then is heard no more. It is a tale
Told by an idiot, full of sound and fury,
Signifying nothing.
Macbeth Act 5, scene 5, 19–28
Is life meaningless? Is living a futile act, like a bad play in which we're all players who "strut and fret"? I occasionally ask my students this question: Why do anything? The question itself is vitally important, I think, because if you seriously believe that nothing is worth doing, then life becomes either a long wait for death or a preparation for suicide.
So I ask you: why do anything? What makes life worth living?
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