Friday, March 30, 2012

do you have free will?

Sam Harris, speaking at Cal Tech, thinks you don't.

Harris's points seem almost to be grounded in Indian philosophy:

• Consciousness is the one thing that can't be illusory.
• The self, meanwhile, is an illusion.*
• Decisions, being based on previous states of affairs that include both previous decisions and random factors, cannot be parsed in such a way as to reveal free will at any point in the decision-making process.

There's more going on in this talk-- much more. If you find yourself with about 80 minutes to spare, I highly recommend watching Harris's spiel and the brief Q&A period that follows it.

My own sense that I have free will is both strong and undeniable, but Harris makes a pretty good case for the idea that a combination of deterministic and random factors can never be a recipe for freedom in the cherished philosophical sense, i.e., that I am somehow the "author" (Harris's term) of my actions. I wish he'd had more time to tease out the moral implications of this way of thinking. The talk heads, somewhat fuzzily, in the direction of emphasizing compassion and understanding-- especially regarding violent criminals-- as core values in this new, post-libertarian ethos, but Harris's spiel does little to unpack these concepts.

I approach these ideas with caution, partly because I'm extremely wary of attempts at social engineering. When people propose new moral paradigms, I feel as if I'm witnessing a sort of top-down attempt at restructuring human interaction. Of course, Harris isn't seriously proposing a thorough, comprehensive reparadigming; the lack of detail in his talk is enough to make that clear. But as a prominent author and respected neuroscientist, he's in a position to influence many people, and his facility for accessible explanations means he can insert his ideas into the pop-cultural nomos with ease. There is indeed a top-down dynamic at work here, and it's worrisome.

All of this has made me want to read more Herbert Fingarette. Fingarette has done a lot of work in the areas of freedom and responsibility, and I think he comes down on the side of moral agency: there is some sense in which we are morally responsible for what we do. He talks about two senses of the word "responsibility": (1) being the locus of action, and (2) being the locus of moral agency. In the first sense, being responsible means being the locus of a given action. In the second sense, it refers to being an accountable moral agent. The first sense applies when we think of, say, a bear attacking someone: no one seriously attributes malice to the bear. The second sense is more in line with how we approach premeditated murder: the killer is not only the enactor of the murder; he is also someone who can be held accountable for having done wrong.

Harris's way of thinking detracts nothing from sense (1), but it certainly complicates our evaluation of sense (2). I may watch this talk again soon. If I do, I'll likely have more to say on the matter.



*This is somewhat unfortunately phrased, since the term "illusion" requires a self that grounds the perspective from which illusions can be perceived. Harris might have done better to say that the self doesn't exist.


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Thursday, March 29, 2012

vive le cancre!

cancre:

1. Vx [P. réf. aux pinces du crabe] Personne méprisable par son extrême rapacité. Quel cancre! fit Rodolphe en se sauvant. Ah çà! fit-il, il manque encore trente et un sous (Murger, Scènes de la vie de bohème,1851, p. 100).
2. Usuel [P. allus. à la marche oblique du crabe, dont la progression est lente et difficile] Élève nul et paresseux :
1. Le triomphe du cancre restera ce prodige de la dernière minute grâce auquel le génie souffle à l'élève le moyen de sauver sa peau. En France le cancre règne et le fort en thème donne des résultats médiocres. Cocteau, Le Foyer des artistes,1947, p. 26.
− Emploi adj., au fig. Sot, niais. Pinette ricanait d'un air cancre (Sartre, La Mort dans l'âme,1949, p. 169):
2. Devant le compliment, ce n'est pas la fierté qui me donne cet air cancre et ingrat que je connais bien, mais (en même temps que cette profonde indifférence qui est en moi comme une infirmité de nature) un sentiment singulier qui me vient alors : « Ce n'est pas cela... » Camus, L'Envers et l'endroit,1937, p. 25.

Quelques extraits de La foire aux cancres (recueil d'écrits des cancres, publié en 1962):

En ce qui concerne LES MATHEMATQIUES:

Il faut simplifier les fractions sinon elles atteignent des proportions gastronomiques.

Un cercle est une ligne ronde, sans angles, et fermée pour qu'on ne voie pas où elle commence. Pour trouver la surface, on multiplie le milieu par le centre.

Le carré est une figure qui a un angle droit dans chaque coin.

Un octogone est une sorte de carré qui a huit côtés.

Un parallélépipède est un animal dont les deux pieds sont parallèles.

Un cône est une chose idiote. Il y en a donc de toutes sortes.


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Wednesday, March 28, 2012

David Gelernter on "cyber-English"

From here:

Social networking, texting, email and digital messages have borrowed the keys to the English language and are joy-riding all over the landscape, smashing body panels and junking up the fancy interior. Many thoughtful people are worried. But it's good for English to get shaken up occasionally—by people who are using it in new ways, not by academics ordaining from on high.

In the 1980s and '90s, email saved the personal letter from extinction by moving it online. Email-writers have leaned heavily for decades on abbreviations, which suit this quick-and-casual medium. Thus the celebrated "lol," "laughing out loud," and many others.

When the young members of Generation-i use their phones to send text messages, the small keyboards make typing awkward and abbreviations even more important: "b4n" (bye for now), "cu" (see you). Texters, social-network posters and emailers are all prone to write (as their messages go zipping and hurtling back and forth) in sharp-edged shards and slivers of language.

Abbreviations and fragments are a language's normal response to stress. Medieval language is dense with abbreviations, because writing material was expensive and books could be published only by copying. Today the stresses are different but the response is familiar.

When you are forced to compress your message into fewer words, each word works harder, carries more meaning on its shoulders and, accordingly, becomes more important and interesting. Digital English is no good for poetry or novels, but on balance it's refreshing.

What are your thoughts on the evolution of English? Linguists take it as axiomatic that English-- as with any language-- is constantly evolving. Language purists, however, bemoan the various ways in which the language changes. The difference between these detached observers (the linguists), on one hand, and the so-called "language Nazis" (the purists), on the other, is the difference between descriptivism and prescriptivism. A linguistic descriptivist simply describes what's happening to language; a prescriptivist, by contrast, considers him- or herself to be an authority on the proper forms of that language: s/he prescribes the correct forms and usage.

Every English teacher is at least a partial prescriptivist in that sense, concerning him- or herself with proper and coherent forms of self-expression. Every dictionary, meanwhile, is both descriptivistic and prescriptivistic: dictionaries describe language as it's spoken and written in that dictionary's era (invoking histories and etymologies along the way), but they also act as authorities on proper usage, spelling, pronunciation, etc. We don't merely read dictionaries; we consult them.

I've written quite a few posts on this blog that are prescriptivistic in tone. It might surprise students to learn that I'm also a bit of a descriptivist: I believe that language has a structure, and that there are proper and improper forms of expression, but I also think it's only natural for language to evolve. That is the way of things-- the way of the Force, as Yoda might say. Shakespeare sounds old because language constantly changes; the 1950s expression "Daddy-o" sounds old to young ears (it sounds old to my ears, since I was born in the late 1960s!); even expressions from the 70s, like "Right on!" and "Keep on truckin'!" sound antiquated. How many students nowadays would be able to use 1980s high-school slang with a straight face? "You dweeb!" "You spaz!" Who talks like that anymore? Even 1990s slang like "Whoop-- my bad" sounds a bit hackneyed. In 2012, portmanteaux rule: slammed-together word combos that express complex concepts in a single compound. In 2012, we've got frenemies and we're chillaxin'; ambivalent people can be forgainst something. By 2020, those same portmanteaux might seem embarrassingly cliché.

Take a step back from the lexical swirl, though, and notice that most of the linguistic evolution is occurring only at the superficial level of slang. Basic structures-- e.g., syntax-- take much longer to change. Shakespeare is still comprehensible after 500 years because we moderns still use the same basic grammar and most of the same basic vocabulary.

So I don't think Mr. Gelernter is wrong to note that English needs to be shaken up every now and then. But we also need to remember that speaking and writing a language don't mean speaking or writing whatever we want, however we want. If I point at a bird and yell "Police car! Police car!", who can blame any observers for thinking I'm crazy? Language evolves, but this doesn't remove the notion of right and wrong from language learning.


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Tuesday, March 27, 2012

this week's MGRE Math Beast Challenge: blind edition

MGRE's website is undergoing some sort of facelift, which is playing havoc with certain parts of the site. This week's Math Beast Challenge has been affected: I can no longer see the illustration that accompanies the problem, nor can I see most of the answer choices, except for the first choice, which is 8. So this week, we're going to fly blind and just use our imagination to try to draw the illustration accompanying the problem. The problem itself is pretty clearly worded, and we needn't worry about the unseeable answer selections: we'll just figure things out on our own.

A solid cube with edge length 2 is sliced by a plane passing through two opposite corners of the cube. This creates a cut surface, the shaded rhombus shown [below]. What is the perimeter of the shaded rhombus?

I've attempted to make an illustration, which you see below. Note that the illustration is in two parts: a drawing based on the above description, plus a "closeup" that will help us analyze the problem.




I'm of the opinion that the perimeter of the rhombus in question is 4√5. Segment AC is the hypotenuse of a right triangle whose legs measure, respectively, 2 (Segment AB) and 1 (Segment BC). We can check visually that all the other edges of the rhombus are the same length, so this rhombus is a square with perimeter 4√5.

I bet that, once MGRE's site is back in order, one of the answer choices will indeed be 4√5.

By the way, here's a horizontally squished version of what I currently see at the MGRE page:




As you see, there's no illustration, and only one visible answer choice.


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Monday, March 26, 2012

SAT-style geometry problems

A good set of geometry problems for the SAT can be found here. I discovered these while planning a geometry tutoring session for my goddaughter. The Khan Academy website also has its own fairly comprehensive geometry section, as well as a massive SAT Math prep section.

Before I forget: this Cliffs Notes page does a very good job of explaining the relationship between circles, chords, secants, and tangents.


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the solution to last week's MGRE Math Beast Challenge

I was right! The answer to last week's MGRE Math Beast Challenge problem is indeed (A): Quantity A is greater. Here's MGRE's rationale:

Notice that the 10th and 11th terms (the two middle terms in a set of 20 terms) are arithmetic inverses, that is, their sum is zero. Likewise, the 1st and 20th terms sum to zero, as do the 2nd and 19th terms. In the first 20 terms of the sequence, we can make 10 pairs that each sum to zero. Thus, Quantity A is zero.

For the sum of the first 19 terms, we could either
(1) Subtract a20 from the sum of the first 20 terms: 0 – (220 – 21) = 21 – 220 = 2 – a very large positive number = negative, or
(2) Realize that in the first 19 terms, all terms except a1 can be paired such that the pair sums to zero, so the sum of the first 19 terms = a1 = 21 – 220 = 2 – a very large positive number = negative.

Thus, Quantity B is negative, which is less than zero.

The correct answer is A.

This isn't far removed from what I said in this comment.


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Friday, March 23, 2012

"How does the brain secrete morality?"

Here.

Interesting excerpt:

“The brain secretes thought as the liver secretes bile,” asserted 18th century French physiologist Pierre Cabanis. Last week, the Potomac Institute for Policy Studies convened a conference of neuroscientists and philosophers to ponder how our brains secrete thoughts about ethics and morality. The first presenter was neuroeconomist Gregory Berns from Emory University whose work peers into brains to see in which creases of gray matter those values we hold sacred lodge. The study, “The Price of Your Soul: neural evidence for the non-utilitarian representation of sacred values,” was just published in the Philosophical Transactions of the Royal Society B.

Philosophers often frame arguments over the bases of ethics in terms of deontology (right v. wrong irrespective of outcomes) and utilitarianism (costs v. benefits of potential outcomes). Both utilitarians and deontologists would argue that it is wrong to kill innocent human beings. A utilitarian might tote up the costs of being caught in murder or the harms to a victim’s family, whereas a deontologist would assert it is moral duty to avoid killing the innocent. For most people, a utilitarian reckoning in this case seems cold and psychologically broken (e.g., the kind of calculation that a psychopath would make). The researchers define personal sacred values as those for which individuals resist trade-offs with other values, particularly economic or materialistic incentives.

It is this distinction that Berns probes using functional magnetic imaging (fMRI) to see in which parts of subjects’ brains their moral decision-making is localized. Such scans identify areas of the brain that are activated by measuring blood flow.

I've generally heard the dichotomy referred to as deontology versus consequentialism. The first term comes from the Greek deon, which means "duty," a beloved concept of the philosopher Immanuel Kant, who wove duty into his Grounding for the Metaphysics of Morals. (The term ontology comes from a different Greek root: on or ontos, which means "being" or "existence." Don't confuse ontology with deontology; they aren't the same animal!) There is, when you think about it, something deontological about the consequentialist stance, and there's also something consequentialist about the deontological stance. As they might say in Zen Buddhism, the concepts are not-two (不二), i.e., they're distinct yet inseparable-- nondual.


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Thursday, March 22, 2012

tueur "djihadiste" cerné: qui est Mohamed Merah?
exploration de l'homme et de sa mouvance

Extrait d'un article sur Mohamed Merah, le tueur de sept personnes (dont des militaires, un rabbin, et des écoliers juifs) à Montauban et à Toulouse, et sur "la mouvance djihadiste en France":

(REUTERS)

Le tueur de Toulouse et de Montauban, toujours cerné par le Raid ce mercredi, avait séjourné en Afghanistan et au Pakistan dans des camps d'entrainements djihadistes. L'Express revient sur les ramifications de la mouvance djihadiste en France.

Mohamed Merah, le présumé tueur de Toulouse et de Montauban, avait séjourné en Afghanistan et au Pakistan dans des camps d'entrainements djihadistes, selon le ministre de l'intérieur Claude Guéant. Ce Français d'origine algérienne dit "être un moudjahidine", et "appartenir à Al-Qaïda". Que sait-on de la mouvance djihadiste en France?


Mohamed Merah, le parcours d'un djihadiste

Ce que l'on sait jusqu'à présent de Mohamed Merah correspond au parcours type du djihadiste, selon Samir Amghar, auteur de Salafisme d'aujourd'hui. Mouvements sectaires en Occident. D'origine algérienne, donc véhiculant un certain contentieux historique avec la France. Comme lui, ces jeunes proviennent souvent de familles déstructurées (parents divorcés): ils choisissent une "famille d'adoption" qui leur offre une autorité retrouvée, explique le sociologue. Il ont souvent un contentieux à régler avec la société: Mohamed Merah, passé par la prison pour de petits faits de délinquance, aurait essayé de s'engager dans l'armée mais son dossier a été rejeté.

Il serait passé par des camps d'entrainement en Afghanistan et au Pakistan. Plusieurs cas similaires ont été de nombreuses fois décrits, comme ces deux "apprentis du djihad", en route pour l'Irak, dont L'Express dressait le portrait en 2007: "les deux hommes se rencontrent en 2002, dans une mosquée toulousaine. Très vite, ils se radicalisent et rejoignent une petite communauté de fidèles. Divers jeunes gens se retrouvent régulièrement au sein de ce groupe dirigé par un "gourou" d'origine syrienne".

Ce type de "jeune radicalisé, fait son stage dans un camp d'Al-Qaïda ou pas, mais en tous cas dans les zones tribales du Pakistan, entre en contact avec des gens d'Al-Qaïda et ce contact est maintenu" avec des groupes qui l'imprégnent de l'idée suivante:" 'le moment venu, passe à l'action' au nom des valeurs que nous t'avons inculqué ici", explique Jean-Pierre Filiu, professeur à l'Institut d'études politiques de Paris.

"Nous connaissons bien ce type de profil de jeunes délinquants qui se radicalisent. Ils peuvent entrer dans une forme de discours et d'action violente avec une cohérence toute relative. Ils se nourrissent d'un peu tout: la présence française en Afghanistan, au Sahel, le vote contre la burka... Dans les dix dernières années, plusieurs individus de ce genre ont été arrêtés", explique de son côté Louis Caprioli, ancien sous-directeur chargé de la lutte contre le terrorisme à la Direction de la surveillance du territoire (DST), interrogé par FranceTV info. "Le suspect de Toulouse était fiché, repéré mais rien n'indiquait qu'il pouvait ainsi passer à l'acte, observe Louis Caprioli. Et c'est bien toute la difficulté dans le suivi de ces gens qui peuvent à tout moment devenir extrêmement dangereux".

Lisez le reste.


MISE A JOUR: Mohamed Merah est mort.


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Wednesday, March 21, 2012

the varying dignity of letters

I respect the letter "i"
Which I find more dignified
Than "y" or "ee"

When I spell Korean words
On the page they're seen, not heard:
I write "kimchi"

Same is true when I write "u"
It's superior to "oo"
Ask Noh Moo Hyeon

Would you rather be a "Wu"?
Or instead a lowly "Woo"?
That can't be fun

Letters know their place and rank
Like the fishes in a tank
They dominate

Change a spelling, add some verve
Set your words upon the curve
From good to great

"Chattahoochee," lacking wit
Fails with dignity to sit
Upon the page

"Chatahuchi," by contrast--
There's a name that's meant to last
Through every age!

It's an orthographic game
But some spellings are too lame
To greet the eye

Know your letters! Treat them well!
Don't consign your words to hell
With glyphs awry!


I admit I like "y" when it's pronounced "ih" as in "dysfunction" or "nymph"-- or the aforementioned "glyph." "Y" acquires an aura of power and mystery(!) in such contexts.

But spelling a foreign word with unsavory letter choices leaves me cold: I don't like "kimchee," which looks infantile, but I do like "kimchi." While I'm used to seeing surnames romanized as "Lee" and "Woo," I prefer "Li" and "Wu." True: the "Lee" versus "Li" distinction is often useful in distinguishing Korean versus Chinese surnames, even though the respective surnames are derived from the same Chinese character. If, back in the beginning, the Koreans and Chinese had some sort of contest to decide who got to use which spelling, I think the Koreans got the short end of the stick. But I've also seen Koreans deliberately choose the lamer orthography, as in "Jee-young" instead of the far more dignified "Ji-yeong." That unsavory "ee" combination should be reserved for childish utterances: "Oh, gee!" or "Hee hee hee!" (which can't be rendered in English as "Hi! Hi! Hi!" for obvious reasons).

My orthographic sensibility kicks into overdrive whenever I see names like "Sarkozy" and "Grozny." Wouldn't Sarko's name be cooler as "Sarkozi?" The change from "y" to "i" would give it a sort of mafioso cachet. And "Grozny" is just plain sad, whereas "Grozni" is, at least, not totally prostrate.

For Koreans, the inconsistent romanization of Korean names has led to some intractable problems. What's the valence of "u," for example? In the official ROK romanization scheme, it's clearly an "ooh" sound, but so many Koreans use it to mean "uh" that it's hard to tell who means what (e.g., "Sun-hee," where "Sun" sounds like the English "sun," not "soon"). That's why a dude with the surname "Yoon" is probably trapped into writing it that way: were he to write "Yun," it'd be hard for a non-Korean to know whether the name should rhyme with "tune" or with "fun." (Officially speaking, "Yun" should be pronounced "yoon," and if the name rhymed with "fun," it would/should be romanized "Yeon.") "Yoon" looks too close to "cartoon" for my taste. The most infamous example of the Korean surname problem? "Moon."

Does anyone else share this aesthetic, or am I all alone on this one? If you do feel similarly about letters, do you deplore, as I do, the change of that cable channel's name from "Sci-Fi" to "SyFy"? I just can't take the new spelling seriously.


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Tuesday, March 20, 2012

this week's MGRE Math Beast Challenge

From here:


Go to it! My attempt at an answer will eventually appear in the comments. (NB: The above image can be clicked to magnify.)

By the way, in case you're finding the mathematical expression difficult to read, I'm rewriting it here:

an = 2n - 1/(2n - 21)

Enjoy.


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Monday, March 19, 2012

last week's Math Beast Challenge: correct!

The answer to last week's MGRE Math Beast Challenge problem is indeed (B), 7/12. MGRE's explanation:

This is an Overlapping Sets problem that contains an increased level of difficulty because the variable x is used to represent two completely different things (a number of students and a percent of some other group of students). Keep in mind that x can represent two different things, but is the same number in both cases.

An overlapping sets problem in which everything in the set can be categorized as being a member of one of two groups and also one of two other groups (for instance, everyone is a man or woman and also a junior or a senior, or all the vehicles are either cars or trucks and are also manual or automatic transmission) fits well in a type of chart called a double-set matrix.



Now, let’s place the numbers from the problem into the chart. The overall total is x. The total of honors students is 36. The number of males in the honors program is 15. We are also told that x% of the 35 female students are in the honors program. So, [(x/100)•35] can be placed into the chart.



Since this is an additive chart (all rows and columns can be added), let’s sum the top row. We'll solve the resulting equation for x:



Now that we have x, we can fill in the rest of the chart. The number of female honors students, [(x/100)•35] = 60% of 35 = 21. The total is simply 60. Before we unnecessarily complete the entire chart, however, let’s determine which information we actually need.

MANY people misread the final question in problems like this one. The question "What fraction of all the non-honors students are female?" means that all the "non-honors" students go on the bottom and the "female non-honors" students on the top. (Note that the sentence pattern "What fraction of m is n?" always means n/m, not m/n.) Let’s indicate with bold text the boxes we want (on paper, you could circle these boxes).



Subtract 36 from 60 to get 24. Subtract 21 from 35 to get 14.

The answer is 14/24 or 7/12.

The correct answer is B.

Very interesting method. I'll have to study it further to see whether it really saves time.


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Friday, March 16, 2012

Sam Harris on Islam and Western liberalism

From here:

The ferocious response to my discussion with [Joe] Rogan about the war on terror has, once again, caused me to worry about the future of liberalism. It is one thing to think that the war in Afghanistan has been an excruciating failure (which I believe), but it is another to think that we had no moral right to attack al-Qaeda and the Taliban in the first place. A significant percentage of liberals seem to hold the latter view, and consider President Obama to be nothing more than a neocon stooge and Islam to be an unfairly maligned religion of peace. I regularly hear from such people, and their beliefs genuinely trouble me. It doesn’t take many emails containing sentences like “The United States and Israel are the greatest terrorist states on earth” to make me feel that liberalism is simply doomed.

[...]

As I tried to make clear on Rogan’s podcast, we know that intolerance within the Muslim world extends far beyond the membership of “extremist” groups. Recent events in Afghanistan demonstrate, yet again, that ordinary Afghans grow far more incensed when a copy of the Qur’an gets defaced than when their own children are accidentally killed by our bombs—or intentionally murdered. I doubt there is a more ominous skewing of priorities to be found in this world.

Should people be free to draw cartoons of the Prophet? There must be at least 300 million Muslims spread over a hundred countries who think that a person should be put to death for doing so. (This is based on every poll assessing Muslim opinion I have seen over the past ten years.) Should Ayaan Hirsi Ali be killed for her apostasy? Millions of Muslim women would applaud her murder (to say nothing of Muslim men). These attitudes must change. The moral high ground here is clear, and we are standing on it.

Your thoughts?


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Thursday, March 15, 2012

why do dogs have wet noses?

Explication en français ici.

NB: la truffe = nose, but also means "truffle."


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Wednesday, March 14, 2012

"everyday" vs. "every day"

Remember that "every day" functions as an adverb of frequency, whereas "everyday" is an adjective meaning "ordinary."

I brush my teeth every day.

Brushing my teeth is an everyday occurrence.


We good?


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Tuesday, March 13, 2012

this week's MGRE Math Beast Challenge

From here:

In a school of x students, 36 are in the honors program, and x% of the 35 female students are in the honors program. If 15 male students are in the honors program, what fraction of all the non-honors students are female?

(A) 5/12

(B) 7/12

(C) 6/15

(D) 7/15

(E) 8/15

Go to it! My answer will eventually appear in the comments.


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Monday, March 12, 2012

last week's MGRE Math Beast Challenge

I was indeed correct in answering (A) to last week's MGRE Math Beast Challenge. Here's MGRE's official explanation, in two parts: non-algebraic and algebraic. Neither explanation seems to rely on similar triangles, strangely enough.

NB: I have changed all subscript notation to capitals and lowercase: h0 is now H; h1 is now h; r0 is now R; r1 is now r.

The first explanation:

The best way to solve this problem may be one that involves little math. Notice that the cone is much wider at the top than it is at the bottom. Because the bottom of the cone is so narrow, filling up the cone to 40 percent of its height would fill less than 40 percent of its volume. The cone must be filled above 40 percent of h0 to reach 40 percent of the original volume, so h/H > 0.4.

The second explanation:

To solve this problem algebraically, we’ll use the volume formula provided.

Volume at H:

1000π = (1/3)π(R2)H

We’ll solve this for H, as it is one part of the expression in Quantity A:

H = 1000π • (3/πR2) = 3000/R2

Volume at h:

0.4(1000π) = 400π = (1/3)πr2h

We’ll solve this for h, as it is the other part of the expression in Quantity A:

h = 400π • 3/πr2 = 1200/r2

Putting it together, Quantity A is

h/H = (1200/r2)/(3000/R2)

= (1200/3000) • (R2/r2)

= 0.4 • (R/r)2

To compare Quantity A to 0.4, the question is simply whether R/r is greater or less than 1. Similar to how H/h > 1, we can see that R/r > 1, so Quantity A is greater than 0.4.

To be honest, although I love the non-algebraic explanation, I don't like MGRE's algebraic explanation. They'd have done a lot better to go with similar triangles as their strategy. MGRE's algebraic explanation culminates in the ratios H/h and R/r, but the point is to compare h/H (the reciprocal of the aforementioned H/h) with 0.4. I think a few explanatory steps are missing in MGRE's writeup of this problem. "We can see that" is a non-explanation, and to say that "the question is... whether R/r is greater or less than 1" is really to say that no algebra was needed at all: we can compare visually, even if the drawing isn't done to scale. But having compared radii in this way, can the average GRE-taker leap deductively to a conclusion about h/H? I don't think so. Similar triangles give us those relationships most directly.


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Friday, March 9, 2012

do they worship "the same God"?

Lee M., at his excellent blog A Thinking Reed, ponders what it means when people ask whether Christians and Muslims worship the same God. Be sure to read the interesting comments appended to the post.


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Thursday, March 8, 2012

"trop d'étrangers sur notre territoire" ?

Pour tous les pays industrialisés, un des facteurs démographiques qui caractérise une société et une culture robustes est le pluralisme. Mais existe-t-il un point au delà duquel il y a "trop d'étrangers"? Et qu'est-ce qu'on entend par ce terme, étranger? Président Nicolas Sarkozy a récemment déclaré qu'il y a "trop d'étrangers sur notre territoire"-- un propos qui divise la France en deux catégories: le "nous/notre" ("notre territoire") et le "eux/étrangers," c'est-à-dire l'Autre. Voir cet extrait:

Le président français Nicolas Sarkozy, candidat à sa succession à la présidentielle, a estimé qu'il y avait "trop d'étrangers" en France pour que le système d'intégration fonctionne bien et promis de diviser par deux le nombre d'immigrés accueillis chaque année s'il était élu.

"Notre système d'intégration fonctionne de plus en plus mal car nous avons trop d'étrangers sur notre territoire et que nous n'arrivons plus à leur trouver un logement, un emploi, une école", a déclaré M. Sarkozy dans une émission télévisée sur la chaîne de télévision France 2.

"Sur le quinquennat, je considère que pour relancer dans de bonnes conditions l'intégration, il faut diviser par deux le nombre de gens que nous accueillons, c'est-à-dire passer de 180.000 (à) autour de 100.000", a-t-il proposé.

Il est vrai que l'influx des étrangers peut créer des problèmes pour les systèmes d'accueil et d'intégration qui sont en place en France, aux Etats-Unis, etc. Alors que faut-il faire pour amortir l'impact (social, économique) de cet influx?


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Wednesday, March 7, 2012

¡Ay, caramba!

From my Twitter feed, I was led to an article by Katy Meyers on the GradHacker blog about Stoicism in Grad School. Unfortunately, the article is horribly written, and I've highlighted, in red font, every instance of a mistake. Feel free to type a list of corrections in the comments. NB: one or two mistakes are minor in nature, but most are obvious, objective errors that should have been excised in a single wave of proofreading.

The piece has other problems as well (omitted colons, poor spelling and diction, etc.); feel free to fix those. I've reprinted the article below:

I used to be kind of a control freak, I think many grad students can attest to a similar personality trait. Sadly this tends to go along with the perfectionism that Julie talked about last week. Control is important, we need to be able to balance a number of lives as grad students, maintain multiple fellowships and jobs, work on our research as well as ace our classes, and make a good impression in the department as well as the broader discipline. Our success comes from the close control over every aspect of our professional and academic lives: mapping out every minute of our week into our Google calendars, tracking assignments through various iPhone apps, using Zotero to organize every bibliographic reference, and keeping up with the professionals through every social media site we can think of. This is good, it keeps us grounded.

So here’s the problem, you can’t control everything. This may come as a shock to some, I honestly thought in my first year of grad school that I could control every aspect of my life. I extended the necessity to control my academic world to my personal world. This personal control led to anxiety over family and friend relationships for not conforming exactly to the plans I had made up in my head, and massive fears about my department’s view of myself. I wasted precious energy and time worrying about things that I had no control over. I would lose sleep over things that were external to me. It got so bad that it led to physical damage when I starting unconsciously clenching my teeth at night, I now have a wonderful click sound in my jaw (TMJ for those who want the medical term).

That’s when my little brother suggested stoicism. Joel Mendez wrote “Contrary to common perception, being stoic doesn’t mean being emotionless. The real quality of Stoicism is far more masculine than not caring about anything – it’s about knowing when to care, when to be upset, and how to accept the inescapable with your head held higher than you thought possible.”

According to Mendez, if nature gives you a metaphorical slap in the face you can either get all worked up about wondering why this occurred to you or you can accept what occurred and realize there’s no use in crying over it, because you can’t control nature. There’s no point in freaking out because a freak snowstorm prevented you from getting to a presentation, its nature and you obviously couldn’t have done anything to prevent it from occurring. The second part of this is that you accept what things are occurring, you don’t let it affect your emotion, and you don’t retalitate or react. Using nature as an example is good because you can’t retaliate... I guess you could punch the snow, but it’s not going to change anything.

This is all well and good for interactions with nature, but how do we apply this to our lives in grad school? Stocism is about knowing and accepting your limitations. We can control our lives, our emotions, and our reactions to these metaphorical slaps in the face. We can’t control other people’s lives, emotions, or when they chose to slap us in the face. By giving up trying to control things in our life that we have no control over we end up gaining control over ourselves.

We have to accept that sometimes not everyone in your department will like us, we have to accept that some of our students are going to review us badly regardless of how well we teach, we have to accept that we can’t get funding for every thing we do, and we have to accept that our friends and family are not part of our sphere of control. This doesn’t mean giving in and going with the flow completely. Sometimes you do need to fight against funding agencies, and you can work harder to make some people in your department like you. But you need to know your limits, where you can affect change and where you cannot.

Stocism is about finding inner strength, and letting go of the necessity to control the views and actions of others. I leave you with this quote by Seneca the Younger: “Let Nature deal with matter, which is her own, as she pleases; let us be cheerful and brave in the face of everything, reflecting that it is nothing of our own that perishes.”

For a great summary of stocism check out Mendez’s article: The Modern Wimp’s Introduction to Stoicism.

What's most disturbing is that the article is written by someone who wants to talk about perfectionism as a stressor, but I see little evidence of perfectionism in her prose. The repeated misspelling of "stoicism" is a prime example of this sloppiness.


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Tuesday, March 6, 2012

this week's MGRE Math Beast Challenge

From here:



Go to it! My answer will eventually appear in the comments, but right now I suspect the correct response is (D)-- cannot be determined. Why? Because there are four pieces of data we need to know, and we don't know any of them:

1. initial height
2. "diminished" height
3. initial radius
4. "diminished" radius

Still, that's just a conjecture at this point.* When I finally write out my attempted solution, I may disagree with what I've just written. Stay tuned-- but feel free to leave your answer in the comments if you think you've arrived at it before I have.


*If we think of the problem two-dimensionally, i.e., in terms of similar triangles, it may be that there is a solution. Again, I'm typing all this in a rush, so I really don't know yet. Will have to stare hard at the problem before I give it a go.


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Monday, March 5, 2012

elegant solution

I had mentioned, last week, that I don't like summing problems. MGRE's solution to last week's problem is simple and elegant. To wit:

Let’s number the rows top-to-bottom such that the top row is “Row 1” and the bottom row is “Row 24.”

Row 1 has 4 blocks.
Row 2 has 4 + 8(1) = 12 blocks.
Row 3 has 4 + 8 + 8 = 4 + 8(2) = 20 blocks.
Row 4 has 4 + 8 + 8 + 8 = 4 + 8(3) = 28 blocks.

We can generalize the pattern at this point. Row n has 4 + 8(n – 1) blocks. Thus, Row 24 has 4 + 8(23) = 188 blocks.

When we sum the number of blocks in Rows 1 through 24, we are summing an evenly spaced set, for which we have a formula:

Sum = Average Value × Number of Terms, where

Average Value = (first term + last term)/2 = (4 + 188)/2 = 192/2 = 96
Number of Terms = 24, which is just the number of rows.

So, the Sum = (96)(24) = 2,304.

I admit it! This is a much simpler method than mine was.


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Friday, March 2, 2012

almost everything you ever wanted to know about panentheism, but were afraid to ask

The Stanford Encyclopedia of Philosophy (a.k.a. the SEP) has an excellent article summarizing the salient themes and concepts found in panentheism (lit. "all-in-God"-ism). See here.


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Thursday, March 1, 2012

Ave, Guy Sorman!

Article très intéressant de l'économiste pro-marché-libre Guy Sorman (auteur de L'économie ne ment pas) à propos de "comment meurent les démocraties." Extrait:

Dans le monde « occidental » enfin, à ressasser nos crises, on en oublie que sur les dix dernières années, le revenu par habitant en Allemagne par exemple, a crû de 1,3% par an, ce qui est conséquent dans une société prospère, parce que l'Allemagne s'en est tenue au démo-capitalisme, sans céder à des pulsions étatistes. Enfin, par-delà les statistiques, le démo-capitalisme, seul, procure les biens non quantifiés que nous respirons sans nous en apercevoir tant ils nous semblent acquis, comme la liberté d'expression, la recherche de l'équité ou l'égalité des sexes. Tandis que, dans l’ordo-capitalisme, chacun retient son souffle et contrôle ses paroles. Tout ceci n'est pas suffisamment dit, ni dans les pays de l’ordre parce qu’il est imprudent de parler ni dans le monde démo-capitaliste quand les idiots utiles confisquent la parole.


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