MGRE Math Beast Challenge problem!

Here's this week's Math Beast Challenge problem:

This Week's Problem: "Lunch Combos"

Q:

The standard lunch price at a cafeteria buys either a combination of 1 entree, 2 different side dishes, and 1 drink or a combination of 1 soup, 3 different side dishes, and 1 drink. Substitutions are not allowed, and customers cannot order multiple servings of any one side dish. If customers can choose from among 3 entree, 4 side dish, 3 soup, and 7 drink options, how many different lunch combinations are available for the standard lunch price?


A:

(A) 54
(B) 84
(C) 126
(D) 210
(E) 252

Go for it. My answer will appear in the comments, and MGRE will publish the official answer next week. My first impression is that we're dealing with a typical permutations/combinations problem... but we'll see. I need to stare at it for a moment.


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Bonne Fête des Morts!

Have fun with these two spooky videos:

1. Big Spider Attacks Daddy


2. Le Serpent Mort (Dead Snake)
(The comments to this second video, though in French, have a very American tenor.)



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conjugation, and the most basic irregular verbs in French

European languages usually come with a cluster of crucial irregular verbs that are essential for the conveyance of information. This includes English, which is, after all, a European language. Think about the verb to be, which doesn't conjugate in a regular manner:

I am
You are
He/She/It/One is
We are
You (all) are
They are

Compare that to some typical regular verbs in English, such as to walk and to talk:

I walk, I talk
You walk, You talk
He walks, He talks
We walk, We talk
You (all) walk, You (all) talk
They walk, They talk

Notice that regular verbs in English barely change form at all: only the third-person singular form (he, she, it, one) adds an "s." By contrast, an irregular verb like to be has three different forms.

The same holds true for French: irregular verbs have their own idiosyncratic conjugations. But before I go any further, we need to talk about what conjugation is and how it works.

To conjugate a verb means to put a form of the verb together with a subject (conjugate comes from two Latin roots that, together, mean conjoin). The subject pronoun "he," for example, needs to be paired up with the appropriate form of a given verb: He has. The unconjugated form of a verb is called the infinitive. For example:

to have
to be
to do
to think
to walk
to barf

The bare infinitive is the infinitive form without the to particle. In French, where the infinitive is often seen by how a verb ends, there is no bare infinitive, but once you take away the infinitive's ending, you're left with an infinitive stem. Examples:

INFINITIVE: parler (to speak)
STEM: parl-

INFINITIVE: choisir (to choose)
STEM: chois-

INFINITIVE: vendre (to sell)
STEM: vend-

The above verbs-- parler, choisir, and vendre-- are all regular verbs. Irregular verbs, by contrast, don't always map out so neatly. Here's the verb to be in French:

être (to be)
Je suis (I am)
Tu es (You are)
Il est/Elle est/On est (He/She/It/One is)
Nous sommes (We are)
Vous êtes (You are)
Ils sont/Elles sont (They are)

There's no verb chart in the world that can help you here; you simply have to memorize the conjugation!

Along with to be, then, here are some basic irregular French verbs that are essential if you're to express almost anything in the language:

avoir (to have)
aller (to go)
savoir (to know, or to know how to)
vouloir (to want or wish)
pouvoir (to be able to)
devoir (should, must)

Let's conjugate them, shall we?




While there are many, many irregular verbs in French, it's best to start off with this set. In my upcoming posts, I'll be writing about (1) why verb conjugation charts are ordered the way they are, and (2) how to use the irregular verbs mentioned here. In the meantime, a quick re-listing of the Magnificent Seven irregular French verbs:

être (to be)
avoir (to have)
aller (to go)
savoir (to know, or to know how to)
vouloir (to want or wish)
pouvoir (to be able to)
devoir (should, must)

Remember: by definition, irregular verbs follow no rules. The only way to master them is to go old-school and memorize them.



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"if" conditional grammar in French and English, and other remarks on tense

While I wouldn't use this as a rule of thumb, I think it's important to point out that European languages often bear striking resemblances to each other, thanks to their common history. Case in point: how to handle "if" conditional sentences in French and English.*

[NB: This post assumes a certain level of knowledge of both languages.]

The basic format in French looks like this, with the "si (if)" clause coming first:

1. présent --> présent/futur

2. imparfait --> conditionnel

3. plus-que-parfait --> conditionnel passé

Examples:

1. S'il pleut, j'apporterai mon parapluie. (cas réel)

2. Si j'étais roi, tu ne m'aimerais pas. (cas irréel/hypothétique)

3. Si j'avais su, je ne l'aurais jamais fait. (description d'un passé alternatif/hypothétique/contrefactuel)


In English, the grammar works exactly the same way. To wit:

1. present --> future

2. past --> conditional

3. pluperfect (i.e., past perfect) --> conditional past

Examples:

1. If it rains, I'll take my umbrella. (real case: planning an action that will definitely happen)

2. If I were king, you wouldn't like me. (unreal/hypothetical case: we're just speculating/imagining)

3. If I had known, I'd never have done it. (description of an alternative/hypothetical/counterfactual past)

So if you've learned the grammar in French for "if" conditional sentences, you can apply it to English, because it maps onto English perfectly. And let this be a warning to all the ungrammatical people who start a sentence with "If I could have..." or "If I would have...": you're not doing it right.

WRONG: If I would have known, I'd have been there sooner.
RIGHT (1): If I had known, I'd have been there sooner.
RIGHT (2): Had I known, I'd have been there sooner. (Inversion takes the place of writing "if.")

Had you not read this blog post, you might have made some critical errors in that essay you're writing. While I'm at it, how well do you know your past tenses?

Simple past (le passé simple in French**):

John ate a huge breakfast.
Meg slept like the dead.
Roger swam the English Channel yesterday.
You farted!

NB: The verb is a single unit expressing a fixed action set firmly in the past.

Present perfect (le passé composé, or "compound past," in French):

John has eaten a huge breakfast, so he's not hungry.
Meg has slept like the dead since she stumbled into the apartment last night.
Roger has swum the English Channel before.
You have farted your last fart in this house, young lady!

NB: Even though this is a past tense, it's called present perfect because the helping verb, "to have," is conjugated in the present tense: has eaten, has slept, has swum, etc. This tense usually describes a past action or event that somehow connects to the present. For example, when someone says "I have been to France," they're implying that the experience of having gone to France remains alive in them. Compare that to the simple past construction "I went to France last year," which merely refers to a specific event locked firmly in the past. Is this an absolute distinction between the tenses? Of course not. But it's a very good general guideline.

Past perfect, also known as the pluperfect tense (le plus-que-parfait in French):

John had eaten far too much.
Meg had slept like the dead through many hurricanes in her youth.
Roger had swum the English Channel five times before he took up BASE jumping.
I moved out of the bedroom and into the parlor on the other side of the mansion because you had farted in your sleep so many times.

NB: The pluperfect tense generally suggests a contrast between two events in the past: the event that's further back in the past is the one that takes the pluperfect. In the fart example above, the incessant and intolerable farting came before the other person's disgusted move to the parlor, which is why the construction is "you had farted." The pluperfect is called the past perfect because the helping verb is conjugated in the past tense.

Practice what you've learned!

I. Finish (or begin) these sentences:

1. Had you not arrived in time...

2. She would have married you...

3. If I see that man again today, ...

4. If Slavoj Žižek were president of the European Union...

5. ...Emmanuelle Mimieux won't love you, Frederick.


II. What's the correct answer? Choose TWO! (Highlight the space below the last multiple choice option to see the correct answers.)

1. If Gerald the tiger _____ , none of these poor villagers would have been eaten.
a. had been fed on schedule
b. hadn't gotten so angry
c. was feeling tranquil
d. wouldn't be provoked
Correct answers: A, B.

2. I'll do it if you _____ .
a. do
b. would
c. shall
d. don't
Correct answers: A, D.

3. What would you do if _____ ?
a. you would have a year's free time
b. you could make yourself invisible
c. you had a million dollars
d. hadn't stolen that circular saw blade
Correct answers: B, C.

4. I'd be all over her if _____ !
a. only she had more money
b. you might have pointed her out to me
c. she would have paid attention to me
d. her eyes weren't so crazy-looking
Correct answers: A, D.

5. _____ had he not caught Rachel Dawes in flagrante delicto in a hotel room with the Joker.
a. Batman won't apologize for what he did
b. Batman wouldn't have gone insane
c. Batman cannot blind himself
d. Batman would have stayed away from a career in stand-up comedy
Correct answers: B, D.

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*French is a Romance language while English is classified as Germanic, but both belong to the much larger Indo-European family of languages. English and French both also share a large number of Latin- and Greek-derived words.

**Le passé simple is considered more of a written/literary form than a spoken form of French, although I have heard some older French folks use le passé simple during lectures. We English-speakers are freer in our use of the simple past tense in spoken English, which makes the English simple past and the French passé simple a bit difficult to compare.


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my dirty secret

Well, if I write about it here, my "dirty secret" can't be much of a secret, can it?

All the same, my dirty secret is this: I teach for a tutoring center that does a lot of test and essay prep work for students of all ages, especially for high schoolers looking to do well on the SAT and to write kick-ass college application essays.

But I never used any such services when I was in high school.

I applied to three schools based on my ambition at the time (to become a French teacher): Georgetown, the University of Virginia, and Middlebury College, Vermont. UVA was my "fallback" school; GU and MC were my real targets.* I wrote my essays and may have passed them around to my parents to look over, but that was the extent of my efforts to seek outside help. On the strength of my academic record, my standardized test scores, and my essays, I was accepted to all three schools. To me, getting in was a breeze: it was hard to imagine not being accepted. Was I overprivileged? Have I been gifted with a 200 IQ? Nope. I consider myself to be of pretty average intelligence, and I came from a very middle-class background. Perhaps I would have felt more stress had I applied to some Ivy League schools, but as things were, I was confident that I would get into every school I had applied to.

My point-- the reason why I call all this a dirty secret-- is that I often feel that many of the students who come to me for advice don't really need my help. I've heard from my supervisor that times have changed, though: she contends that competition for schools has become more intense over the past two decades: students need all the help they can get. I squirm when I hear this; it seems like such an obvious play at justifying our center's existence.

As an inveterate teacher, I can't argue with the notion of being there to help students who need help. Helping is what a tutor does. The point of this post isn't that students should forgo all tutoring and fend for themselves: it's that part of a student's maturation process involves embracing independence, and teachers-- like parents-- ultimately have to be ready and able to let students go their own way and do their own thing. So, yeah: I think that most of my seniors are already able to function fantastically without me. They have bright futures ahead of them.

And that's my dirty secret: I think most of these kids don't really need my help. It might lose me some business to write about this, but it's also the truth.

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*Georgetown comes with a reputation that dates back to its founding in 1789. Middlebury is well-known for its magnificent "language houses," in which students must speak in the target language on a 24/7 basis. Language training at Middlebury is some of the best training in the world. I sometimes regret not having gone there. UVA is, of course, a solid school all around, and many of its faculty members are both nationally and internationally reputed. In the end, though, I chose Georgetown and am glad I did. The Ignatian ideal of radical inquiry was a tonic to me; many of my own basic views about the world shifted significantly as a result of my time at GU.


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a difficult grammar point regarding who(m)ever

Which of the following should you say?

a. Give this prize to whomever won the race.
b. Give this prize to whoever won the race.

Did you guess A? Then you're wrong. But why?

We naturally assume, when dealing with who and whom, or whoever and whomever, that whom is what follows a preposition, because a preposition requires an object: To whom were you speaking, young lady?

Normally, that's true. But here's the catch: the preposition to, in the sentences above, introduces a clause. Since a clause has to have both a subject and a predicate, the subject needs to be in the nominative (i.e., subject) case, not the accusative (i.e., direct object) or dative (i.e., indirect object).

So if the boss says something like, "I'll congratulate whomever brings in the most cash for the company," then you know you're dealing with a grammatical idiot. He should have said "whoever."

RULE OF THUMB: ask yourself-- is who(m)ever introducing the clause, or is it the subject of the clause?

We're not done, though. What about a sentence like this:

I'll congratulate whomever the crowd cheers loudest.

Is whomever correct? Yes, it is. Why?

It's because whomever is, in this case, functioning as a relative pronoun introducing a clause. The subject of the clause in question is the crowd, and whomever is actually the object of the verb cheers. (By the way: you see relative pronouns all the time.)

Hope this helps. Here's a quick quiz.

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QUIZ

In the following sentences, are the words whoever and whomever being used correctly?
(Highlight the answers inside the parentheses to see them.)

1. "I'll French kiss whoever I want!" Meredith snarled at her husband Jim.
(Incorrect: it should be whomever, which is the object of the verb kiss. Note, too, that whomever is not the subject of a clause.)

2. "Oh, yeah?" replied Jim. "In that case, I'll kiss whoever comes through the door next!"
(Correct. Whoever is the subject of the clause.)

3. An angry German shepherd trotted in, bloodshot eyes rolling wildly in different directions, fangs dripping with blood and mysterious ribbons of flesh. "Ha ha! A kiss to whoever comes in next!" Meredith hissed spitefully.
(Correct. Again, whoever is the subject of the clause.)

4. "Whomever invented marriage ought to be shot," Jim growled as he bent to kiss the rabid dog.
(Incorrect. Because the word is the subject of a clause, it should be Whoever.)

5. Jim kissed the dog, which immediately transformed into the most gorgeous woman on earth. "I'm Delila," the woman said, "and I'm a gift from Zeus to whomever kisses me."
(Incorrect. Delila might be a gift from the Olympians, but she's having trouble with English. Whoever, not Whomever, is the subject of a clause.)

6. "But-- but--" Meredith sputtered as Jim began to walk out the door with Delila. "What about me?" Jim turned. "We'll divorce. You can marry whoever."
(Incorrect! This was a clear-cut case of whoMever as the object of a verb! A "whom" word would have been perfect here.)


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beware nonsense

English teachers sometimes pass along the nonsense they learned from their own teachers. Here are two myths I sometimes hear parroted by my students at my day job:

1. "You can't end a sentence with a preposition."

This is a myth. Certain petrified expressions (i.e., expressions that can be written only one way, with no change in word order) demand that a sentence end with a preposition. A classic example from linguistics:

RIGHT: That's not something I can put up with.

WRONG: That's not something up with which I can put.

Only Mr. Spock might attempt the second locution. Keep that in mind. Only aliens talk this way.

Put up with is a petrified expression. Being petrified, it governs the structure of the part of the sentence in which it appears. You can't shoehorn it into a mythological grammatical schema.


2. "You can't start a sentence with because."

Oh, yeah? Watch me:

Because I love the rebooted Battlestar Galactica, I've left the Presbyterian Church and have become a Caprican polytheist.

I imagine that the "rule" proscribing the use of because at the beginning of a sentence stems from the occurrence of sentence fragments. A teacher will be understandably horrified to see a "sentence" like:

Because it was the right thing to do.

Why is the above wrong? It's not a real fragment, is it? How can it be, when there's an obvious subject (it) and verb (was)?

Keep in mind that because generally functions as a conjunction introducing a subordinate clause (i.e., a subordinating conjunction). If a sentence has a subordinate clause, it's got to have a main clause. Look at these two sentences:

I love you. You've got eleven fingers.

Join them with because:

I love you because you've got eleven fingers.

The main clause is I love you, and the subordinate clause is you've got eleven fingers. The main clause can stand alone as an independent clause; a subordinate clause, by contrast, never stands alone. And that, ladies and gentlemen, is why a stranded subordinate clause beginning with because is, for all intents and purposes, a fragment.

Keep this in mind as well: it's fine to stick because at the beginning of a sentence since you can reverse the order of the clauses and preserve the sentence's meaning. To wit:

I love you because you've got eleven fingers. (is the same as)

Because you've got eleven fingers, I love you.


Watch out for those language myths. Learn how to look up grammar and usage points yourself by consulting authoritative resources both in the library and online.


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language rant: feel bad, not badly

I hear a lot of people say, "I feel badly about X." Wrong! You feel bad about X, not badly. Why?

What I'm about to say may sound a bit sexual, but it isn't meant to be. The verb feel, in the way it's used in the above example, is a copula-- that is to say, a linking verb. Linking verbs take predicate adjectives or predicate nominatives, not adverbs, which is why badly (an adverb) doesn't work.

You may be wondering, at this point, what a linking verb is. Generally speaking, we can distinguish linking verbs from action verbs. A linking verb establishes some sort of equivalence or identity connecting the sentence's subject to a noun or adjective after the main verb. The verb feel can serve as either a linking verb or an action verb. Examples:

Garrett felt the horrifying alien parasite stirring inside his chest.
(felt = action verb meaning something like "detect")

The alien felt fantastic when it burst out of Garrett's chest and scampered through the ship's labyrinthine corridors.
(felt = linking verb indicating the experience of an emotion, not the execution of an action; in this case, fantastic modifies the subject, The alien)

It may be tempting to engage in a pointless debate over why feeling an emotion doesn't count as a sort of action, but I'm not the one who made the rules, and languages aren't always logical. The point is that a linking verb connects an adjective or a noun directly to the subject, and linking verbs tend to be intransitive in nature-- i.e., they don't transfer any action to an object outside of the subject. Them's the rules.

Here's an example of just such a linking verb: grow. In its intransitive sense, grow is a copula:

The plant grew large. (Not: The plant grew largely.)

However, grow has a transitive sense, in which case it's an action verb that takes a direct object and isn't a linking verb:

Hector Laplante grew tomatoes for a living. (The direct object of grew is tomatoes, which is not modifying or standing in for Hector Laplante.)

The verb grow can, however, take an adverb after it, in which case it's not a linking verb. See here:

The plant grew fast. (Fast modifies the verb, not the subject.)

In case you're still not clear on what's going on here, these are the key concepts mentioned in this post:

1. linking verb = also called a copula; a verb that establishes an equivalence or identity between (a) the subject of the sentence and (b) a noun (predicate nominative) or adjective (predicate adjective) following the verb

2. action verb = a verb that conveys the sense of an observable physical action or a definitive mental action

3. predicate nominative = a noun in the predicate of a sentence that is directly related to, or that somehow modifies/qualifies/stands in for, the subject

4. predicate adjective = an adjective in the predicate that directly modifies the subject

5. transitive verb = a verb whose action is transferred from the subject to a direct object (Kevin lays the book on the table.)

6. intransitive verb = a verb whose action applies only to the subject and is transferred nowhere else (Kevin lies down.)

Keep in mind that many verbs can be used either as linking or action verbs; many verbs can also have transitive or intransitive senses, depending on the context.

Here's a little quiz for you. Highlight the space beneath each sentence to see the correct answer.

PART 1: TRANSITIVE OR INTRANSITIVE?
Look at the verb in context and decide whether it's transitive or intransitive.

1. Gorillas sometimes shave sheep.
Transitive: the word sheep is the direct object of shave. If a verb takes a direct object, it's transitive.

2. Gorillas sometimes shave.
Intransitive: the action of shaving is being transferred nowhere else.

3. Sheila thinks quickly.
Intransitive: all that is reported is the mere action of thinking.

4. Sheila thinks cruel thoughts.
Transitive: the verb now has a direct object: thoughts.

5. Carl carefully considers his options.
Transitive: the direct object is options.

6. If I want your opinion, I'll beat it out of you. (2 verbs)
Both are transitive: the direct object of want is opinion; the direct object of beat is it.

PART 2: PREDICATE NOMINATIVE OR NOT?
Look at the noun or nouns after the main verb and decide whether it or they can be labelled predicate nominatives.

1. Kevin ponders his next move.
No: the verb isn't a linking verb: ponders is transitive in this instance.

2. Paolo is the boss.
Yes. The verb is is a linking verb, making boss a predicate nominative.

3. Lucinda has been working for five years.
No. Years doesn't modify Lucinda. Also, although working is intransitive in this instance, it's an action verb. Finally: the prepositional phrase for five years actually functions as an adverb of time-- another reason why years can't be a predicate nominative.

4. Bishop Berkeley has two dogs.
No. Dogs doesn't modify Bishop Berkeley, and the verb has is transitive: it takes a direct object in this case.

5. To err is human.
This is something of a trick question. The verb is is indeed a linking a verb, and the subject of the sentence, the action to err, can be restated as the gerund erring. But the word human, in this case, is actually functioning as a predicate ADJECTIVE, not a predicate nominative.

PART 3: PREDICATE ADJECTIVE OR NOT?
Look at the adjective or adjectives after the main verb and decide whether it or they can be labelled predicate adjectives.

1. She's pretty hot.
Yes. The adjective hot modifies the subject she, and is connected via the linking verb is. Meanwhile, the word pretty is functioning as an adverb in the same spirit as very. Did you get fooled into thinking that pretty was an adjective?

2. Polar bears enjoy the cold.
Trick question! Cold, in this instance, is a noun, as evidenced by the definite article the. Also, the verb enjoy takes an object, making it transitive, and therefore not a linking verb.

3. My pants are on fire.
Yes. The word are is a linking verb, and the phrase on fire is functioning as the predicate adjective.

4. Dragons eat nubile virgins.
No. The verb eat is both transitive and an action verb; as you can see, it takes a direct object (virgins). Also, the adjective nubile modifies virgins, not dragons.

5. In the alternate universe of Thraxiverm, dragons are nubile virgins.
Another trick question, but you should have been able to reason out that nubile modifies virgins, not dragons. The answer is NO.

6. To a dragon, nubile virgins taste salty and delicious.
Yes. The verb taste is a linking verb, not an action verb, and both salty and delicious are most definitely predicate adjectives.

7. Gandalf feels well.
Yes. Be careful: well is, in this case, an adjective, not an adverb. It refers to one's bodily condition, usually implying a lack of sickness. The verb feel is a copula, making well a predicate adjective.

8. Gandalf feels good.
Yes. As above. In this case, good may refer to something clinical/medical (e.g. Gandalf doesn't have gas today), or to an emotional state. Either way, it's a predicate adjective.

9. Gandalf feels bad about Gollum.
Yes. As above. Bad, not badly. The copula demands a predicate adjective.

I hope this post has cured you of your bad habit of saying "feel badly" when you mean "feel bad." Don't feel bad if it hasn't: just come on back and reread the post until all the information sinks in.


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language rant: the vocative comma

A reader once wrote me:

correct me if I'm wrong, but shouldn't it be:

"Thanks Anne, for stopping by" versus "Thanks, Anne, for stopping by"?

Anyone who has studied a bit of Latin knows that it's a language with a gazillion different cases-- nominative, accusative, dative, genitive, ablative, etc. These cases can be found in all languages, but they're either difficult to see or morphologically invisible, as is often the case in modern American English. Example:

He brings the kid the ball.

He = nominative case (subject of the sentence)

the kid = dative case (indirect object of the action "brings")

the ball = accusative case (direct object of "brings")

Compare the above with German, where the cases are more visible because you have to change the articles to reflect changes in case.

Er bringt dem Kind den Ball.

Er = he, in the nominative

dem Kind = originally das Kind (the word "child" is grammatically neuter in German), but in the dative case, der and das become dem

den Ball = originally der Ball in the nominative, but because Ball is the direct object of the action (accusative case), der becomes den

Sorry for the grammar lesson, but my point is that languages have cases, and different languages show those cases in ways ranging from invisible to quite visible. Languages like German, Latin, Greek, and Russian often show differences in case quite clearly. English, by contrast, doesn't normally change the form of words to indicate variations in case.*

But there's one major exception: the vocative comma.

The vocative case is all about calling or addressing people or things. In English, we indicate the relationship between the speaker and the one spoken to by inserting commas.

Examples:

Hey, dude. What's up? (Not: Hey dude.)

Thanks, Janeane.

Annette, I don't get why you keep dropping vocative commas.

Dammit, Spock, I'm a doctor, not an astrophysicist!

Hear, O Israel!

Buy, minions! Buy!


The last example gives us a chance to see how the vocative comma is helpful. With the comma in place, we have a despot commanding his minions to save the economy by shopping more. Without the comma, we have a despot (or somebody) telling some unknown person to go out and buy him (the despot) some minions:

"Buy minions!" = "You! Buy some minions for me!"

It's possible that the vocative comma may drop out of modern American English altogether, simply as a matter of "common usage," with people intuiting the vocative case through context. I'll be one of the holdouts, though; just as older folks still refuse to split infinitives (despite the fact that most current grammar and style manuals these days claim there's no damage in doing so), I'll be holding on to** those vocative commas until the barbarians come and pry them from my cold, dead brain cells.

In the meantime, I find it excruciating to read vocative locutions that lack vocative commas. I've seen "Hey Kevin" at the start of more emails than I can count, and it's all I can do to keep from weeping and smashing everything around me with a baseball bat.

As the "Buy, minions!" example indicates, vocative commas have their use. Instead of letting the barbarians erode the language further, take a stand and use the comma.

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*For the purposes of this discussion, I'm considering the pronominal shift from "he" to "him" (or "she" or "her," or "they" to "them") to be so common as not to merit discussion. In English overall, very little morphological change occurs when switching cases. Beyond these basic pronouns, it becomes very difficult to cite examples of such changes. Only one other example comes to mind right away: the use of prepositions to indicate case, e.g., "She threw the ball to Clara." Clara is marked as the indirect object of "threw."

**Not "holding onto"! But that's a rant for another time.


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spelling rant

STUDENTS! Here are three words that don't have an "a" in them:

definitely (not "definately")

independence (not "independance")

persistence (not "persistance")

Please don't make me pull my hair out. Make an effort to check your spelling. Don't do the sloppy thing and assume you're spelling correctly-- especially if you have a history of poor spelling. My own analogy for this sort of mental slovenliness is that of the litterer: a person who litters thinks to himself, "Meh... someone else'll come along and clean up my mess." And so he keeps right on littering, thereby demonstrating laziness and a lack of pride. By the same token, many people who fail to check their own spelling think to themselves, "Meh... I'll get a proofreader to look over my work. What are a few misspellings, after all?"

Don't be sloppy. Take pride in your work.

More language rants on the way.


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on writing logically and clearly

It may sound tautological, but bad writing sucks. There are so many ways to write badly that I thought I'd focus on only two major problems today: poor overall organization and lack of clarity. Both of these pitfalls are avoidable.

I. Outlines as the Backbone of Logical Organization

The basic template for writing in the Western world is the outline. This structure has been with us for centuries, if not millennia, and it's the foundation of all modern expository and persuasive writing in English and other European languages. The outline is the structure on which we hang our systematic thoughts, and it relies on a very mundane, commonsense intuition: everything has a beginning, a middle, and an end.

The format for any piece of expository (i.e., for explaining) or persuasive (i.e., for convincing) writing, then, looks like this:

1. Beginning
2. Middle
3. End

Students who routinely write essays probably know the above by different names:

I. Intro
II. Body
III. Conclusion

--but it's the same concept, and for an outline, the concept unfurls this way:

I. Intro (hook, buildup, thesis-- not necessarily in that order)

II. Body (everything in support of the thesis)
  A. First main idea
    1. Supporting detail
    2. Supporting detail
    3. Supporting detail (+ transition)

  B. Second main idea
    1. Supporting detail
    2. Supporting detail
    3. Supporting detail (+ transition)

  C. Third main idea
    1. Supporting detail
    2. Supporting detail
    3. Supporting detail (+ transition?)

III. Conclusion (summary of the argument/explanation that got us to this point; restatement of thesis)

The above schema generally plays out as the infamous five-paragraph essay: an intro paragraph, three body paragraphs, and a concluding paragraph. While extremely practical for writing essays on the SAT I, the schema can also be expanded for more extended writing projects, such as long essays or research papers: simply add more paragraphs to the body. In all cases where the student needs to write expositorily or persuasively, the outline provides the framework for logical expression.

A lot of students will say something like, "But I don't like outlining. I just start writing and go with that." My response to this is twofold: (1) if you're mentally organized enough to produce essays and research papers that come out in beautifully organized form, then bravo! You've already mastered outlining, even if you're not writing your outlines down. But, (2) if you're like most other students, your initial attempts at "going with that" will result in mushy, disorganized writing-- arguments that start but reach no conclusion, or arguments with conclusions arrived at through no discernible logical process. My rule of thumb: better safe than sorry. Get into the habit of outlining your arguments and expositions before you even begin writing. It's hard work-- I remember disliking doing this as a young student-- but it's a valuable skill that will stand you in good stead later on, especially if you're planning to get through college, and maybe even graduate school.

NB: I've avoided talking about another form of writing-- narrative-- because such writing is less inherently logical and more about the evocation of feelings than the crystallizing of thoughts. Asking a creative writer to follow a rigid outline is like asking trees to grow in perfect geometric shapes. This isn't to say that creative writing doesn't require any organization at all; such writing still depends on eloquence, structural harmony, and internal consistency, and may even benefit from something like an outline-style schema. But creative writing is more organic than systematic, which is why I'm not focusing on it here.


II. The Need for Clarity

Many people who should know better-- and these are often, ironically, people in academe like philosophers and English professors-- write horribly. What makes their writing so poor is their inability (or unwillingness?) to strive for clarity of expression. Below is an embarrassing mess of a paragraph, excerpted from the final chapter of an anthology titled The Matrix and Philosophy: Welcome to the Desert of the Real (William Irwin, ed.). The paper's author is Slovenian "philosopher" Slavoj Žižek. His paper for this anthology is "The Matrix: Or, The Two Sides of Perversion." Take a look:

In "Le prix du progès," one of the fragments that conclude The Dialectic of Enlightenment, Adorno and Horkheimer quote the argument of the nineteenth-century French physiologist Pierre Flourens against medical anesthesia with chloroform. Flourens claims that it can be proven that the anesthetic works only on our memory's neuronal network. In short, while we are butchered alive on the operating table, we fully feel the terrible pain, but later, after awakening, we do not remember it ... For Adorno and Horkheimer, this, of course, is the perfect metaphor of the fate of Reason based on the repression of nature in itself: his body, the part of nature in the subject, fully feels the pain, it is only that due to repression, the subject does not remember it. Therein resides the perfect revenge of nature for our domination over it: Unknowingly, we are our own greatest victims, butchering ourselves alive ... Isn't it also possible to read this as the perfect fantasy scenario of inter-passivity, of the Other Scene in which we pay the price for our active intervention into the world? There is no active free agent without this phantasmic support, without this Other Scene in which he is totally manipulated by the Other. A sado-masochist willingly assumes this suffering as the access to Being.

The above strikes me as incoherent-- and reading that paragraph in context with the rest of the paper doesn't help matters. I'll admit the first two-thirds of the above paragraph makes sense, more or less, but things rapidly degenerate as the paragraph blunders drunkenly toward its "conclusion." Were you able to follow Žižek's logic? You should have been. That's what happens with good, clear writing: even when you find yourself in medias res (in the middle of the thing), you should at least be able to understand the writer's reasoning. But how exactly does Žižek go from "We feel pain during surgery but don't remember it" to "human freedom (agency) requires participation in an ironic sadomasochistic fantasy in which Nature has the last laugh"? (Come to think of it: what's the connection between surgery and sadomasochism?)

Confused? Me, too.

Granted: academics, when they write their papers, aren't usually writing for the general public. If we're to be charitable, we have to assume that Žižek's audience is composed mostly of fellow postmodernist scholars (then again, The Matrix and Philosophy is an anthology for popular consumption). But even by the shaky standards of postmodernist scholarship, you'd expect Žižek to write more clearly, wouldn't you? Alas, postmodernists are infamous for their half-baked fusions of Freud and Nietzsche and other disparate sources; coherence is rarely their strong point. I say: the more time and effort you, as a reader, have to waste "unpacking" or "unraveling" what a writer is trying to say, the more likely it is that you're dealing with a bad writer.

Don't be that type of writer. Express yourself clearly. Make sure your conclusions follow neatly from your premises. Make sure your arguments flow and aren't obscured by an insane love of complexity. Keep your sentences crisp and direct. They don't necessarily have to be short, but they should never be overburdened with clauses and connectors that make the reader feel he's on a Möbius-looped roller coaster, or on a slog through the brimstone-reeking wastes of hell. Your writing should be engaging, even to readers outside the compass of your readership. Aim to write for an audience somewhat wider than the one you think you're writing for.

Upshot: keep your thoughts organized, and express them clearly and accessibly.


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Math Beast Challenge!

Manhattan GRE is a GRE test prep company that puts out a weekly "Math Beast Challenge." A new challenge appears every Monday.

Here's the latest one-- "Slash and Burn":



My answer will eventually appear in the comments. Try to figure the problem out for yourself before peeking.



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on tackling some aspects of the TOEFL

Excerpted from an email to a friend who will soon be taking the TOEFL:

The TOEFL rating scale for Integrated and Independent Writing is roughly:

5 = nearly perfect English (very good, natural flow, almost no errors, almost native-quality, excellent organization/coherence)
4 = very good English, with several grammar/spelling/mechanics mistakes and some weakness in essay structure; good coherence
3 = moderate English; many frequent mistakes, unnatural-sounding English, but ideas and content are fairly clear; some coherence
2 = below-average English; the frequency of mistakes impedes comprehension; little coherence
1 = nearly-incomprehensible English; no coherence at all
0 = wrote in a foreign language, or merely re-copied the prompt, or wrote nothing

The key to getting through the Integrated Writing section is to remember that the reading section covers three main points, and the listening section covers those same three points, but the person speaking is REBUTTING the points made in the reading. To write the essay correctly, you have to understand both the three points in the reading and the three points in the audio lecture. Otherwise, it's impossible to get a 5.

Hypothetical Integrated Writing Example:

Let's assume the reading passage covers these three points:

We know global warming is problematic because (a) the rise in global temperatures is directly correlated to the rise in industrial waste heat; (b) according to many scientists, the accumulation of carbon dioxide is trapping the sun's heat in our atmosphere; and (c) cold regions that used to enjoy low average temperatures are now experiencing dangerous melts.

The speaker might respond this way:

It is not obvious that global warming is problematic because (a) first, correlation is not causation, so it is illogical to assume that industrial waste heat is the direct cause of any warming trend; (b) second, there is good scientific evidence that solar activity is the cause of the periodic release of carbon dioxide in our atmosphere, and that this effect is far more powerful than anything humankind has produced; and (c) finally, it is not obvious that a warming-up of colder regions is necessarily a bad thing for humanity or for other forms of life.

Your job will be to write a quick essay that summarizes all six points from the reading and the audio lecture.

The two best essay formats for this are

[Format 1]
1st Paragraph: Point A (reading passage), Rebuttal A (lecture)
2nd Paragraph: Point B (reading passage), Rebuttal B (lecture)
3rd Paragraph: Point C (reading passage), Rebuttal C (lecture)

(or)

[Format 2]
1st Paragraph: Points A, B, and C (reading)
2nd Paragraph: Rebuttals A, B, and C (lecture)

Example of a good 5-level essay:

In the reading passage, the author notes that global warming is problematic. He gives three reasons for this. First, he claims that the rising of worldwide temperatures corresponds to a rise in industrial waste heat, which is produced by people. Second, he argues that there is scientific evidence that carbon dioxide in the earth's atmosphere is retaining the sun's heat, thereby increasing global temperatures. Third, he contends that cold regions of the planet are becoming warmer, resulting in dangerous melting.

The lecturer, however, disagrees with the author of the reading passage. She first counters that "correlation is not causation," which means that it is not logical to assume that two rising trends, global temperature and industrial waste heat, are necessarily associated with each other. Second, she refutes the scientific arguments of the author by saying that other scientists believe the sun itself is responsible for the release of more carbon dioxide than human activity can produce. Third, the lecturer does not feel that the warming-up of previously cold regions is necessarily a bad thing for people, plants, or animals.

Kevin's comment: The above essay covers all six points-- the three points in the reading and the three rebuttals-- clearly and effectively, with no errors in grammar, usage, or mechanics. The summary is logically structured using Format 2; the English is flowing and natural.

Example of a 2- or 3-level essay:

In passage author is argue that global warming is cause the problem. First problem is rising world temperture and undustry heat temperture (people). But lectuer says this is not true because two events together is not causing, is not logical to think so. Second problem is CO2 is rising and causing suns heat to stay in atmosfere. But speaker deny this, and say the sun is first cause of CO2 release. Writter says third problem is danger because cold parts of earth are getting hot, but speak er says why is this problem?

Kevin's comment: The errors in the above essay are so frequent and so severe that a 3 would be a generous score. But a 3 is possible, because the essay writer was able to catch most of the crucial points from the lecture using a Format 1 structure. The quality of the English is what drags this down to a 2 or 3; lack of clarity is what might make this more of a 2.

The point of the Integrated Writing task is to prove that you have fully understood both the reading and audio portions, as well as how those portions relate to each other. The audio lecture will always be a rebuttal of the reading, and will always include three clear points.

For the Independent Writing task, you will have to write briefly on a given topic. Be logical and clear; use a good variety of words, a good variety of sentence structures and locutions (don't be repetitive-- this is death on the TOEFL!), and arguments that don't rely too much on statistics and surveys. Use logic instead. Too many Asian writers on the TOEFL will write things like "A recent survey found that 75% of adult males prefer... (etc., etc.)" TOEFL essay raters don't like this. Keeps stats to a bare minimum; use wide-ranging examples: personal examples, examples from history or literature or film, etc.

To practice your listening skills, I highly recommend you visit the TED Talks website. The TED project is a public forum that invites inspiring people (technological innovators, successful entrepreneurs, etc.) to give short lectures (under 20 minutes) about a topic relevant to human progress and/or enrichment. Subject matter is extremely varied, but most of the speakers are fascinating people. Try this method:

1. Go to the TED website ( http://www.ted.com/talks ).

2. Select and watch a video lecture.

3. Wait a couple hours, then listen to the video lecture again, without watching the screen. Take notes while you listen. Force yourself to recognize important points. Learn to take notes quickly; this will be an important skill in US grad school.

Looking to master the TOEFL? Why not hire me as a tutor? See the test prep page here for more information, then visit the rate charts and the rates/registration page (scroll to the bottom for registration procedure).


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"A Web Whiteboard"

For those of us who tutor via Skype, it's vitally important that we have access to an online whiteboard. A physical whiteboard isn't nearly as convenient: it would have to sit behind me in the webcam view, and I'd have to shift out of my chair every time I wanted to use it. The student might also want to see the notes on the board, and would have to ask me to move. While I definitely need the exercise, I don't think all that standing and sitting and standing is productive in a class context.

Just today, on my Twitter feed, I saw someone link to a new, super-stripped-down type of online whiteboard, called very simply "A Web Whiteboard." No installation necessary-- not that this is unique to A Web Whiteboard, but it does make the app more convenient. I tried the app out for a few minutes... and came away a bit disappointed. While AWW has the advantage of being cross-platform (you can use it just as easily on your smart phone or iPad as you can on your computer), it's missing features that are vital to tutoring, such as the ability to write text or to create clean geometric shapes when visualizing math problems. As far as I can tell, and I may be wrong about this, the whiteboard is geared entirely toward freehand work.

A much better whiteboard for tutors is, in my opinion, Dabbleboard. Dabbleboard is almost as easy to use as AWW is, but it comes with far more features. You can write text on Dabbleboard, for example, and can adjust the size of the text. The text palette includes simple mathematical symbols (pi, square root, some exponents, etc.). You can draw freehand or use a shape-recognizing "orthogonal" tool to create geometric shapes.* The board's animation quality is also much better than AWW's. Dabbleboard includes a video chat function (is this a recent addition?), which makes Skyping a bit redundant, but since I'd normally have to "meet" my students via Skype before referring to the whiteboard during a session, it's better for me simply to remain with Skype.

All in all, if you're an online tutor, I can't recommend AWW in its current state. Once AWW adds more features, I may change my tune. But for now, of the various online whiteboards I've tried, Dabbleboard is the best fit for me.

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*Unfortunately, Dabbleboard interprets your attempts to draw trapezoids as attempts to draw rectangles. To make a trapezoid, you have to draw each line segment separately-- a difference of only a few seconds, so it's no more than a minor annoyance.


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testing Google Docs

I've just written up and uploaded a registration form that has been converted to Google Doc format. Here is the link. You can use the form to register for my classes after we've had an email discussion about your academic needs and your preferred schedule.

Let's see whether this works...

UPDATE: The form seems to work. People simply need to download it as a Word document, fill it out, then send the completed form to me as a file attachment. The form doesn't require anyone to divulge credit card information; payment is through PayPal (using my email address, kevin.timeeffortfocus@gmail.com, as their payee reference), which is encrypted. I use PayPal all the time for eBay; it hasn't failed me yet.

NB: Please remember to double the "e"s in "timeeffortfocus." It's very easy to write "timeffortfocus" by mistake.



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two math problems!

These are examples of the types of math problems one might encounter on the SAT or the GRE. Feel free to have a go at them, but try not to overthink them. That's what usually gets people into trouble on such standardized tests.











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makes you think

My most recent Craigslist ad-- I've created two thus far-- was flagged for deletion for some reason. I read over the Craigslist Terms of Service, and couldn't see what I'd done wrong. No porn, nothing defamatory, no improper use of trademarked or copyrighted material... what exactly was the problem? The ad might be guilty of excessive corniness, but since when has that been a TOS matter?

I suspect that some insecure competitor had my ad flagged as a way of knocking off the competition. It's a low and dirty tactic, if so.

My response: repost.


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