Nobody seems to know what mathematics truly is. Here’s something that involves a lot of mathematical thinking, i.e. deduction.

The Zebra Puzzle

1. There are five houses.
2. The Englishman lives in the red house.
3. The Spaniard owns the dog.
4. Coffee is drunk in the green house.
5. The Ukrainian drinks tea.
6. The green house is immediately to the right of the ivory house.
7. The Old Gold smoker owns snails.
8. Kools are smoked in the yellow house.
9. Milk is drunk in the middle house.
10. The Norwegian lives in the first house.
11. The man who smokes Chesterfields lives in the house next to the man with the fox.
12. Kools are smoked in the house next to the house where the horse is kept.
13. The Lucky Strike smoker drinks orange juice.
14. The Japanese smokes Parliaments.
15. The Norwegian lives next to the blue house.

Suppose someone drinks water. Who is it? Suppose someone owns a zebra. Who is it?

Notes: The houses are arranged in a row. Each of the five houses is painted a different color, and their inhabitants are of different national extractions, own different pets, drink different beverages and smoke different brands of American cigarettes. In the sixth statement, right refers to the reader’s right.

Happy (Chinese) New Year! I am a Rat in the Chinese Zodiac, and this is its year.

Personality profiles from zodiacs are totally arbitrary. Yet I provide my Rat profile, courtesy of Wikipedia:

Being the first sign of the Chinese zodiacs, rats are leaders, pioneers and conquerors. They are charming, passionate, charismatic, practical and hardworking. Rat people are endowed with great leadership skills and are the most highly organized, meticulous, and systematic of the twelve signs. Intelligent and cunning at the same time, rats are highly ambitious and strong-willed people who are keen and unapologetic promoters of their own agendas, which often include money and power. They are energetic and versatile and can usually find their way around obstacles, and adapt to various environments easily. A rat’s natural charm and sharp demeanor make it an appealing friend for almost anyone, but rats are usually highly exclusive and selective when choosing friends and so often have only a few very close friends whom they trust.

Behind the smiles and charm, rats can be terribly obstinate and controlling, insisting on having things their way no matter what the cost. These people tend to have immense control of their emotions, which they may use as a tool to manipulate and exploit others, both emotionally and mentally. Rats are masters of mind games and can be very dangerous, calculative and downright cruel if the need arises. Quick-tempered and aggressive, they will not think twice about exacting revenge on those that hurt them in any way. Rats need to learn to relax sometimes, as they can be quite obsessed with detail, intolerant and strict, demanding order, obedience, and perfection.

Rats consider others before themselves, at least sometimes, and avoid forcing their ideas onto others. Rats are fair in their dealings and expect the same from others in return, and can be deeply affronted if they feel they have been deceived or that their trust has been abused. Sometimes they set their targets too high, whether in relation to their friends or in their career. But as the years pass, they will become more idealistic and tolerant. If they can develop their sense of self and realize it leaves room for others in their life as well, Rats can find true happiness.

According to tradition, Rats often carry heavy karma and at some point in life may face an identity crisis or some kind of feeling of guilt. Rats are said to often have to work very long and hard for everything they may earn or have in life. However, a Rat born during the day is said to have things a bit easier than those who are born at night. Traditionally, Rats born during the night may face extreme hardships and suffering throughout life. Rats in general should guard themselves against hedonism, as it may lead to self-destruction. Gambling, alcohol and drugs tend to be great temptations to Rat natives.

The blog remained absent for more than a month because I neglected to renew my domain. I thought that I forked over the money to my host, but lo and behold it was not so.

Since I’ve been gone, we have a black president with a real shot at the White House. The Clintons are scared . . . they expected to march through the caucuses and primaries with a legion of Democratic voters. Instead, a black dude by the name of Barack Obama has risen to take more electoral delegates than Senator Clinton. Does anyone realize how unbelievable this is?

If indeed Senator Obama can capture enough hearts to take the White House, then he could be one of the greatest role models in U.S. history. He certainly would be in a position to make his tenure one of the most distinguished: the economy is going down the toilet, the Muslim fundamentalists hate us more than ever, and we are losing the hegemony that we’ve enjoyed since the fall of the Berlin Wall. If he can turn this country around and win a second term in a landslide, we would have a black man in office for eight years. Seeing a black man as the most powerful man in the world would do wonders not just for blacks, but for every minority in this country as well . . . provided, of course, that the morons of this country don’t revolt against this man.

A friend of mine tells me that if he gets the nomination, then every white person in the midwest and south will vote against him, because a black man does not belong in office.

Suppose, miraculously, that he is elected. He had better get the greatest Secret Service detail of all time. White people will try to kill him.

Suppose he is assassinated. This country could fall apart. Even if he is merely an average president, black people will lionize him. He would be a kind of demigod to them. To see him die would trigger untold grief and rage . . . far worse than Martin Luther King’s death.

Suppose we are attacked again while he is in office. Say a nuke goes off in D.C., a catastrophe on the scale of a Tom Clancy novel. What the hell would he do then? His country would scream for blood, and he could not possibly maintain his overtures to global diplomacy.

What if the economy continues its nosedive next year? Could he implement the progressive policies that Democrats have been trumpeting the past couple of years? The middle and upper classes are not going to care about the poor in the midst of a recession, or god-forbid, a depression.

What if the Democrats lose both houses of Congress? I’d like to see him solidify his bipartisan coalition then.

Whatever happens, this man needs to be President for the next eight years. And he needs to be the best since Lincoln, and the most endearing since Reagan.

Equality this, equality that. Please.

The goal is not to achieve equality. The goal is to attain inequality.

Black people should not bitch and moan about how unfair the world is toward them and how all things should be equal. The human imperative demands that not all things be equal.

Black people should strive to be the ones at the very top; they should become the ones who have a vested interest in conserving as much as possible their social standing. They should place themselves in a position to screw over everybody else, just like the wealthy white men do right now.

We acquire an identity for ourselves by being different in some sense. Whether those differences are given individualistically or collectively, we find ourselves by encountering those who are not like ourselves. It is a fundamental human characteristic, and it is one that we enjoy in many senses.

We all want inequality in one respect or another. We want to make more money than others. We want to be more attractive than others. Smarter. Funnier. Sexier. We want a better house, a better family, a better job, a better car, a better lifestyle. Some insist on eating different food, or speaking a different language, or practicing a different religion.

That’s insisting on inequality. And yet people demand that they be treated equally? That is contradictory. You can’t at once be different and the same. It makes no sense.

It’s stupid to rail against the world for its inequalities. It’s retarded to do so only when it is you who are on the wrong side of social judgment, because you have prejudices as well. Just accept that they are out there and do what is necessary to alter circumstances in your favor.

I ran into a cute, tall lass outside one of the medical buildings today. We had a pleasant conversation about all the police and federal agents that surrounded us. A caller from some animal protection group dialed my school and informed us that there was a bomb in a medical building. Police initially regarded the bomb threat as bogus . . . until they found something looking like a bomb on the ground floor. This lovely lady and I exhibited a spirited, sarcastic wit about it all, a miracle considering that I was in math mode.

Moving away from the girl . . . animal rights activists are annoying. They are self-righteous underdogs who have precious little hope of getting the rest of carnivorous humanity to stop tearing into flesh. If you get between me and my steak, you are placing your life in serious jeopardy. Be prepared to be Jason Bourne-ified, with me slathering Peter Luger on my T-Bone, standing in victory over you. It is my duty as an American to consume as much beef, chicken, pork, lamb, duck, horse, dog, cat, and Native American as my stomach will allow. If a bomb actually detonates somewhere, we’ll convert the Nathan’s Hot Dog Eating Contest into the USDA 100% Approved Sirloin Challenge, with first prize a cool million bucks and a spot for one hundred contestants. They shall eat meat, as required by the Eleventh Commandment.

How to understand a mathematical definition.

1. Know it. If you can’t recite a definition without thinking about it, then you are sunk. Treat a mathematical definition in a theory as a word in a language. You don’t have to think about what words you’re going to use when you speak; hence you shouldn’t have to think about the mathematical objects with which you play.
2. If there are two or more equivalent definitions, completely understand why they are equivalent. Seek as many equivalent definitions as possible. (E.g., A topological space is disconnected if and only if there exists an open set that is also closed.)
3. Produce (at least) three examples, one of them dumb, another ingenious. For each condition of the definition, produce (at least) three examples of objects that fail to satisfy the condition. Can you use these basic examples to construct new ones? (E.g., if G is a set with a group structure, then we can impose a group structure on the cartesian product, G x G, by exploiting the group structure of G.)
4. Find analogies. Is this object “like” some other object? By relating a given object to other objects, you provide context for that object. A rough analogy is better than no analogy, but an accurate analogy is better than a rough one.
5. Whenever possible, visualize. Draw diagrams. Construct mnemonics that encode the information you wish to retain.
6. Surmise what may have motivated such a definition. Why do we care about the object in question? What properties do we wish to investigate? Which properties do we ignore?

How to understand a theorem.

1. Memorize its statement. Just like knowing a definition. Know the contrapositive if applicable. Do not memorize the proof. Understand and memorize the strategy of the proof — then derive the proof from it.
2. Contextualize. How does this theorem relate to other theorems? If it’s a structure theorem, how comprehensive is it? If it provides a method of calculation, how may it be applied?
3. Deconstruct. For each assumption, find an example which demonstrates that the conclusion does not hold.
4. Anticipate. How can you use this theorem to solve potential problems?

Analyze, analyze, analyze . . . and never give up.

Writers have their blocks, musicians their fruitless jam sessions, and mathematicians their proof-less days. I’m enduring one, right now, in the same manner as I endure them all — I seriously doubt whether I should pursue this as a career.

It amuses me when others compliment my intellect. Nearly everyone else in my program is far more adept than I am. To make matters more depressing, in mathematics most great minds do mediocre work. Worse still, some great minds do great work, but that work is never heralded.

There is one student who drags his feet across the halls, apparently unmindful of the relation between his body and the ground, ensnared in a mental world of endless abstraction, of innumerable premises and necessary truths. He seems like a man who has had sleep stolen from him every night. His drawn visage, to which his left hand rises in rescue from unanticipated conversation, is speckled with unshaved whiskers. He is one of our best students. I don’t want to be that person.

I want the theorems and their proofs to come easily, perhaps bestowed upon me by some deity as Ramanujan claimed had happened to him. I want to play with mathematics, not to work with it. I want to bend it to my will as I do with words. I want to turn the kaleidoscope and have everything arrive inexorably, as though these truths were my birthright.

There is a moment in the movie Amadeus where Salieri toils with a composition, the notes inching into his mind. The film cuts to a scene with Salieri and Mozart. Salieri tells Mozart of his composition, and Mozart, immediately inspired, begins to compose instantly a piece of his own. Phrases and harmonies pour from the man onto a harpsichord, and Salieri glares at him with enraged jealousy.

I am not Salieri, but I sympathize with him.

I’ve got to hand it to Washington Mutual for being a beneficent bastion of capitalism. Today came their third invitation to throw away my money: accidental death insurance of a lucrative $3000. I appreciate the offer. Being a budding mathematician is rife with life-threatening danger. Chalk dust. Pointy pencils. Cerebral hemorrhage. Insanity. These and other ponderous perils frequent the lives of mathematicians daily. WaMu, doubtlessly understanding that black mathematicians possess a higher mortality rate than their white colleagues, have come yet again to the rescue, and I am proud to be associated with an institution that places the welfare of its consumers above all else. I wiped a tear from my eye as I ripped apart the letter and sniffed my nose during its plunge from my hand into the recycling bin. These guys really tug on the heartstrings.

Tuesday was Juggler’s birthday, and we hit up a nice spot near the airport. It was a soccer bar, and it was all but dead that night. Nevertheless, I had an awesome time — considering that our waitress was a tall, thick Brit with a great smile and a mesmerizing accent. (What is it about those accents from the UK? Scottish, Irish, Welsh, and British . . . I could listen to their women endlessly.) I stared at her throughout half of the night as we paid tribute to our friend by talking about pretty much everything else except him. The real pleasure came in explaining the nature of mathematics to the non-mathematicians in the crowd. Our explanation amounted to stating that mathematics is complete bullshit, and yet no matter what new bullshit mathematicians cook up, it somehow discovers a way to permeate society.

Tomorrow will suck, for it brings my first true test of the quarter, which I’m fairly sure will leave my ass black and blue.

Meh.

There are times when I wish with all my heart that sleep were completely unnecessary. I’m typing this up after having risen at 2:30 in the AM from a mere five hours of rest. I couldn’t pay Sandman a return visit, so I’m slamming a Rockstar and heading out exceptionally early today.

A couple of nights ago, I was at Lexus’ place watching Game Two of what’s turning out to be an insipid World Series. After the Red Sox dispatched the Rockies for a second straight night, a trailer for the seventh season of 24 aired.

Tony Almeida is alive. He’s one of the villains this season.

Anyone who follows this show knows that my profound disgust and disappointment need not be expressed. Tony died two seasons ago. Now he’s alive again. The show has deteriorated into a soap-operatic disaster. Apparently the producers had designs on filming part of the season in Africa, but they wound up scrapping an entire story arc for this season and started anew. They had three weeks to dream up something, and time was too precious. I’ll watch the show nevertheless, but the experience may be akin to watching a train wreck — it’s extraordinarily painful, yet you can’t deprive yourself of it.