# Logic in Math and in the Arts

This post is prompted mainly from my first-year writing seminar, English 1170: Short Stories. A couple days ago we discussed “The Necklace” and “Araby,” by Guy de Maupassant and James Joyce respectively. Being a math/logic person, I found there’s just something uncanny about literary analysis—something similar, yet not the same—as if it requires a subtly different kind of logic. I felt I was thinking in a completely different manner in that class, and asked myself, are logic in math and logic in literary analysis the same? Today, in a discussion on “The Cask of Amontillado” by Edgar Allan Poe, I think I found my answer.

The discovery is not that the logic is different: logic is when one thing follows another, and this chain is the same for mathematics and literature. Rather, the primary difference is in the direction of the chain.

In math, we often have to prove a theorem. We know exactly what it is we’re trying to prove: we’re just supplying what gets us there. Of course, this can get very tough sometimes, but we know at least what the end result is.

The difference in analyzing literature is that we at first don’t know what we’re trying to prove—we don’t know what argument about the work we want to make.

Literary analysis is therefore more open-ended. I’m not saying mathematical proofs are easy—many of them are unsolved or have taken centuries to solve—but they are defined problems that can be solved (or be shown to be unsolvable). Analyzing literature is really weird since I’m so used to mathematical logic.

Also, the reason I made this post and not earlier is that I’ve never done literary analysis on this level before. In this case there is a noticeable difference between high school and college.

# Young Goodman Brown

All right, I must first get this out of the way: I don’t like Nathaniel Hawthorne’s writing style. I mean, he’s the guy who wrote The Scarlett Letter.

But I’ll have to admit that his short story “Young Goodman Brown” is a very intriguing piece of work. The context? I’m taking an English class (ENGL 1170: Short Stories) for my writing seminar, and our primary book is 40 Short Stories compiled by Beverly Lawn. “Young Goodman Brown” is the first story. Of course, I don’t intend to write a blog post on each one, but I will share the ones I find the most awesome. This means I will be adding to this blog another category: Short Stories.

I would encourage you to read “Young Goodman Brown” if you haven’t already. In case, here is an online copy of the text: http://www.online-literature.com/hawthorne/158/.

Dream or Reality?

In the fifth to last paragraph, Goodman Brown wakes up in a forest and doesn’t know whether the previous events of his being at a devil worship in the forest were real or a dream. Hawthorne leaves it ambiguous. (Remember, this was published in 1835, fully 175 years before Inception.)

I would argue it’s a dream.

First, the story is too supernatural. The devil figure in the woods carries a serpentine staff that seems to animate twice. The first time Brown dismisses it as an “ocular deception” (p. 2 of 40 Short Stories). The second time, though still uncertain, is quite vivid:

So saying, he threw it [the staff] at her feet, where, perhaps, it assumed life, being one of the rods which its owner had formerly lent to the Egyptian magi. Of this fact, however, Goodman Brown could not take cognizance. (5)

The fact that Brown sees the staff coming to life twice may imply it isn’t just by mistake. And even if you don’t take the staff’s animation as a sign of the supernatural, perhaps you will take the actual devil figure as supernatural.

Second, it’s too coincidental. Of course, most literature have those moments when the right thing happens at the right place, at the right time, but here, one scene does seem very contrived. It is scene in which Goodman Brown sees the pink ribbon fall from the sky, the pink being ribbon a part of Faith, his wife. It is an extreme coincidence that the ribbon happens to fall in the middle of the woods precisely where Brown is sitting, and at precisely the time he calls out for Faith. (Then again, the very much real ‘A’ that appeared in the sky in The Scarlett Letter was a super coincidence as well.)

Third, when Goodman Brown wakes up he is in an uncorrupted forest. The most telling sentence is this:

He staggered against the rock, and felt it chill and damp; while a hanging twig, that had been all on fire, besprinkled his cheek with the coldest dew. (12)

So, when just before, the twig had been on fire and the rock had been hot and dry, they are now cool and moist. This isn’t even in the morning. He wakes up to find himself here in the middle of the calm night. Thus, we have sufficient reason to believe the journey of Goodman Brown is but a dream.

# Do Androids Dream of Electric Sheep?

A great work of imagination, with some very intriguing questions. The story is set in a post-apocalyptic future: owning animals is a sign of social status though many animals are fake, i.e., electric; a radioactive dust cloud envelopes Earth, causing many to emigrate; and bounty hunters find and “retire” illegal androids. The novel focuses on the day of one bounty hunter, Rick Deckard.

The Will to Live

Yet, the dark fire waned; the life force oozed out of her, as he had so often witnessed before with other androids. The classic resignation. Mechanical, intellectual acceptance of that which a genuine organism—with two billion years of the pressure to live and evolve hagriding it—could never have reconciled itself to.

An android coldly accepts death. It is programmed. A human fights to live. It is evolved.

But does this alone mean an android is less alive than a human? Is the will to live a prerequisite to life? It seems not. Androids, we learn, are capable of committing suicide via holding their breath. But human beings at times, when the cause is sufficient, sacrifice themselves as well. In Orson Scott Card’s Ender’s Shadow (parallel of Ender’s Game), for example, we learn that the only reason Ender is able to defeat the Buggers is that the Bugger queen thought humans, as sentient beings, were incapable of self-sacrifice. His final attack was a mass sacrifice.

In Do Androids Dream of Electric Sheep?, the androids die for different reasons, however, than humans. Some androids, on learning they are to be retired, give that “mechanical, intellectual acceptance.” They don’t fight back or argue for the truth. It would be analogous to a criminal being ordered the death sentence. Rarely do they immediately accept death.

“Will you kill me in a way that won’t hurt? I mean, do it carefully. If I don’t fight; okay? I promise not to fight. Do you agree?”

“I can’t stand the way you androids give up.”

Artificial Intelligence, and the Turing Test

The Turing Test is an abstract, hypothetical test on artificial intelligence. If a computer can successfully pass off as a human, it passes the test. If not, it fails.

In Do Androids Dream of Electric Sheep?, two such tests exist. The more prominent is the Voigt-Kampff Empathy Test. The tester asks the subject various questions drawing emotional responses to determine whether the subject is an android. More specifically, it measures response times in the eye. A human responds much faster to emotional stimuli than does a android. This is how Rick determines whether Rachael is an android.

The other is the Boneli Reflex-Arc Test, which is only mentioned, not used. According to another bounty hunter, Phil Resch, this test is “simpler” in that it does not require a tester to ask questions. It is fairly automatic and tests the inner biology of the subject. In a way, it almost cheating, and is not truly a Turing Test.

Intelligence

Right now, humans are still far more intelligent than computers. Douglas Hofstadter in Gödel, Escher, Bach points out that we humans are able to “jump out” of our thinking, thus starting a process of meta-thinking. For instance, we might be in the middle of calculating an 3-digit by 3-digit multiplication problem in our heads, and half way through, we suddenly realize, why don’t we just search the answer on Google? A computer calculating this problem, however, would never (at least our current generation of computers) think of doing that; it would simply go through the calculation. But at least it can do it in a split second.

Perhaps a more relevant example is the game of chess. A human grandmaster can look at a position, pick out three or four moves that seem good, analyze a few moves deep into one line, and then based on intuition, decide that the line is not worth analyzing any further, and then switch to analyzing a different line. The computer isn’t so smart. It has to go through EVERY possible move in the position, calculating EVERY possible reply to that move, and then EVERY possible reply to that too, and so on. The number of positions to calculate rises exponentially with each step, and eventually the computer is forced by programing to a stop. The computer, when analyzing an unpromising line, doesn’t say, “Oh, this looks bad, I won’t analyze it any more.” Instead, it will do as it’s been programmed to. The human will. The human can jump out of the current thinking process (analyzing one line) into a higher level of thought (this line is bad, so I’ll look at a different one).

In the same chess example, humans can jump out even further. Supposing the game is lasting very long, the human might need to go to the restroom at some point. At that point, the human’s subconscious, which machines don’t yet have, will tell him to do something other than stare at the chessboard. What if a fire starts? Our current machine won’t even notice. It’ll just continue analyzing the position. The human player would have long been gone. The human has jumped completely out of chess thought. The computer can’t.

In Do Androids Dream of Electric Sheep?, the androids are often distinguishable from humans by this trait, that they cannot think at higher levels as humans can. Only one time I remember does an android demonstrate this human-like feat (correct me if I’m wrong):

“When I used the word ‘human,”‘ Roy Baty said to Pris, “I used the wrong word.”

Roy Baty realizes that by using the word “human,” he has betrayed the fact that he is an android, he catches himself. But other than that, androids seem to be characterized by their straightforward, mechanical thinking.

What is Deckard?

Is Rick Deckard himself an android? We have no idea. I strongly suspect he is. At one point, he asks himself a question from the Voigt-Kampff test and tells the other bounty hunter, Phil Resch, to watch the degree of the emotional response but not his reaction time. And as we know, Rick earlier used the method of measuring reaction time on Rachael to determine whether she was an android. Plus, Rick does not show much emotion in the book. The androids he retires seem to be more lively than him.

Blade Runner (1982) is the film adaptation of Do Androids Dream of Electric Sheep?. It’s brilliant. 9/10.

It keeps the spirit of the book but changes much of the story, completely leaving out some themes. But that was necessary, and the filmography is excellent—they’ve created a convincing new world. Screenplay isn’t supposed to be the same thing as the original (I’m reading Syd Field’s Screenplay right now).

Blade Runner makes the question of whether Rick is a human or android even more prominent. It does so via an origami unicorn that Rick remembers from his dreams. In the end he sees one in front of his door. If he were an android with implanted memories, it would make sense how somebody knew about the origami unicorn dream.

I actually watched the film first. The book is Cornell University’s summer reading assignment, and the first time, I believe, I have ever read a science fiction book for school. Anyway, both the book and the film are outstanding.

# The Picture of Dorian Gray

Oscar Wilde’s only novel, The Picture of Dorian Gray, is a beautiful work of art, and it tells us—according to the book’s epigram and preface—that “all art is quite useless.” Therefore, I shall try not to dig far into the meaning, but rather, present some of the most funny and quotable material from the book.

The following passage comes from the very beginning of the book, where the painter Basil Hallward refuses to send his portrait of Dorian Gray anywhere. Lord Henry Wotton is of the opposite opinion:

“Not send it anywhere! My dear fellow, why? Have you any reason? What odd chaps you painters are! You do anything in the world to gain a reputation. As soon as you have one, you seem to want to throw it away. It is silly of you, for there is only one thing in the world worse than being talked about, and that is not being talked about. A portrait like this would set you far above all the young men in England, and make the old men quite jealous, if old men are ever capable of emotion.” (page 4)

Basil is an eccentric artist in other respects as well, for example, on secrecy:

“Dorian Gray? Is that his name?” asked Lord Henry, walking across the studio toward Basil Hallward.

“Yes, that is his name. I didn’t intend to tell it to you.”

“But why not?”

“Oh, I can’t explain. When I like people immensely I never tell their names to any one. It is like surrendering a part of them. I have grown to love secrecy. It seems to be the one thing that can make modern life mysterious or marvelous to us. The commonest thing is delightful if one only hides it. When I leave town now I never tell my people where I am going. If I did, I would lose all my pleasure. IT is a silly habit, I dare say, but somehow it seems to bring a great deal of romance into one’s life. I suppose you think me awfully foolish about it?” (page 6)

This starts a chain of witty remarks:

“Not at all,” answered Lord Henry, “not at all, my dear Basil.” You seem to forget that I am married, and the one charm of marriage is that it makes a life of deception absolutely necessary for both parties. I never know where my wife is, and my wife never knows what I am doing. When we meet—we do meet occasionally, when we dine out together, or go down to the Duke’s—we tell each other the most absurd stories with the most serious faces. My wife is very good at it—much better, in fact, than I am. She never gets confused over her dates, and I always do. But when she does find me out, she makes no row at all. I sometimes wish she would; but she merely laughs at me.”

“I hate the way you talk about your married life, Harry,” said Basil Hallward, strolling toward the door that led into the garden. “I believe that you are really a very good husband, but that you are thoroughly ashamed of your own virtues. You are an extraordinary fellow. You never say a moral thing, and you never to a wrong thing. Your cynicism is simply a pose.

Being natural is simply a pose, and the most irritating pose I know,” cried Lord Henry, laughing. (page 6)

Some more amusing lines:

The whole thing was a fiasco. The last act was played to almost empty benches. The curtain went down on a titter, and some groans.

As soon as it was over, Dorian Gray rushed behind the scenes into the greenroom. The girl was standing there alone, with a look of triumph on her face. Her eyes were lit with an exquisite fire. There was a radiance about her. Her parted lips were smiling over some secret of their own.

When he entered she looked at him, and an expression of infinite joy came over her. “How badly I acted to-night, Dorian!” she cried.

“Horribly!” he answered, gazing at her in amazement—”horribly! It was dreadful. Are you ill? You have no idea what it was. You have no idea what I suffered!” (page 89)

“I should think it was, Harry. But according to your category I must be merely an acquaintance.”

“My dear old Basil, you are much more than an acquaintance.”

“And much less than a friend. A sort of brother, I suppose?”

Oh, brothers! I don’t care for brothers. My elder brother won’t die, and my younger brothers seem never to do anything else.” (page 10)

To be good is to be in harmony with one’s self,” he replied, touching the thin stem of his glass with his pale, fine pointed fingers. “Discord is to be forced to be in harmony with others. One’s own life—that is the most important thing. As for the lives of one’s neighbors, if one wishes to be a prig or a Puritan, one can flaunt one’s moral views about them, but they are not one’s concern. Besides, Individualism has really the higher aim. Modern morality consists in accepting the standard of one’s age. I consider that for any man of culture to accept the standard of his age is a form of the grossest immorality.”

“But, surely, if one lives merely for one’s self, Harry, one pays a terribly price for doing so?” suggested the painter.

“Yes, we are overcharged for everything nowadays. I should fancy that the real tragedy of the poor is that they can afford nothing but self-denial. Beautiful sins, like beautiful things, are the privilege of the rich.” (page 82)

Anyway, the novel was quite unlike anything I had ever read. I’m not exactly sure I liked it, but it is certainly an amusing read.

# Lady Windermere’s Fan

A typical Oscar Wilde play, this is one of the wittiest works imaginable, and is the origin of many famous quotes such as “I can resist everything except temptation” and “Life is far too important a thing ever to talk seriously about it.” Although this play might not be as famous as The Importance of Being Earnest, and it might not have as sophisticated a plot, it is most certainly as witty, and has also more social commentary.

LORD WINDERMERE: Ah, Margaret, only trust me! A wife should trust her husband!

LADY WINDERMERE: London is full of women who trust their husbands. One can always recognise them. They look so thoroughly unhappy. I am not going to be one of them.

Here is another awesome passage, this time on superficiality:

LADY WINDERMERE: Lord Darlington, you annoyed me last night at the Foreign Office. I am afraid you are going to annoy me again.

LORD DARLINGTON: I, Lady Windermere? […] I am quite miserable, Lady Windermere. You must tell me what I did.

LADY WINDERMERE: Well, you kept paying me elaborate compliments the whole evening.

LORD DARLINGTON: Ah, nowadays we are all of us so hard up, that the only pleasant things to pay are compliments. They’re the only things we can pay.

LADY WINDERMERE: No, I am talking very seriously. You mustn’t laugh, I am quite serious. I don’t like compliments, and I don’t see why a man should think he is pleasing a woman enormously when he says to her a whole heap of things he doesn’t mean.

LORD DARLINGTON: Ah, but I did mean them.

LADY WINDERMERE: I hope not. I should be sorry to have to quarrel with you, Lord Darlington. I like you very much, you know that. But I shouldn’t like you at all if I thought you were what most other men are. Believe me, you are better than most other men, and I sometimes think you pretend to be worse.

LORD DARLINGTON: We all have our little vanities, Lady Windermere.

LADY WINDERMERE: Why do you make that your special one?

LORD DARLINGTON: Oh, nowadays so many conceited people go about Society pretending to be good, that I think it shows rather a sweet and modest disposition to pretend to be bad. Besides, there is this to be said. If you pretend to be good, the world takes you very seriously. If you pretend to be bad, it doesn’t. Such is the astounding stupidity of optimism.

It is Lady Windermere’s very dislike of compliments that leads to the farcical temptation quote:

LORD DARLINGTON: Ah. what a fascinating Puritan you are, Lady Windermere!

LADY WINDERMERE: The adjective was unnecessary, Lord Darlington.

LORD DARLINGTON: I couldn’t help it. I can resist everything except temptation.

Another charming line is Lord Darlington’s speech on good and bad:

LORD DARLINGTON: Do you know I am afraid that good people do a great deal of harm in the world. Certainly the greatest harm they do is that they make badness of such extraordinary importance. It is absurd to divide people into good and bad. People are either charming or tedious. I take the side of charming, and you, Lady Windermere, can’t help belonging to them.

Also, near the end of Act 3 are three now-very-famous quotes, quite close together:

DUMBY: I congratulate you, my dear fellow. In this world there are only two tragedies. One is not getting what one wants, and the other is getting it. The last is much the worst; the last is a real tragedy! But I am interested to hear she does not love you,. How long could you love a woman who didn’t love you, Cecil?

CECIL GRAHAM: A woman who didn’t love me? Oh, all my life!

DUMBY: So could I. But it’s so much different to meet one.

LORD DARLINGTON: How can you be so conceited, Dumby?

DUMBY: I didn’t say it was a matter of conceit. I said it as a matter of regret. I have been wildly, madly adored. I am sorry I have. It has been an immense nuisance. I should like to be allowed a little time to myself now and then.

LORD AUGUSTUS: Time to educate yourself, I suppose.

DUMBY: No, time to forget all I have learned. That is much more important, dear Tuppy.

LORD DARLINGTON: What cynics you fellows are!

CECIL GRAHAM: What is a cynic?

LORD DARLINGTON: A man who knows the price of everything and the value of nothing.

CECIL GRAHAM: And a sentimentalist, my dear Darlington, is a man who sees an absurd value in everything, and doesn’t know the market price of any single thing.

LORD DARLINGTON: You always amuse me, Cecil. You talk as if you were a man of experience.

CECIL GRAHAM: I am.

LORD DARLINGTON: You are far too young!

CECIL GRAHAM: That is a great error. Experience is a question of instinct about life. I have got it. Tuppy hasn’t. Experience is the name Tuppy gives to his mistakes. That is all.

DUMBY: Experience is the name every one gives to their mistakes.

I had certainly known of all three quotes before, but I never thought they were all located within a page of one another. Now, here are two more Wilde quotes, both located on the page before the previous passage:

DUMBY: Good heavens! how marriage ruins a man! It’s just as demoralising as cigarettes, and far more expensive.

and

LORD DARLINGTON: No, we are all in the gutter, but some of us are looking at the stars.

That makes for five infamous quotes in the span of two pages.

By the way, the title Lady Windermere’s Fan is actually a sort of pun, as the fan could refer to both her physical fan, which Lord Windermere gave to her as a present, and Lord Darlington, who likes her. Again, it is maybe not as funny a pun as The Importance of Being Earnest, but the content is just as clever.

# The Count of Monte Cristo

I read this book in a truly Westwood style: about 10 pages a day for the first 10 days, 50 pages a day for the next five days, then 250 pages on the last day, today. That is, the Barnes & Nobel Classics edition of the book, which I have, is abridged to 591 pages—most unabridged versions of the story are well over a thousand pages.

Alexander Dumas’ work is a real page turner. Nevermind my slow start—it took me a few days to get through Edmond Dantès’ betrayal and unjust imprisonment because I was rather occupied by other activities, which may be seen from my last few blog posts (though I assure you they are not at all comprehensive). It turns out that this imprisonment, which lasts 14 years, also constitutes the majority of the story’s time. But once Edmond escapes from the Château d’If and acquires massive treasure, the book becomes very interesting and exceedingly difficult to put down. (In this edition he finds the treasure on page 143.)

At that point it is the story of what an honorable but vengeful soul can do with infinite wealth. The count can manipulate the feelings and actions of others, and eventually controls even life and death. This causes him to carry with him a mystical, God-like aura. For instance, when Edmond is overly confident about winning a duel against Albert de Morcerf, Albert’s friend Beauchamp was “somewhat disconcerted, for he could not make up his mind whether he had to deal with an arrogant braggadocio or a supernatural being” (p. 466).

Does this alone make the book a page turner? Not at all! Edmond has three main enemies to upon which to invoke revenge, and the three have families and are connected, so the reader desperately wants to know how Edmond’s plans will affect all three families simultaneously. And with unlimited wealth with which to bribe, to impress, or to deceive, Edmond can guarantee that his cunning plans will succeed.

The most powerful quotation from this book, for me, is actually before he finds his treasure—or rather, it is the search for the treasure itself. On page 141, he still does not know whether the treasure is real or imaginary.  He uncovers the entrance to the treasure’s cave and sees a staircase, whence Dumas inserts the following line:

Dantès descended, murmuring the supreme word of human philosophy: ‘Perhaps.’

After this moment, Dantès, with his unimaginable wealth, can obtain anything he desires. So ironically, the word ‘perhaps’ becomes obsolete.

# Summer Reading List

I’m trying to read some real literature this summer, so here’s what I have tentatively planned.

Books which I have and plan to read:

• Slaughterhouse-Five by Kurt Vonnegut
• Brave New World by Aldous Huxley
• The Picture of Dorian Gray by Oscar Wilde
• The Collected Oscar Wilde by Oscar Wilde The Count of Monte Cristo by Alexander Dumas*

*Barnes and Nobel sent the wrong book, but with the correct cover. That’s right, the cover and the pages don’t match. I’m perfectly fine with this however, as this is a book which I have also been wanting to read.

Plays which I have and plan to read:

• Lady Windermere’s Fan by Oscar Wilde
• A Woman of No Importance by Oscar Wilde
• An Ideal Husband by Oscar Wilde
• Salomé by Oscar Wilde

These four plays are all in a collection titled The Importance of Being Earnest and Four Other Plays. I have already read—and seen in both movie rendition and live performance—The Importance of Being Earnest.

Nonfiction books which I have and plan to read:

• Screenplay by Syd Field
• Writing with Style by John R. Trimble
• Gates by Stephen Manes and Paul Andrews

The last title is of course a reference to Bill Gates, not garden gates.

Books which I don’t have but plan to read:

• Do Androids Dream of Electric Sheep? by Philip K. Dick**

**This is Cornell’s summer reading book, which they’re shipping soon.

Books which I don’t have but do want to read:

• Catch-22 by Joseph Heller
• Don Quixote by Miguel de Cervantes
• Nobody’s Fool by Richard Russo (at friend’s recommendation)

• Straight Man by Richard Russo (at friend’s recommendation)
• The Man in the High Castle by Philip K. Dick (at friend’s recommendation)

Well, that’s it for now—there’s a heck of a lot of other books I want to read at some point.

&

Finally, for the sake of completeness, below is a list of books which I have read so far in 2010, in approximate forward chronological order (many of these appear as posts on my blog).

Books which I have read so far in 2010:

• The Metamorphosis by Franz Kafka*** (actually I read this on Dec. 25, 2009, but eh, close enough!)
• QED by Richard Feynman (and I read this on Dec. 29, 2009, oh well)
• Perfect Rigor by Masha Gessen
• The Elements of Style by William Strunk Jr. and E.B. White
• Viva la Repartee by Mardy Grothe
• Oxymoronica by Mardy Grothe
• Candide by Voltaire
• Othello by Shakespeare***
• The Pirate Hunter by Richard Zacks
• The Pursuit of WOW! by Tom Peters
• Innumeracy by John Allen Paulos
• I Know Why the Caged Bird Sings by Maya Angelou***
• I Never Metaphor I Didn’t Like by Mardy Grothe
• Ifferisms by Mardy Grothe
• Introduction to Graph Theory by Richard J. Trudeau
• Alice’s Adventures in Wonderland by Lewis Carroll
• Through the Looking Glass by Lewis Carroll
• On Writing Well by William Zinsser
• Siddhartha by Herman Hesse
• The Aims of Education by The University of Chicago
• The Great Gatsby by F.S. Fitzgerald***
• Never Let a Fool Kiss You or a Kiss Fool You by Mardy Grothe
• Plato and a Platypus Walk into a Bar by Tom Cathcart and Dan Klein
• xkcd: volume 0 by Randall Munroe
• The Annotated Alice by Martin Gardner and Lewis Carroll
• Gödel, Escher, Bach by Douglas Hofstadter
• “The Hunting of the Snark” by Lewis Carroll

***Assigned readings for school

By the way, the size of this list is rather unusual for me, as I used to not read this much. I went through most years of my life reading maybe five or six books outside of school per year; only this year (and the latter half of 2009) did I really start enjoying literature.

If I had to recommend five books from this list—actually a tough decision—I would choose Viva la Repartee, Candide, Siddhartha, Alice in Wonderland, and Through the Looking Glass. Yes, Lewis Carroll is just that awesome.