You are currently browsing jeff’s articles.

There’s someone you want to hook up with.  How do you find out if the attraction is mutual while avoiding the risk of rejection?  That is simply not possible no matter how sophisticated a mechanism you use.  Because in order for the mechanism to determine whether the attraction is mutual you must communicate your desire to hook up but she’s not that into you, well you are going to be rejected.

But rejection per se is not the real risk. Because if she rejects you without ever actually knowing it, you will be disappointed but you won’t be embarrassed.  The real cost of rejection comes only when rejection is common knowledge between the rejector and the rejected.

So to design a mechanism that maximizes the number of hookups you need to give people maximal incentives to reveal whom they want to hook up with and to do that you need to insure them against common-knowledge rejections.

And that’s where Bang With Friends comes in.

Bang With Friends is a Facebook app, coded by a few college kids in a weekend, that facilitates no-risk hookups with people on your friends list. You say you’d like to bang them, and no one ever knows, unless they happen to say that they’d like to bang you, too.

Now this indeed takes care of one side of the incentive problem, but I worry about the other side.  Suppose I want to know who wants to bang with me even if I don’t have the same lust for them. I can find out by putting all of my friends on my Down To Bang list.  The only cost I pay for this information is that all of those who are down to bang with me will be told that I am down to bang with them. In some cases this could be lead to some embarrassment and awkwardness but I imagine some people would pay that price just to find out. And anticipating this possibility everyone is again reluctant to be truthful about who they do want to Bang for fear of being caught out this way.

One way to mitigate the problem is to replace the flat list with a ranking of your friends from most to least Bang-able, and then establish a hookup only with the friend who is highest on your ranking among those who want to Bang back. Then if you do decide to pad your list, you will put the reconnaissance Bangage low on your list. Of course this will allow you to find out those friends who put you highest on their ranking, but at least this is less information than you can get with the existing system.

The Magic Kingdom of Data:

The Walt Disney Co. recently announced its intention to “evolve” the experience of its theme park guests with the ultimate goal of giving everyone an RFID-enabled bracelet to transform their every move through the company’s parks and hotels into a steady stream of information for the company’s databases.

…Tracking the flow through the parks will come next. Right now, the park prints out pieces of paper called “FastPasses” to let people get reservations to ride. The wristbands and golden orbs will replace these slips of paper and most of everything else. Every reservation, every purchase, every ride on Dumbo, and maybe every step is waiting to be noticed, recorded, and stored away in a vast database. If you add up the movements and actions, it’s easy to imagine leaving a trail of hundreds of thousands of bytes of data after just one day in the park. That’s a rack of terabyte drives just to record this.

Theory question:  Suppose Disney develops a more efficient rationing system than the current one with queues and then adjusts the price to enter the park optimally.  In the end will your waiting time go up or down?

Eartip:  Drew Conway

photo


 

  1. Talking about inlaws with your spouse is a minefield of higher-order beliefs that its really just veiled criticism of those traits of your spouse that have yet to assimilate into the relationship.
  2. Kids love to play games with grownups in large part because they infer that if the grownup is playing then the game must be super fun.  The problem is that games for kids are usually boring for grownups.  So someone should invent a game where there are effectively two sets of rules.  The simple kids rules and the more subtle rules for grownups.  Think of Pixar movies with inside jokes aimed over the heads of kids and at the adults.
  3. We have recently discovered a great exception to the boring-for-grownups rule for games.  Its called Escape:  The Curse of the Temple.  Highly recommended.
  4. On Economics Job Market Rumors the only threads worth reading are the ones that have many Likes and also many Dislikes.  Its gotta have both.
  5. When you send out emails pitching your students to departments that are hiring, you recycle the text but cut and paste the name of the recipient and the department to customize the email. When you send it to, say LRMU, address it to Harvard pretending it was a cut-and-paste omission.
  6. Someone should collect data on coughing in concert halls over time.  I hypothesize that they are clustered rather than uniformly distributed.  (There’s a simple theory behind it.)

Arthur Robson wrote this on Facebook:

If am peacefully working out, and someone else arrives in the gym, they usually grab the TV remote to bathe in the inane chatter of preternaturally perky news shows. What if I were to arrive while they were watching TV and switched it off?

Which is a good point but still I think that a case can be made that it is morally allowed to turn on the TV but not to turn it off.

If you walk into the gym and the TV is on, that fact is a strong signal that somebody is watching it and would be harmed if you turned it off.  On the other hand when the TV is off you have much less information about what people are paying attention to.  You only know that nobody turned the TV on.  This is consistent with everybody being indifferent to the TV being on and off.

The point being that a utilitarian calculation based only on the signal of whether the TV is on or off will always make it strictly more permissible to turn the TV on than to turn it off.

But note that the inference is a function of the moral code. And if people are following the turn-on-but-not-off code then the TV will be on even if nobody is watching it.

So what we need is an equilibrium code:  a code that works even in equilbirium when it is expected to be followed by others.

Congratulations to our colleague Aviv Nevo on his appointment to this position which Thomson-Reuters says will make him the top non-lawyer at the Department of Justice (there’s a joke in there somewhere).

Aviv joined our department the same year I rejoined and we both wanted the same office.  Highest seniority in our department determines priority for choosing offices and to break the tie there was a coin toss.  I was in Boston and couldn’t actually witness the coin toss but they tell me I lost.

So Aviv got the office, but he also got seniority which means he is in line to be chairman before me.  I am sure he will be back with us in time to take his turn.

Imagine a genie which randomly imposes across-the-board budget cuts unless Congress votes to stop them before they happen.  This would be a good genie.

Its easy to blame the other side for not coming to an agreement.  The genie’s cuts will happen because both sides will blame the other for not reaching an agreement to stop them.  This is different than proposing and approving of cuts yourself because you would get the blame for that.

And of course a random genie is blameless.

It’s not a first-best genie.  The cuts are random and across the board.  But because of the asymmetry of blame they wouldn’t happen otherwise.

Sadly its not even a real genie so the cuts never happen.  But Congress and President Obama have now learned how to replicate the genie:  impose the cuts on a future congress.  From the point of view of the future congress the previous congress is essentially a random genie.

The previous congress, not being an actual genie, nevertheless avoids blame because everyone expects the next Congress to do the sane thing and replace the sequester with something sensible.

All we can hope now is that the current Congress looks at this sequester “debacle” and concludes that in order to make it work as intended the next time the threatened cuts have to be even bigger.

Consider a team selling tickets for its upcoming baseball season. Before the season begins it offers a bundle of tickets for every game. Some of these games however are certain to have very low attendance (games on a Tuesday, games against poor opponents, etc.) The tickets for these games will be placed on the secondary market at very low prices. Indeed one of the biggest problems for teams is the inability to prevent those secondary market prices from falling so low that they cannibalize single-game box office sales. The problem is so severe that many baseball teams are making arrangements with StubHub to enforce a price floor on that exchange.

The problem has a much simpler solution: stop selling season tickets. The team should instead offer the following type of bundle:  you may purchase tickets for all of the predictably high-demand games at the usual season ticket discount.Then you may add to that bundle any subset of the low-demand games you desire but each at a price equal to the face value of the ticket.

This arrangement will make both season ticket holders and the team better off. Season ticket holders will opt not to add the low demand games (unless the opponent is a team they really like for example) and since they weren’t going to those games anyway they are saving money.

The team will increase revenue: supply of tickets to low demand games will be controlled. Secondary market tickets will be priced at or near face value because nobody will buy a ticket at face value for a lousy game unless they actually plan to use the tickets. This enables the team to hold prices at their desired (i.e. revenue maximizing) level without cannibalism.

Since you’ve only ever been you and you’ve had to listen to yourself talk about your own thoughts for all this time, by now you are bored of yourself.  Your thoughts and acts seem so trite compared to everyone else so instead you try to be like them. But you fail to account for the fact that to everybody else you are pretty much brand new and indeed you would be a refreshing break from their boring selves if only you would just be you.

There are two actions, A and B, and there are two observable types of people L and R.  Everybody is the same in the following sense:  for any single individual either A or B is the optimal action but which one it is depends on an unknown state of the world.

But in another sense people are heterogeneous.  It is common knowledge that in the state of the world where A is best for people of type L then B is best for people of type R.  And in the other state its the other way around.  Each person observes a private signal that contains information about the state of the world.

Acting in isolation everybody would do exactly the same thing:  pick the action that is best according to their belief (based on the private signal) about the state of the world.  But now embed this in a model of social learning.  People make their choices in sequence and each observes the choices made by people who went before.

Standard herding logic tells us that L’s and R’s will polarize and choose the opposite action even if they get it completely wrong (with L’s choosing the action that is best for R’s and R’s choosing the action that is best for L’s)

(A reminder of how that works.  Say that an L moves first.  He chooses the action that looks the best to him say A.  Now suppose the next guy is an R and by chance action B looks best to him.  The third guy is going to look at the previous two and infer from their choices that there is strong information that the true state is such that A is good for L’s and B is good for R’s. This information can be so strong that it swamps his one little private signal and he follows the herd:  choosing A if he is L or B if he is R.  This perpetuates itself with all subsequent decision makers.)

In effect the L’s choose A just because the R’s are choosing B and vice versa.

via The Morning News:

More info here.

This is an interesting article, albeit breathless and probably completely deluded, about acquired savantism:  people suffering traumatic brain injury and as a result developing a talent that they did not have before.  Here’s at least one bit that sounds legit:

Last spring, Snyder published what many consider to be his most substantive work. He and his colleagues gave 28 volunteers a geometric puzzle that has stumped laboratory subjects for more than 50 years. The challenge: Connect nine dots, arrayed in three rows of three, using four straight lines without retracing a line or lifting the pen. None of the subjects could solve the problem. Then Snyder and his colleagues used a technique called transcranial direct current stimulation (tDCS) to temporarily immobilize the same area of the brain destroyed by dementia in Miller’s acquired savants. The noninvasive technique, which is commonly used to evaluate brain damage in stroke patients, delivers a weak electrical current to the scalp through electrodes, depolarizing or hyperpolarizing neural circuits until they have slowed to a crawl. After tDCS, more than 40 percent of the participants in Snyder’s experiment solved the problem. (None of those in a control group given placebo tDCS identified the solution.)

(I know this problem because it was presented to us as a brain teaser when I was in 2nd grade.  Nobody got it. The solution while quite simple is “difficult” to see because you instinctively self-impose the unstated rule that your pencil cannot leave the square.)

The suggestion is that with some drugs or surgery we could all unlock some hidden sensitivity or creativity that is latent within us. Forget about whether any of the anecdotes in the article are true examples of the phenomenon (the piano guy almost certainly is not.  Watch the video, he’s doing what anyone with some concentrated practice can do.  There is no evidence that he has acquired a natural, untrained facility at the piano.  And anyway even if we accept the hypothesis about brain damage and perception/concentration why should we believe that a blow to the head can give you a physical ability that normally takes months or years of exercise to acquire?)

The examples aside, there is reason to believe that something like this could be possible.  At least the natural counterargument is wrong:  our brains should already be using whatever talents they have to their fullest.  It would be an evolutionary waste to build the structure to do something useful and not actually use it.  This argument is wrong but not because playing the piano and sculpting bronze bulls are not valuable survival skills.  Neither is Soduku but we have that skill because its one way to apply a deeper, portable skill that can also be usefully applied.  No, the argument is wrong because it ignores the second-best nature of the evolutionary optimum.

It could be that we have a system that takes in tons of sensory information all of which is potentially available to us at a conscious level but in practice is finely filtered for just the most relevant details.  While the optimal level of detail might vary with the circumstances the fineness of the filter could have been selected for the average case.  That’s the second best optimum if it is too complex a problem to vary the level of detail according to circumstances.  If so, then artificial intervention could improve on the second-best by suppressing the filter at chosen times.

The case of The Oscars:

BEST PICTURE

“This is a preferential system. I’m putting Amour at No. 9 because I’m just pissed off at that film. Beasts of the Southern Wild is a movie that I just didn’t understand, so that’s my No. 8. Les Miserables goes in seventh place — it’s not just the most disappointing film of the year but the most disappointing film in many years. Above that I’m putting Silver Linings Playbook, which is just a “blah” film. Django Unchained will go into my fifth slot — it’s a fun movie, but it’s basically just Quentin Tarantino masturbating for almost three hours. Next up is Life of Pi because of how unique it is and for holding my attention up until its irritating ending. Argo is gonna go in third place, but I don’t want it to win because I don’t think it deserves to win and am annoyed that it is on track to win for the wrong reasons. Actually, come to think of it, do we have to put a film in every slot? Because what I want is for my best picture choice to have the best possible shot, so why even give any support to the others? [He has his assistant call the Oscar voting helpline, finds out that voters can leave slots blank and promptly removes all of the aforementioned selections.] I’m basically OK with one of two films winning. Lincoln is going in my second slot; it’s a bore, but it’s Spielberg, it’s well-meaning, and it’s important. Zero Dark Thirtyis my No 1.”

Vote: (1) Zero Dark Thirty, (2) Lincoln, (3) [blank], (4) [blank], (5) [blank], (6) [blank], (7) [blank], (8) [blank], (9) [blank]

Read the whole article for the inside view of Oscar balloting, including beating the shit out of Ann Hathaway, spinnng the iPhone, and filleting the neighbor’s dog.

Gatsby grip:  Alex Frankel

  1. The WaxVac
  2. How the Pope Is Chosen
  3. Check out the Spicoli on this hatchet-wielding homeless false-savior vanquishing savior
  4. Hacking my vagina (not actually mine)

A fascinating article I found after digging through Conor Friedersdorf’s best of journalism.

What distinguishes a great mnemonist, I learned, is the ability to create lavish images on the fly, to paint in the mind a scene so unlike any other it cannot be forgotten. And to do it quickly. Many competitive mnemonists argue that their skills are less a feat of memory than of creativity. For example, one of the most popular techniques used to memorize playing cards involves associating every card with an image of a celebrity performing some sort of a ludicrous — and therefore memorable — action on a mundane object. When it comes time to remember the order of a series of cards, those memorized images are shuffled and recombined to form new and unforgettable scenes in the mind’s eye. Using this technique, Ed Cooke showed me how an entire deck can be quickly transformed into a comically surreal, and unforgettable, memory palace.

The author documents his training as a mental athlete and his US record breaking performance memorizing a deck of cards in 1 minute 40 seconds.  I personally have a terrible memory, especially for names, but I don’t think this kind of active memorization is especially productive.  The kind of memory enhancement we could all benefit from is the ability to call up more and more ideas/thoughts/experiences related to whatever is currently going on.  We need more fluid relational memory, RAM not so much.

Look at married female academics and whether or not they use their maiden name. See how this depends on

1. Which of the two names comes earlier in the alphabet.

2. Whether their field uses the lexicographic convention of ordering authors names.

People don’t like to be idle.  They are willing to spend energy on pointless activities just to avoid idleness.  But they are especially willing to do that if they can make up fake reasons to justify the unproductive busyness.  That’s the conclusion from a clever experiment Emir Kamenica told me about.

In this experiment subjects who had just completed a survey were told they had to deliver the survey to one of two locations before being presented with the next survey 15 minutes later.  They could walk and deliver to a faraway location, about a 15 minute roundtrip, or deliver it nearby, in which case they would have to stand around for the remainder of the 15 minutes.

There was candy waiting for them at the delivery point.  In a benchmark treatment it was the same candy at each location.  In that treatment the majority of subjects opted for the short walk and idleness.

In a second treatment two different, but equally attractive (experimentally verified) types of candy were available at the two locations and the subjects were told this.  In this treatment the majority of subjects walked the long distance.

The researchers conclude that the subjects wanted to avoid idleness and rationalized the effort spent by convincing themselves that they were getting the better reward.  Indeed the subjects who traveled far reported greater happiness than their idle counterparts regardless of what candy was available.

In my first year as an Assistant Professor I was assigned the job of teaching Microeconomic Principles, aka Econ 1, aka the Freshman economics class which is for most students the first introduction to economics they will have and for a large fraction of them also the last.  I sucked at it.  But not because I didn’t care.  I cared a lot and I put a lot of effort into preparing each class and making the whole sequence of classes fit together as a coherent whole.  But that first year of teaching my evaluations were absolutely awful.

So I tried harder the next year, and put more and more effort into the class each year and yet each year my evaluations got worse and worse.  The lowest point for me was when I decided I would write out every lecture word for word to make sure I was saying everything I needed to say and saying it right.  That year my evaluations hit bottom and it was the last time I taught the course.

The next undergraduate course I taught was Intermediate Microeconomics and when I was planning how to teach it I decided to go to the completely opposite extreme and not prepare anything at all except for the topics of each lecture and how they would fit together.  Apart from knowing what I needed to teach them I went into each class with no preparation at all, just chalk and a board.  It couldn’t be any worse than before.

I discovered that when you are teaching something that you know very well, preparation only gets in the way.  Improvisation

  1. Forces you to develop the ideas from scratch out loud which gives the students a glimpse at how to arrive at those ideas rather than just seeing them fully baked on an overhead.
  2. Creates an element of danger that you naturally respond to by digging deeper and finding your way through.
  3. Gets the students’ attention.  They can tell you are doing it without a net and the drama of that hooks them in.
  4. Makes it less like a lecture and more like a conversation.

Google discontinued their appointment slots feature of Google Calendar.  I was using that to schedule meetings with students.  It was really nice because I could just block out some time for meetings and send a link to students and they would just sign up for 30 minute slots in the block.  But no more.  Does anybody know of a good alternative?

Comes from being able to infer that since by now you have not found any clear reason to favor one choice over the other it means that you are close to indifferent and you should pick now, even randomly.

  1. Plagiarize this:  unquotations.
  2. Portrait of the artist falling from various heights.
  3. Highland Park, IL allows Billy Corgan to keep his 49 sq. ft. neon sign.
  4. You probably already saw this, but its a hilarious bad lip reading of NFL players on the field.
  5. How to make a cocktail, and many other simple howto videos.

From Catherine Rampell:

In several computer science courses at Johns Hopkins University, the grading curve was set by giving the highest score on the final an A, and then adjusting all lower scores accordingly. The students determined that if they collectively boycotted, then the highest score would be a zero, and so everyone would get an A. Amazingly, the students pulled it off:

Her analysis of the problem would be the starting point for a nice introductory example in a game theory class (although it appears what she is saying is that taking the test is weakly dominant, but I doubt that is true if there is a positive opportunity cost of time.)

Kava tembel tumble:  Arthur Robson

You know how after you just saw a really cool movie with a friend and you and your friend run into a mutual friend and you two are so excited about the movie you describe it in great detail elaborating on one another’s account getting yourselves more and more excited about the movie just through your own process of recalling it and meanwhile your friend is bored to tears and really when you think about it the guy’s only real role here is to be a third party who hasn’t seen the movie so that you and your friend can talk to each other about the movie through him because it wouldn’t really make sense for the two of you to describe the movie to each other because, right, you both just saw it together but still there is something for the two of you to communicate to each other, to relive it and make the experience more common and indeed when you milk that to its fullest you are talking about subtleties that really only someone who has had the experience can relate to and appreciate so your third party gets progressively more estranged from the conversation at the same time that the two of you get more involved.

Well, that’s kinda what articles like this one about the Grateful Dead  are like. Giving stories that anyone who doesn’t already know them isn’t going to be interested in but nevertheless there is a sense that this way of writing the article, pretending that the reader is someone else, is the most effective way to reminisce with the actual readers.

It was the way he treated last-second, buzzer-beating three-pointers. Not close shots at the end of a game or shot clock, but half-courters at the end of each of the first three quarters. He seemed to be purposely letting the ball go just a half-second after the buzzer went off, presumably in order to shield his shooting percentage from the one-in-100 shot he was attempting. If the shot missed, no harm all around. If it went in? Then the crowd would go nuts and he’d get a few slaps on the back, even if he wouldn’t earn three points for the scoreboard.

In Baseball, a sacrifice is not scored as an at-bat and this alleviates somewhat the player/team conflict of interest.  The coaches should lobby for a separate shooting category “buzzer-beater prayers.” As an aside, check out Kevin Durant’s analysis:

“It depends on what I’m shooting from the field. First quarter if I’m 4-for-4, I let it go. Third quarter if I’m like 10-for-16, or 10-for-17, I might let it go. But if I’m like 8-for-19, I’m going to go ahead and dribble one more second and let that buzzer go off and then throw it up there. So it depends on how the game’s going.”

This seems backward.  100% (4-4) is much bigger than 80% (4/5) whereas the difference between 8 for 19 and 8 for 20 is just 2 percentage points.

When I was back home over Winter Break my Mom tried to get me to throw away all the old papers and junk that I left behind in a box but it didn’t work.  Still I rummaged through and I found this gem.  Its an essay assignment in a Freshman history class about racism in Joseph Conrad’s Heart of Darkness.  This is very typical of my work in college.  The grader’s comments in red are especially entertaining, again quite typical.

 

The paper doesn’t seem to exist yet but here are slides from talk by Raj Chetty, Emmanual Saez and Lazlo Sander.  They randomly altered the incentives for referees at the Journal of Public Economics to see what it takes to get referees to give timely reports.  Some referees were offered cash.  Some were simply given shorter deadlines with no carrots.  Still others were threatened with public shame if they did not submit reports on time.  Not surprisingly the threat of humiliation caused many referees to refuse the contract altogether.  Perhaps less surprisingly, cash didn’t do much better than simply shortening the deadline.  The latter did help a bit.

Kofia krumple:  Tobias Schmidt

Ever seen this?  There’s a panel of experts and every couple weeks they are presented with a policy statement like “The debt ceiling creates too much uncertainty” and each one has to say individually whether they agree or disagree.

Randomize whether you put the statement in the affirmative or the negative:  “The debt ceiling creates too much uncertainty” versus “The debt ceiling doesn’t create too much uncertainty”, and see how that affects how that affects which experts agree or disagree.

This is sublime writing.  It will make your week, go and read it.  Thanks to The Browser for the pointer.

Another good one from Scott Ogawa.  It’s the Creampuff Dilemma.  A college football coach has to set its pre-season non-conference schedule, thinking ahead to the end-of-season polling that decides Bowl Bids.  A schedule stocked with creampuffs means lots of easy wins.  But holding fixed the number of wins, a tough schedule will bolster your ranking.

Here’s Scott’s model.  Each coach picks a number p between 0 and 1.  He is successful (s=1) with probability p and unsuccessful (s=0) with probability 1-p.  These probabilities are independent across players.  (Think of these as the top teams in separate conferences.  They will not be playing against each other.)

Highest s-p wins.

Lee Childs gets asked that question a lot.

But it’s a bad question. Its very form misleads writers and pushes them onto an unhelpful and overcomplicated track.

Because “How do you create suspense?” has the same interrogatory shape as “How do you bake a cake?” And we all know — in theory or practice — how to bake a cake. We need ingredients, and we infer that the better quality those ingredients are, the better quality the cake will be. We know that we have to mix and stir those ingredients, and we’re led to believe that the more thoroughly and conscientiously we combine them, the better the cake will taste. We know we have to cook the cake in an oven, and we figure that the more exact the temperature and timing, the better the cake will look.

So writers are taught to focus on ingredients and their combination. They’re told they should create attractive, sympathetic characters, so that readers will care about them deeply, and then to plunge those characters into situations of continuing peril, the descent into which is the mixing and stirring, and the duration and horrors of which are the timing and temperature.

But it’s really much simpler than that. “How do you bake a cake?” has the wrong structure. It’s too indirect. The right structure and the right question is: “How do you make your family hungry?”

And the answer is: You make them wait four hours for dinner.

As novelists, we should ask or imply a question at the beginning of the story, and then we should delay the answer. (Which is what I did here, and you’re still reading, right?)

It’s a great article but I agree with Emir Kamenica (deerstalker doff) who says that there’s one thing in there the author gets completely wrong.

The clocks in Grand Central are off by 1 minute:

But Grand Central, for years now, has relied on a system meant to mitigate, if not prevent, all the crazy. It is this: The times displayed on Grand Central’s departure boards are wrong — by a full minute. This is permanent. It is also purposeful.

The idea is that passengers rushing to catch trains they’re about to miss can actually be dangerous — to themselves, and to each other. So conductors will pull out of the station exactly one minute after their trains’ posted departure times. That minute of extra time won’t be enough to disconcert passengers too much when they compare it to their own watches or smartphones … but it is enough, the thinking goes, to buy late-running train-catchers just that liiiiiitle bit of extra time that will make them calm down a bit. Fast clocks make for slower passengers. “Instead of yelling for customers to hurry up,” the Epoch Times notes, “the conductors instead tell everyone to slow down.”

Not everyone is going to equilibrate, just the regulars.  But that’s exactly what you want.  If you set the clock right then everyone is rushing to the train just when its departing.  If you set the clock 1 minute off and everyone equilibrates then still everyone rushes to the train when its departing.

The system works because some of the people adjust to the clock and others don’t.  So the rush is spread over two minutes rather than one.