Thursday, July 25, 2013

NBA AM: The Free Agent Update

Suns guard Kendall Marshall talks about his team, whats he's been working on and what he expects from Phoenix this season.

Watch More Video Here

The Free Agent Update:? NBA free agency has now passed from the frantic ?get ?em signed? phase into the bargain shopping phase. The worst values in free agency occur within the first five days of the process. This is typically when teams have to overpay to get the players they covet. When you look at the contracts that players like Tyreke Evans, Zaza Pachulia or even Monta Ellis received ? all were the results of multiple offers and the teams that wanted them understanding that they either had to offer a million or two more or an additional contract year in order to secure those players.

The most expensive players in sports are someone else?s? players. Equally the most expensive players to retain are players other teams covet, and that plays out in the first week or so of free agency.

So now that the ?mad money? is spent, let?s take a look at some of the guys who are left:

Jennings_DeadlineTitleBrandon Jennings:? The Milwaukee Bucks tried to sign Atlanta Hawks? restricted free agent Jeff Teague, mainly because they thought they could get him cheaper and felt he fit the direction the team was heading under new head coach Larry Drew. The Bucks tried to do a contract extension with Jennings last year only to have the table turned and the price jacked way up. The price tag for Jennings is what has the Bucks looking at other options.

Sources close to the process explained that the team has never wavered in their desire to ink Jennings to a new deal, they just won?t massively overpay Jennings and it seems that?s what his camp is seeking.

The Bucks issued a $4.5 million Qualifying Offer to Jennings at the start of free agency in order to restrict his free agency. With most of the major free agent money off the table, Jennings looks to have two options ? make a reasonable deal with the Bucks or pick up the offer year and play out another season for the Bucks.

Both Jennings and the Bucks have entertained sign-and-trade scenarios, but sources close to the situation say Milwaukee is not going to sandbag their season to move Jennings for basically nothing and that any deal made would have to return a legitimate starting point guard.

Both sides are talking, and a deal to keep Jennings in Milwaukee could be had in the $8 million per season range. The question is will Jennings take a deal at that price? He wants significantly more considering his peers received deals in the $11 to $12 million per season range last year by way of extensions.

If Jennings picks up his Qualifying Offer, he would become untradeable this season without his consent and he?d become an unrestricted free agent in July, something he and his camp are strongly considering.

The Bucks and Jennings have a dialogue going. Will they reach a deal?

Mo_Williams_Tile_USAT_1Mo Williams:? Utah Jazz guard Mo Williams has no shortage of suitors, but what he does not have is a long list of big-dollar offers.

Williams is said to be weighing a number of scenarios, but is holding out hope that a solid multi-year offer will come his way.

Williams has told friends in the league that if the offers don?t improve, he may opt for a one-year deal for a contending team like Miami, who has expressed interest.

Unfortunately for Williams, the market doesn?t have a ton of money left and those teams with cash to spend are not teams Williams is actively considering.

There is no doubt that Williams lands somewhere, but the question is which would-be contender gets his services and how much will that cost them?

GeraldHenderson_TileGerald Henderson:? The Charlotte Bobcats have been talking with Gerald Henderson about a new deal, but as you can imagine the numbers and years on the table are not in Henderson?s favor.

Sources close to the process say there is no question the team wants Henderson back, but they are not about to overpay for him.

The problem for the former Duke star is that most of the league views him the same way. There are several teams that would do a mid-level exception based offer sheet, but the Bobcats almost certainly match that kind of number.

Eventually, some team will set the price on Henderson and that?s the unfortunate side of restricted free agency. Once that happens, Charlotte will then make their decision, mainly because they don?t have to do anything until then.

Like Jennings, Charlotte did issue a $4.53 million Qualifying Offer to restrict Henderson?s free agency and the Bobcats have talked about sign-and-trade scenarios with Henderson and other teams, so moving him in a trade is a consideration. However, sources say that seems somewhat unlikely at this point unless it?s a good deal for Charlotte.

When teams reach a pricing impasse like Charlotte has with Henderson and Milwaukee has with Jennings, they often turn to the trade market to make sure they are not over or under valuing a player.

It is telling that no one has tendered a major offer for Henderson (or Jennings). Rather than bid against themselves, the Bobcats, like most teams with restricted free agents, are letting the marketplace do their negotiating.

Henderson could opt to pick up his Qualifying Offer and head into unrestricted free agency next year, but sources close to the process say it?s far more likely Henderson reaches a new deal in Charlotte than play out next season on his Qualifier.

DeJuanBlair_DeadlineTile1DeJuan Blair:? There?s no shortage of interested teams inquiring about DeJuan Blair. In fact, most of the league has called about Blair in some capacity. The issue for Blair is how can he get a multi-year deal or a deal that preserves his Bird Rights via sign-and-trade with the San Antonio Spurs.

Blair?s time in San Antonio was far from ideal for a free agent since he played sparingly in the postseason and didn?t have a huge role in the last two years. This makes landing a significant free agent deal tough, especially for a guy with no anterior cruciate ligaments in his knees.

Teams are more than willing to do one-year, low-dollar deals for Blair, mainly because when he did play in San Antonio, he played extremely well. The issue is how to get him a multi-year deal or how to preserve his Bird Rights.

The Spurs are not closed to a sign-and-trade with Blair, but like all things with San Antonio the deal has to favor them and that?s tough to construct.

Free agency comes in tiers and with most of the upper-tier guys off the board, Blair?s window for a deal is open and there are no shortage of scenarios, especially for a guy that could be playing for less than $2 million next season.

Timofey_Mozgov_Tile_USAT_1Timofey Mosgov:? Mosgov has been a regular at Impact Basketball in Las Vegas, going hard daily against the likes of Oklahoma City?s Serge Ibaka. The word around Summer League was that Mozgov was headed to the Sacramento Kings as a free agent, although the Denver Nuggets were trying to re-sign him.

There were reports this week that after signing guard Nate Robinson to a free agent deal, the Nuggets could be working on a sign-and-trade deal for Mozgov.

The Spurs have emerged as a team interested in Mozgov and they could be the team trying to construct a deal with Denver.

Like Blair, the window for a deal for Timofey is open and it seems like he could come off the free agent board fairly soon.

NikolaPekovic_TileNikola Pekovic:? The Timberwolves and Pekovic have been working on a multi-year deal that would keep the seven-footer in Minnesota for the next four seasons.

Sources close to the situation say retaining Pekovic is a virtual lock and all that?s remaining is for the Wolves to finish their offseason.

Because of how the cap rules work, Pekovic has to be the last player signed as his number could push the Wolves into the luxury tax and that would limit any other roster moves the team can make.

The deal that?s expected for Pekovic is in the four-year, $50 million range, which should put his first year?s salary at roughly $10.7 million. This would give the Wolves a committed salary of $65.812 million, assuming they don?t make any other deals.

The Wolves still have roughly $650,000 remaining on their mid-level exception and $516,000 left on their bi-annual exception, and at least one open roster spot.

Gary Neal:? GaryNeal_FinalsTileWord has it that the San Antonio Spurs have considered rescinding the Qualifying Offer of free agent guard Gary Neal.

The move would be strictly about cap management to allow the Spurs to potentially add another player via sign-and-trade.

Dropping Neal and possibly DeJuan Blair?s cap holds would allow the Spurs to make such a move.

Neal has had interest from other teams and like most free agents, he has to play the waiting game. San Antonio removing his restricted status will help.

We Want To Know:?

More Than Just 48 Minutes:? Someone asked me on Twitter yesterday why new Denver Nuggets guard Nate Robinson didn?t receive a bigger deal, agreeing to a two-year deal worth $4.03 million after what was an impressive postseason with the Chicago Bulls.

NateRobinson_InsideOnly1The truth of the situation is that while some players are uber-appealing on the floor, they are incredibly tough to manage off the floor. Enter Nate Robinson.

There is no question that Robinson is an impressive basketball player, but the problem for Robinson and many free agents who are still unsigned is that their history and their reputation for being disruptive limits what teams are willing to offer.

Robinson is a clown around guy off the court. If you spend 10 minutes in a locker room with him you?ll eventually see it. That kind of stuff surfaces in practice, on the team plane and in meetings.

For the most part, it?s harmless. However, for teams with culture issues or control issues, Robinson can be a distraction and he?s not alone. Free agent guard Delonte West is in the same boat; talented player on the court, an eventual distraction off the court.

It?s not a surprise that Robinson had success in Chicago. They are a tough veteran team with a controlled environment. The structure in place (and fear of Tom Thibodeau, according to sources) was great for Robinson. Unfortunately for these players, there are not a lot of those kinds of teams willing to take on someone who could be a distraction.

NBA teams have to live with each other for roughly 200 days a year when you factor in training camp, preseason and the regular season.

They have to practice together, travel together and live around each other for more than the 48 minutes of game time we see on the court.

So when you ask yourself, ?Why doesn?t this guy get a deal? Why is this guy out of the NBA? Why didn?t this guy get a major contract?? a lot of times it boils down to how teams see a player fitting into their culture.

The good teams really value that; the great teams cultivate that. And guys that could be a distraction tend to find themselves looking for jobs more often than not.

It?s About Improving:? Staying on the topic of Twitter questions ? yesterday someone asked me, what?s the Orlando Magic?s plan?

While surely the question was trying to solicit a complex answer, the truth of the matter is the Magic, like many teams outside the playoff picture, have a very basic answer ? get better.

Mo_Harkless_Inside_USAT_1Making the playoffs or getting a high draft picks isn?t a goal most teams have. It?s a result. You make the playoffs because you are good, typically better than the teams you play against.

Getting a high draft pick is typically the result of being bad, or having less talent or maturity than the teams you play against.

The Magic are trying to build a culture of winning. They are not willfully losing games; in fact they really don?t want to lose games at all. No one stays employed in the NBA very long if all they do is lose games, regardless of the players you draft with high draft picks.

Is the 2014 NBA Draft class appealing? Sure. There is no question that some of the roster decisions being considered have the 2014 draft in mind, but the Magic are not fielding a D-League team just to land a 25 percent chance at Andrew Wiggins.

They want to see Tobias Harris improve. They want to see Maurice Harkless come into his own as a star-level talent. They want Nikola Vucevic to develop the same kind of impact on a game defensively as he showed last year offensively. They want Jacque Vaughn to grow as a coach and they want their new free agents and draft additions to make them a better team.

The Magic won 20 games last year, but were in a lot of those games. The goal this year is to win a few more of those and if that results in a playoff berth, great. If that results in a high draft pick, that?s not going to be a problem either.

The goal for the Magic, like most teams, is to work at getting better. For Orlando, as they enter year two of this new regime and program, they are expecting more from themselves.

While that certainly isn?t the sexy answer, it?s the truth of what they are doing.

More Twitter:? Make sure you are following all of our guys on Twitter to ensure you are getting the very latest from our team: @stevekylerNBA, @AlexKennedyNBA, @TheRocketGuy, @LangGreene, @EricPincus, @joelbrigham, @SusanBible @TommyBeer, @JabariDavisNBA , @NateDuncanNBA , @MokeHamilton and @YannisHW.

Source: http://www.hoopsworld.com/nba-am-the-free-agent-update?utm_source=rss&utm_medium=rss&utm_campaign=nba-am-the-free-agent-update

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'Law & Order' star Dennis Farina had cancer at time of death

Law & Order star Dennis Farina was battling cancer at the time of his death, it has been revealed.

Farina died at the age of 69 at a Scottsdale, AZ hospital due to developing blood clots in his lungs.

Dennis Farina attends a screening of new HBO Original Series LUCK at the Mandalay Bay Hotel and Casino in Las Vegas

? PA Images / AJM/EMPICS Entertainment

His physician Dr Marc A Kates has now released a statement to clarify that Farina had been undergoing treatment for cancer at the time of his passing.

"He had a small cancer 13 years ago that was treated and cured with surgery," Dr Kates commented. "Over the last several months, he unfortunately experienced a recurrence of the cancer which was being treated."

He continued: "Despite treatment, over the weekend a blood clot developed in Mr Farina's lung which unexpectedly and suddenly took his life."

Farina was survived by his three sons and long-time partner Marianne Cahill.

His former Law & Order boss Dick Wolf said that he was "stunned" by Farina's death, and called the actor a "great guy".

Watch a clip of Dennis Farina in Law & Order below:

View all of today's best celebrity pictures:

Celebrity Pictures: 20/07/13 - 26/07/13

Avril Lavigne wears an over-sized knitted jumper, baseball cap and sunglasses as she hops in Beverly Hills. The star recently wed Nickelback singer Chad Kroeger.

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Police officer dies during rescue of hiker outside of Vegas

AP via Las Vegas Metropolitan Police Dept.

Search & rescue officer David Vanbuskirk, 36, died last night, when he fell during the helicopter rescue of a stranded hiker outside of Las Vegas.

By Hannah Dreier, The Associated Press

LAS VEGAS ? A Las Vegas police officer, who was rescuing a hiker stranded in an off-limits area of a mountain northwest of the city, died after falling from a helicopter hoist line Monday night.

At an emotional news conference Tuesday, police offered details about the accident that killed search and rescue officer David Vanbuskirk, 36, at Mount Charleston.

"We're a big family, a close family, and this is going to be trying on us for quite a while," Las Vegas police Assistant Sheriff Joseph Lombardo told reporters shortly after the accident. "We will survive it. We'll come back together, and hopefully in my lifetime, it will never happen again."

Rescuers responded shortly before 9 p.m. to reports that a hiker was disoriented and stranded on a rocky ledge just above Mary Jane Falls. The area was marked with signs warning hikers to stay out or face fines, according to Jay Nichols, spokesman for Spring Mountains National Recreation Area.

Compounding the issue, a wildfire now entering its third week has been burning in the area, and park workers have closed some trails in the interest of public safety.

After landing, Vanbuskirk attached a safety harness to the stranded man, who was hiking alone. He signaled to the four rescue workers in the helicopter above to hoist them both up from the craggy ledge, but then Vanbuskirk somehow detached from the line in midair and fell a "non-survivable" distance to the ground below, officials said.

The hiker was safely rescued and is being interviewed, police said.

The mood was somber among officers, who have not lost one of their own in the line of duty since 2009. Officers Tuesday wore black bands over their badges in honor of their fallen comrade.

The Occupational Safety and Health Administration and other agencies are investigating.

Julie Jacobson, AP

Clark County Sheriff Doug Gillespie gives details about the death of Las Vegas Metropolitan search and rescue police officer David Vanbuskirk during a news conference on Tuesday in Las Vegas.

Vanbuskirk grew up in the Las Vegas area, was married and lived in Henderson. He had worked for the department since 1999, and had served on the search and rescue team since 2007.

Clark County Sheriff Doug Gillespie said Vanbuskirk had performed "dozens" of rescues like the one that killed him Monday. Las Vegas rescue workers have completed 130 helicopter rescues in the past 12 months.

Nevada Gov. Brian Sandoval said Vanbuskirk's death was "a tragic reminder of the dangers our first responders are exposed to on a daily basis."

"His service to his community, state, and country will not be forgotten," Sandoval said in a statement.

On Twitter, U.S. Sen. Dean Heller of Nevada called Vanbuskirk a hero.

Others in the police department also praised him.

"He was an exceptionally fine officer," police spokesman Bill Cassell said.

? 2013 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.

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Thursday, May 30, 2013

Estate Planning Is Important For Your Online Assets, Too

NY Times:

IT'S tough enough to write an ordinary will, deciding how to pass along worldly goods like your savings, your real estate and that treasured rocking chair from Aunt Martha in the living room.

But you may want to provide for your virtual goods, too. Who gets the photographs and the e-mail stored online, the contents of a Facebook account, or that digital sword won in an online game?

Read the whole story at NY Times

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Source: http://www.huffingtonpost.com/2013/05/28/estate-planning-is-import_n_3347190.html

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Monday, May 20, 2013

Childhood ADHD Linked to Obesity in Adulthood

Identification and treatment issues surrounding attention deficit hyperactivity disorder (ADHD) are challenging enough. Now research is shedding light on long-term outcomes for people with ADHD. A recent study in Pediatrics reports that men who had ADHD in childhood are twice as likely to be obese in middle age, even if they no longer exhibit symptoms of ADHD. ADHD is a mental disorder characterized by hyperactivity, impulsivity, inattention and inability to focus. It affects approximately 6.8 percent of U.S. children ages 3 to 17 in any given year, according to a recent report by the CDC. Medications used to treat ADHD, such as Ritalin (methylphenidate) or Adderall (dextroamphetamine and amphetamine), are stimulants that can suppress appetite, however, a couple recent retrospective studies have pointed to a possible increased risk for obesity among adults diagnosed with ADHD as children. The new 33-year prospective study started with 207 healthy middle-class white boys from New York City between 6 and 12 years old, who had been diagnosed with ADHD. When the cohort reached an average age of 18, another 178 healthy boys without ADHD were recruited for comparison. At the most recent follow-up when the participants were an average age of 41, a total of 222 men remained in the study. A troubling pattern emerged: A comparison of the men?s self-reported height and weight revealed that twice as many men with childhood ADHD were obese than those without childhood ADHD. The average body mass index (BMI) of the men with childhood ADHD was 30.1 and 41.4 percent were obese, whereas those without the condition as kids reported an average BMI of 27.6 and an obesity rate of 21.6 percent. The association held even after the researchers controlled for socioeconomic status, depression, anxiety and substance abuse disorders. The results have implications for parents currently raising kids with ADHD. ?Many parents are concerned that their children may not be gaining as much weight as they should because [ADHD] medications can decrease appetite in the short run, but these results would lead me to be much less worried about that now,? says corresponding author F. Xavier Castellanos of the Phyllis Green and Randolph Cowen Institute of Pediatric Neuroscience at NYU Langone Medical Center. ?It helps us to realize that over the long run, the potential risks of obesity, of overeating and of dysregulation, are a more prominent long-term concern.? The study is case-controlled, which means researchers identified participants (cases) with the condition and then matched them to a control population to compare outcomes and look for risk factor differences. Therefore, it cannot prove causation because it?s observational. Only a randomized, controlled trial could show that obesity is caused by ADHD, but it?s impossible to randomize participants to have ADHD, both because it?s unethical and because researchers do not know precisely what causes ADHD. Possible causes could include genetics, nutrition, environmental factors or brain injuries. These findings, however, are similar to results in other studies that have found links between ADHD and obesity. The previous studies, however, were retrospective (relying on participants? recall), did not focus exclusively on ADHD (included other conduct disorders) or compared only men with adult ADHD to men with remitted childhood ADHD, rather than to controls without ADHD. This prospective study is the most long-term and the first to focus exclusively on adult obesity rates in men with childhood ADHD compared to men without childhood ADHD. Its findings therefore contribute to the growing evidence base for an association between obesity and childhood ADHD.? An unclear mechanism A link between obesity and childhood ADHD could be explained by either a neurobiological or a psychological mechanism, the authors proposed. With the former, it is possible that something similar genetically underlies both ADHD and obesity; Castellanos and his colleagues note that dysfunction in the dopamine pathways of the brain have been found among both people who are obese and people with ADHD. As for the psychological mechanism, the impulsive behaviors and diminished inhibitions associated with ADHD ?may foster poor planning and difficulty in monitoring eating behaviors, leading to abnormal eating patterns and consequent obesity,? the team wrote. ?One of the aspects of ADHD is this tendency to focus on ?I want it now? and not waiting for something, not delaying gratification, so we think that may lead people to eat more than they physiologically might need,? Castellanos says. Eating just an extra 100 calories a day than the total burned can easily lead one to accumulate extra pounds. Appetite regulation is complex but usually balances out in healthy individuals?unless they eat when they?re not actually hungry. Some researchers are dubious about both the neurobiological and the psychological explanations. Lawrence Diller, a behavioral developmental pediatrician at the University of California, San Francisco, and author of Remembering Ritalin and Running on Ritalin, says he finds the idea of dysregulation in adulthood unlikely for adults who no longer have symptoms of ADHD. ?The finding is real?no question about it?but the explanations are poor,? says Diller. ?If the ADHD is remitted, then why should the impulsivity and poor judgment still be there?? Of the 111 men with childhood ADHD in this study, 87 no longer had ADHD symptoms (remitted) and 24 still had ADHD (persistent). Those with remitted ADHD had relatively higher obesity rates than the persistent-ADHD men, though the small number of men with persistent ADHD makes it difficult to draw any substantial conclusions about this difference. Diller suggested that the long-term impact of ADHD medication may play a part. ?We know that stimulants very much affect the satiety thermostat in people who take them,? he says. ?There is the question of whether or not the long-term suppression of appetite somehow affects the brain so that when you?re no longer taking the drugs, it takes more [food] to make you feel full.? Diller pointed to research showing that long-term use of ADHD stimulants can lead to an inch or two of lower-than-predicted height in adults, although the adults in this new study showed no significant differences in height. ?That doesn?t mean you shouldn?t take the medicine, but in weighing the pros and cons, it?s one more thing for parents to think about in treatment,? Diller says. ?The idea that impulsivity and poor judgment may play a role is possible, but I think my idea of adjusting the satiety thermostat long-term is just as plausible as theirs.? A different possible mechanism, proposed by Juan Salinas, a lecturer specializing in the neuropharmacology of learning and memory at the University of Texas at Austin, resembles the neurobiological hypothesis, given that ADHD involves a dysfunctional release of dopamine in the brain. ?From more basic research into the neurobiology of reward, it?s suggestive that maybe somehow these people who do not have ADHD anymore may have an alteration in the dopamine pathways, and maybe some of the eating may be a way to self-medicate to increase dopamine release,? Salinas says. ?It?s not so much impulse control, but it?s a self-medicating idea.? The implications of the study, then, Salinas says, are that parents need to train their children with ADHD early to eat healthily, exercise and practice a healthy lifestyle. Another line of thought, proposed by Stephen Hinshaw, a psychology professor specializing in ADHD at the University of California at Berkeley and at San Francisco, extends the poor impulse control hypothesis. ?It?s plausible that there are biological underpinnings of both ADHD and obesity,? he says, ?but the more parsimonious explanation from other research is that ADHD portends problems in self-regulation over time.? In other words, adults who once had ADHD might later be able to sit in a chair and refrain from fidgeting, but emotional and physical regulation issues could linger in the form of less-than-ideal eating habits. 'Devastating? long-term consequences Hinshaw?s own work with ADHD in girls and other research into long-term outcomes support this idea that the challenges of self-regulation may not fade when the outwardly clinical symptoms of hyperactivity do. His 10-year study of 140 girls with ADHD found much higher rates of self-cutting, self-burning and suicide attempts in this group than were found in a control group. Additionally, he says, recent research has found high levels of unemployment and underemployment and poorer work productivity among adults who had childhood ADHD than among those who did not. The men with childhood ADHD in the new study also had significantly lower socioeconomic status than those in the control group, even though the groups had been matched initially for parental socioeconomic status and geography. ?ADHD still gets ridiculed in the press?saying it?s a made-up disease or that we just don?t tolerate fidgety kids?but it has really devastating long-term consequences, and we have to take it seriously,? Hinshaw says. Rising rates of ADHD diagnoses could be related to both improved health care access for more children and possible misdiagnoses due to the inadequate time spent on assessments in pediatricians? offices. ?We need to insist upon a much higher level of diagnosis and evaluation so that we?re really sure that it?s ADHD and not maltreatment or family conflict or normal-range behavior,? Hinshaw says. For those who really suffer from ADHD, this study provides more evidence of the challenges those children will face in adulthood. ?ADHD has staying power,? he says, ?regardless of whether the symptoms on the surface improve or not.?? Follow Scientific American on Twitter @SciAm and @SciamBlogs. Visit ScientificAmerican.com for the latest in science, health and technology news.
? 2013 ScientificAmerican.com. All rights reserved.

Source: http://news.yahoo.com/childhood-adhd-linked-obesity-adulthood-090000730.html

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Math Trek: One of the most abstract fields in math finds application in the 'real' world

By Julie Rehmeyer

Web edition: May 20, 2013

Every pure mathematician has experienced that awkward moment when asked, ?So what?s your research good for?? There are standard responses: a proud ?Nothing!?; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding application that maybe, perhaps, someday, it will turn out to be useful.

That last possibility is now proving itself to be dramatically true in the case of category theory, perhaps the most abstract area in all of mathematics. Where math is an abstraction of the real world, category theory is an abstraction of mathematics: It describes the architectural structure of any mathematical field, independent of the specific kind of mathematical object being considered. Yet somehow, what is in a sense the purest of all pure math is now being used to describe areas throughout the sciences and beyond, in computer science, quantum physics, biology, music, linguistics and philosophy.

Samuel Eilenberg of Columbia University and Saunders Mac Lane of the University of Chicago developed category theory in the 1940s to build a bridge between abstract algebra (the generalization of high school algebra) and topology (the qualitative study of shapes, including those in very high dimensions). Very similar arguments repeatedly cropped up in the two fields in different contexts, so the mathematicians reasoned that some deeper structure must unite these situations.

They created an organizing framework that any field of mathematics could be put in. A ?category? is a collection of mathematical objects together with arrows connecting them. So, for example, the natural numbers are the objects of a category, and one particular arrow in that category would connect each number to its double. Eilenberg and Mac Lane could then analyze maps between entire categories, and maps between those maps. This allowed the connections between different fields of mathematics to be formulated precisely.

Mathematicians sardonically dubbed the field ?abstract nonsense.? Its extreme level of abstraction drains all the content out of the theory, since the objects can represent nearly anything. Draining the content, many expected, would also drain its power: What can anyone possibly say that will apply to essentially all mathematical objects?

Surprisingly, a lot. The recurrent arguments that had spurred the theory were ones that applied to all categories. Eilenberg and Mac Lane?s framework revealed an entire world of theorems that could be applied throughout mathematics.

Logicians started using category theory, viewing a deduction of one theorem from another as an arrow connecting the two. Then computer scientists carried category theory further still, viewing programs as maps connecting input of one category to output of another. A program that multiplies two numbers, for example, would go from the category of pairs of numbers (the numbers being multiplied) to the category of numbers (their product).

These connections turned out to be extraordinarily deep ? indeed, the theory of programming languages and the field of logic can be seen as essentially identical to category theory. Computer scientist Robert Harper of Carnegie Mellon University jokingly calls this ?computational trinitarianism,? imitating the Christian notion that God is a trinity of Father, Son and Holy Ghost.

?The central dogma of computational trinitarianism,? he wrote on his blog, ?holds that Logic, Languages, and Categories are but three manifestations of one divine notion of computation.? There is no preferred route to enlightenment: each aspect provides insights that comprise the experience of computation in our lives. Computational trinitarianism entails that any concept arising in one aspect should have meaning from the perspective of the other two.? Porting ideas between the fields has led to profound insights for all three.

Category theory?s spread has continued. Many results in quantum information theory turn out to follow directly from category theory. Category theory?s hierarchical structure has made it useful for modeling complex biological systems. Category theoretic models of language have outperformed conventional ones in distinguishing, for example, the meaning of ?saw? in sentences like ?I saw a man with a saw.? It?s even proving valuable in developing rigorous models of music theory.

David Spivak of MIT has perhaps the boldest vision for category theory?s potential. In a paper posted February 27 on arXiv.org, he argues that all scientific thought can be expressed in a structured way using category theory. Both ideas and the data supporting them can be encoded in the universal language of category theory, allowing scientists to present a database with their full work. Spivak even imagines a Facebook-like interface with people?s full thoughts and experiences presented in a category theoretic database that would connect people whose databases overlap.

?If people adopt the level of rigor of category theory,? he says, ?it will provide a precise language for science as a whole, and it will help individual scientists to clarify their thinking. My ultimate dream is that communication problems would only happen because someone is trying to lie.??

Source: http://www.sciencenews.org/view/generic/id/350567/title/One_of_the_most_abstract_fields_in_math_finds_application_in_the_real_world

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