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National Baseball Hall of Fame and Museum

The National Baseball Hall of Fame and Museum is a history museum and hall of fame in Cooperstown, New York, operated by private interests. It serves as the central point of the history of baseball in the United States and displays baseball-related artifacts and exhibits, honoring those who have excelled in playing, managing, and serving the sport. The Hall's motto is "Preserving History, Honoring Excellence, Connecting Generations". Cooperstown is often used as shorthand (or a metonym) for the National Baseball Hall of Fame and Museum.

The Hall of Fame was established in 1939 by Stephen Carlton Clark, an heir to the Singer Sewing Machine fortune. Clark sought to bring tourists to the village hurt by the Great Depression, which reduced the local tourist trade, and Prohibition, which devastated the local hops industry. Clark constructed the Hall of Fame's building, which was dedicated on June 12, 1939. (His granddaughter, Jane Forbes Clark, is the current chairman of the board of directors.) The erroneous claim that Civil War hero Abner Doubleday invented baseball in Cooperstown was instrumental in the early marketing of the Hall.

An expanded library and research facility opened in 1994. Dale Petroskey became the organization's president in 1999. In 2002, the Hall launched Baseball as America, a traveling exhibit that toured ten American museums over six years. The Hall of Fame has since also sponsored educational programming on the Internet to bring the Hall of Fame to schoolchildren who might not visit. The Hall and Museum completed a series of renovations in spring 2005. The Hall of Fame also presents an annual exhibit at FanFest at the Major League Baseball All-Star Game.

Inductees
Among baseball fans, "Hall of Fame" means not only the museum and facility in Cooperstown, New York, but the pantheon of players, managers, umpires, executives, and pioneers who have been inducted into the Hall. The first five men elected were Ty Cobb, Babe Ruth, Honus Wagner, Christy Mathewson and Walter Johnson, chosen in 1936; roughly 20 more were selected before the entire group was inducted at the Hall's 1939 opening. , 343 people had been elected to the Hall of Fame, including 241 former Major League Baseball players, 39 Negro league baseball players and executives, 23 managers, 10 umpires, and 36 pioneers, executives, and organizers. One hundred eighteen members of the Hall of Fame have been inducted posthumously, including four who died after their selection was announced. Of the 39 Negro league members, 31 were inducted posthumously, including all 26 selected since the 1990s. The Hall of Fame includes one female member, Effa Manley.

The newest members, soon to be inducted on July 21, 2024, are Adrián Beltré, Todd Helton, Jim Leyland, and Joe Mauer.

In 2019, former Yankees closer Mariano Rivera became the first player to be elected unanimously. Derek Jeter, Marvin Miller, Ted Simmons, and Larry Walker were to be inducted in 2020, but their induction ceremony was delayed by the COVID-19 pandemic until September 8, 2021. The ceremony was open to the public, as COVID restrictions had been lifted.

Selection process
Players are currently inducted into the Hall of Fame through election by either the Baseball Writers' Association of America (or BBWAA), or the Veterans Committee, which now consists of four subcommittees, each of which considers and votes for candidates from a separate era of baseball. Five years after retirement, any player with 10 years of major league experience who passes a screening committee (which removes from consideration players of clearly lesser qualification) is eligible to be elected by BBWAA members with 10 years' membership or more who also have been actively covering MLB at any time in the 10 years preceding the election (the latter requirement was added for the 2016 election). From a final ballot typically including 25–40 candidates, each writer may vote for up to 10 players; until the late 1950s, voters were advised to cast votes for the maximum 10 candidates. Any player named on 75% or more of all ballots cast is elected. A player who is named on fewer than 5% of ballots is dropped from future elections. In some instances, the screening committee had restored their names to later ballots, but in the mid-1990s, dropped players were made permanently ineligible for Hall of Fame consideration, even by the Veterans Committee. A 2001 change in the election procedures restored the eligibility of these dropped players; while their names will not appear on future BBWAA ballots, they may be considered by the Veterans Committee. Players receiving 5% or more of the votes but fewer than 75% are reconsidered annually until a maximum of ten years of eligibility (lowered from fifteen years for the 2015 election).

Under special circumstances, certain players may be deemed eligible for induction even though they have not met all requirements. Addie Joss was elected in 1978, despite only playing nine seasons before he died of meningitis. Additionally, if an otherwise eligible player dies before his fifth year of retirement, then that player may be placed on the ballot at the first election at least six months after his death. Roberto Clemente set the precedent: the writers put him up for consideration after his death on New Year's Eve, 1972, and he was inducted in 1973.

The five-year waiting period was established in 1954 after an evolutionary process. In 1936 all players were eligible, including active ones. From the 1937 election until the 1945 election, there was no waiting period, so any retired player was eligible, but writers were discouraged from voting for current major leaguers. Since there was no formal rule preventing a writer from casting a ballot for an active player, the scribes did not always comply with the informal guideline; Joe DiMaggio received a vote in 1945, for example. From the 1946 election until the 1954 election, an official one-year waiting period was in effect. (DiMaggio, for example, retired after the 1951 season and was first eligible in the 1953 election.) The modern rule establishing a wait of five years was passed in 1954, although those who had already been eligible under the old rule were grandfathered into the ballot, thus permitting Joe DiMaggio to be elected within four years of his retirement.

Contrary to popular belief, no formal exception was made for Lou Gehrig (other than to hold a special one-man election for him): there was no waiting period at that time, and Gehrig met all other qualifications, so he would have been eligible for the next regular election after he retired during the 1939 season. However, the BBWAA decided to hold a special election at the 1939 Winter Meetings in Cincinnati, specifically to elect Gehrig (most likely because it was known that he was terminally ill, making it uncertain that he would live long enough to see another election). Nobody else was on that ballot, and the numerical results have never been made public. Since no elections were held in 1940 or 1941, the special election permitted Gehrig to enter the Hall while still alive.

If a player fails to be elected by the BBWAA within 10 years of his eligibility for election, he may be selected by the Veterans Committee. Following changes to the election process for that body made in 2010 and 2016, the Veterans Committee is now responsible for electing all otherwise eligible candidates who are not eligible for the BBWAA ballot — both long-retired players and non-playing personnel (managers, umpires, and executives). From 2011 to 2016, each candidate could be considered once every three years; now, the frequency depends on the era in which an individual made his greatest contributions. A more complete discussion of the new process is available below.

From 2008 to 2010, following changes made by the Hall in July 2007, the main Veterans Committee, then made up of living Hall of Famers, voted only on players whose careers began in 1943 or later. These changes also established three separate committees to select other figures:
 * One committee voted on managers and umpires for induction in every even-numbered year. This committee voted only twice—in 2007 for induction in 2008 and in 2009 for induction in 2010.
 * One committee voted on executives and builders for induction in every even-numbered year. This committee conducted its only two votes in the same years as the managers/umpires committee.
 * The pre–World War II players committee was intended to vote every five years on players whose careers began in 1942 or earlier. It conducted its only vote as part of the election process for induction in 2009.

Players of the Negro leagues have also been considered at various times, beginning in 1971. In 2005, the Hall completed a study on African American players between the late 19th century and the integration of the major leagues in 1947, and conducted a special election for such players in February 2006; seventeen figures from the Negro leagues were chosen in that election, in addition to the eighteen previously selected. Following the 2010 changes, Negro leagues figures were primarily considered for induction alongside other figures from the 1871–1946 era, called the "Pre-Integration Era" by the Hall; since 2016, Negro leagues figures are primarily considered alongside other figures from what the Hall calls the "Early Baseball" era (1871–1949).

Predictably, the selection process catalyzes endless debate among baseball fans over the merits of various candidates. Even players elected years ago remain the subjects of discussions as to whether they deserved election. For example, Bill James' 1994 book Whatever Happened to the Hall of Fame? goes into detail about who he believes does and does not belong in the Hall of Fame.

Non-induction of banned players
The selection rules for the Baseball Hall of Fame were modified to prevent the induction of anyone on Baseball's "permanently ineligible" list, such as Pete Rose or "Shoeless Joe" Jackson. Many others have been barred from participation in MLB, but none have Hall of Fame qualifications on the level of Jackson or Rose.

Jackson and Rose were both banned from MLB for life for actions related to gambling on their own teams—Jackson was determined to have cooperated with those who conspired to intentionally lose the 1919 World Series, and for accepting payment for losing, and Rose voluntarily accepted a permanent spot on the ineligible list in return for MLB's promise to make no official finding in relation to alleged betting on the Cincinnati Reds when he was their manager in the 1980s. (Baseball's Rule 21, prominently posted in every clubhouse locker room, mandates permanent banishment from MLB for having a gambling interest of any sort on a game in which a player or manager is directly involved.) Rose later admitted that he bet on the Reds in his 2004 autobiography. Baseball fans are deeply split on the issue of whether these two should remain banned or have their punishment revoked. Writer Bill James, though he advocates Rose eventually making it into the Hall of Fame, compared the people who want to put Jackson in the Hall of Fame to "those women who show up at murder trials wanting to marry the cute murderer".

Changes to Veterans Committee process
The actions and composition of the Veterans Committee have been at times controversial, with occasional selections of contemporaries and teammates of the committee members over seemingly more worthy candidates.

In 2001, the Veterans Committee was reformed to comprise the living Hall of Fame members and other honorees. The revamped Committee held three elections, in 2003 and 2007, for both players and non-players, and in 2005 for players only. No individual was elected in that time, sparking criticism among some observers who expressed doubt whether the new Veterans Committee would ever elect a player. The Committee members, most of whom were Hall members, were accused of being reluctant to elect new candidates in the hope of heightening the value of their own selection. After no one was selected for the third consecutive election in 2007, Hall of Famer Mike Schmidt noted, "The same thing happens every year. The current members want to preserve the prestige as much as possible, and are unwilling to open the doors." In 2007, the committee and its selection processes were again reorganized; the main committee then included all living members of the Hall, and voted on a reduced number of candidates from among players whose careers began in 1943 or later. Separate committees, including sportswriters and broadcasters, would select umpires, managers and executives, as well as players from earlier eras.

In the first election to be held under the 2007 revisions, two managers and three executives were elected in December 2007 as part of the 2008 election process. The next Veterans Committee elections for players were held in December 2008 as part of the 2009 election process; the main committee did not select a player, while the panel for pre–World War II players elected Joe Gordon in its first and ultimately only vote. The main committee voted as part of the election process for inductions in odd-numbered years, while the pre-World War II panel would vote every five years, and the panel for umpires, managers, and executives voted as part of the election process for inductions in even-numbered years.

Further changes to the Veterans Committee process were announced by the Hall in July 2010, July 2016, and April 2022.

Current structure
Per the latest changes, announced on April 22, 2022, the multiple eras previously utilized were collapsed to three, to be voted on in an annual rotation (one per year): A one-year waiting period beyond potential BBWAA eligibility (which had been abolished in 2016) was reintroduced, thus restricting the committee to considering players retired for at least 16 seasons.
 * Contemporary Baseball Era (1980–present) players
 * Contemporary Baseball Era (1980–present) non-players (managers, executives, and umpires)
 * Classic Baseball Era (prior to 1980)

Eligibility
The eligibility criteria for Era Committee consideration differ between players, managers, and executives.
 * Players: When a player is no longer eligible on the BBWAA ballot (either 15 years after retirement—five-year period and the 10 years after he first becomes eligible to appear on the BBWAA ballot or when the player is not eligible after earning less than five percent of the BBWAA ballot during a year), he will be considered by the respective committee.
 * The Hall has not yet established a policy on when players who die while active or during the standard five-year waiting period for BBWAA eligibility will be eligible for committee consideration. As noted earlier, such players become eligible for the BBWAA ballot six months after their deaths.
 * Managers and umpires who have served at least 10 seasons in that role are eligible five years after retirement, unless they are 65 or older, in which case the waiting period is six months.
 * Executives are eligible five years after retirement, or upon reaching age 70. For those who meet the age cutoff, they are explicitly eligible for consideration regardless of their current position in an organization or their status as active or retired. Before the 2016 changes to the committee system, active executives 65 years or older were eligible for consideration.

Players and managers with multiple teams
While the text on a player's or manager's plaque lists all teams for which the inductee was a member in that specific role, inductees are usually depicted wearing the cap of a specific team, though in a few cases, like umpires, they wear caps without logos. (Executives are not depicted wearing caps.) Additionally, as of 2015, inductee biographies on the Hall's website for all players and managers, and executives who were associated with specific teams, list a "primary team", which does not necessarily match the cap logo. The Hall selects the logo "based on where that player makes his most indelible mark."

Although the Hall always made the final decision on which logo was shown, until 2001 the Hall deferred to the wishes of players or managers whose careers were linked with multiple teams. Some examples of inductees associated with multiple teams are the following:
 * Frank Robinson: Robinson chose to have the Baltimore Orioles cap displayed on his plaque, although he had played ten seasons with the Cincinnati Reds and six seasons with Baltimore. Robinson won four pennants and two World Series with the Orioles and one pennant with Cincinnati. His second World Series ring came in the 1970 World Series against the Reds. Robinson also won an MVP award while playing for each team.
 * Catfish Hunter: Hunter chose not to have any logo on his cap when elected to the Hall of Fame in 1987. Hunter had success for both teams for which he played – the Kansas City/Oakland Athletics (his first ten seasons) and the New York Yankees (his final five seasons). Furthermore, both during and after his career he maintained good relations with both teams and their respective owners (Charles Finley and George Steinbrenner), and did not wish to slight either team by selecting the other.
 * Nolan Ryan: Born and raised in Texas, Ryan entered the Hall in 1999 wearing a Texas Rangers cap on his plaque, although he spent only five seasons with the Rangers, while raised in the Houston area and having longer and more successful tenures with the Houston Astros (nine seasons, 1980–88 and his record-setting fifth career no-hitter) and California Angels (eight seasons, 1972–79 and the first four of his seven career no-hitters). Ryan's only championship was as a member of the New York Mets in 1969. Ryan finished his career with the Rangers, reaching his 5,000th strikeout and 300th win, and throwing the last two of his no-hitters. He had personally chosen the Rangers due to these figures as well as because Texas encompasses the city of Houston, thereby representing both teams. Despite this, his biography on the Hall's website lists his primary team as the Angels. Ryan later took ownership of the Rangers when they were sold to his Rangers Baseball Express group in 2010. He sold his Rangers interest in 2013. From 2014 to 2019, Nolan was in the Astros' front office as a special assistant. In 2020 Ryan discontinued his executive role with the Astros. The minor-league team in which he has an ownership interest, the Round Rock Express of Round Rock, Texas outside of Austin, will be the AAA franchise of the Texas Rangers.
 * Reggie Jackson: Jackson chose to be depicted with a Yankees cap over an Athletics cap. As a member of the Kansas City/Oakland A's, Jackson played ten seasons (1967–75, '87), winning three World Series (1972, 1973, 1974) and the 1973 AL MVP Award. During his five years in New York (1977–81), Jackson won two World Series (1977–78), with his crowning achievement occurring during Game Six of the 1977 World Series, when he hit three home runs on consecutive pitches and earned his nickname "Mr. October".
 * Carlton Fisk: Fisk went into the hall with a Boston Red Sox cap on his plaque in 2000 despite having played with the Chicago White Sox longer and posting more significant numbers with the White Sox. Fisk's choice of the Red Sox was likely due to his being a New England native, as well as his famous "Stay fair!" walk-off home run in Game Six of the 1975 World Series for which he is most associated.
 * Sparky Anderson: Also in 2000, Anderson entered the Hall with a Cincinnati Reds cap on his plaque despite managing almost twice as many seasons with the Detroit Tigers (17 in Detroit; nine in Cincinnati). He chose the Reds to honor that team's former general manager Bob Howsam, who gave him his first major-league managing job. Anderson won two World Series with the Reds and one with the Tigers.
 * Dave Winfield: Winfield had spent the most years in his career with the Yankees and had great success there, though he chose to go into the Hall as a member of the San Diego Padres due to his feud with Yankees owner George Steinbrenner.

In all of the above cases, the "primary team" is the team for which the inductee spent the largest portion of his career except for Ryan, whose primary team is listed as the Angels despite playing one fewer season for that team than for the Astros.

In 2001, the Hall of Fame decided to change the policy on cap logo selection, as a result of rumors that some teams were offering compensation, such as number retirement, money, or organizational jobs, in exchange for the cap designation. (For example, though Wade Boggs denied the claims, some media reports had said that his contract with the Tampa Bay Devil Rays required him to request depiction in the Hall of Fame as a Devil Ray.) The Hall decided that it would no longer defer to the inductee, though the player's wishes would be considered, when deciding on the logo to appear on the plaque. Newly elected members affected by the change include the following:
 * Gary Carter: Inducted in 2003, Carter was the first player to be affected by the new policy. Carter won his only championship with the 1986 New York Mets, and wanted his induction plaque to depict him wearing a Mets cap, though he had spent twelve years (1974–84, 1992) with the Montreal Expos and five (1985–89) with the Mets. The Hall of Fame decided that Carter's impact on the Montreal franchise warranted depicting him with an Expos cap.
 * Wade Boggs: Boggs's only title was as a member of the 1996 New York Yankees, for whom he played from 1993 to 1997, but his best career numbers were posted during his 11 years (1982–92) with the Boston Red Sox. Boggs would eventually be depicted wearing a Boston cap for his 2005 induction.
 * Andre Dawson: Dawson's cap depicts him as a member of the Expos, his team for eleven years, despite his expressed preference to be shown as a member of the Chicago Cubs. While Dawson played only six years with the Cubs, five of his eight All-Star appearances were as a Cub, and his only MVP award came in his first year with the team in 1987.
 * Tony La Russa: Manager La Russa chose not to have a logo after managing three teams over 33 years—the Chicago White Sox, Oakland Athletics, and St. Louis Cardinals. His greatest successes were with the A's (three pennants and a World Series title in 10 years) and Cardinals (three pennants and two World Series in 16 years). Nonetheless, La Russa felt that his induction to the Hall was due to his tenures with all three teams, and stated that not including a logo meant that "fans of all [three] clubs can celebrate this honor with me." La Russa's biography on the Hall's website lists his primary team as the Cardinals.
 * Greg Maddux: Although Maddux had his greatest success while with the Atlanta Braves for 11 seasons, he had two stints with the Chicago Cubs for a total of 10 seasons, including the first seven of his MLB career. Maddux believed that both fanbases were equally important in his career, and so the cap on his plaque does not feature any logo. His biography on the Hall's website lists his primary team as the Braves.
 * Randy Johnson: Johnson played for six teams in a 22-year career, but spent the bulk of it with the Seattle Mariners (10 seasons) and Arizona Diamondbacks (8 seasons). While enjoying great success with both teams, he had more significant honors with the Diamondbacks. Four of Johnson's five Cy Young Awards (consecutively from 1999 to 2002), his only title (in 2001), his pitching triple crown (2002), and his perfect game (2004) all came with Arizona. Accordingly, he and the Hall agreed his plaque should feature a Diamondbacks logo. His biography on the Hall's website lists his primary team as the Mariners.
 * Vladimir Guerrero: Guerrero played the majority of his career with the Montreal Expos, spending eight of his sixteen seasons with the team. However, he recorded the majority of his success during his time with the Angels, including five out of his nine All-Star selections, his MVP award, four out of his eight Silver Slugger awards, and all five of his playoff berths. Guerrero ultimately had an Angels logo on his plaque, becoming the only member of the team to have as such. His biography on the Hall's website lists his primary team as the Expos.
 * Mike Mussina, who played 10 seasons with the Baltimore Orioles and eight seasons with the New York Yankees, decided to go into the Hall without a logo on his plaque, saying "I don't feel like I can pick one team over the other because they were both great to me. I did a lot in Baltimore and they gave me the chance and then in New York we went to the playoffs seven of eight years, and both teams were involved. To go in with no logo was the only decision I felt good about". Mussina's biography at the Hall lists his primary team as the Orioles.
 * Roy Halladay was posthumously elected to the Hall on January 22, 2019, in his first year of eligibility, garnering 85.4 percent of the vote. Halladay was a six-time All-Star and won a Cy Young award with the Toronto Blue Jays from 1998 to 2009, and then was a two-time All-Star and won a Cy Young award with the Philadelphia Phillies over his final four seasons. He spent 12 of his 16 MLB seasons with the Blue Jays and earned 148 of his 203 victories with them, although his team never reached the playoffs. For the Phillies, he threw a perfect game and a postseason no-hitter, though his final two seasons were injury-plagued. Halladay was quoted as saying after he retired in 2013 that he'd like to enter the Hall of Fame as a Blue Jay, and he signed a ceremonial contract to retire with Toronto. However, he died in a plane crash on November 7, 2017. The Hall deferred to the wishes of his wife and sons who chose not to have a logo for his cap, which leaves Roberto Alomar as the sole Cooperstown inductee as a Blue Jay.  Halladay's biography on the Hall's website lists his primary team as the Blue Jays.

The museum
Sam Crane (who had played a decade in 19th century baseball before becoming a manager and sportswriter) had first approached the idea of making a memorial to the great players of the past in what was believed to have been the birthplace of baseball: Cooperstown, New York, but the idea did not muster much momentum until after his death in 1925. In 1934, the idea for establishing a Baseball Hall of Fame and Museum was devised by several individuals, such as Ford Frick (president of the National League) and Alexander Cleland, a Scottish immigrant who decided to serve as the first executive secretary for the Museum for the next seven years that worked with the interests of the Village and Major League Baseball. Stephen Carlton Clark (a Cooperstown native) paid for the construction of the museum, which was planned to open in 1939 to mark the "Centennial of Baseball", which included renovations to Doubleday Field. William Beattie served as the first curator of the museum.

According to the Hall of Fame, approximately 260,000 visitors enter the museum each year, and the running total has surpassed 17 million. These visitors see only a fraction of its 40,000 artifacts, 3 million library items (such as newspaper clippings and photos) and 140,000 baseball cards.

The Hall has seen a noticeable decrease in attendance in recent years. A 2013 story on ESPN.com about the village of Cooperstown and its relation to the game partially linked the reduced attendance with Cooperstown Dreams Park, a youth baseball complex about 5 mi away in the town of Hartwick. The 22 fields at Dreams Park currently draw 17,000 players each summer for a week of intensive play; while the complex includes housing for the players, their parents and grandparents must stay elsewhere. According to the story,

"Prior to Dreams Park, a room might be filled for a week by several sets of tourists. Now, that room will be taken by just one family for the week, and that family may only go into Cooperstown and the Hall of Fame once. While there are other contributing factors (the recession and high gas prices among them), the Hall's attendance has tumbled since Dreams Park opened. The Hall drew 383,000 visitors in 1999. It drew 262,000 last year."

First floor

 * Baseball at the Movies houses baseball movie memorabilia while a screen shows footage from those movies.
 * The Bullpen Theater is the site of daily programming at the museum (trivia games, book discussions, etc.) and is decorated with pictures of famous relief pitchers.
 * Inductee Row features images of Hall of Famers inducted from 1937 to 1939.
 * The Perez-Steele Art Gallery features art of all media related to baseball. Dick Perez served as an artist for various projects at the National Baseball Hall of Fame and Museum for 20 years, starting in 1981
 * The Plaque Gallery, the most recognizable site at the museum, contains induction plaques of all members. Since 2016, sculptor Tom Tsuchiya has been creating the bas-relief likeness plaques due to a commission from Matthews International.
 * The Sandlot Kids Clubhouse has various interactive displays for young children.
 * Scribes and Mikemen honors BBWAA Career Excellence Award and Ford C. Frick Award winners with a photo display and has artifacts related to baseball writing and broadcasting. Floor-to-ceiling windows at the Scribes and Mikemen exhibit face an outdoor courtyard with statues of Johnny Podres and Roy Campanella (representing the Brooklyn Dodgers 1955 championship team), and an unnamed All-American Girls Professional Baseball League player. A Satchel Paige statue was unveiled and dedicated during the 2006 Induction Weekend.
 * An Education Gallery hosts school groups and, in the summer, presentations about artifacts from the museum's collection.

Second floor

 * The Grandstand Theater features a 12-minute multimedia film. The 200-seat theater, complete with replica stadium seats, is decorated to resemble old Comiskey Park.
 * The Game is the major feature of the second floor. It is where the most artifacts are displayed. The Game is set up in a timeline format, starting with baseball's beginnings and culminating with the game we know today. There are several offshoots of this meandering timeline:
 * The Babe Ruth Room
 * Diamond Dreams (women in baseball)
 * ¡Viva Baseball! (a bilingual exhibit, in English and Spanish, that celebrates baseball in Latin America)
 * Pride and Passion (Negro leagues exhibit)
 * Taking The Field (19th century baseball)
 * Whole New Ballgame, the Museum's newest permanent exhibit, opened in 2015 and is located in the Janetschek Gallery. This exhibit completes the timeline of baseball through the last 45 years into the game we know today. It features environmental video walls and new interactive elements to go along with artifacts from the Museum's collection.
 * The Today's Game exhibit is built like a baseball clubhouse, with 30 glass-enclosed locker stalls, one for each Major League franchise. In each stall there is a jersey and other items from the designated big league team, along with a brief team history. A center display case holds objects donated to the Hall of Fame from the past year or two. Fans can also look into a room designed to look like a manager's office. Outside is a display case with rotating artifacts. Currently the space is devoted to the World Baseball Classic.

Third floor

 * Autumn Glory is devoted to post-season baseball and has, among other artifacts, replicas of World Series rings.
 * Hank Aaron: Chasing the Dream
 * A theater area continually plays the popular Abbott and Costello routine "Who's on First?"
 * One for the Books tells the story of baseball's most cherished records through more than 200 artifacts. The exhibit allows fans to search records dating back through baseball history via an interactive Top Ten Tower while giving visitors a look at exciting moments throughout the years via a multimedia wall.
 * BBWAA awards: Replicas of various awards distributed by the BBWAA at the end of each season, along with a list of past winners.
 * A case dedicated to Ichiro Suzuki setting the major league record for base hits in a single season, with 262 in 2004, after George Sisler had held the record for 84 years with 257.
 * A case full of World Series rings from prior years from the 1900s to present.
 * An inductee database touch-screen computer with statistics for every inductee.
 * Programs from every World Series.
 * Sacred Ground is devoted entirely to ballparks and everything about them, especially the fan experience and the business of a ballpark. The centerpiece is a computer tour of three former ballparks: Boston's South End Grounds, Chicago's Comiskey Park, and Brooklyn's Ebbets Field.

1982 unauthorized sales
A controversy erupted in 1982, when it emerged that some historic items given to the Hall had been sold on the collectibles market. The items had been lent to the Baseball Commissioner's office, gotten mixed up with other property owned by the Commissioner's office and employees of the office, and moved to the garage of Joe Reichler, an assistant to Commissioner Bowie Kuhn, who sold the items to resolve his personal financial difficulties. Under pressure from the New York Attorney General, the Commissioner's Office made reparations, but the negative publicity damaged the Hall of Fame's reputation, and made it more difficult for it to solicit donations.

2014 commemorative coins

In 2012, Congress passed and President Barack Obama signed a law ordering the United States Mint to produce and sell commemorative, non-circulating coins to benefit the private, non-profit Hall. The bill,, was introduced in the United States House of Representatives by Rep. Richard Hanna, a Republican from New York, and passed the House on October 26, 2011. The coins, which depict baseball gloves and balls, are the first concave designs produced by the Mint. The mintage included 50,000 gold coins, 400,000 silver coins, and 750,000 clad (nickel-copper) coins. The Mint released them on March 27, 2014, and the gold and silver editions quickly sold out. The Hall receives money from surcharges included in the sale price: a total of $9.5 million if all the coins are sold.


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BPP (complexity)

In computational complexity theory, a branch of computer science, bounded-error probabilistic polynomial time (BPP) is the class of decision problems solvable by a probabilistic Turing machine in polynomial time with an error probability bounded by 1/3 for all instances. BPP is one of the largest practical classes of problems, meaning most problems of interest in BPP have efficient probabilistic algorithms that can be run quickly on real modern machines. BPP also contains  P, the class of problems solvable in polynomial time with a deterministic machine, since a deterministic machine is a special case of a probabilistic machine.

Informally, a problem is in BPP if there is an algorithm for it that has the following properties:
 * It is allowed to flip coins and make random decisions
 * It is guaranteed to run in polynomial time
 * On any given run of the algorithm, it has a probability of at most 1/3 of giving the wrong answer, whether the answer is YES or NO.

Definition
A language L is in BPP if and only if there exists a probabilistic Turing machine M, such that Unlike the complexity class ZPP, the machine M is required to run for polynomial time on all inputs, regardless of the outcome of the random coin flips.
 * M runs for polynomial time on all inputs
 * For all x in L, M outputs 1 with probability greater than or equal to 2/3
 * For all x not in L, M outputs 1 with probability less than or equal to 1/3

Alternatively, BPP can be defined using only deterministic Turing machines. A language L is in BPP if and only if there exists a polynomial p and deterministic Turing machine M, such that In this definition, the string y corresponds to the output of the random coin flips that the probabilistic Turing machine would have made. For some applications this definition is preferable since it does not mention probabilistic Turing machines.
 * M runs for polynomial time on all inputs
 * For all x in L, the fraction of strings y of length p(|x|) which satisfy $M(x,y) = 1$ is greater than or equal to 2/3
 * For all x not in L, the fraction of strings y of length p(|x|) which satisfy $M(x,y) = 1$ is less than or equal to 1/3

In practice, an error probability of 1/3 might not be acceptable, however, the choice of 1/3 in the definition is arbitrary. Modifying the definition to use any constant between 0 and 1/2 (exclusive) in place of 1/3 would not change the resulting set BPP. For example, if one defined the class with the restriction that the algorithm can be wrong with probability at most 1/2100, this would result in the same class of problems. The error probability does not even have to be constant: the same class of problems is defined by allowing error as high as 1/2 − n−c on the one hand, or requiring error as small as 2−n c on the other hand, where c is any positive constant, and n is the length of input. This flexibility in the choice of error probability is based on the idea of running an error-prone algorithm many times, and using the majority result of the runs to obtain a more accurate algorithm. The chance that the majority of the runs are wrong drops off exponentially as a consequence of the Chernoff bound.

Problems
All problems in P are obviously also in BPP. However, many problems have been known to be in BPP but not known to be in P. The number of such problems is decreasing, and it is conjectured that P = BPP.

For a long time, one of the most famous problems known to be in BPP but not known to be in P was the problem of determining whether a given number is prime. However, in the 2002 paper PRIMES is in P, Manindra Agrawal and his students Neeraj Kayal and Nitin Saxena found a deterministic polynomial-time algorithm for this problem, thus showing that it is in P.

An important example of a problem in BPP (in fact in co-RP) still not known to be in P is polynomial identity testing, the problem of determining whether a polynomial is identically equal to the zero polynomial, when you have access to the value of the polynomial for any given input, but not to the coefficients. In other words, is there an assignment of values to the variables such that when a nonzero polynomial is evaluated on these values, the result is nonzero? It suffices to choose each variable's value uniformly at random from a finite subset of at least d values to achieve bounded error probability, where d is the total degree of the polynomial.

Related classes
If the access to randomness is removed from the definition of BPP, we get the complexity class P. In the definition of the class, if we replace the ordinary Turing machine with a quantum computer, we get the class BQP.

Adding postselection to BPP, or allowing computation paths to have different lengths, gives the class BPPpath. BPPpath is known to contain NP, and it is contained in its quantum counterpart PostBQP.

A Monte Carlo algorithm is a randomized algorithm which is likely to be correct. Problems in the class BPP have Monte Carlo algorithms with polynomial bounded running time. This is compared to a Las Vegas algorithm which is a randomized algorithm which either outputs the correct answer, or outputs "fail" with low probability. Las Vegas algorithms with polynomial bound running times are used to define the class ZPP. Alternatively, ZPP contains probabilistic algorithms that are always correct and have expected polynomial running time. This is weaker than saying it is a polynomial time algorithm, since it may run for super-polynomial time, but with very low probability.

Complexity-theoretic properties

It is known that BPP is closed under complement; that is, BPP = co-BPP. BPP is low for itself, meaning that a BPP machine with the power to solve BPP problems instantly (a BPP oracle machine) is not any more powerful than the machine without this extra power. In symbols, BPPBPP = BPP.

The relationship between BPP and NP is unknown: it is not known whether BPP is a subset of NP, NP is a subset of BPP or neither. If NP is contained in BPP, which is considered unlikely since it would imply practical solutions for NP-complete problems, then NP = RP and PH ⊆ BPP.

It is known that RP is a subset of BPP, and BPP is a subset of PP. It is not known whether those two are strict subsets, since we don't even know if P is a strict subset of PSPACE. BPP is contained in the second level of the polynomial hierarchy and therefore it is contained in PH. More precisely, the Sipser–Lautemann theorem states that $$\mathsf{BPP} \subseteq \Sigma_2 \cap \Pi_2 $$. As a result, P = NP leads to P = BPP since PH collapses to P in this case. Thus either P = BPP or P ≠ NP or both.

Adleman's theorem states that membership in any language in BPP can be determined by a family of polynomial-size Boolean circuits, which means BPP is contained in P/poly. Indeed, as a consequence of the proof of this fact, every BPP algorithm operating on inputs of bounded length can be derandomized into a deterministic algorithm using a fixed string of random bits. Finding this string may be expensive, however. Some weak separation results for Monte Carlo time classes were proven by, see also.

Closure properties
The class BPP is closed under complementation, union and intersection.

Relativization
Relative to oracles, we know that there exist oracles A and B, such that PA = BPPA and PB ≠ BPPB. Moreover, relative to a random oracle with probability 1, P = BPP and BPP is strictly contained in NP and co-NP.

There is even an oracle in which $\mathsf P \overset{?}{=} \mathsf{BPP}$ (and hence $\mathsf{BPP}=\mathsf{EXP}^\mathsf{NP}$), which can be iteratively constructed as follows. For a fixed ENP (relativized) complete problem, the oracle will give correct answers with high probability if queried with the problem instance followed by a random string of length kn (n is instance length; k is an appropriate small constant). Start with n=1. For every instance of the problem of length n fix oracle answers (see lemma below) to fix the instance output. Next, provide the instance outputs for queries consisting of the instance followed by kn-length string, and then treat output for queries of length ≤(k+1)n as fixed, and proceed with instances of length n+1.

$\mathsf{P<NP<BPP=EXP=NEXP}$ $$

The lemma ensures that (for a large enough k), it is possible to do the construction while leaving enough strings for the relativized $$ answers. Also, we can ensure that for the relativized $$, linear time suffices, even for function problems (if given a function oracle and linear output size) and with exponentially small (with linear exponent) error probability. Also, this construction is effective in that given an arbitrary oracle A we can arrange the oracle B to have $$ and $^{A}≤^{B}$. Also, for a $^{{{sans-serif|NP}}^{A}}=^{{{sans-serif|NP}}^{B}}=^{B}|undefined$ oracle (and hence $$), one would fix the answers in the relativized E computation to a special nonanswer, thus ensuring that no fake answers are given.

Derandomization
The existence of certain strong pseudorandom number generators is conjectured by most experts of the field. Such generators could replace true random numbers in any polynomial-time randomized algorithm, producing indistinguishable results. The conjecture that these generators exist implies that randomness does not give additional computational power to polynomial time computation, that is, P = RP = BPP. More strongly, the assumption that P = BPP is in some sense equivalent to the existence of strong pseudorandom number generators.

László Babai, Lance Fortnow, Noam Nisan, and Avi Wigderson showed that unless EXPTIME collapses to MA, BPP is contained in
 * $$\textsf{i.o.-SUBEXP} = \bigcap\nolimits_{\varepsilon>0} \textsf{i.o.-DTIME} \left (2^{n^\varepsilon} \right).$$

The class i.o.-SUBEXP, which stands for infinitely often SUBEXP, contains problems which have sub-exponential time algorithms for infinitely many input sizes. They also showed that P = BPP if the exponential-time hierarchy, which is defined in terms of the polynomial hierarchy and E as EPH, collapses to E; however, note that the exponential-time hierarchy is usually conjectured not to collapse.

Russell Impagliazzo and Avi Wigderson showed that if any problem in E, where
 * $$\mathsf{E} = \mathsf{DTIME} \left( 2^{O(n)} \right),$$

has circuit complexity 2Ω(n) then P = BPP.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: BPP (complexity)


text:
BQP

In computational complexity theory, bounded-error quantum polynomial time (BQP) is the class of decision problems solvable by a quantum computer in polynomial time, with an error probability of at most 1/3 for all instances. It is the quantum analogue to the complexity class BPP.

A decision problem is a member of BQP if there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem with high probability and is guaranteed to run in polynomial time. A run of the algorithm will correctly solve the decision problem with a probability of at least 2/3.

Definition
BQP can be viewed as the languages associated with certain bounded-error uniform families of quantum circuits. A language L is in BQP if and only if there exists a polynomial-time uniform family of quantum circuits $$\{Q_n\colon n \in \mathbb{N}\}$$, such that
 * For all $$n \in \mathbb{N}$$, Qn takes n qubits as input and outputs 1 bit
 * For all x in L, $$\mathrm{Pr}(Q_{|x|}(x)=1)\geq \tfrac{2}{3}$$
 * For all x not in L, $$\mathrm{Pr}(Q_{|x|}(x)=0)\geq \tfrac{2}{3}$$

Alternatively, one can define BQP in terms of quantum Turing machines. A language L is in BQP if and only if there exists a polynomial quantum Turing machine that accepts L with an error probability of at most 1/3 for all instances.

Similarly to other "bounded error" probabilistic classes, the choice of 1/3 in the definition is arbitrary. We can run the algorithm a constant number of times and take a majority vote to achieve any desired probability of correctness less than 1, using the Chernoff bound. The complexity class is unchanged by allowing error as high as 1/2 − n−c on the one hand, or requiring error as small as 2−n c on the other hand, where c is any positive constant, and n is the length of input.

Relationship to other complexity classes

BQP is defined for quantum computers; the corresponding complexity class for classical computers (or more formally for probabilistic Turing machines) is BPP. Just like P and BPP, BQP is low for itself, which means $$. Informally, this is true because polynomial time algorithms are closed under composition. If a polynomial time algorithm calls polynomial time algorithms as subroutines, the resulting algorithm is still polynomial time.

BQP contains P and BPP and is contained in AWPP, PP and PSPACE. In fact, BQP is low for PP, meaning that a PP machine achieves no benefit from being able to solve BQP problems instantly, an indication of the possible difference in power between these similar classes. The known relationships with classic complexity classes are:
 * $$\mathsf{P \subseteq BPP \subseteq BQP\subseteq AWPP \subseteq PP \subseteq PSPACE\subseteq EXP}$$

As the problem of $\mathsf{P}\ \stackrel{?}{=}\ \mathsf{PSPACE}$ has not yet been solved, the proof of inequality between BQP and classes mentioned above is supposed to be difficult. The relation between BQP and NP is not known. In May 2018, computer scientists Ran Raz of Princeton University and Avishay Tal of Stanford University published a paper which showed that, relative to an oracle, BQP was not contained in PH. It can be proven that there exists an oracle A such that $$\mathsf{BQP}^\mathrm{A}\nsubseteq\mathsf{PH}^\mathrm{A}$$. In an extremely informal sense, this can be thought of as giving PH and BQP an identical, but additional, capability and verifying that BQP with the oracle (BQPA) can do things PHA cannot. While an oracle separation has been proven, the fact that BQP is not contained in PH has not been proven. An oracle separation does not prove whether or not complexity classes are the same. The oracle separation gives intuition that BQP may not be contained in PH.

It has been suspected for many years that Fourier Sampling is a problem that exists within BQP, but not within the polynomial hierarchy. Recent conjectures have provided evidence that a similar problem, Fourier Checking, also exists in the class BQP without being contained in the polynomial hierarchy. This conjecture is especially notable because it suggests that problems existing in BQP could be classified as harder than NP-Complete problems. Paired with the fact that many practical BQP problems are suspected to exist outside of P (it is suspected and not verified because there is no proof that P ≠ NP), this illustrates the potential power of quantum computing in relation to classical computing.

Adding postselection to BQP results in the complexity class PostBQP which is equal to PP.

A complete problem for Promise-BQP
Promise-BQP is the class of promise problems that can be solved by a uniform family of quantum circuits (i.e., within BQP). Completeness proofs focus on this version of BQP. Similar to the notion of NP-completeness and other complete problems, we can define a complete problem as a problem that is in Promise-BQP and that every other problem in Promise-BQP reduces to it in polynomial time.

APPROX-QCIRCUIT-PROB
The APPROX-QCIRCUIT-PROB problem is complete for efficient quantum computation, and the version presented below is complete for the Promise-BQP complexity class (and not for the total BQP complexity class, for which no complete problems are known). APPROX-QCIRCUIT-PROB's completeness makes it useful for proofs showing the relationships between other complexity classes and BQP.

Given a description of a quantum circuit $C$ acting on $n$ qubits with $m$ gates, where  $m$ is a polynomial in $n$ and each gate acts on one or two qubits, and two numbers $$\alpha, \beta \in [0,1], \alpha > \beta$$, distinguish between the following two cases:
 * measuring the first qubit of the state $$C|0\rangle^{\otimes n}$$ yields $$|1\rangle$$ with probability $$\geq \alpha$$
 * measuring the first qubit of the state $$C|0\rangle^{\otimes n}$$ yields $$|1\rangle$$ with probability $$\leq \beta$$

Here, there is a promise on the inputs as the problem does not specify the behavior if an instance is not covered by these two cases.

Claim. Any BQP problem reduces to APPROX-QCIRCUIT-PROB.

Proof. Suppose we have an algorithm $A$ that solves APPROX-QCIRCUIT-PROB, i.e., given a quantum circuit $C$ acting on  $n$ qubits, and two numbers $$\alpha, \beta \in [0,1], \alpha > \beta$$, $A$ distinguishes between the above two cases. We can solve any problem in BQP with this oracle, by setting $$\alpha = 2/3, \beta = 1/3$$.

For any $$L \in \mathsf{BQP} $$, there exists family of quantum circuits $$\{Q_n\colon n \in \mathbb{N}\}$$ such that for all $$n \in \mathbb{N}$$, a state $$ |x\rangle $$ of $$n $$  qubits, if $$x \in L, Pr(Q_n(|x\rangle)=1) \geq 2/3$$; else if  $$x \notin L, Pr(Q_n(|x\rangle)=0) \geq 2/3 $$. Fix an input $$ |x\rangle $$ of $n$ qubits, and the corresponding quantum circuit $$Q_n$$. We can first construct a circuit $$C_x$$ such that $$C_x|0\rangle^{\otimes n} = |x\rangle$$. This can be done easily by hardwiring $$ |x\rangle $$ and apply a sequence of CNOT gates to flip the qubits. Then we can combine two circuits to get $$C' = Q_nC_x$$, and now $$C'|0\rangle^{\otimes n} = Q_n|x\rangle$$. And finally, necessarily the results of $$Q_n$$ is obtained by measuring several qubits and apply some (classical) logic gates to them. We can always defer the measurement and reroute the circuits so that by measuring the first qubit of $$C'|0\rangle^{\otimes n} = Q_n|x\rangle$$, we get the output. This will be our circuit $C$, and we decide the membership of $$x \in L$$ by running $$A(C)$$ with $$\alpha = 2/3, \beta = 1/3$$. By definition of BQP, we will either fall into the first case (acceptance), or the second case (rejection), so $$L \in \mathsf{BQP} $$ reduces to APPROX-QCIRCUIT-PROB.

BQP and EXP
We begin with an easier containment. To show that $$\mathsf{BQP} \subseteq \mathsf{EXP}$$, it suffices to show that APPROX-QCIRCUIT-PROB is in EXP since APPROX-QCIRCUIT-PROB is BQP-complete.

$$

$$

Note that this algorithm also requires $$2^{O(n)}$$ space to store the vectors and the matrices. We will show in the following section that we can improve upon the space complexity.

BQP and PSPACE
Sum of histories is a technique introduced by physicist Richard Feynman for path integral formulation. APPROX-QCIRCUIT-PROB can be formulated in the sum of histories technique to show that $$\mathsf{BQP} \subseteq \mathsf{PSPACE}$$.

Consider a quantum circuit $C$, which consists of $t$ gates, $$g_1, g_2, \cdots, g_m$$, where each $$g_j$$ comes from a universal gate set and acts on at most two qubits. To understand what the sum of histories is, we visualize the evolution of a quantum state given a quantum circuit as a tree. The root is the input $$|0\rangle^{\otimes n}$$, and each node in the tree has $$2^n$$ children, each representing a state in $$\mathbb C^n$$. The weight on a tree edge from a node in $j$-th level representing a state $$|x\rangle$$ to a node in $$j+1$$-th level representing a state $$|y\rangle$$ is $$\langle y|g_{j+1}|x\rangle$$, the amplitude of $$|y\rangle$$ after applying $$g_{j+1}$$ on $$|x\rangle$$. The transition amplitude of a root-to-leaf path is the product of all the weights on the edges along the path. To get the probability of the final state being $$|\psi\rangle$$, we sum up the amplitudes of all root-to-leave paths that ends at a node representing $$|\psi\rangle$$.

More formally, for the quantum circuit $C$, its sum over histories tree is a tree of depth $m$, with one level for each gate $$g_i$$ in addition to the root, and with branching factor $$2^n$$.

$$

$$

$$

$$

$$

$$

$$

Notice in the sum over histories algorithm to compute some amplitude $$\alpha_x$$, only one history is stored at any point in the computation. Hence, the sum over histories algorithm uses $$O(nm)$$ space to compute $$\alpha_x$$ for any $x$ since $$O(nm)$$ bits are needed to store the histories in addition to some workspace variables.

Therefore, in polynomial space, we may compute $$\sum_x |\alpha_x|^2$$ over all $x$ with the first qubit being $1$, which is the probability that the first qubit is measured to be 1 by the end of the circuit.

Notice that compared with the simulation given for the proof that $$\mathsf{BQP} \subseteq \mathsf{EXP}$$, our algorithm here takes far less space but far more time instead. In fact it takes $$O(m\cdot 2^{mn} )$$ time to calculate a single amplitude!

BQP and PP
A similar sum-over-histories argument can be used to show that $$\mathsf{BQP} \subseteq \mathsf{PP}$$.

P and BQP
We know $$ \mathsf{P} \subseteq \mathsf{BQP} $$, since every classical circuit can be simulated by a quantum circuit.

It is conjectured that BQP solves hard problems outside of P, specifically, problems in NP. The claim is indefinite because we don't know if P=NP, so we don't know if those problems are actually in P. Below are some evidence of the conjecture:

 * Integer factorization (see Shor's algorithm)
 * Discrete logarithm
 * Simulation of quantum systems (see universal quantum simulator)
 * Approximating the Jones polynomial at certain roots of unity
 * Harrow-Hassidim-Lloyd (HHL) algorithm

title: BQP


text:
Blade Runner 3: Replicant Night

Blade Runner 3: Replicant Night is a science fiction novel by an American writer K. W. Jeter, first published in 1996. It is a continuation of Jeter's novel Blade Runner 2: The Edge of Human, which was itself a sequel to both the film Blade Runner and the novel upon which the film was based, Philip K. Dick's Do Androids Dream of Electric Sheep?

Plot introduction
Living on Mars, Deckard is acting as a consultant to a movie crew filming the story of his days as a blade runner. He finds himself drawn into a mission on behalf of the replicants he was once assigned to kill. Meanwhile, the mystery surrounding the beginnings of the Tyrell Corporation is being exposed.

Characters

 * Rick Deckard, a former bounty hunter, now working as a film consultant
 * Sarah Tyrell, the niece of Eldon Tyrell; she has been living on Mars since the events of Blade Runner 2
 * Anson Tyrell, Sarah's father
 * Ruth Tyrell, Sarah's mother
 * Rachael, a ten-year-old girl
 * Roy Batty, the human template for the replicant Deckard fought in the previous novel. That replicant's personality now resides inside Deckard's briefcase.
 * Sebastien, a dehydrated deity
 * Urbenton, director of the movie Blade Runner on which Rick Deckard is a consultant
 * Dave Holden, Deckard's former police partner.

Film adaptation
The plot element of a replicant giving birth served as the basis for the 2017 film Blade Runner 2049.

title: Blade Runner 3: Replicant Night


text:
Blade Runner 2: The Edge of Human

Blade Runner 2: The Edge of Human (1995) is a science fiction novel by American writer K. W. Jeter. It is a continuation of both the film Blade Runner and the novel upon which the film was based, Philip K. Dick's Do Androids Dream of Electric Sheep?

Plot
Several months after the events depicted in Blade Runner, Deckard has retired to an isolated shack outside the city, taking the replicant Rachael with him in a Tyrell transport container, which slows down the replicant aging process. He is approached by a woman who explains she is Sarah Tyrell, niece of Eldon Tyrell, heiress to the Tyrell Corporation and the human template ("templant") for the Rachael replicant. She asks Deckard to hunt down the "missing" sixth replicant. At the same time, the templant for Roy Batty hires Dave Holden, the blade runner attacked by Leon, to help him hunt down the man he believes is the sixth replicant—Deckard.

Deckard and Holden's investigations lead them to re-visit Sebastian, Bryant, and John Isidore (from the book Do Androids Dream Of Electric Sheep?), learning more about the nature of the blade runners and the replicants.

When Deckard, Batty, and Holden finally clash, Batty's super-human fighting prowess leads Holden to believe he has been duped all along and that Batty is the sixth replicant, leading to Holden shooting him. Deckard returns to Sarah with his suspicion: there is no sixth replicant. Sarah, speaking via a remote camera, confesses that she invented and maintained the rumor herself in order to deliberately discredit and eventually destroy the Tyrell Corporation because her uncle Eldon had based Rachel on her and then abandoned the real Sarah. Sarah brings Rachael back to the Corporation to meet with Deckard, and they escape.

However, Holden, recovering from his injuries during the fight, later uncovers the truth: Rachael has been killed by Tyrell agents, and the "Rachael" who escaped with Deckard was actually Sarah. She has completed her revenge by both destroying Tyrell and taking back Rachael's place.

Characters

 * Rick Deckard: The Tyrell Corporation finally locates him, residing at a cabin in the woods with the frozen Rachael. In exchange for getting Rachael back, Deckard agrees to hunt the missing sixth replicant.
 * Roy Batty: The man which Tyrell used as the template for his combat replicants is in fact a man of considerable instability, suffering from a brain disorder that prevents him from experiencing fear.
 * Sarah Tyrell: The niece of Eldon Tyrell, Sarah locates and hires Deckard to eliminate the final replicant in order to retain her corporation's hold over the market.
 * Dave Holden: Starting off bed-ridden after his attack by the replicant Leon, Holden is rescued by Roy who in turn leads him to some startling revelations.
 * J.R. Isidore: A lowly employee of a vet's office, Isidore also works as an underground replicant sympathizer, having made modifications to replicants in order to help them escape detection.

Relationship to other works
The book's plot draws from other material related to Blade Runner in a number of ways:
 * Deckard, Pris, Sebastian, Leon, Batty, and Holden all appeared in Blade Runner.
 * Many of the parts of the "conspiracy" are based on errors or plot holes identified by fans of the original movie, such as Leon's ability to bring a gun into the Tyrell building, or the reference to the sixth replicant.
 * The character of John Isidore, and his "pet hospital", is taken from Dick's original novel Do Androids Dream of Electric Sheep?, although that book contained no suggestion that the shop ran a sideline in modifying replicants.
 * Blade Runner ' s Sebastian was based on Electric Sheep ' s Isidore, though Jeter features them as separate characters in The Edge of Human.
 * The idea of replicant models being mass-produced, and in particular a woman identical to Rachael existing, is also from Do Androids Dream of Electric Sheep?; although in that book, Pris was the replicant double of Rachael, and there was no suggestion that replicants were constructed based on human templates.
 * The etymology of the term "blade runner" is revealed to come from the German phrase bleib ruhig, meaning "remain calm." It was supposedly developed by the Tyrell Corporation to prevent news about replicants malfunctioning.

However, it also contradicts material in some ways:
 * Sebastian was stated as being dead in the movie, yet he is alive in The Edge of Human.
 * Pris was clearly stated as being a replicant in both the movie and the original novel, yet The Edge of Human claims she was human.
 * Pris was clearly destroyed by Deckard in both the movie and the original novel. Sebastian's ability to bring Pris back to life as a replicant introduces numerous problems: the book implies that Sebastian was able to do this without realising that her original body was human. It is likewise unclear why Deckard would have left her, or any suspected replicant he retired, in a state from which they could be repaired.
 * "The Final Cut" of Blade Runner removed the reference of a surviving sixth replicant, as it was normally considered a leftover from an early script.

Reception
Michael Giltz of Entertainment Weekly gave the book a "C−", feeling that "only hardcore fans will be satisfied by this tale" and saying Jeter's "habit of echoing dialogue and scenes from the film is annoying and begs comparisons he would do well to avoid." Tal Cohen of Tal Cohen's Bookshelf called The Edge of Human "a good book", praising Jeter's "further, and deeper, investigation of the questions Philip K. Dick originally asked", but criticized the book for its "needless grandioseness" and for "rel[ying] on Blade Runner too heavily, [as] the number of new characters introduced is extremely small..."

Ian Kaplan of BearCave.com gave the book three stars out of five, saying that while he was "not entirely satisfied" and felt that the "story tends to be shallow", "Jeter does deal with the moral dilemma of the Blade Runners who hunt down beings that are virtually human in every way." J. Patton of The Bent Cover praised Jeter for "[not] try[ing] to emulate Philip K. Dick", adding, "This book also has all the grittiness and dark edges that the movie showed off so well, along with a very fast pace that will keep you reading into the wee hours of the night."

Failed film adaptation
In the late 1990s, Edge of Human had been adapted into a screenplay by Stuart Hazeldine, Blade Runner Down, that was to be filmed as the sequel to the 1982 film Blade Runner. Ultimately neither this script nor the Jeter novel were used for the eventual sequel, Blade Runner 2049, which follows a different story.

title: Blade Runner 2: The Edge of Human


text:
Talk:Big O notation

Query
What's "sup" in the "Limit Definitions" of "Big Oh" and "Big Omega (HLw)" at #Family of Bachmann–Landau notations ?? $$\limsup_{n \to \infty} \frac{\left|f(n)\right|}{g(n)} < \infty $$ and $$\limsup_{n \to \infty} \frac{\left|f(n)\right|}{g(n)} > 0 $$ Yashpalgoyal1304 (talk) 13:40, 6 June 2022 (UTC)

 * The source says , and searching for it fetches this: Limit inferior and limit superior which researching on this page itself, is also mentioned in the sections: #Formal definition and #See also. Yashpalgoyal1304 (talk) 13:55, 6 June 2022 (UTC)
 * You seem to be disturbed by the space between "lim" and "sup" that you get when typing "limsup" in LaTeX, like in $$\limsup$$. Well, you better get used to it... --Sapphorain (talk) 14:21, 6 June 2022 (UTC)
 * No, it was not that. I had never even consciously encountered these terms: superior/inferior limits. Looking at it's wikip article's illustration now, I understand that it's just a fancy term for upper limit and lower limit lol. But yeah, thanks for the tip too, t'll definitely help me in future when using it in LaTex. Yashpalgoyal1304 (talk) 17:01, 6 June 2022 (UTC)
 * No, they are not just fancy terms for upper and lower limit. Maybe you should check the definitions again.2405:6E00:1ED2:1700:9DBE:839C:30C6:CE68 (talk) 09:36, 18 May 2023 (UTC)

Use in computer science
It seems, from the opening of this section, that it is meant to discuss the fact that some computer scientists use O where $$\Theta$$ should be used instead (i.e., for a tight bound); I'm not sure if it is desirable to discuss improper usages in the article. At any rate, the rest of the section does not match its beginning, as it illustrates the proper use. It should be edited, perhaps removed. AmirOnWiki (talk) 14:07, 30 June 2023 (UTC)

Determining if a binary number is even or odd changed to finding median
"Determining if a binary number is even or odd" isn't a particularly useful example, because there will only one number being tested. Finding the median value for a sorted list of measurements is a better example. SlowJog (talk) 02:32, 29 October 2023 (UTC)

Big O and data structures
My note on this topic disapeared, but I still think there is common misinterpretation there. Suppose you have algorithm which \Theta(n) times calls a method of a data structure. The assymptotic complexity of the method is described as O(\log s) where s is the size of the data structure. The actual use of the data structure is such that s never exceeds 1. (Weird case) If you simply multiply the number of method calls by their complexity you obtain bound 0.

There are several solutions of this wrong calculation ... I recommend considering the minimal complexity of a call be 1 what changes the result to \Theta(n). I do not think we would change all complexity descriptions to O(1+\log s) ..., but one should know about this use asymptotic when the size does not go to infinity problem.Hippo.69 (talk) 13:50, 12 December 2023 (UTC)

 * Are you talking about this discussion from three years ago? --JBL (talk) 17:11, 12 December 2023 (UTC)
 * Oh yes, and seems nobody else considers using assymptotic complexity for tiny data structures be a problem. Let us hope people are smart enough not to think n calls to a data structure could take constant/zero time in total and there is no need to emphasize that.

Hippo.69 (talk) 21:04, 14 December 2023 (UTC)

 * It makes no sense for the size of a data structure to be a positive number less than one. These sizes are generally integers: integer numbers of memory cells (bits, bytes, words, whatever) or number of elements stored. Occasional care needs to be taken with logs when the size can equal one, and people are often sloppy about that, but it's harmless.
 * In the meantime, the much bigger problem with O-notation is the use of it with more than one variable, without any specification of how the two variables are assumed to go to infinity together or separately. It's safe for the most common usage, for graph algorithms on connected graphs as a function of vertex and edge counts, because those two things are tied to each other in both directions, but even for disconnected multigraphs one runs into this issue. —David Eppstein (talk) 21:51, 14 December 2023 (UTC)
 * Yes, I was refering to the sloppiness with size 1 and log(s) (s not meaning the number of bytes or cells, but the number of represented items) (and I do not see a problem with data structure state representing 0 elements).
 * I actually am not sure where is the problem with the complexity bounded by more parameters going to infinity.
 * I interpret f(n_1,n_2,...,n_k)\in O(g(n_1,n_2,...,n_k)) as ... there exists c and n_0 that for all i 1<=i<=k and n_i>n_0 f(n_1,n_2,....,n_k)<c g(n_1,n_2,...,n_k). What problems it causes? Hippo.69 (talk) 08:00, 15 December 2023 (UTC)
 * So you are assuming that all n_i go to infinity at the same rate? But what if they don't? If an algorithm takes time O(f(x)+g(y)) according to your definition, and you hold x fixed while letting y grow, how much time does it take? —David Eppstein (talk) 08:13, 15 December 2023 (UTC)
 * No, I am assuming all n_i going to infinity where the rate does not matter. Of course there could be other constraints (typically m<n^2 ... edges and vertices) or (h<=n Kirkpatrick–Seidel h subset of n points), but it seems to me they are not relevant. Oh I have not read the x, y example ... if x is hold fixed, it does not go to infinity, but if goes to infinity, it seems to me it is fine using O as I have written. ... End of course there could be constants in the expressions f,g, but there is no variable and n_i connected to them ... may be try to show the confusing use in an exampleHippo.69 (talk) 08:38, 15 December 2023 (UTC)
 * But if you assume that all n_i are greater than some n_0, then you are assuming the rate does matter. Consider the function f(x,y) that is 2^y for x=1 but x^2+y^2 for x,y>1. For all x,y>n_0 (for instance n_0=2), it is less than some constant times x^2+y^2. Does that mean you can write that it is O(x^2+y^2)? It is, according to your definition. What if you plug in that time bound to an algorithm that, say, loops over all pairs (x,y) up to n? Can you just add the O(x^2+y^2) bound and get a valid answer? —David Eppstein (talk) 18:28, 15 December 2023 (UTC)
 * OK, I get your point. When the function is not monotone, the relative grow rate matters. Hippo.69 (talk) 21:02, 15 December 2023 (UTC)

title: Talk:Big O notation


text:
Brainfuck

Brainfuck is an esoteric programming language created in 1993 by Swiss physics student Urban Müller. Designed to be extremely minimalistic, the language consists of only eight simple commands, a data pointer and an instruction pointer.

Brainfuck is an example of a so-called Turing tarpit: it can be used to write any program, but it is not practical to do so, because it provides so little abstraction that the programs get very long or complicated. While Brainfuck is fully Turing complete, it is not intended for practical use, but to challenge and amuse programmers. Brainfuck requires one to break commands into microscopic steps.

The language takes its name from the slang term brainfuck, which refers to things so complicated or unusual that they exceed the limits of one's understanding, as it was not meant or made for designing actual software but to challenge the boundaries of computer programming.

Because the language's name contains profanity, many substitutes are used, such as brainfsck, branflakes, brainoof, brainfrick, BrainF, and BF.

History
Müller designed Brainfuck with the goal of implementing the smallest possible compiler, inspired by the 1024-byte compiler for the FALSE programming language. Müller's original compiler was implemented in machine language and compiled to a binary with a size of 296 bytes. He uploaded the first Brainfuck compiler to Aminet in 1993. The program came with a "Readme" file, which briefly described the language, and challenged the reader "Who can program anything useful with it? :)". Müller also included an interpreter and some examples. A second version of the compiler used only 240 bytes.

Language design
The language consists of eight commands. A brainfuck program is a sequence of these commands, possibly interspersed with other characters (which are ignored). The commands are executed sequentially, with some exceptions: an instruction pointer begins at the first command, and each command it points to is executed, after which it normally moves forward to the next command. The program terminates when the instruction pointer moves past the last command.

The brainfuck language uses a simple machine model consisting of the program and instruction pointer, as well as a one-dimensional array of at least 30,000 byte cells initialized to zero; a movable data pointer (initialized to point to the leftmost byte of the array); and two streams of bytes for input and output (most often connected to a keyboard and a monitor respectively, and using the ASCII character encoding).

The eight language commands each consist of a single character:

and  match as parentheses usually do: each   matches exactly one   and vice versa, the   comes first, and there can be no unmatched   or   between the two.

Brainfuck programs are usually difficult to comprehend. This is partly because any mildly complex task requires a long sequence of commands and partly because the program's text gives no direct indications of the program's state. These, as well as Brainfuck's inefficiency and its limited input/output capabilities, are some of the reasons it is not used for serious programming. Nonetheless, like any Turing complete language, Brainfuck is theoretically capable of computing any computable function or simulating any other computational model, if given access to an unlimited amount of memory. A variety of Brainfuck programs have been written. Although Brainfuck programs, especially complicated ones, are difficult to write, it is quite trivial to write an interpreter for Brainfuck in a more typical language such as C due to its simplicity. Brainfuck interpreters written in the Brainfuck language itself also exist.

Adding two values
As a first, simple example, the following code snippet will add the current cell's value to the next cell: Each time the loop is executed, the current cell is decremented, the data pointer moves to the right, that next cell is incremented, and the data pointer moves left again. This sequence is repeated until the starting cell is 0.

This can be incorporated into a simple addition program as follows:

Hello World!
The following program prints "Hello World!" and a newline to the screen:

For readability, this code has been spread across many lines, and blanks and comments have been added. Brainfuck ignores all characters except the eight commands  so no special syntax for comments is needed (as long as the comments do not contain the command characters). The code could just as well have been written as:

ROT13
This program enciphers its input with the ROT13 cipher. To do this, it must map characters A-M (ASCII 65–77) to N-Z (78-90), and vice versa. Also it must map a-m (97-109) to n-z (110-122) and vice versa. It must map all other characters to themselves; it reads characters one at a time and outputs their enciphered equivalents until it reads an EOF (here assumed to be represented as either -1 or "no change"), at which point the program terminates.

Simulation of abiogenesis
In 2024, a Google research project used Brainfuck as the basis of an artificial digital environment. In this environment, they found that replicators arose naturally and competed with each other for domination of the environment.

title: Brainfuck


text:
Bartolomeo Ammannati

Bartolomeo Ammannati (18 June 1511 – 13 April 1592) was an Italian architect and sculptor, born at Settignano, near Florence, Italy. He studied under Baccio Bandinelli and Jacopo Sansovino (assisting on the design of the Library of St. Mark's, the Biblioteca Marciana, Venice) and closely imitated the style of Michelangelo.

He was more distinguished in architecture than in sculpture. He worked in Rome in collaboration with Vignola and Vasari), including designs for the Villa Giulia, but also for works at Lucca. He labored during 1558–1570, in the refurbishment and enlargement of Pitti Palace, creating the courtyard consisting of three wings with rusticated facades, and one lower portico leading to the amphitheatre in the Boboli Gardens. His design mirrored the appearance of the main external façade of Pitti. He was also named Consul of Accademia delle Arti del Disegno of Florence, which had been founded by the Duke Cosimo I in 1563.

In 1569, Ammannati was commissioned to build the Ponte Santa Trinita, a bridge over the Arno River. The three arches are elliptic, and though very light and elegant, has survived, when floods had damaged other Arno bridges at different times. Santa Trinita was destroyed in 1944, during World War II, and rebuilt in 1957.

Ammannati designed what is considered a prototypic Mannerist sculptural ensemble in the Fountain of Neptune (Fontana del Nettuno), prominently located in the Piazza della Signoria in the center of Florence. The assignment was originally given to the aged Bartolommeo Bandinelli; however when Bandinelli died, Ammannati's design, bested the submissions of Benvenuto Cellini and Vincenzo Danti, to gain the commission. From 1563 and 1565, Ammannati and his assistants, among them Giambologna, sculpted the block of marble that had been chosen by Bandinelli. He took Grand Duke Cosimo I as model for Neptune's face. The statue was meant to highlight Cosimo's goal of establishing a Florentine Naval force. The ungainly sea god was placed at the corner of the Palazzo Vecchio within sight of Michelangelo's David statue, and the then 87-year-old sculptor is said to have scoffed at Ammannati— saying that he had ruined a beautiful piece of marble— with the ditty: "Ammannati, Ammanato, che bel marmo hai rovinato!" Ammannati continued work on this fountain for a decade, adding around the perimeter a cornucopia of demigod figures: bronze reclining river gods, laughing satyrs and marble sea horses emerging from the water.

In 1550 Ammannati married Laura Battiferri, an elegant poet and an accomplished woman. Later in his life he had a religious crisis, influenced by Counter-Reformation piety, which resulted in condemning his own works depicting nudity, and he left all his possessions to the Jesuits.

He died in Florence in 1592.

Works

 * Victory (1540), marble, Museo Nazionale del Bargello, Florence
 * Leda with the Swan, marble, also in Bargello, Florence
 * Venus (1558–59), marble, Prado Museum, Madrid
 * Parnassus (1563), marble, Museo Nazionale del Bargello, Florence
 * Allegory of Winter (1563–65), stone, Villa Medici, Castello
 * Goddess Opi (1572–75), bronze, Palazzo Vecchio, Florence

General references

 * Bartolomeo Ammannati in the "History of Art"

title: Bartolomeo Ammannati