romikgosai/squad_modified_2 huggingface dataset:
The reason for this is that a quantum disjunction, unlike the case for classical disjunction, can be true even when both of the disjuncts are false and this is, in turn, attributable to the fact that it is frequently the case, in quantum mechanics, that a pair of alternatives are semantically determinate, while each of its members are necessarily indeterminate. This latter property can be illustrated by a simple example. Suppose we are dealing with particles (such as electrons) of semi-integral spin (angular momentum) for which there are only two possible values: positive or negative. Then, a principle of indetermination establishes that the spin, relative to two different directions (e.g., x and y) results in a pair of incompatible quantities. Suppose that the state ɸ of a certain electron verifies the proposition "the spin of the electron in the x direction is positive." By the principle of indeterminacy, the value of the spin in the direction y will be completely indeterminate for ɸ. Hence, ɸ can verify neither the proposition "the spin in the direction of y is positive" nor the proposition "the spin in the direction of y is negative." Nevertheless, the disjunction of the propositions "the spin in the direction of y is positive or the spin in the direction of y is negative" must be true for ɸ. In the case of distribution, it is therefore possible to have a situation in which , while .

Q1: What is the difference of quantum disjunction from classic?
A1: can be true even when both of the disjuncts are false
Q2: What is frequently the case in quantum mechanics when a pair of alternatives are semantically determinate?
A2: each of its members are necessarily indeterminate
Q3: How can quantum disjuction be illustrated?
A3: illustrated by a simple example
Such strategies, which minimize the maximum loss for each player, are called optimal. Von Neumann showed that their minimaxes are equal (in absolute value) and contrary (in sign). Von Neumann improved and extended the minimax theorem to include games involving imperfect information and games with more than two players, publishing this result in his 1944 Theory of Games and Economic Behavior (written with Oskar Morgenstern). Morgenstern wrote a paper on game theory and thought he would show it to von Neumann because of his interest in the subject. He read it and said to Morgenstern that he should put more in it. This was repeated a couple of times, and then von Neumann became a coauthor and the paper became 100 pages long. Then it became a book. The public interest in this work was such that The New York Times ran a front-page story. In this book, von Neumann declared that economic theory needed to use functional analytic methods, especially convex sets and topological fixed-point theorem, rather than the traditional differential calculus, because the maximum-operator did not preserve differentiable functions.

Q1: What is optimal strategy?
A1: minimize the maximum loss for each player
Q2: What von Neumann work was published in 1944?
A2: Theory of Games and Economic Behavior
Q3: Who was co-author with von Neman on the Theory of Games and Economic Behavior?
A3: Oskar Morgenstern
Von Neumann raised the intellectual and mathematical level of economics in several stunning publications. For his model of an expanding economy, von Neumann proved the existence and uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem. Von Neumann's model of an expanding economy considered the matrix pencil  A − λB with nonnegative matrices A and B; von Neumann sought probability vectors p and q and a positive number λ that would solve the complementarity equation

Q1: How did von Neumann raise the level of economics?
A1: several stunning publications
Q2: What did von Neumann prove with his model of expanding economy?
A2: uniqueness of an equilibrium using his generalization of the Brouwer fixed-point theorem
Q3: What did von Neumann consider for his model of expanding economy?
A3: matrix pencil  A − λB with nonnegative matrices A and B
along with two inequality systems expressing economic efficiency. In this model, the (transposed) probability vector p represents the prices of the goods while the probability vector q represents the "intensity" at which the production process would run. The unique solution λ represents the growth factor which is 1 plus the rate of growth of the economy; the rate of growth equals the interest rate. Proving the existence of a positive growth rate and proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann.

Q1: In von Neumann's model what does p represent?
A1: p represents the prices of the goods
Q2: In von Neumann's model what does q represent?
A2: q represents the "intensity" at which the production process would run
Q3: What is the rate of qrowth equal to?
A3: rate of growth equals the interest rate
Q4: Was the economic model successful?
A4: proving that the growth rate equals the interest rate were remarkable achievements, even for von Neumann
Von Neumann's results have been viewed as a special case of linear programming, where von Neumann's model uses only nonnegative matrices. The study of von Neumann's model of an expanding economy continues to interest mathematical economists with interests in computational economics. This paper has been called the greatest paper in mathematical economics by several authors, who recognized its introduction of fixed-point theorems, linear inequalities, complementary slackness, and saddlepoint duality. In the proceedings of a conference on von Neumann's growth model, Paul Samuelson said that many mathematicians had developed methods useful to economists, but that von Neumann was unique in having made significant contributions to economic theory itself.

Q1: What were von Neumann's model an example of?
A1: viewed as a special case of linear programming
Q2: What was the significance of von Neumann's model of expanding economy?
A2: unique in having made significant contributions to economic theory itself.
Q3: What ideas were utilized in von Neumann's ecocomic model?
A3: fixed-point theorems, linear inequalities, complementary slackness, and saddlepoint duality
Von Neumann's famous 9-page paper started life as a talk at Princeton and then became a paper in Germany, which was eventually translated into English. His interest in economics that led to that paper began as follows: When lecturing at Berlin in 1928 and 1929 he spent his summers back home in Budapest, and so did the economist Nicholas Kaldor, and they hit it off. Kaldor recommended that von Neumann read a book by the mathematical economist Léon Walras. Von Neumann found some faults in that book and corrected them, for example, replacing equations by inequalities. He noticed that Walras's General Equilibrium Theory and Walras' Law, which led to systems of simultaneous linear equations, could produce the absurd result that the profit could be maximized by producing and selling a negative quantity of a product. He replaced the equations by inequalities, introduced dynamic equilibria, among other things, and eventually produced the paper.

Q1: When did von Neumann's interest in economics begin?
A1: When lecturing at Berlin in 1928 and 1929
Q2: What economist did von Neumann get to know that spurred the interest in economics?
A2: Nicholas Kaldor
Q3: In who's book did von Neuman find errors in the author's equations?
A3: Léon Walras
Later, von Neumann suggested a new method of linear programming, using the homogeneous linear system of Gordan (1873), which was later popularized by Karmarkar's algorithm. Von Neumann's method used a pivoting algorithm between simplices, with the pivoting decision determined by a nonnegative least squares subproblem with a convexity constraint (projecting the zero-vector onto the convex hull of the active simplex). Von Neumann's algorithm was the first interior point method of linear programming.

Q1: What was the new method of linear programming that von Neumann suggested?
A1: homogeneous linear system of Gordan
Q2: What did von Neuman's method use?
A2: pivoting algorithm between simplices
Q3: What was von Neumann's method known to be the first of?
A3: algorithm was the first interior point method of linear programming.
Von Neumann made fundamental contributions to mathematical statistics. In 1941, he derived the exact distribution of the ratio of the mean square of successive differences to the sample variance for independent and identically normally distributed variables. This ratio was applied to the residuals from regression models and is commonly known as the Durbin–Watson statistic for testing the null hypothesis that the errors are serially independent against the alternative that they follow a stationary first order autoregression.

Q1: When did von NEumann establish mean square ratio?
A1: 1941
Q2: How has mean square ratio been applied?
A2: Durbin–Watson statistic
Q3: what does null hypothesis test against?
A3: alternative that they follow a stationary first order autoregression
Von Neumann made fundamental contributions in exploration of problems in numerical hydrodynamics. For example, with Robert D. Richtmyer he developed an algorithm defining artificial viscosity that improved the understanding of shock waves. A problem was that when computers solved hydrodynamic or aerodynamic problems, they tried to put too many computational grid points at regions of sharp discontinuity (shock waves). The mathematics of artificial viscosity smoothed the shock transition without sacrificing basic physics. Other well known contributions to fluid dynamics included the classic flow solution to blast waves, and the co-discovery of the ZND detonation model of explosives.

Q1: The algorithm defining artificial viscosity is a fundamental contribution to what area?
A1: numerical hydrodynamics
Q2: What did the math of artificial viscosity do?
A2: smoothed the shock transition without sacrificing basic physics
Q3: What was the problem of computers solving fluid dynamics?
A3: they tried to put too many computational grid points at regions of sharp discontinuity (shock waves)
Von Neumann's principal contribution to the atomic bomb was in the concept and design of the explosive lenses needed to compress the plutonium core of the Fat Man weapon that was later dropped on Nagasaki. While von Neumann did not originate the "implosion" concept, he was one of its most persistent proponents, encouraging its continued development against the instincts of many of his colleagues, who felt such a design to be unworkable. He also eventually came up with the idea of using more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly".

Q1: What principal contribution did von Neumann make to atomic bomb?
A1: concept and design of the explosive lenses needed to compress the plutonium core
Q2: Did von Nemann think that the atomic bomb design was not workable?
A2: he was one of its most persistent proponents, encouraging its continued development
Q3: What additional ideas did von Neumann contribute to Atomic bomb?
A3: more powerful shaped charges and less fissionable material to greatly increase the speed of "assembly"
When it turned out that there would not be enough uranium-235 to make more than one bomb, the implosive lens project was greatly expanded and von Neumann's idea was implemented. Implosion was the only method that could be used with the plutonium-239 that was available from the Hanford Site. He established the design of the explosive lenses required, but there remained concerns about "edge effects" and imperfections in the explosives. His calculations showed that implosion would work if it did not depart by more than 5% from spherical symmetry. After a series of failed attempts with models, this was achieved by George Kistiakowsky, and the construction of the Trinity bomb was completed in July 1945.

Q1: what change was made when shortage of uranium 235 was apparent?
A1: implosive lens project was greatly expanded
Q2: What was the tolerance limit for implosion "edge effect"?
A2: not depart by more than 5% from spherical symmetry
Q3: Who constructed Trinity bomb?
A3: George Kistiakowsky
Q4: In what year was Trinity bomb completed?
A4: 1945
Along with four other scientists and various military personnel, von Neumann was included in the target selection committee responsible for choosing the Japanese cities of Hiroshima and Nagasaki as the first targets of the atomic bomb. Von Neumann oversaw computations related to the expected size of the bomb blasts, estimated death tolls, and the distance above the ground at which the bombs should be detonated for optimum shock wave propagation and thus maximum effect. The cultural capital Kyoto, which had been spared the bombing inflicted upon militarily significant cities, was von Neumann's first choice, a selection seconded by Manhattan Project leader General Leslie Groves. However, this target was dismissed by Secretary of War Henry L. Stimson.

Q1: What other people worked with von Neumann on target selection?
A1: four other scientists and various military personnel
Q2: What role did von Neuman play in the selection of targets?
A2: oversaw computations
Q3: What was von Neumann's first choice for target city?
A3: Kyoto
Q4: Who dismissed von Neuamann's primary target city?
A4: Secretary of War Henry L. Stimson.
On July 16, 1945, with numerous other Manhattan Project personnel, von Neumann was an eyewitness to the first atomic bomb blast, code named Trinity, conducted as a test of the implosion method device, at the bombing range near Alamogordo Army Airfield, 35 miles (56 km) southeast of Socorro, New Mexico. Based on his observation alone, von Neumann estimated the test had resulted in a blast equivalent to 5 kilotons of TNT (21 TJ) but Enrico Fermi produced a more accurate estimate of 10 kilotons by dropping scraps of torn-up paper as the shock wave passed his location and watching how far they scattered. The actual power of the explosion had been between 20 and 22 kilotons. It was in von Neumann's 1944 papers that the expression "kilotons" appeared for the first time. After the war, Robert Oppenheimer remarked that the physicists involved in the Manhattan project had "known sin". Von Neumann's response was that "sometimes someone confesses a sin in order to take credit for it."

Q1: On what day was the first atomic blast?
A1: July 16, 1945
Q2: Where did the first atomic blast test take place?
A2: Alamogordo Army Airfield,
Q3: What was the power of the first atomic blast?
A3: between 20 and 22 kilotons
Von Neumann continued unperturbed in his work and became, along with Edward Teller, one of those who sustained the hydrogen bomb project. He then collaborated with Klaus Fuchs on further development of the bomb, and in 1946 the two filed a secret patent on "Improvement in Methods and Means for Utilizing Nuclear Energy", which outlined a scheme for using a fission bomb to compress fusion fuel to initiate nuclear fusion. The Fuchs–von Neumann patent used radiation implosion, but not in the same way as is used in what became the final hydrogen bomb design, the Teller–Ulam design. Their work was, however, incorporated into the "George" shot of Operation Greenhouse, which was instructive in testing out concepts that went into the final design. The Fuchs–von Neumann work was passed on, by Fuchs, to the Soviet Union as part of his nuclear espionage, but it was not used in the Soviets' own, independent development of the Teller–Ulam design. The historian Jeremy Bernstein has pointed out that ironically, "John von Neumann and Klaus Fuchs, produced a brilliant invention in 1946 that could have changed the whole course of the development of the hydrogen bomb, but was not fully understood until after the bomb had been successfully made."

Q1: With whom did von Neumann collaborate for further development of the hydrogen bomb?
A1: Klaus Fuchs
Q2: What improvement did von Neumann see in the nuclear weaponry?
A2: using a fission bomb to compress fusion fuel to initiate nuclear fusion
Q3: What country was afforded access to design of improved nuclear weapon through espionage?
A3: Soviet Union
In 1950, von Neumann became a consultant to the Weapons Systems Evaluation Group (WSEG), whose function was to advise the Joint Chiefs of Staff and the United States Secretary of Defense on the development and use of new technologies. He also became an adviser to the Armed Forces Special Weapons Project (AFSWP), which was responsible for the military aspects on nuclear weapons.Over the following two years, he also became a consultant to the Central Intelligence Agency (CIA), a member of the influential General Advisory Committee of the Atomic Energy Commission, a consultant to the newly established Lawrence Livermore National Laboratory, and a member of the Scientific Advisory Group of the United States Air Force.

Q1: In 1950 von Neumann became a consultant for what organization?
A1: Weapons Systems Evaluation Group
Q2: What military organization did von NEumann also consult with for military aspect of nuclear weapons?
A2: Armed Forces Special Weapons Project
Q3: What committee did von Neumann serve on within the Atomic Energy Commission?
A3: General Advisory Committee
In 1955, von Neumann became a commissioner of the AEC. He accepted this position and used it to further the production of compact hydrogen bombs suitable for Intercontinental ballistic missile delivery. He involved himself in correcting the severe shortage of tritium and lithium 6 needed for these compact weapons, and he argued against settling for the intermediate range missiles that the Army wanted. He was adamant that H-bombs delivered into the heart of enemy territory by an ICBM would be the most effective weapon possible, and that the relative inaccuracy of the missile wouldn't be a problem with an H-bomb. He said the Russians would probably be building a similar weapon system, which turned out to be the case. Despite his disagreement with Oppenheimer over the need for a crash program to develop the hydrogen bomb, he testified on the latter's behalf at the 1954 Oppenheimer security hearing, at which he asserted that Oppenheimer was loyal, and praised him for his helpfulness once the program went ahead.

Q1: In what year did von Neumann become commissioner of the AEC?
A1: 1955
Q2: What were compact hydrogen bombs useful for?
A2: Intercontinental ballistic missile delivery
Q3: What was the concern with longer range ICBM with Hbomb?
A3: relative inaccuracy of the missile
Q4: Von Neumann testified at whose hearing about loyalty and help?
A4: Oppenheimer
Shortly before his death, when he was already quite ill, von Neumann headed the United States government's top secret ICBM committee, and it would sometimes meet in his home. Its purpose was to decide on the feasibility of building an ICBM large enough to carry a thermonuclear weapon. Von Neumann had long argued that while the technical obstacles were sizable, they could be overcome in time. The SM-65 Atlas passed its first fully functional test in 1959, two years after his death. The feasibility of an ICBM owed as much to improved, smaller warheads as it did to developments in rocketry, and his understanding of the former made his advice invaluable.

Q1: What was the purpose of top secret ICBM committee?
A1: decide on the feasibility of building an ICBM large enough to carry a thermonuclear weapon
Q2: What argument did von Neumann make about ICBMs?
A2: while the technical obstacles were sizable, they could be overcome in time
Q3: In what year did SM-65 Atlas pass its first fully functional test?
A3: 1959
Von Neumann is credited with the equilibrium strategy of mutual assured destruction, providing the deliberately humorous acronym, MAD. (Other humorous acronyms coined by von Neumann include his computer, the Mathematical Analyzer, Numerical Integrator, and Computer—or MANIAC). He also "moved heaven and earth" to bring MAD about. His goal was to quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR, and he knew the Soviets were doing similar work because the CIA interviewed German rocket scientists who were allowed to return to Germany, and von Neumann had planted a dozen technical people in the CIA. The Russians believed that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the ne plus ultra of weapons, and they believed that whoever had superiority in these weapons would take over the world, without necessarily using them. He was afraid of a "missile gap" and took several more steps to achieve his goal of keeping up with the Soviets:

Q1: What was MAD?
A1: mutual assured destruction
Q2: What was the goal of MAD?
A2: quickly develop ICBMs and the compact hydrogen bombs that they could deliver to the USSR
Q3: What were Russians opinions of future weaponry?
A3: Russians believed that bombers would soon be vulnerable, and they shared von Neumann's view that an H-bomb in an ICBM was the ne plus ultra of weapons
Q4: What was the concern of a missile gap?
A4: keeping up with the Soviets
Von Neumann entered government service (Manhattan Project) primarily because he felt that, if freedom and civilization were to survive, it would have to be because the US would triumph over totalitarianism from Nazism, Fascism and Soviet Communism. During a Senate committee hearing he described his political ideology as "violently anti-communist, and much more militaristic than the norm". He was quoted in 1950 remarking, "If you say why not bomb [the Soviets] tomorrow, I say, why not today? If you say today at five o'clock, I say why not one o'clock?"

Q1: Why did von Neumann join government work?
A1: felt that, if freedom and civilization were to survive, it would have to be because the US would triumph over totalitarianism
Q2: How did von Neumaan describe his political ideology?
A2: violently anti-communist, and much more militaristic than the norm
Q3: What was the project that von Neumann first participated in government?
A3: Manhattan Project
Von Neumann was a founding figure in computing. Donald Knuth cites von Neumann as the inventor, in 1945, of the merge sort algorithm, in which the first and second halves of an array are each sorted recursively and then merged. Von Neumann wrote the sorting program for the EDVAC in ink, being 23 pages long; traces can still be seen on the first page of the phrase "TOP SECRET", which was written in pencil and later erased. He also worked on the philosophy of artificial intelligence with Alan Turing when the latter visited Princeton in the 1930s.

Q1: Who was the inventor of the merge-sort algorithm?
A1: Von Neumann
Q2: With whom did von Neumann work on the philosophy of artificial intelligence?
A2: Alan Turing
Q3: What does a merge sort algorithm do?
A3: the first and second halves of an array are each sorted recursively and then merged
Von Neumann's hydrogen bomb work was played out in the realm of computing, where he and Stanislaw Ulam developed simulations on von Neumann's digital computers for the hydrodynamic computations. During this time he contributed to the development of the Monte Carlo method, which allowed solutions to complicated problems to be approximated using random numbers. His algorithm for simulating a fair coin with a biased coin is used in the "software whitening" stage of some hardware random number generators. Because using lists of "truly" random numbers was extremely slow, von Neumann developed a form of making pseudorandom numbers, using the middle-square method. Though this method has been criticized as crude, von Neumann was aware of this: he justified it as being faster than any other method at his disposal, and also noted that when it went awry it did so obviously, unlike methods which could be subtly incorrect. "Anyone who considers arithmetical methods of producing random digits is, of course, in a state of sin."

Q1: Where were the computations for hydrogen bomb worked out?
A1: von Neumann's digital computers
Q2: What was the Monte Carlo method?
A2: allowed solutions to complicated problems to be approximated using random numbers
Q3: Due to slow use of random numbers what was developed?
A3: pseudorandom numbers