Jun 29, 2023 01:21 PM
What math can teach us about standing up to bullies
https://www.eurekalert.org/news-releases/993759
INTRO: In a time of income inequality and ruthless politics, people with outsized power or an unrelenting willingness to browbeat others often seem to come out ahead.
New research from Dartmouth, however, shows that being uncooperative can help people on the weaker side of the power dynamic achieve a more equal outcome—and even inflict some loss on their abusive counterpart.
The findings provide a tool based in game theory—the field of mathematics focused on optimizing competitive strategies—that could be applied to help equalize the balance of power in labor negotiations or international relations and could even be used to integrate cooperation into interconnected artificial intelligence systems such as driverless cars.
Published in the latest issue of the journal PNAS Nexus, the study takes a fresh look at what are known in game theory as "zero-determinant strategies" developed by renowned scientists William Press, now at the University of Texas at Austin, and the late Freeman Dyson at the Institute for Advanced Study in Princeton, New Jersey... (MORE - details)
How math achieved transcendence
https://www.quantamagazine.org/recountin...-20230627/
INTRO: In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides the ones used to count, and they have labored to understand their properties.
Although each type of number has its own fascinating and complicated history, today they are all so familiar that they are taught to schoolchildren. Integers are just the whole numbers, plus the negative whole numbers and zero. Rational numbers are those that can be expressed as a quotient of integers, such as 3, −1/2 and 57/22. Their decimal expansions either terminate (−1/2 = −0.5) or eventually repeat (57/22 = 2.509090909…). That means if a number has decimal digits that go on forever without repeating, it’s irrational. Together the rational and irrational numbers comprise the real numbers. Advanced students learn about the complex numbers, which are formed by combining the real numbers and imaginary numbers; for instance, i=√−1.
One set of numbers, the transcendentals, is not as well known. Paradoxically, these numbers are both plentiful and exceedingly difficult to find. And their history is intertwined with a question that plagued mathematicians for millennia.. (MORE - details)
https://www.eurekalert.org/news-releases/993759
INTRO: In a time of income inequality and ruthless politics, people with outsized power or an unrelenting willingness to browbeat others often seem to come out ahead.
New research from Dartmouth, however, shows that being uncooperative can help people on the weaker side of the power dynamic achieve a more equal outcome—and even inflict some loss on their abusive counterpart.
The findings provide a tool based in game theory—the field of mathematics focused on optimizing competitive strategies—that could be applied to help equalize the balance of power in labor negotiations or international relations and could even be used to integrate cooperation into interconnected artificial intelligence systems such as driverless cars.
Published in the latest issue of the journal PNAS Nexus, the study takes a fresh look at what are known in game theory as "zero-determinant strategies" developed by renowned scientists William Press, now at the University of Texas at Austin, and the late Freeman Dyson at the Institute for Advanced Study in Princeton, New Jersey... (MORE - details)
How math achieved transcendence
https://www.quantamagazine.org/recountin...-20230627/
INTRO: In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides the ones used to count, and they have labored to understand their properties.
Although each type of number has its own fascinating and complicated history, today they are all so familiar that they are taught to schoolchildren. Integers are just the whole numbers, plus the negative whole numbers and zero. Rational numbers are those that can be expressed as a quotient of integers, such as 3, −1/2 and 57/22. Their decimal expansions either terminate (−1/2 = −0.5) or eventually repeat (57/22 = 2.509090909…). That means if a number has decimal digits that go on forever without repeating, it’s irrational. Together the rational and irrational numbers comprise the real numbers. Advanced students learn about the complex numbers, which are formed by combining the real numbers and imaginary numbers; for instance, i=√−1.
One set of numbers, the transcendentals, is not as well known. Paradoxically, these numbers are both plentiful and exceedingly difficult to find. And their history is intertwined with a question that plagued mathematicians for millennia.. (MORE - details)