# Science

Related: About this forum# When Math Gets Impossibly Hard {article w/surprising connection to Gerrymandering ! } (Quanta)

David S. Richeson

Contributing Columnist

September 14, 2020

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People use the term “impossible” in a variety of ways. It can describe things that are merely improbable, like finding identical decks of shuffled cards. It can describe tasks that are practically impossible due to a lack of time, space or resources, such as copying all the books in the Library of Congress in longhand. Devices like perpetual-motion machines are physically impossible because their existence would contradict our understanding of physics.

Mathematical impossibility is different. We begin with unambiguous assumptions and use mathematical reasoning and logic to conclude that some outcome is impossible. No amount of luck, persistence, time or skill will make the task possible. The history of mathematics is rich in proofs of impossibility. Many are among the most celebrated results in mathematics. But it was not always so.

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Many states require that districts be “compact,” a term with no fixed mathematical definition. In 1991, Daniel Polsby and Robert Popper proposed 4?A/P² as a way to measure the compactness of a district with area A and perimeter P. Values range from 1, for a circular district, to close to zero, for misshapen districts with long perimeters.

Meanwhile, Nicholas Stephanopoulos and Eric McGhee introduced the “efficiency gap” in 2014 as a measure of the political fairness of a redistricting plan. Two gerrymandering strategies are to ensure that the opposition party stays below the 50% threshold in districts (called cracking), or near the 100% level (stacking). Either tactic forces the other party to waste votes on losing candidates or on winning candidates who don’t need the votes. The efficiency gap captures the relative numbers of wasted votes.

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more: https://www.quantamagazine.org/when-math-gets-impossibly-hard-20200914/

Not much more on Gerrymandering, but lots of interesting background.

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#### ihas2stinkyfeet

(1,400 posts)my son has a phd in theoretical math.

he posted a vid once of someone demonstrating some topology thing w a dance.

he bypassed my math knowledge at about 10. i took calculus on college but got c's. but i had hidden epilepsy until recently and now that that is treated, this shit all makes a lot more sense to me. amazing how hard math and physics can be when you dont know your left from your right.