Book: Numbers and the Making of Us: Counting and the Course of Human Cultures

“Carved into our past, woven into our present, numbers shape our perceptions of the world and of ourselves much more than we commonly think. Numbers and the Making of Us is a sweeping account of how numbers radically enhanced our species’ cognitive capabilities and sparked a revolution in human culture. Caleb Everett brings new insights in psychology, anthropology, primatology, linguistics, and other disciplines to bear in explaining the myriad human behaviors and modes of thought numbers have made possible, from enabling us to conceptualize time in new ways to facilitating the development of writing, agriculture, and other advances of civilization.

“Number concepts are a human invention―a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.

“Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.”

https://www.amazon.com/Numbers-Making-Us-Counting-Cultures/dp/0674504437/ref=sr_1_1?ie=UTF8&qid=1490024639&sr=8-1&keywords=numbers+and+the+making+of+us

Why Do We Count?

“Numbers may feel instinctual. They may seem simple and precise. But Everett synthesizes the latest research from archaeology, anthropology, psychology and linguistics to argue that our counting systems are not just vital to human culture but also were invented by that culture. “Numbers are not concepts that come to people naturally and natively,” he writes. “Numbers are a creation of the human mind.””

https://fivethirtyeight.com/features/why-do-we-count/?ex_cid=538twitter

 

How can we use math to help us understand sports?

There are some interesting debates raging within the sports community about the ways in which statistics can help us understand athletic performance and the value of different players to a team. These statistics also are used to evaluate what are effective strategies and which are not.

Though some of the debate is about whether we should or should not rely on these statistical models, there are some interesting differences among those models themselves. Each model relies on different assumptions and maps the reality of the game differently. Sometimes, as in the case discussed in the article below, different models give us wildly different answers about a player’s value. Which is correct? What does this case tell us about the ability and limits of using math to understand reality? Is it possible to resolve this debate?

http://www.espn.com/mlb/story/_/id/18114272/miller-going-war-mystery-robbie-ray

How does the quote below apply to this case?

“A man with a watch knows what time it is. A man with two watches is never sure.”

The Billion-Dollar Jackpot: Engineered to Drain Your Wallet

“Consider that for state-run lotteries as a whole, only about 60 cents of every dollar goes back to ticket buyers in the form of winnings, an analysis of United States Census Bureau data shows. The flip side is that in the long run, players as a group lose about 40 percent of the money they put into the lottery, and the chances of a big win are vanishingly small.”

http://www.nytimes.com/2016/08/14/your-money/the-billion-dollar-lottery-jackpot-engineered-to-drain-your-wallet.html?ribbon-ad-idx=11&rref=homepage

In N.F.L., Deeply Flawed Concussion Research and Ties to Big Tobacco

This article connects to some interesting TOK issues. Clearly we can discuss the ethics, or lack of ethics, in the NFL’s manipulation of data to disprove conclusions that undermine its business.

This also illustrates how math can help us understand and possibly prove complex issues like the connection between football and health issues like concussions and CTE.  Rather than observing or intuiting a causal relationship between two phenomenon, we have to use math along with the methods of proof in the natural sciences to establish truth and construct knowledge. By misrepresenting data, one might reach incorrect conclusions, which seems to have been the case here.

http://www.nytimes.com/2016/03/25/sports/football/nfl-concussion-research-tobacco.html

A second article about how flawed data undermines our ability to construct knowledge.

“Researchers primed to believe that the NFL has concussions under control, a data set that’s missing important information, and publication in a journal edited by a consultant to the NFL — it looks more like an attempt to create evidence for a predetermined message than good science. But even if we throw out these studies, we can’t yet conclude that football inevitably leads to lasting brain damage.”

http://fivethirtyeight.com/features/the-nfls-shoddy-science-means-we-know-even-less-about-concussions/

Human cycles: History as science Advocates of ‘cliodynamics’ say that they can use scientific methods to illuminate the past. But historians are not so sure.

“What is new about cliodynamics isn’t the search for patterns, Turchin explains. Historians have done valuable work correlating phenomena such as political instability with political, economic and demographic variables. What is different is the scale — Turchin and his colleagues are systematically collecting historical data that span centuries or even millennia — and the mathematical analysis of how the variables interact.”

http://www.nature.com/news/human-cycles-history-as-science-1.11078

The Pursuit of Beauty: Yitang Zhang solves a pure-math mystery.

“The problem that Zhang chose, in 2010, is from number theory, a branch of pure mathematics. Pure mathematics, as opposed to applied mathematics, is done with no practical purposes in mind. It is as close to art and philosophy as it is to engineering. “My result is useless for industry,” Zhang said. The British mathematician G. H. Hardy wrote in 1940 that mathematics is, of “all the arts and sciences, the most austere and the most remote.” Bertrand Russell called it a refuge from “the dreary exile of the actual world.” Hardy believed emphatically in the precise aesthetics of math. A mathematical proof, such as Zhang produced, “should resemble a simple and clear-cut constellation,” he wrote, “not a scattered cluster in the Milky Way.” Edward Frenkel, a math professor at the University of California, Berkeley, says Zhang’s proof has “a renaissance beauty,” meaning that though it is deeply complex, its outlines are easily apprehended. The pursuit of beauty in pure mathematics is a tenet. Last year, neuroscientists in Great Britain discovered that the same part of the brain that is activated by art and music was activated in the brains of mathematicians when they looked at math they regarded as beautiful.”

http://www.newyorker.com/magazine/2015/02/02/pursuit-beauty

The Beauty of Bounded Gaps
A huge discovery about prime numbers—and what it means for the future of math.

http://www.slate.com/articles/health_and_science/do_the_math/2013/05/yitang_zhang_twin_primes_conjecture_a_huge_discovery_about_prime_numbers.html