Is People’s Behavior Predictable?

1. Is People’s Behavior Predictable? Gary Rockswold, Ph.D Emeritus Professor of Mathematics Minnesota State University, Mankato PEARSON MATHEMATICS WEBINAR April 7, 2011

2. Taking Care of the Details • In mathematics we spend a lot of time covering the details. • After all, putting the decimal point in the “correct place” can make a big difference! Photo by Wonderlane

3. Teaching a Rich Curriculum • Arithmetic, factoring, solving equations, … • It’s tough to “do it all”. • Most of our time is spent studying the trees. Less time is spent studying the forest. By Grant MacDonald

4. The View Above the Trees • In this presentation we will “look at the forest”. • This view is essential—particularly when we are communicating with students and public! Travis S. Flickr

5. Math in the Natural Sciences

6. Natural Sciences • Mathematics usage in the natural sciences is more well-known. • Many of these examples showhow we are interpreting the world more and more in terms of mathematics. Large Hadron Collider (LHC) By CERN

7. Why Are They Building the LHC? In one word: “Higgs” • The Higgs particle is important because it gives objects in the universe mass. • There is no experimental evidence for the Higgs particle.

8. Why Do They Think Higgs Exists? • The symmetry in the equations suggests that it exists. • In 1964 Peter Higgs proposed the “Higgs particle” in a paper that contained only 79 lines and 5 equations.

9. Mathematics Says That It Is Safe. • Scientists hope to create black holes in the LHC. • Fortunately, Stephen Hawking (1974) has shown mathematically that tiny black holes will disintegrate in a fraction of a second. Scientists really do trust mathematics!

10. A Nobel Laureate’SObservation “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” by Eugene Wigner in Communications in Pure and Applied Mathematics, February 1960

11. Mathematics Guides Us. Mathematics can lead us in a direction we would not take if we only followed up physical ideas by themselves. --Paul Dirac

12. Mathematics in the Social Sciences

13. Social sciences Next we will concentrate on the amazing impact that mathematics is having in the social sciences. Social sciences often deal with human behavior and the choices that people make. By Viola Damiani

14. Are Math and Behavior Related? By MinivanNinja Flickr • We often think that behavior is unpredictable. • But is behavior outside the realm of math? • Modeling the choices that people make is one way to predict behavior. By OrphanJones flickr

15. Meaningful Mathematics Most of our students major in humanities or social sciences. Math is meaningful… and it is important to show how math relates to their lives.

16. Modeling Social Situations Consider teaching the concept of intersection in a Venn diagram in today’s classroom. People wearing sandals People wearing socks MY DAD!!!

17. A Famous Example

18. Modeling a Pool Player Mathematics can predict the next shot that an excellent pool player will make with a high degree of accuracy. By misswired flickr

19. Important Questions Does this mean that a pool player is actually using trigonometry, algebra, vectors, and properties of physics to determine the next shot? Probably not But does this mean that our mathematical model is incorrect and not worthwhile? By sbma44 flickr

20. Math Modeling Choice Math is not modeling “reality” in that math is not modeling how the pool player does it, but somehow mathematics is modeling the pool player’s choices. Whatever is happening, there is an equivalency: Pool player’s choices vs. Mathematical calculations By sbma44 flickr By misswired flickr

21. Modeling Non-Rational Choice

22. Losses and Gains Question: Is it better to give your significant other two $100 presents or is it better to give one $200 present? Next Question: If a person wins $50 and then gets a $25 parking ticket, do they feel happy because the net gain is $25? By Bahi P Flickr By puggles flickr

23. Behavior and Losses People weigh losses significantly more than they do gains. (About double) People demonstrate loss-averse behavior. This somewhat non-rational behavior is modeled by the following value function. By Dale Moore

24. Concave Value Function Modeling: Losses and Gains versus Value

25. Why Give Rebates? Yes, people forget to send them in, but there’s more. The small rebate (gain) gives more value than does tacking on the additional small loss to the already “high” price. People’s value functions are concave not linear!

26. The Recent Debate in Economics

27. The Recent Economic Collapse How Did Economists Get It So Wrong? byPaul Krugman, Nobel Laureate The New York Times 9/6/2009 By David_Shankbone flickr

28. Mathematics in Economics “As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth.” --Paul Krugman, Nobel Laureate

29. Shocked by the Economy I am in “shocked disbelief” because “the whole intellectual edifice” has “collapsed”. By trackrecord flickr --Alan Greenspan, October 2008

30. However, Math Is Important. Math continues to guide our thinking: “Only after doing the math, was I able to express my models in plain English. It really took the equations to understand what was happening.” --Paul Krugman, Nobel Laureate

31. Social Networking

32. Social Networking Social networking is transforming our society. Social networking is generational. Should this affect how we teach math? By Emilie Ogez flickr

33. Gmail However, Google reads our email and sends us advertisements based on keywords in our private messages. By Gubatron Flickr Our privacy is a currency. For example, Google charges nothing for gmail.

34. Facebook Three-quarters of Facebook users do not live in the U.S. The privacy issues surrounding Facebook are global issues. In some sense: Sharing data is the point of Facebook. By @superamit flickr

35. What’s the Fuss About? Using mathematics, it is possible to analyze a person’s facebook friends and determine with “reasonable certainty” things like hobbies, interests, health issues, and even sexual orientation. This information is used to target advertisements toward a subset of consumers. If businesses analyze social networks they can know exactly where to insert their campaign so that it fuels itself and reaches people who care. More effective than 30-second TV commercials

36. The Mathematics of Social Networks

37. Mathematics And Media Max Levchin (CEO of Slide) is the number one creator of applications for Facebook. He stated the following about his success. “Our competitive advantage is actually our math skills, which is probably not something you would expect from a media company.” --Max Levchin, CEO of Slide

38. Social Networks as Directed Graphs People are vertices tied by friendship, interest, membership, or beliefs. Person 1 and 2 are friends with each other. Person 3 “likes” everyone, but no one “likes” Person 3. 2 3 1 5 4

39. Adjacency Matrices A square adjacency matrix can be used to summarize this simple social network: 2 3 1 5 4

40. Structure in a Network Matrix Matrices are often square, but not necessarily symmetric. If aij = aji, then “friendships” are mutual. By looking at each row and column, people with larger social networks can be identified as having many 1’s. The sums of columns and rows have meaning.

41. Calculating Social Distance The computation A² can be used to determine people who have a social distance of 2. 2 3 1 5 4

42. Visualization of Social Networks The following graph shows a social network. People with centrality become apparent, as do loners.

44. The Essence of Mathematics One conceptcan be used to simplify a vast array of complicated problems. Problems solved by adjacency matrices: Transportation problems/shortest paths Internet pages and links Social networks By ButchLebo Flickr By HH-Michael flickr

45. Mathematics, Data, and Social Networks VIDEO: From Vermont Public Television: Features Peter Dodds, University of Vermont

47. Using Mathematics to Keep Secrets Safe

48. Keeping Information Secret Cryptography as been around for a long time as a way to hide information. Using math, groups of people now compute virtually anything from their collective data without revealing any individual data.

49. Secure Function Evaluation • Suppose that three people have individual weights of 155 lb., 210 lb., and 184 lb. They want to calculate the groups total weight without revealing their individual weights. 155 + 210 + 184 = 549 lb

50. Applying Modular Arithmetic Each person privately selects three numbers between 0 and 1000, whose sum equals their weight modulo 1000. For example, the 155 lb. person could use That is, 1155 mod 1000 = 155 255 + 563 = 1155 155 + 337