The M Word

The talk I gave to the Oklahoma Atheists in June of 2012 about math literacy.

Transcript

1. The M Word
2. Math Literacy
3. Math Literacy There’s public shame if you walk out now
4. Math Quiz A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
5. Did you pick 10¢?
6. Did you pick 10¢?
7. Word Problems A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
8. Word Problems 1 Ball A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
9. Word Problems 1 Ball + 1 Bat A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
10. Word Problems = $1.10 1 Ball + 1 Bat A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
11. Word Problems = $1.10 1 Ball + (1 Ball + $1.00) A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost?
12. Word Problems = $1.10 1 Ball + (1 Ball + $1.00) A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost? 1 Ball + 1 Ball + $1.00 = $1.10
13. Word Problems = $1.10 1 Ball + (1 Ball + $1.00) A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost? 1 Ball + 1 Ball + $1.00 = $1.10 2 Balls + $1.00 = $1.10
14. Word Problems = $1.10 1 Ball + (1 Ball + $1.00) A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost? 1 Ball + 1 Ball + $1.00 = $1.10 2 Balls + $1.00 = $1.10 2 Balls = 10¢
15. Word Problems = $1.10 1 Ball + (1 Ball + $1.00) A baseball and bat together cost $1.10. The bat costs $1.00 more than the ball. What does the ball cost? 1 Ball + 1 Ball + $1.00 = $1.10 2 Balls + $1.00 = $1.10 2 Balls = 10¢ 1 Ball = 5¢
16. Who the Heck am I to Talk About Math?
17. James Edward Gray II • I’m a programmer • We use at least a little math in our jobs • I’m an atheist • Good atheists use a little math too • I’m not a math whiz
18. Better Qualified
19. Better Qualified
20. Better Qualified
21. Why Math? Is this really Disbelief Discourse material?
22. Skepticism
23. Skepticism Logic
24. Skepticism Logic Math
25. Branches of Math • Combinatorics: dealing with combinations of objects • Estimation: rough calculations of value, quantity, or extent • Probability: the extent to which an event is likely to occur
26. Math Quiz How many people would you need to gather to be absolutely certain (a 100% chance) that two people in the group share a birthday (month and day only)?
27. Did you pick 365?
28. Did you pick 365?
29. 366?
30. 366?
31. It’s actually 367.
32. Math Quiz: Round 2 How many people do we need to gather if we are willing to accept half the odds (a 50% chance) that two people in the group share a birthday?
33. Did you pick 183?
34. Did you pick 183?
35. Would you believe 23?
36. Would you believe 23? Believe it
37. Birthday Combinatorics • Ignoring Leap Year to keep this simple… • The possible combinations of five different birthdays: 365 × 365 × 365 × 365 × 365 (or 3655) • The ways you can select five birthdays without repeats: 365 × 364 × 363 × 362 × 361
38. Birthday Probability • The ratio (fraction) of events we’re interested in to the total possible events • Chance five people don’t share a birthday: (365 × 364 × 363 × 362 × 361) / (365 × 365 × 365 × 365 × 365) • Subtract from one to get the chance of the opposite occurrence (a birthday is shared)
39. Chance Five People Share a Birthday 365 × 364 × 363 × 362 × 361 365 × 365 × 365 × 365 × 365
40. Chance Five People Share a Birthday 365 × 364 × 363 × 362 × 361 365 × 365 × 365 × 365 × 365 = 0.972…
41. Chance Five People Share a Birthday 365 × 364 × 363 × 362 × 361 365 × 365 × 365 × 365 × 365 = 0.972… 1 - 0.972… = 0.027…
42. Chance Five People Share a Birthday 365 × 364 × 363 × 362 × 361 365 × 365 × 365 × 365 × 365 = 0.972… 1 - 0.972… = 0.027… About 3%
43. Chance Twenty Three Share a Birthday 365 × 364 × … × 344 × 343 365 × 365 × … × 365 × 365
44. Chance Twenty Three Share a Birthday 365 × 364 × … × 344 × 343 365 × 365 × … × 365 × 365 = 0.492…
45. Chance Twenty Three Share a Birthday 365 × 364 × … × 344 × 343 365 × 365 × … × 365 × 365 = 0.492… 1 - 0.492… = 0.507…
46. Chance Twenty Three Share a Birthday 365 × 364 × … × 344 × 343 365 × 365 × … × 365 × 365 = 0.492… 1 - 0.492… = 0.507… About 50%
47. It’s Not That Amazing It’s just math
48. Why Second Movies Suck
49. First Movie Second Movie 0 25 50 75 100 Why Second Movies Suck
50. First Movie Second Movie 0 25 50 75 100 Why Second Movies Suck
51. First Movie Second Movie 0 25 50 75 100 Why Second Movies Suck
52. “Plane crashes always happen in threes!”
53. “Plane crashes always happen in threes!” Over what time period?
54. All Measurements are some level of estimate Image from http://iruler.net/
55. All Measurements are some level of estimate Image from http://www.1234tools.com/caliper-measuring/
56. All Measurements are some level of estimate Image from http://www.mitutoyo.com/producttyperesultform.aspx?type=1066
57. Just Understanding Scale can be Valuable
58. Water Depth
59. Water Depth
60. Water Depth
61. Water Depth
62. Water Depth
63. Money
64. Money
65. Money
66. Money
67. Money
68. Money
69. Radiation
70. Radiation
71. Radiation
72. Radiation
73. Radiation
74. http://xkcd.com/ A webcomic of romance, sarcasm, math, and language.
75. Is Math Cool? This is where the war is being fought
76. Heard Any of These? • “I’m terrible at Math” • “Math was always my worst subject” • “A million dollars, a billion, a trillion, whatever”
77. xkcd: “Forgot Algebra”
78. xkcd: “Forgot Algebra”
79. Girls Suck at Math Anyway, Right?
80. Girls Suck at Math Anyway, Right? No: http://www.sciencedaily.com/releases/ 2011/12/111212153123.htm
81. Math Quiz: Girl’s Only! A woman is about to give birth to her first child. What are the odds that it’s a boy?
82. Math Quiz: Girl’s Only! A woman is about to give birth to her first child. What are the odds that it’s a boy? ½
83. Math Quiz: Round 2 A woman is about to give birth to her eighth child. The first seven were all boys. What are the odds that this child is a boy too?
84. Math Quiz: Round 2 A woman is about to give birth to her eighth child. The first seven were all boys. What are the odds that this child is a boy too? ½
85. Math Quiz: Round 3 You visit a friend, knowing she has two children but not the gender of the children. A young girl answers the door, so that’s one child. What are the odds that the other child is a boy?
86. Math Quiz: Round 3 You visit a friend, knowing she has two children but not the gender of the children. A young girl answers the door, so that’s one child. What are the odds that the other child is a boy? ⅔
87. Possible Combinations of Two Children • Boy boy • Boy girl • Girl boy • Girl girl
88. Possible Combinations of Two Children • Boy boy • Boy girl • Girl boy • Girl girl
89. Champions of Math We hope
90. Are They on Our Side? Image from http://sharetv.org/shows/the_big_bang_theory #1: http://tvbythenumbers.zap2it.com/2012/04/17/syndicated-tv-ratings-big-bang-theory-on-top-again-dr-phil-leads-talk-shows/129421/
91. Is He on Our Side? Image from http://www.boston.com/bigpicture/2008/11/the_next_president_of_the_unit.html
92. Danica McKellar is on Our Side • Actress (Wendy on The Wonder Years) • Sex symbol • Math degree (with honors) • Published author • Chayes-McKellar-Winn theorem Image from http://allinone1-z.blogspot.com/2010/12/danica-mckellar-hotdanica-mckellar.html
93. Danica’s Books Images from http://www.amazon.com/
94. It’s Very Important to be Cool Just ask Apple and Microsoft
95. U.S. Math Literacy • The U.S. is below a 34 country average • 17 of those 34 countries score better than we do while only 5 score below us (11 are roughly even with us) • Ranking math proficiency from level 1 to level 6, only 27% of U.S. students score 4 or higher 2009 statistics for 15-year-olds from http://nces.ed.gov/surveys/pisa/pisa2009highlights_3.asp
96. Is Math Important? The consequences of mathematical illiteracy
97. Writing on This Subject Images from http://www.amazon.com/
98. My Book Club Pick Image from http://www.amazon.com/
99. A Biblical Flood • “…all the high mountains under the entire heavens were covered.”—Genesis 7:19 NIV • 10,000 to 20,000 feet of water • “And rain fell on the earth forty days and forty nights.”—Genesis 7:12 NIV • 960 hours of rainfall • That’s water rising about 15 feet per hour
100. Will it Sink?
101. Will it Sink? Image from http://www.naval-technology.com/projects/cvn-21/
102. Will it Sink? Image from http://www.naval-technology.com/projects/cvn-21/ Image from http://www.whybaptism.org/Creation-HTML/NoahArk.htm
103. "The State Department is infested with communists. I have here in my hand a list of 205— a list of names that were made known to the Secretary of State as being members of the Communist Party and who nevertheless are still working and shaping policy in the State Department."—Joe McCarthy, U.S. Senator
104. Are Exact Numbers More True? Internal Human Body Temperature: 98.6°F
105. Are Exact Numbers More True? Internal Human Body Temperature: 98.6°F 37.0°C
106. $100,000 Average $100,000 $101,000 $98,500 $99,700 $103,200 $100,300 $99,000 $96,800 $100,000 $101,500
107. $100,000 Average $1 $1 $1 $1 $1 $1 $1 $1 $1 $999.991 $100,000 $101,000 $98,500 $99,700 $103,200 $100,300 $99,000 $96,800 $100,000 $101,500
108. Mean Verses Median $1 $1 $1 $1 $1 $1 $1 $1 $1 $999.991 $100,000 $101,000 $98,500 $99,700 $103,200 $100,300 $99,000 $96,800 $100,000 $101,500
109. Mean Verses Median $1 $1 $1 $1 $1 $1 $1 $1 $1 $999.991 $100,000 $101,000 $98,500 $99,700 $103,200 $100,300 $99,000 $96,800 $100,000 $101,500 =$100,000 =$100,000
110. Mean Verses Median $1 $1 $1 $1 $1 $1 $1 $1 $1 $999.991 $100,000 $101,000 $98,500 $99,700 $103,200 $100,300 $99,000 $96,800 $100,000 $101,500 =$100,000 =$100,000 =$1 =$100,000
111. Math Quiz Judy is thirty-three, unmarried, and quite assertive. A magna cum laude graduate, she majored in political science in college and was deeply involved in campus social affairs, especially in anti-discrimination and anti-nuclear issues. Which statement is more probable? (a) Judy works as a bank teller. (b) Judy works as a bank teller and is active in the feminist movement.
112. Occam’s Razor (a) Judy works as a bank teller. (b) Judy works as a bank teller and is active in the feminist movement.
113. Occam’s Razor (a) Judy works as a bank teller. (b) Judy works as a bank teller and is active in the feminist movement.
114. Occam’s Razor (a) Judy works as a bank teller. (b) Judy works as a bank teller and is active in the feminist movement. Bank Teller Odds * Feminist Odds < Bank Teller Odds
115. Voting and Polls
116. Polling • Any kind of polling is subject to statistical errors • This is where our margin of error comes from • Even that can (rarely) be off • You also have to worry about systemic errors
117. How Many People Have You Slept With? A famously problematic poll question
118. Gerrymandering • Nick had to move to even try to get elected • That’s because politicians use packing and cracking to distribute votes • Nick’s district looks like a dinosaur • The Voting Rights Act made this illegal, but only when racial (political is fine)
119. The Census • The constitution requires an “actual enumeration” of the population every 10 years • This process costs billions • It contains known systemic errors
120. Sampling
121. Is Sampling Legal? • In the past, the U.S. Census used both approaches • This has been fought out in the Supreme Court: • Sampling was declared unconstitutional • Imputation is still allowed
122. The Truth: Humans Can’t Count Well, not exactly
123. Did Bush or Gore win the popular vote in 2000?
124. Neither It was a tie, mathematically speaking
125. It Takes More Than Just Math • Two gamblers wager $100 on coin flips • The first to win six flips takes the pot • Their game is interrupted when the score is five to three • How do we fairly divide the pot?
126. Payout Arguments • Pay $100 to the gambler with five wins since he’s leading and the prize is all or nothing • Payout ⅝ and ⅜ of the pot for their respective wins • Pay ⅞ and ⅛ for the odds each man will win (½ × ½ × ½ = ⅛ and 1 - ⅛ = ⅞)
127. How Do We Improve? My recommendations for where we go from here
128. A Traditional Approach Images from http://www.amazon.com/
129. For Puzzle Fans Images from http://www.amazon.com/
130. Math Quiz You need to test the blood of 100 patients for a disease. On average one in a 100 will have the disease. Can you find those that have the disease by doing less than 100 tests? (Givens: you have enough of each patient’s blood to test them several times and you can test multiple patients at once by combining samples.)
131. Binary Search 100
132. Binary Search 100 50 50
133. Binary Search 100 50 25 50 25
134. Binary Search 100 50 25 13 50 25 12
135. Binary Search 100 50 25 13 7 50 25 12 6
136. Binary Search 100 50 25 13 7 4 50 25 12 6 3
137. Binary Search 100 50 25 13 7 4 2 50 25 12 6 3 2
138. Binary Search 100 50 25 13 7 4 2 1 50 25 12 6 3 2 1
139. A Secret/Fun Cheat Images from http://www.amazon.com/
140. Back to Front 3 4 1 3 ×
141. Back to Front 3 4 1 3 × 2 1
142. Back to Front 3 4 1 3 × 2 1 0 1
143. Back to Front 3 4 1 3 × 2 1 0 1 0
144. Back to Front 3 4 1 3 × 2 1 0 1 0 4
145. Back to Front 3 4 1 3 × 2 1 0 1 0 4 3
146. Back to Front 3 4 1 3 × 2 1 0 1 0 4 3 +
147. Back to Front 3 4 1 3 × 2 1 0 1 0 4 3 + 2 4 4
148. Front to Back 3 4 1 3 ×
149. Front to Back 3 4 1 3 × 3 0 0
150. Front to Back 3 4 1 3 × 3 0 0 0 9
151. Front to Back 3 4 1 3 × 3 0 0 0 9 0 4
152. Front to Back 3 4 1 3 × 3 0 0 0 9 0 4 1 2
153. Front to Back 3 4 1 3 × + 3 0 0 0 9 0 4 1 2
154. Front to Back 3 4 1 3 × + 2 4 4 3 0 0 0 9 0 4 1 2
155. In Your Head 34 × 13
156. In Your Head 34 × 13 30 × 10 = 300
157. In Your Head 34 × 13 30 × 10 = 300 30 × 3 = 90 + 300 = 390
158. In Your Head 34 × 13 30 × 10 = 300 30 × 3 = 90 + 300 = 390 4 × 10 = 40 + 390 = 430
159. In Your Head 34 × 13 30 × 10 = 300 30 × 3 = 90 + 300 = 390 4 × 10 = 40 + 390 = 430 4 × 3 = 12 + 430 = 442
160. A Good Rule of Thumb • A lot of people choose to look up a new word when they first encounter it • It’s an equally good idea to look up new math when you encounter it • http://www.wolframalpha.com/ • Ask a math geek
161. How Does a Home Mortgage Loan Work? What’s the formula?
162. Wolfram|Alpha
163. Wolfram|Alpha
164. Wolfram|Alpha
165. Wolfram|Alpha
166. The Formulas P = L(i(1 + i)m) / ((1 + i)m - 1) B = L(1 + i)m - (1 + i)p) / ((1 + i)m - 1) P = Monthly payment L = Loan amout i = Monthly interest (6% loan: 0.06 / 12 = 0.005) m = Length of the loan in months B = Balance remaining p = Payments made
167. Please, Help Bring Back the Cool in Math If we do nothing else
168. Thanks
169. Questions? Slides: https://speakerdeck.com/u/jeg2/p/the-m-word