The M Word

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June 18, 2012

The M Word

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

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jeg2

June 18, 2012
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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