jeg2
June 18, 2012
970

# The M Word

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

June 18, 2012

## Transcript

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?

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¢

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

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)?

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?

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%

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

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”

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

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

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

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

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

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

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

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

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)

from here

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.)

6

12 6 3

25 12 6 3 2
138. ### Binary Search 100 50 25 13 7 4 2 1

50 25 12 6 3 2 1

0 1

0 1 0

0 1 0 4

0 1 0 4 3

0 1 0 4 3 +
147. ### Back to Front 3 4 1 3 × 2 1

0 1 0 4 3 + 2 4 4

0

0 0 9

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

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

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