jeg2
June 18, 2012
900

# The M Word

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

June 18, 2012

## 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

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…

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…

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

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?

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

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

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
• 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

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

34 × 13

34 × 13
30 × 10 = 300

34 × 13
30 × 10 = 300
30 × 3 = 90 + 300 = 390

34 × 13
30 × 10 = 300
30 × 3 = 90 + 300 = 390
4 × 10 = 40 + 390 = 430

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/

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