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Mathematics & Reason
Mathematics & Reason
How understanding maths and reason changes your view of the World.
How understanding maths and reason changes your view of the World.
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What is Mathematics?
What is Mathematics?
The search for pattern.
The search for pattern.
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Betrand RussellBetrand Russell
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”
“Mathematics, rightly viewed, possesses not only truth, but supreme beauty.”
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Monty Hall ProblemMonty Hall Problem
1 2 3
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Monty Hall ProblemMonty Hall Problem
1
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Simpson’s ParadoxSimpson’s Paradox
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Simpson’s ParadoxSimpson’s Paradox
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Bayes’s TheoremBayes’s Theorem
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
A patient goes to see a doctor. The doctor performs a test with 99 percent reliability--that is, 99 percent of people who are sick test positive and 99 percent of the healthy people test negative. The doctor knows that only 1 percent of the people in the country are sick. Now the question is: if the patient tests positive, what are the chances the patient is sick?
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Bayes’s TheoremBayes’s Theorem
9900
100
9801
99
1
99
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Penney Ante Game
Penney Ante Game
Mathematics in Gambling
Mathematics in Gambling
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Penney Ante Rules
1. You pick a 3-coin sequence (e.g. H T H)
2. I pick a 3 coin sequence (e.g. T T H)
3. We toss a coin repeatedly
4. Whoever’s sequence appears first wins. T H H H H T H you win
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H H H T T TH H T T T
HH T H T H
TH T T T H
H
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Penny Ante is a scam ! Imagine you choose H H
H . Eventually we get the
first appearance of H H H :
. . . . . . . . . . . ? H H H
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Was OJ Simpson Guilty?
Was OJ Simpson Guilty?
Mathematics & Statistics in the
Courtroom
Mathematics & Statistics in the
Courtroom
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O.J. Simpson abused his wifeand she was murdered.
1 in 1,000 abused womenare killed by their
husbands. But 80% of murdered abused
womenare killed by the husbands.
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3 Dice… which one would you choose?
3 Dice… which one would you choose?
33
33
33
33
33
66
22
22
22
55
55
55
11
44
44
44
44
44
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MC EsherMC Esher
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Are there examples of this way of thinking in
mathematics?
Are there examples of this way of thinking in
mathematics?
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33
33
33
33
33
66
22
22
22
55
55
55
vs
BLUEBLUE beats GREENGREEN on average
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22
22
22
55
55
55
vs
GREENGREEN beats REDRED on average
11
44
44
44
44
44
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33
33
33
33
33
66
22
22
22
55
55
55
11
44
44
44
44
44
?
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vs
REDRED beats BLUEBLUE!!
11
44
44
44
44
44
33
33
33
33
33
66
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625625
671671
Two blues beat two reds
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Benford’s LawBenford’s Law
• Take a list of data.• Examine how many of the numbers start with a 1, 2, 3, etc
• Take a list of data.• Examine how many of the numbers start with a 1, 2, 3, etc
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Benford’s LawBenford’s Law
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Understanding Mathematics
Understanding Mathematics
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Picasso’s GuernicaPicasso’s Guernica
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Perelman’s PoincarePerelman’s Poincare
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Why do we study such old maths?
Why do we study such old maths?