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Pat Hanrahan's Tapestry Conference 2013 short story slide presentation
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Showing is not Explaining
Pat Hanrahan
Stanford and Tableau
Tapestry
Euclid’s Algorithm**First known algorithm
Greatest Common Divisor
2, 3, 4, 6 divide 12
2, 3, 6, 7 divide 42
6 is the GCD
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
Demonstration
Problems with Animation [Tversky et al.]
Motion is fleeting and transient
Cannot simultaneously attend to multiple
motions
People try to parse motion into events,
actions and behaviors
We strive to infer causality and intention
Anthropomorphizing: physical motion may
cause confusion or lead to incorrect
conclusions
Difficult to estimate paths and trajectories
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
a=15, b=6
a=15
b=6
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
a=9, b=6
a=15
b=6
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
a=9, b=6
a=3, b=6
a=15
b=6
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
a=9, b=6
a=3, b=6
a=3, b=3
a=15
b=6
Euclid’s Algorithm
def gcd(a,b):
while b != 0:
if a > b:
a = a-b
else:
b = b-a
return a
a=9, b=6
a=3, b=6
a=3, b=3
a=3, b=0
a=15
b=6
?
Why Greatest Common Divisor?
Fact 1
Consider the answer r
a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
Consider b
a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
Consider b
a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
Consider b
r divides a a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
Consider b
r divides a
Therefore, r divides a & b
a
b
r
Why Greatest Common Divisor?
Fact 1
Consider the answer r
r divides b
Consider b
b divides a
Therefore, r divides a & b
Hence, r <= GCD
a
b
r
Why Greatest Common Divisor?
Fact 2
Suppose d divides a
a
Why Greatest Common Divisor?
Fact 2
Suppose d divides a
Suppose d divides b
b
Why Greatest Common Divisor?
Fact 2
suppose d divides a & b
a
b
Why Greatest Common Divisor?
Fact 2
suppose d divides a & b
a
b
r
Why Greatest Common Divisor?
Fact 2
suppose d divides a & b
then d must divide r
a
b
r
Why Greatest Common Divisor?
Fact 2
suppose d divides a & b
then d must divide r
Any divisor d of a & b
must divide r a
b
r
Why Greatest Common Divisor?
Fact 2
suppose d divides a & b
then d must divide r
Any divisor d of a & b
must divide r
Therefore, GCD <= r
a
b
r
Why Greatest Common Divisor?
Fact 1: r <= GCD
Fact 2: GCD <= r
Therefore r = GCD
Cool math reasoning! a
b
r
Recording and Showing
Getting Easier with
Computers
“Showing is not Explaining”
Thanks to Barbara Tversky
for explaining this maxim to me
Aftermath of Hurricane Katrina
By Emmett Mayer III
Principles
1. Perceiving is hard, graphics design to the rescue
2. Need to add the invisible forces of cause and effect, intention and consequences
3. People produce better visuals if they are told to explain
Software needs to support these principles
