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