Section 9 - Diversity and Innovation

Problem Solving and Innovation

Use Landscape to begin to get to the best value (hills and valleys)

Perspectives and Innovation

Perspective - how you represent a problem, to be able to encode it

Perspective - representation of all possible solutions, with encoding, by applying values, we get the landscape

Rugged Landscape - many peaks and valleys
Local Optima - peaks within the landscape
Mt Fuji - A landscape with one peak

Good Perspective - few local optima,

Shovel Size Landscape - by Taylor

Sum-to-Fifteen - Herb Simon
-  Cards 1-9 face up on the table
-  Player alternate selecting cards
- Win if you get to exactly 15

Magic Square - all rows add up to 15, all columns add up to 15 and all diagonals add up to 15

Savant Existence Theorem - for any problem there exists a Mt Fuji Landscape

Heuristics

Heuristics - how you move on the landscape (hill climbing, random search, etc)

Hill climb to get to local optima

Heuristic 1 - Do the Opposite - think about the current solution and do just the opposite
Heuristic 2 - Big Rocks First - Do important things first
Heuristic 3 - No Free Lunch (Wolpert  & McCready) - Algorithms that search the same number of points  with the goal of locating the maximum value of a function defined on a finite set perform exactly  the same when averages over  all possible functions
                  -  If you don't know if your perspective, no algorithm or heuristic performs better than any other.

Diverse heuristics provide better solutions

Teams and Problem Solving

Groups of people are better at solving problems - based on diversity of thought

Using Caloric Perspective
A = 10
B = 8
C = 6

Average = 8

Using the Masticity Perspective
A=10
B= 8
D =6
E = 4
F = 2

Average = 6

If they work as a team, then if they the person on Caloric finds C, then the person doing Masticity will not get stuck.  In this case the only place the team can get caught is A & B.

Claim: The team can only get stuck on solution that's a local optimum for every  member of the team.

So we want people with different perspectives and different heuristics

Assumptions
1) when you have a team, they are assumed to be able to communicate
2) There is some ability to recognize an error in our solution.  I propose something and people may actually not see the value.

Recombination

Recombination - take solutions from multiple problems, bring them together to recombine them to better and better solutions 

Innovation comes from recombination of many solutions.

How many ways to pick 3 objects from 10?

10 things to pick 1st, 9 to pick second, 8 to pick 3rd, .....

divided by 3 chances for 1st pick, 2 chances for 2nd, and 1 for third.

leaving 120 ways

Picking 20 cards from a deck ==> 52 x 51 x 50 x 49... / 20 x 19 x 18 x ...... leaving 125 trillion possibilities

Martin Weitzman - Recombinant Growth - whereby things continuously get recombined new growth. 

Ex: car - steering wheel, wheels, brakes, etc coming together to make a car.

Exaptation - some innovation comes up for one reason, but then gets applied to another.

Joel Mokyr - Gifts of Athena - how ideas are transferred from one location to another and between people.