Mihnea Moldoveanu Desautels Professor of Integrative Thinking Rotman School of Management

1. From the Age of Science and Manufacturing to the Age of Design and Problem Solving:Integrative Thinking as a Tool for Educational ReformShantou University, Session 5, November, 2010. Mihnea Moldoveanu Desautels Professor of Integrative Thinking Rotman School of Management University of Toronto

2. THE PROBLEMS OF THE WORLD: A MAP “Complex” “Simple” INTEGRATIVE THINKING: RECOGNIZE WICKED PROBLEMS AND TURN THEM INTO (LOCALLY) TRACTABLE PROBLEMS • Well specified, multi-dimensional goals and metrics; • logically deep pathways from statement to solution • Many dependant and independent variables • Convergence tests are either clearly defined or definable as a function of resource availability and problem complexity; fulfillment is independent • Well specified, uni-dimensional goals and metrics; • logically shallow pathways from statement to solution • Few dependant and independent variables • Clearly defined convergence tests and criteria whose fulfillment is independent PROBLEMS THE AGE OF SCIENCE THE AGE OF DESIGN “Wicked” • Goals and objectives have multiple, potentially incommensurable and conflicting specifications • logical sequence from statement to solution depends on specification and choice of logic • number of variables depends on specification and can change as a function of the solution process • Solution criteria are negotiated; their fulfillment conditions are “user-dependent”

3. TRANSFORMATIONAL “Algorithmic” Total New Jobs 1998 – 2004 N = 6.4MM “Super-algorithmic” The Market Opportunity for the High Value Decision Maker NEW JOBS, 1998-2004 (Adapted from Johnson, Manyika & Yee, 2004) TRANSACTIONAL TACIT

4. SUPPORTING DISCIPLINES Analog Circuit Design RF Circuit Design Logic Circuit Design EXPLICIT EXPERTISE RF Antenna Design RF system design System Testing Hardware systems design Competitive Analysis TACIT EXPERTISE Strategy negotiate motivate Network Theory Network Design INTEGRATE Market Demand Analysis communicate Programming Languages and Logics Marketing Software Design Financial Reporting Financial Analysis Operating System Design Accounting Science Finance Theory Auditing Science The Integrative Gap: Consider the Expertise Map of General Manager in Large Telecommunications Equipment Manufacturer (eg: Nokia, Cisco, Huawei, etc.) Linear Systems Theory SUPPORTING BASIC SCIENCES Boolean Logic Electromagnetic Wave Theory Statistical Analysis Game Theory Queuing Theory Psychology Logic Sociology Linguistics Microeconomics Stochastic System Theory

5. Two Views of Education “INFORMATION” (KNOW-WHAT) [current state: what do I know/remember?] “KNOWING” EDUCATION “BEING, DOING” “TRANSFORMATION” (KNOW-HOW) [desired state: what problems can I solve with what I know?]

6. What Is “Know-How”? SOLVE PROBLEMS FRAME PROBLEMS KNOW-HOW “MAKE IT WORK”: IMPLEMENT SOLUTIONS COMMUNICATE AND LEGITIMIZE SOLUTIONS

7. The Problems of the World: A Unified Picture Forecasting/Prediction: Given n points in a time series, what is the n+1st point? Strategic Manager: What problem am I solving? Optimization: Given objective  and constraints {Ci}, find a function (structure, process, procedure, algorithm) that maximizes  and obeys {Ci} Analysis: Given a data set {d}, find a model, M (causal, functional), that is most likely to have generated {d} Adaptation: Given model M (structure, procedure), that is consistent with data {dk}, find optimal update rule R(M) that preserves consistency with new and possibly unforeseeable evidence {en}

8. What Is a Problem? Path 1 Initial Conditions (Current) Desired Conditions Path 2 Path 3 Path 4 Path 5 Observable and Measurable or Auditable and Relevant Time Bounded Observable and Measurable or Auditable Search Space of Possible Paths that Connect Current to Desired Conditions

9. The Goal: A Bigger, Nimbler Mind N The Integrator’s mind: mile wide, mile deep Inch-deep, mile-wide mind How many things you think about Integrative thinking training path Inch-wide mile-deep mind K possible links among N variables K How deeply do you think about it N variables

10. Problems: A Value Map Easy (Linear or constant) Value Added Transformation 4 Tractable Hard (nonlinear) Value Added Transformation 3 Well Structured Intractable (NP hard) Value Added Transformation 2 Well Defined Ill Structured (wicked) (Search space defined but changes as a function of search process Problems Value Added Transformation 1 Ill Defined (No well defined current, desired state, search space)

11. Thinking about Thinking about Problems:A General Framework Representation of problem statement in algorithmic language Problem statement in everyday language FEEDBACK Revision of algorithmic problem statement Measurement of problem complexity

12. Stop and Think: What Does This Mean? What Does This Mean for the Way We Design Problem Solving Organizations?

13. Search: A Simple Distinction x₁ Solution (optimum point) Deterministic Trajectory of search x₂ Search Solution (optimum point) Probabilistic Pick a point at random then search around it for T hours. If S not found, pick another point at random.

14. Types of Search: Properties of the Search Method Exact Deterministic Approximate Exact Local Stochastic Approximate Search Exact Deterministic Global Approximate Exact Stochastic Approximate

15. Types of Search: Properties of the Search Architecture Directed Serial Autonomous Directed Central Parallel Autonomous Search Directed Serial Distributed Autonomous Directed Parallel Autonomous

16. How to Put the Disciplines to Work: Get Them Working on Real Problems! Neural Networks Time Series Analysis Statistics Computational Linguistics Signal Processing Prediction Problems Operations Research Dynamical Systems Modeling Dynamical Systems Design Problem Solver Analysis Problems Optimization Problems Computational Complexity Theory Nonlinear filtering General Equlibrium Analysis Inverse scattering problems Adaptation Problems Evolutionary Algorithms Statistical Signal Processing Time Series Synthesis Neural Networks

17. Real Business Problems: What do they look like? Technology constraints Competitive constraints How to increase revenue by 15% over 2A mos subject to maintaining 15% EBITDA? Strategic Plane Cost constraints Cash constraints Demand constraints How to optimize production function to deliver growth plan? Lock-in constraints Complexity constraints Operational Plane Labor constraints Cash constraints Cultural constraints How to change / optimize organizations to deliver on growth plan? Talent constraints Organizational Plane Incentive constraints Coordination constraints Psychological constraints How to design / change / adjust top management team / board of directors for growth plan? Incentive constraints Interpersonal Plane Interaction constraints How to structure / sell / execute w/k – w/k engagement? Cost constraints Pragmatic Plane Skill constraints Logistical constraints

18. Thinking about the way you think about the world I-Mode (Intelligent) Surveying the predicament Choosing the problem Parsing the problem Thinking about the world M-Mode (Mechanical) ‘chugging through’ ‘solving the problem’ The World Intelligence does not equate to computational ability, but to the clever deployment of computational ability (!!)

19. US National Academy of Engineering Grand Challenges 2010: Can you turn them into well-defined problems? • Make solar energy economical; • Manage the nitrogen cycle; • Advance health informatics; • Prevent nuclear terror; • Advance personalized learning; • Provide energy from fusion; • Provide access to clean water; • Engineer better medicines; • Secure cyberspace; • Engineer the tools of scientific discovery; • Develop carbon sequestration methods; • Restore and improve urban infrastructure; • Reverse engineer the brain; • Enhance virtual reality.

20. Stop and Think: How Do You Make This Work in a University?

21. How Hard is Hard? Measuring the Complexity of a Problem

22. Illustrating the dependence on time complexity of a problem on the number of salient variables of the problem (N), for three different complexity growth profiles: square growth (column 2), cubic growth (column 3) and exponential growth (column 4)

23. Complexity Regimes: I. The P-Class Constant complexity K = C Linear complexity K = AN + C Quadratic (K = AN2 + C) and quasi-quadratic complexity K = AN log N + C Super-quadratic complexity K > AN2 + BN + C belong to belong to belong to belong to belong to Correlation Gaussian elimination One-shot heuristic search procedures Recognition or ‘pick the highest-’ ranking procedures Ranking or sorting a list from ‘high’ to ‘low’ reduce reduce reduce reduce reduce reduce Compute degree of similarity Solve N equations for N unknowns ‘Pick the first thing that comes to mind’ ‘Pick the first recognized name/ number from a list’ ‘Pick the highest one name/ number from a list’ Ordering random list from high to low K= complexity of solution algorithm; N= number of variables in problem statement A,B,C are arbitrary constants.

24. Typical ‘tree search’ (P-hard) problem ‘O’ ‘ROOOD’ ‘O’ ‘U’ ‘ROOUD’ ‘N’ ‘ROOND’ ‘O’ ‘ROUUD’ ‘U’ ‘O’ ‘U’ ‘ROUOD’ ‘N’ ‘ROUND’ ‘O’ ‘U’ ‘N’ ‘N’ ‘O’ ‘O’ ‘U’ ‘N’ ‘O’ ‘U’ ‘R’ ‘U’ ‘U’ ‘N’ ‘O’ ‘U’ ‘N’ ‘N’ ‘O’ ‘O’ ‘U’ ‘N’ ‘N’ ‘U’ ‘N’ Fourth letter First letter Second letter Third letter Tree search problems are typically P-hard. Their lower complexity stems from the fact that each node of the tree reduces the search space by a factor that is proportional to the number of branches (3 in this case) that stem from each node. Complexity of the search process is at most log (N), where N is the number of possible end-states of the tree. In this case, the problem is to find the natural-language 5-letter word that starts with ‘r,’ ends in ‘d,’ and has middle letters drawn from the set (O, U, N).

25. Tree Searches: The “OK” Approach Space of possible solutions spanned by tree: Orthogonality (“mutually exclusive”) Completeness (“collectively exhaustive”) A tree search is efficient in that it allows the searcher to classify an entity as one of N possible entities in no more than Log (N) operations. So, for instance, the ‘Five Forces’ model [Porter, 1980] can be represented as a 5 stage binary search tree, that allows one to classify a business in one 32 possible categories. Stages 4 2 1 3 5 TREE

26. Basic Intuition Behind Hard Problems: The Tower of Hanoi Problem Initial Conditions Desired Conditions See this link for a video of the solution: http://www.mazeworks.com/hanoi/index.htm

27. Complexity Regimes: II. The NP-Class. K=a exp(bN) Satisfiability (Cook, 1976) 3 SAT reduces to reduces to Partition Vertex cover reduces to reduces to Hamiltonian circuit Clique models models models models Nash Equilibrium calculation for N≥3 players Clique discovery in social networks Optimal system design, via Knapsack problem Optimal task design, via Knapsack problem Optimal path calculation via Traveling Salesman problem

28. Graph Searches • Given a graph, find: • cliques • minimum vertex covers • maximum centrality nodes • minimum centrality nodes • geodesic paths

29. Typical ‘graph search’ (NP-hard) problem C dBC B dCE dEB dAB D dED E dAE A dEF dAF F Graph searches are typically NP-hard, and their higher complexity arises from the fact that one must take into account all possible combinations of the nodes of the graph when performing the search. The task is to find the shortest route that connects all of the vertices in the graph. The complexity of a systematic search through all of the routes is at most NN where N (in this case, 6) is the number of vertices in the graph.

30. Consider the problem of finding the shortest tour linking together Canada’s 4663 cities…

31. How long would it take you to solve it by brute force using a state of the art RISC processor (10¹²ops / second) • 1. Total number of operations required • K ~ 2⁴⁶⁶³ ~ 5 x 10¹⁴⁰³ calculations • Your computational resources • R ~ 10¹² ops / second • Your computational process • (10¹² ops / second) (3600 sec / H) (24h / day) x(365 days / yr) • ~ 3 x 10²⁰ • So: You can solve this problem in 1.6 x 10¹³⁸³ years

32. Miraculously, however, here is the solution:

33. Best Response Best Response Best Response Best Response Example: Competitive Choice Modeling in a Duopoly Firm 1’s quantity choice/best response Firm 2’s quantity choice/best response a-c 2 a-c 2 a-c 4 a-c 4 Generate using series qN= a-c - qN-1 ; 2 2 qo=0 which results from joint maximization of profits Πi= (a-c-qi-qj)qi So, if firm 1 says, “I will sell (a-c )/2” , firm 2 will credibly retort, “I will sell (a-c )/4“; which would lead to losses relative to the a-c , a-c 3 3 solution 3(a-c) 8 3(a-c) 8 5(a-c) 16 5(a-c) 16 11(a-c) 32 11(a-c) 32 … … a-c 3 NASH EQUILIBRIUM

34. The Benefits of Logical Depth of Computation When Playing a Cournot-Nash Duopoly Game

35. Computational Landscape of Cournot Nash Equilibrium, 2 firms, a=3, c=1. Horizontal axes represent number of iterations for each firm. Vertical axis is the profit level of firm 1. Profit levels of firm 2 are symmetrical. Landscape converges to Nash Equilibrium output of (a-c)/3.

36. Stop and Think!How Do We Make This Work?