Managing Complexity

Managing Complexity In Your Head

Finding it hard to understand a complex phenomenon?

How do you manage complexity in your head?

1. Visualization / Imagination

Language and words are discrete. Visualize, so you see ‘all’, ‘the whole’ at once.

  • Organization
  • Connected Structure – how parts are connected to form the whole; what happens when a part is changed.
  • Chunking

2. Abstraction

Create Abstractions to help you see whole in terms of abstract concepts, when it’s hard to see ‘whole’ at once.

  • Visualization is usually top-down; creating abstractions can be done both bottom-up and top-down.
  • Recursive definitions are one type of abstraction.
  • Naming.

3. Generalization

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‘Have a good day , and a great week , and just a wonderful life in general ! ‘ – Generalization by Katrina Kaif

Abstract classes and classes of behaviors into Generalizations.

Science is all about discovering generalizations.

4. Systems Thinking

Divide the whole into systems and the systems into sub-systems and their interactions – Systems Thinking.

5. Knowledge Ontology

Organize generalizations into Knowledge Ontology.

Move up and down between Multiple Levels Of Abstractions.

6. Point of View / Perspective

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Perspective by Katrina Kaif

Find new Points of view from which to look at the domain under consideration (examples include how Feynman found new way of looking at interactions between light and matter which helped him discard infinities and formulate QED).

 

  • Understand part (representative element / elements) to understand the whole – Part – Whole.
  • Lens tool – “zoom in” to “zoom out”.
  • Problem – Sub-problem
    • Examples
      • Recursion
      • Dynamic Programming
      • Mathematical Induction
  • Individual Element – Whole 
    • Examples
      • Matrix Multiplication: individual element = respective row * column
      • Proof of Inclusion Exclusion Principle.
      • Coloring Principle (Problem Solving Heuristic)
      • Telescoping Tool (Mathematical Problem Solving; Series Summation)
  • Local Behavior – Global Behavior
    • Invariance Principle (Problem Solving Heuristic)
      • Change in individual states – Invariant Global function.
    • Iteration in Computing
      • Thinking in terms of change in state in an iteration.

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