**Managing Complexity In Your Head**

Finding it hard to understand a complex phenomenon?

**1. Visualization / Imagination**

**‘The true sign of intelligence is not knowledge but imagination’ – Imagination by Katrina Kaif**

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.
- Concept borrowed from Computer Science; applicable across disciplines.

**3. Generalization**

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.**

Concept borrowed from Artificial Intelligence (AI).

## 6. Point of View / Perspective

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

**‘Seeing the world through different glasses’ – Point of view, zooming in and out by Katrina Kaif**

- Understand part (representative element / elements) to understand the whole –
**Part – Whole**.

**Lens tool**– “zoom in” and “zoom out”.

**Problem – Sub-problem**- Examples
- Recursion
- Dynamic Programming
- Mathematical Induction

- Examples

**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)

- Examples

**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.

**At the end of the day: ‘Hold on, I’ve gotta overthink about it!’ – Managing complexity by Katrina Kaif**