1. Art and Science

2. Art Goal: Communicate Human perception and aesthetics Grounded in Science Admits Qualitative and Subjective elements ConcreteAbstract Shapes, Relationships, Stories, Experiences, Ideas, Themes

3. Science Goal #1: Establish Facts Objective Quantitative Reproducible Goal #2: Communicate Results Validation: Peer review Citation / related work Proof or Derivation Experimental Evidence (Persuasive Argument) Fact Opinion Historical Observation

4. The Art of Science Choosing the right problem Experiment design Communicate Results Elegant proofs and systems Intuitive diagrams and demonstrations Computer Science fields that study Art Graphics Games, Film, and Scientific Visualization Vision and Perception Quantitative & Objective Art! { Subjective & Qualitative Science! {

5. Computer Science Create algorithms and heuristics (strategies), e.g., Next move in a Chess game Color of every pixel in a 3D image Where to aim to hit a moving target Prove properties of algorithms and rule sets, e.g., Correctness (and termination!) Time required State (“space” or “memory”) required Safe, sound, and complete

6. Game Design Synthesize rule systems that express ideas that are fair and stable under which optimal strategies are engaging ones Requires CS-style of analysis: prove properties of optimal strategies prove properties of rule systems experimentally measure human quantities experimentally validate ideas

7. Establishing Truth Proof/Derivation For cases where inputs have been measured and the complexity is manageable Proof of Bounds For game situations too complex to analyze directly Experimentation For cases are so complex that we cannot prove anything about them from first principles Proof or Derivation Experimental Evidence (Persuasive Argument) Fact Opinion Historical Observation

8. Examples Proof: In God of War, all players will have obtained the Medusa power before fighting the first minotaur. Proof of Bounds: The expected value of a Carcassonne road tile is at least 1 point (for the road itself) and at most 1.34 points (because of farms). Experiments: What fraction of people prefer vanilla to chocolate? What amount of variance in Settlers of Catan resource production optimizes engagement for the average player?

9. Exercises Choose the best approach for each problem: What is the expected value of 3d10? Is Settlers of Catan fair? How long does it take to shuffle a deck of 52 cards? Do piece colors affect a player’s engagement? What is the largest acceptable network lag? What is the minimum network lag between NY and LA? Does a Puerto Rico game always end? Derivation Experiment Bounded proof Derivation Experiment Proof Does the bullet with position x and velocity v hit the character at position p? Derivation