Art and Science

Art•Goal: Communicate

•Human perception and aesthetics

• Grounded in Science

• Admits Qualitative and Subjective elements

Concrete Abstract

Shapes, Relationships, Stories, Experiences, Ideas, Themes

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

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!{

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

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

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

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?

ExercisesChoose 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

Experiment

Proof

Does the bullet with position x and velocity v hit the character at position p? Derivation