AI Discovers Physics in Mind: Measuring Comfort in Mind

Hiroyuki Iida (JAIST)

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Games and the very act of playing have been around since before the cradle of human civilization.

However, games have constantly evolved over time, with various rulesets and modes of play falling in

and out of favor throughout history. In turn, this implies that people at different times enjoyed different

aspects of each game, which may constitute a vivid reflection of the cultural tendencies of each era.

Unfortunately, the attractiveness of games is tied to human psychology, and finding objective evidence in

topics related to the realm of the human mind is a difficult task. Could there possibly be a way to quantify

universal characteristics of games so as to put them under rigorous mathematical analysis?

One key measure in the model of motion in mind is the acceleration or 'gravity in the mind,' in analogy

with the earth's gravitational acceleration. In sufficiently refined games, the model establishes a

relationship between the effort that the player has to make to advance and the degree of challenge a game

represents. The scientists calculated the gravity associated with a wide variety of games as they evolved

through history, including classic board games like Chinese Go, Chess and Shogi, popular sports like

soccer, tennis and basketball, and videogames, such as fighting games and strategy games.

AI Discovers Physics in Mind: Measuring Comfort in Mind in Games

Computing Games and Its Implication to

Measuring Playing ExperienceAnggina Primanita (2021). PhD Thesis, JAIST

Over history, games have served multiple purposes. It serves as a fun activity for players who need the

entertainment to become test-beds for artificial intelligence. Solving games is beneficial in providing a

better understanding of how information is progressing throughout the game. Uncertainty in games affects

the way a game is solved, and the way the game is experienced. Previous works have interpreted

uncertainty in the game progress through various means, but there have been no clear links among those

interpretations. In this study, the probability-based proof number (PPN) and single conspiracy number

(SCN) were used as the domain-independent indicators to analyze how uncertainty affects various game

elements. PPN-search exploits information from certain and uncertain information to reach convergence in

solving games. Meanwhile, SCN evaluates the game states' difficulty and describes game-playing patterns

to understand play positions better. Experiments results demonstrate the link between the search indicators

and the measure of entertainment where uncertainty plays a vital role in both contexts, verified from both

two-person and single-agent games. Such a situation is also crucial for both computation and entertainment

measures since it impacts both the quality of information and the expected game-playing experience.

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HIROYUKI IIDA received the Ph.D. degree in Heuristic Theories on Game-Tree Search from the Tokyo

University of Agriculture and Technology, Tokyo, in 1994. He is currently a Japanese Computer Scientist and a

Computer Games Researcher with a focus on Game Refinement Theory, Opponent Model Search, and

Computer Shogi. He is also the Trustee and the Vice President of Educational and Student Affairs with the

Japan Advanced Institute of Science and Technology (JAIST), the Director of the Global Communication

Center and the Research Center for Entertainment Science, and the Head of the Iida Laboratory. He is also 7-

dan Shogi GM Player and a Co-author of the Shogi Program TACOS, the four times Gold Medal Winner at

Computer Olympiads. He was affiliated with Shizuoka University, Hamamatsu. He was a Guest Researcher

with Maastricht University. His research interests include Artificial Intelligence, Game Informatics, Game

Theory, Mathematical Model, Search Algorithm, Game-Refinement Theory, Game-Tree Search, and

Entertainment Science. He is a member of the Board of the ICGA as a Secretary-Treasurer and a Section Editor

of ICGA Journal. 4

• C.Shannon, A.Turing, Jaap van den Herik

Heuristic Theories on Game-tree Search (1994)

OM-Search, Tutoring strategy in gameplay, etc.

Computer Chess – Treasure for AI

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1950 1997 2018

Look-ahead search: Automatic AI generation:

Program a computer:

winning human champion

Program a computer:

enjoying together with human

New Paradigm: Entertainment Science

2028

Identifying a more stable move

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‘‘Human beings are never more ingenious than in the

invention of games.’’ － Gottfried Wilhelm Leibniz

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Using games to study law of motions in mindHiroyuki Iida; Mohd Nor Akmal Khalid (2020)

IEEE Access, vol. 8, pp. 138701-138709

Establishing several physics quantities (such as mass, speed, and acceleration)

relative to the game progress model allowed for the player's entertainment

experiences for a specific game to be determined through the Newtonian laws

of motion, specifically the Force, Momentum, and Potential Energy. Such a

law of motion reveals the feeling of a player in their mind. Mapping different

games originated from different cultures to the state of the human mind; a

measure of sophistication that leads to a natural yet pleasurable experience.

Uncovering the fundamental mechanisms of game playing mechanisms had been the primary

goal in the IIDA laboratory. Game refinement theory is the fruit of labor for several years--the

relationships between game progress and entertainment experience from the perspective of

game design. Several sub-branch of the study had been explored through board games (e.g.,

Chess, Go, etc.), sports (e.g., Basketball, Table tennis, etc.), and video game (e.g., action games).

From a non-game context had also been previously explored (such as business, education, and

loyalty programs). Interestingly, all of those studies found that game refinement measure

converges to approximately similar "zone" value (a region named as the Noble Uncertainty).8

Physics and Game Play

• Analogy of motion

• Dimension of challenge

• Basic Assumption:

m + v = 1 (zero-sum game)

Notation Physic Game play

y Displacement Solved Uncertainty

t Time Length

v Velocity Win or Score Rate

M Mass Difficulty Rate (m)

a Gravitational Acceleration

Informational Acceleration (a = GR2)

𝒑 Momentum Momentum of Game

U Gravitational Potential Energy

Potential Energy in Game (Ep)

In board games:v = B/2D

In scoring games:v = G/T

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The gravity of play: Quantifying what we enjoy

about gamesK. Xiaohan; Mohd Nor Akmal Khalid; Hiroyuki Iida (2020)

“Player Satisfaction Model and its Implication to Cultural Change,"

IEEE Access, vol. 8, pp. 184375-184382

Games and the very act of playing have been around since before the cradle of human civilization. However,

games have constantly evolved over time, with various rulesets and modes of play falling in and out of favor

throughout history. In turn, this implies that people at different times enjoyed different aspects of each game,

which may constitute a vivid reflection of the cultural tendencies of each era. Unfortunately, the

attractiveness of games is tied to human psychology, and finding objective evidence in topics related to the

realm of the human mind is a difficult task. Could there possibly be a way to quantify universal

characteristics of games so as to put them under rigorous mathematical analysis?

One key measure in the model of motion in mind is the acceleration or 'gravity in the mind,' in analogy with

the earth's gravitational acceleration. In sufficiently refined games, the model establishes a relationship

between the effort that the player has to make to advance and the degree of challenge a game represents. The

scientists calculated the gravity associated with a wide variety of games as they evolved through history,

including classic board games like Chinese Go, Chess and Shogi, popular sports like soccer, tennis and

basketball, and videogames, such as fighting games and strategy games.10

Principle 1.

People feel entertaining or thrilling when the

outcome of an event is uncertain till the very end.

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The gravity of play: Quantifying what we enjoy about games

One key measure in the model of motion in

mind is the acceleration or 'gravity in the

mind,' in analogy with the earth's gravitational

acceleration. In sufficiently refined games, the

model establishes a relationship between the

effort that the player has to make to advance

and the degree of challenge a game represents.

The gravity was calculated associated with a

wide variety of games as they evolved through

history, including classic board games like

Chinese Go, Chess and Shogi, popular sports

like soccer, tennis and basketball, and

videogames, such as fighting games and

strategy games.

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Momentum & Energy in Games

Associated with high playexpectation1 (m = 1/3)

Associated with balance between ability and challenge1 (m = 1/2)

[1] H. Iida, M. N. A. Khalid, Using games to study law of

motions in mind, IEEE Access 8 (2020) 138701–138709.

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Principle 2. (Momentum Conservation)

Potential energy (Ep) is assumed to be conserved over time and

transformed into Momentum of game’s motion ( p1) and Momentum of

mind’s motion ( p2), i.e., Ep = p1 + p2.

Hence, it is expected for p2 to be a reliable measurement of engagement.

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Motion/Momentum

Energy

Law of ConservationE

Ep Eq+

p1 p2+ p1 p2-

Eq = 2m2vp1 = mvp2 = 2m3 – 3m2 + m

15

En

erg

y

Con

serv

ati

on

1

Mo

me

ntu

m

Con

serv

ati

on

1

Law of Conservation (Continued)

Game’s Motion: Change of game scores/moves

p1

Mind’s Motion: Change of winning prediction

p2

Game’s Motivational Potential: Amount of information perceived

Ep

Mind’s Motivational Potential: Amount of information expected Eq

1. A. Einstein, et al., On the electrodynamics of moving bodies, Annalen der physik 17 (10) (1905) 891–921. 16

Law of Conservation (Continued)

Conjecture 1 (Momentum conservation): p2 (momentum’s of mind) is a reliable measure of engagement

Conjecture 2:

𝒎 =𝟑+ 𝟑

𝟔≅ 𝟎. 𝟕𝟗 (high competitive excitement)

𝒎 =𝟑− 𝟑

𝟔≅ 𝟎. 𝟐𝟏 (high-win expectancy)

Conjecture 3 (Energy conservation): Ep (game’s energy) and Eq (mind’s energy) is a reliable measure of motivational potential

Conjecture 4 (Natural Equilibrium): Play experience is in constant state of seesaw; implying greatest attractiveness

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Subjective1

Objective1

“Psychology” and Comfort in Mind

p1 = mv = m - m2

p2 = 2m3 – 3m2 + mv1 = 1 – mv2 = 2m2 – 3m + 1

p1

v1

p2

v2

Third-personPerspective

First-personPerspective

Conjecture 5: Addictive events

postulates condition v2 ≥ ½

and

m ≤ 𝟑 − 𝟓

𝟒

Negative v2 is the “comfort” in mind

for facing lossaversion2

1. T. Constant, G. Levieux, A. Buendia, S. Natkin, From objective to subjective difficulty evaluation in video games, in: IFIP Conference on Human-Computer Interaction, Springer, 2017, pp. 107–127.

2. K. Daniel, T. Amos, Prospect theory: an analysis of decision under risk, Econometrica 47 (2) (1979) 263–291 18

Subjective

Force in Mind and Perception

p2

v2 F2

a2

p2 = 2m3 – 3m2 + mv2 = 2m2 – 3m + 1a2 = 4m – 3F2 = ma2 = m(4m -3)j = 4

j

m

Conjecture 6 (Game’s Inertial Force):

Appropriate challengefor novice (or learning)

when F2 < 0 and m = 3/8 ≈ 0.38

m = 0.38 indicates compelling play

situation

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Principle 3.

The difference between objectivity (v1) and subjectivity (v2) equals

the total energy (E), i.e., E = v1 - v2.

Hence, it is expected that larger the difference is, the higher

attractiveness of the game under the consideration.

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“Physics in Mind”

Real-Physics

Process Dynamics and Gamification

A general activity is depicted as a linearprocess or ∆displacement (v is constant)

A gamified experience is when ∆v occurred (a is constant)

The dynamic challenge and gamified experienceare when there is an interplay of ∆v and ∆a(existence of j)

y v a j

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Summary of Motion in Mind

m Indication Related Events

0.19 v2 = 0.50 Comfort in Loss Aversion1

0.21 Peak p2 High-win Expectancy

0.25 Eq = p2 Pleasure in Uncertainty2

0.33 Peak Ep Objective Motivation

0.38 Peak -F2, v2 ≈ Eq Compelling Play

0.50 Peak E, p1 = Ep = Eq, p2 = 0 Game’s Natural Equilibrium

0.67 Peak Eq Subjective Motivation

0.72 F2 = p2 Player Satisfaction

0.75 Peak -v2, F2 ≥ 0 Perceptive Turnover

0.79 Peak -p2 High-tension Excitement

Motivation to prolong/continueplay due to uncertainty of positive event (Ep > Eq)

Fascination (of play) inmind (p2) meets dedication (of

work) in mind (F2)

The border between brute-force and knowledge-driven of

player’s ability to play

1. K. Daniel, T. Amos, Prospect theory: an analysis of decision under risk, Econometrica 47 (2) (1979) 263–2912. J. L. Kurtz, T. D.Wilson, D. T. Gilbert, Quantity versus uncertainty: When winning one prize is better than winning two, Journal of

Experimental Social Psychology 43 (6) (2007) 979–985

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Pushing the Boundary of the Entertainment Science

Entertainment

AnalyticsBusiness

Education

Psychology

Design

Game with Purpose Data-Driven

Design

BehavioralScience

Knowledge Discovery

Affective Science

Brain Science?

Meta-Learning?

Music Theory?

Play-Driven PCG?

Business Model?

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Going to the future is searching the past!

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