The Scientific Community Game: Education and Innovation Through Survival in a Virtual World of Claims Karl Lieberherr Northeastern University College of Computer and Information Science Boston, MA joint work with Ahmed Abdelmeged and Bryan Chadwick Karl Lieberherr Northeastern University College of Computer and Information Science Boston, MA joint work with Ahmed Abdelmeged and Bryan Chadwick Supported by Novartis

Why Scientific Community Game (SCG) … motives in academic publishing: – desire for recognition and respect from the people one regards as peers, – desire to have impact (on conclusions being reached, on the development of the discipline, etc.), and – desire to participate in significant knowledge- building discourse. e.g., Scardamalia, M., & Bereiter, C. (1994) Bionetics 20102

SCG is Bio-inspired Virtual world of scholars based on natural selection – propose, oppose (refute and strengthen) claims – maximize reputation, weak scholars are removed. Turn problem-solving software into virtual organisms that fend for themselves and survive in a virtual world inhabited by virtual organisms created by your peers. Bionetics 20103

SCG is a web-based implementation of Karl Popper’s science ideas One of the greatest philosophers of science of the 20th century.philosophers of science Falsifiability or refutability is the logical possibility that an assertion could be shown false by a particular observation or physical experiment. Error elimination (refutation), performs a similar function for science that natural selection performs for biological evolution.natural selectionbiological evolution Bionetics from Wikipedia

Comparison Karl Popper: Conjectures and Refutations, 1963 Scientific Community Game: Claims and Refutations, 2007 Bionetics 20105

Recognition in SCG Scholars build their reputation by proposing and opposing claims, by defending their own claims and refuting or strengthening the claims of others. The higher their reputation, the more recognition. Bionetics 20106

Impact in SCG Second-order environment – what one scholar does in adapting, changes the environment so that others must readapt. Developing novel techniques to find superior solutions, challenges others to catch up. Bionetics 20107

Knowledge-Building Discourse in SCG Communication or debate. Refutation protocol defines the structure of the debate and who wins. Claims are defined through a refutation protocol. Knowledge-building: – claims that have been defended predominantly are candidates for truth – claims that have been refuted predominantly are probably false. Bionetics 20108

Goals of SCG Put knowledge-building discourse on the web giving participants the option to gain recognition and to have impact. Focus the discourse through precise definition of claims with refutation protocols. Make knowledge building discourse fun and educational from the high school to the advanced research level. Bionetics SCG = Scientific Community Game = Specker Challenge Game

What do we mean by science? Science consists of the formulation and testing of hypotheses based on observational evidence. Ours: Science consists of the formulation and testing of constructive claims based on observational evidence. Construction is computable. Bionetics

What do we mean by Scientific Method Hypothetico-deductive method: Formulate a hypothesis in a form that could conceivably be falsified by a test on observable data. Ours: Formulate a constructive claim in a form that could conceivably be falsified by a test using a protocol. The refutation protocol is part of the claim to make very explicit when refutation is successful. Bionetics

Bionetics Tartaglia against Fior 1535 Tartaglia was famed for his algebraic solution of cubic equations which was published in Cardan's Ars Magna.

Outline Introduction – Popper Science, Renaissance History: Tartaglia and Fior Definition of SCG – Example (Highest safe rung) Applications: Teaching, Software Development, Research Claims with secrets and other protocol variants Output of SCG, Equilibrium Advantages and Disadvantages Conclusions Bionetics

Definition of SCG: Domain Problem: Set Solution: Set valid: relation(Problem, Solution) quality: function(Problem, Solution)->[0..1] 14Bionetics 2010

Claim(Domain) Problems: Powerset(Domain.Problem) q: Quality = [0,1] r: Resource = N + = positive integer Alice claims to have a technique to solve problems in Problems with at least quality q and using at most resources r. 15Bionetics 2010 makes predictions about the future

Implied Protocol of Claim(Domain) Alice claims (problems,q,r), Bob refutes Bob provides problem prob in Claim.Problems. Alice solves problem prob providing sol in Domain.Solution. check: valid(prob,sol) and quality(prob,sol)>=q and sol.resource<=r. sol.resource returns Alice’ resource consumption to solve problem prob. 16Bionetics 2010 Karl Popper: Only hypotheses capable of clashing with observation reports are allowed to count as scientific.

Claim Problems: subset of problems quality in [0,1] Bionetics quality (how well problems in Problems can be solved)

Claim Bionetics quality strengthening correct valuation over strengthening

Bio-inspired computing: Virtual World of SCG-Avatar SCG-Avatar (Claim(Domain)) – State: Reputation = positive rational number – Activity propose new claims oppose claims of others – refute claim(Problems, q, r) – strengthen claim(Problems, q’, r’), q’>q or r’<r Reputation gain: refute others’ claims and defend own claims (counter refutation attempts) Reputation loss: unsuccessful refutation of other’s claim and refutation of own claims 19Bionetics 2010

Tournament 1.round-robin 2.Swiss-style 3.elimination 1.single 2.double 20Bionetics 2010

Summary of SCG Definitions Domain Problem Solution valid(Problem, Solution) quality(Problem, Solution) → [0,1] 21Bionetics 2010 Claim(Domain) Problems: PowerSet(Domain.Problem) q: Quality = [0,1] r: Resource = N + Rules of the Scientific Community: propose and oppose, be an active scholar, rules for reputation accumulation. Tournaments

Highest Safe Rung You are doing stress-testing on various models of glass jars to determine the height from which they can be dropped and still not break. The setup for this experiment, on a particular type of jar, is as follows. Bionetics

Highest Safe Rung Only two identical bottles to determine highest safe rung Alice Bob 23Bionetics 2010 You have a ladder with n rungs, and you want to find the highest rung from which you can drop a copy of the jar and not have it break. We call this the highest safe rung. You have a fixed ``budget'' of k > 0 jars.

Highest Safe Rung Only two identical bottles to determine highest safe rung HSR(9,2) ≤ 4 I doubt it: refutation attempt! Alice Bob Alice constructs decision tree T of depth 4 and gives it to Bob. He checks whether T is valid. Bob wins if he finds a flaw. 24Bionetics 2010

x yz yes no u highest safe rung Highest Safe Rung Decision Tree HSR(9,2)=5 25Bionetics 2010

Finding solution for HSR(n,2) Approximate min x in [0,n] (n/x) + x Exact – MaxRungs(x,y) =MaxRungs(x-1,y-1)+MaxRungs(x-1,y) – MaxRungs(x, 2) = x + MaxRungs(x – 1, 2) – MaxRungs(0, 2) = 1 – Applied to HSR(9,2) MaxRungs(3,2) = 7 < 9 MaxRungs(4,2) = 11 > 9 26Bionetics 2010 Keith Levin CS 4800 Fall 2010 MaxRungs(x,y) = the largest number of rungs we can test with y jars and x experiments. breaks at rootdoes not break at root Find minimum x, s.t. MaxRungs(x,2) > n

MaxRungs MaxRungs(x,y) = sum [k=0.. y] binomial(x,k) All paths are of length x. At most k branches may be left branches. Note: y = x implies MaxRungs(x,y) = 2 x meaning a complete binary tree of depth x. Example: binomial(3,2)+binomial(3,1)+ binomial(3,0) = 7 Bionetics

Formal: HSR Domain: – Problem: (n,k), k <= n. – Solution: Decision tree to determine highest safe rung. – quality(problem, solution): depth of decision tree / number of rungs – valid(problem, solution): at most k left branches,... 28Bionetics 2010

Formal: HSR Claim(Domain): – Alice claims ({(25,2)},9/25,5 seconds) {(25,2)}: set of problems (singleton) 9/25: quality 5 seconds: resource Refutation Protocol: – Bob refutes: only one problem: (25,2) – Alice: solves problem by providing decision tree t. – predicate: t is a valid decision tree for (25,2) of depth 9 Bionetics

Claim involving Experiment Claim ExperimentalTechnique(X,Y,q,r) I claim, given raw materials x in X, I can produce product y in Y of quality q and using resources at most r. 30Bionetics 2010

Outline Introduction – Popper Science, Renaissance History: Tartaglia and Fior Definition of SCG – Example (Highest safe rung) Applications: Teaching, Software Development, Research Claims with secrets and other protocol variants Output of SCG, Equilibrium Advantages and Disadvantages Conclusions Bionetics

Applications: Software Development Software Development Teaching Constructive Domains Bionetics

Gamification of Software Development etc. Want reliable software to solve a computational problem? Design a game where the winning team will create the software you want. Want to teach a STEM domain? Design a game where the winning students demonstrate superior domain knowledge. Bionetics 2010 Doesn’t TopCoder already do this? STEM = Science, Technology, Engineering, and Mathematics 33

SCG and TopCoder SCG is an abstraction and generalization of what TopCoder does. Bionetics

35 10/16/09Can DM and ML help? Software Development Skills Needed when avatar caregiver is human. Knowledge about domain X needs to be developed by students or taught to them and understood and put into algorithms (propose- oppose-provide-solve) that go into the avatar. This tests both whether the knowledge about X is understood as well as the programming skills of caregiver.

The Traditional Approach Solver A Static Benchmark Solver B Solver C Team A Team B Team C Parameterized by the domain. Software: Solving HSR Problem: construct decision tree of min. depth measure how close to minimum HSR(9,2)=4 HSR(25,2)=7 Ranking 36Bionetics 2010

The Bio-Inspired Approach Team A Solver A prop-opp A Team C Solver C prop-opp C Team B Solver B prop-opp B Virtual World (Game) Ranking Parameterized by the domain. Avatar A Avatar C Avatar B Dynamic Benchmark 37Bionetics 2010

A Virtual World Avatar’s View Administrator Avatar Opponents’ communication, Feedback Claims, Problems, Solutions Results Problems: Benchmark output Solutions: Software output Claims: statements about algorithms 38Bionetics 2010

What Scholars think about! If I propose claim C, what is the probability that – C is successfully refuted – C is successfully strengthened If I try to refute claim C, what is the probability that I will fail. If I try to strengthen claim C, what is the probability that I will fail? 39Bionetics 2010

SCG = Scientific Community Game Make software development more scientific. Software developers build reputation – propose and defend claims about their software – oppose claims made by others refute claims strengthen claims claim includes refutation protocol Bionetics

Who are Alice and Bob? They are avatars developed by real Alice and real Bob. Alice and Bob compete with 10 other avatars in a full-round robin tournament. Who is the winner: The avatar with the highest reputation, i.e., the avatar who has the strongest, not successfully opposed claims (like in a real scientific community). Bionetics Why a web application with avatars? Fair Evaluation.

What is SCG(X) Bionetics no automation human plays full automation avatar plays degree of automation used by scholar our focus some automation human plays 0 1 more applications: test constructive knowledge transfer to reliable, efficient software avatar Bob Alice

Real Scholars and Avatars: Same rules Are encouraged to 1.propose claims that are not easily strengthened. 2.offer claims that they can successfully support. 3.strengthen others’ claims, if possible. 4.stay active and propose new strong claims or oppose others’ claims. 5.become famous! 43Bionetics 2010

What we want Engage software developers – let them produce software that models an organism that fends for itself in a real virtual world while producing the software we want. Have fun. Focus them. – let them propose claims about the software they produce. Reward them when they defend their claims successfully or oppose the claims of others successfully. Bionetics Clear FeedbackSense of Progress Possibility of Success Authenticity (Facebook)

SCG Gamification of software development for computational problems A Sociotechnical System for knowledge dissemination, innovation, and integration 45Bionetics 2010

Life with SCG(X) with SCG structured collaboration between software developers, frequent feedback propose and oppose non- trivial claims to gain reputation. Drive to win knowledge accumulation in claims that have not been opposed successfully management effort goes into X without SCG collaboration is unstructured, less effective reputation gain is delayed knowledge is scattered in s, programs and minds more management effort required 46Bionetics 2010

Software Engineering Properties fostered by SCG Reliable (otherwise the avatar is removed from the game) Flexible, modular (otherwise the avatar cannot be easily updated between tournaments) Efficient (otherwise you cannot defend your claims and oppose the claims of others) Bionetics Adaptive and Aspect-Oriented Software is relevant!

State of Avatar SCG-Avatar: Our Vision Companies come to SCG website and define a competition by defining a claim domain X. Participating teams get baby avatars generated from X that participate in daily competitions. Competition generates a wealth of information: educated employees, good (undefeated) software, good algorithms, good potential employees. Reward is paid to the winner. Bionetics

State of SCG-Avatar: Our Vision Not only companies but faculty members who want to give their students a rich learning experience for computational problem X. Or editors of special issues in journals who want to use a competition to get a real world comparison of all approaches to solve computational problem X. Bionetics

Avatars propose and oppose Bionetics CA1 CA2 CA3 CA4 egoistic Alice egoistic Bob reputation 1000 reputation 10 CB1 CB2 opposes (1) provides problem (2) solves problem not as well as she expected based on CA2 (3) WINS! LOSES proposed claims transfer 200 social welfare Life of an avatar: (propose+ oppose+ provide* solve*)*

What is SCG(X)? Teams Design Problem Solver Develop Software Deliver Avatar Avatar AliceAvatar Bob Administrator SCG police I am the bestNo!! Let’s play constructively 51Bionetics 2010 Team Alice Team Bob

competitive / collaborative Bionetics Avatar Alice: claim C Avatar Bob: opposes C, refutes: provides evidence for !C loses reputation rwins knowledge k wins reputation rmakes public knowledge k

Outline Introduction – Popper Science, Renaissance History: Tartaglia and Fior Definition of SCG – Example (Highest safe rung) Applications: Teaching, Software Development, Research Claims with secrets and other protocol variants Output of SCG, Equilibrium Advantages and Disadvantages Conclusions Bionetics

Protocol Variants secrets: approximation problems involving trusted third party – renaissance: exchange of problems Bionetics

Example: Triple HSR Alice claims ({(25,2,0), (25,2,1), (25,2,2), (25,2,3), …,(25,2,25)},9/25, 5 seconds) Refutation Protocol: – Bob refutes (25,2,17) – Alice solves problems (25,2,*) by providing decision tree to trusted third party which reveals path p from root to 17. – predicate: p is valid and length(p) <= 9 55Bionetics 2010 Highest Safe Rung

Protocol Variation Secrets problem has public and private part, private part is a secret solution predicate has secret as argument 56Bionetics 2010

Protocol Variation Secret Program for SCG-Avatar problem has public and private part, private part is a secret solution and goes to administrator Alice gives her algorithm to administrator who applies it to public part of problem predicate has secret as argument 57Bionetics 2010

Example Claims involving secrets My algorithm can solve more problems using resources r than your algorithm using r. If I create problems for you for which I have a solution, you cannot recreate or approximate the solution with quality q using resources r. 58Bionetics 2010

Output and Equilibrium Rich tournament history What is an equilibrium in SCG? Bionetics

Soundness Theorem SCG is sound: The avatar with the best algorithms / knowledge wins (there is no way to cheat) – best: within the group of participating avatars – issues: Does an avatar win because she is good at solving? Or good at proposing, opposing and providing? Answer: proposing, opposing and providing all reduce to solving. 9/15/2015Games for SD60

SCG Equilibrium reputations of scholars are stable the ranking of the scholars is invariant from tournament to tournament the science does not progress; bugs are not fixed, no new ideas are introduced extreme example: All scholars are perfect: they propose optimal claims C(ps,q) that can neither be strengthened nor refuted. Bionetics

[Scientific Innovation in X] Avatars get skills programmed into them by clever scientists in domain X. Scientists use data mining to learn from competitions and manually improve the avatars. [Machine Learning Innovation in X] Avatars get skills programmed into them by an avatar caregiver programmed with learning skills and data mining skills for domain X. Avatar gets updated automatically. Survival in SCG(X) 62Bionetics 2010 second-order environment!

Blame assignment Where is the proposer to blame? – Bad claim that is refuted. – Bug in problem finding algorithm? – Bug in problem solving algorithm? 63Bionetics 2010

How to use SCG(X) Company AB needs new ideas about how to solve optimization problems in domain X. Define claims language for X – X-problems – claims, includes protocol Submit claims language definition to SCG server. 64Bionetics 2010

How to use SCG(X) Offer prize money for winner with conditions, e.g., performance must be at least 10% higher as performance of avatar XY that AB provides. 10 teams from 6 countries sign up, committing to 6 competitions. Player executables become known to other players after each competition. One team from company AB. The SCG server sends them the basic avatar and the administrator for testing. 65Bionetics 2010

How to use SCG(X) Game histories known to all. Data mining! First competition is at on day 1. Registration starts at on same day. The competition lasts 2.5 hours. Repeat on days 7, 14, … 42. The final winner is: Team Mumbai, winning Euro. Delivers source code and design document describing winning algorithm to AB. 66Bionetics 2010

Benefits for company AB of using SCG(X) Teams perform know-how retrieval and integration and maybe some research. – Participating teams try to find the best knowledge in the area. – Claims language gives control! The non-refuted claims give hints about new X- specific knowledge. A well-tested solver for X-problems that integrates the current algorithmic knowledge in field X. 67Bionetics 2010

Outline Introduction – Popper Science, Renaissance History: Tartaglia and Fior Definition of SCG – Example (Highest safe rung) Applications: Teaching, Software Development, Research Claims with secrets and other protocol variants Output of SCG, Equilibrium Advantages and Disadvantages Conclusions Bionetics

Benefits/Disadvantages Benefits – competitive / collaborative – structured feedback, game history – Teaching – Research – Software Development Dynamic testing and evaluation Disadvantages – addictive Bionetics

Disadvantages of SCG The game is addictive. After Bob having spent 4 hours to fix his avatar and still losing against Alice, Bob really wants to know why! Overhead to learn to define and participate in competitions. The administrator for SCG(X) must perfectly supervise the game. Includes checking the legality of X-problems. – if admin does not, cheap play is possible – watching over the admin 70Bionetics 2010

How to compensate for those disadvantages Warn the scholars. Use a gentleman’s security policy: report administrator problems, don’t exploit them to win. Occasionally have a non-counting “attack the administrator” competitions to find vulnerabilities in administrator. – both generic as well as X-specific vulnerabilities. 71Bionetics 2010

Benefits of SCG Social Welfare – Supported knowledge Claims are refuted and strengthened. Better supported knowledge comes from better algorithms and software. 72Bionetics 2010

Advantage: Democratic Problem to be solved: Develop the best practical algorithms for solving computational problems in domain X. Issue: There are probably hundreds of papers on the topic with isolated implementations. What are the best practical algorithms? Our solution: Use the scientific community game SCG(X) with a suitably designed claims language to compare the software. The winning avatar has the best practical algorithms/software. 73Bionetics 2010

Experience with MAX-CSP MAX-CSP Problem Decompositions T-Ball (one relation), Softball (several relations, one implication tree), Baseball (several relations). ALL, SECRET 74Bionetics 2010

Stages for SECRET T-Ball MAXCUT – R(x,y)= x!=y – fair coin ½ – maximally biased coin ½ – semi-definite programming / eigenvalue minimization Bionetics 2010

Stages for SECRET T-Ball One-in-three – R(x,y,z) = (x+y+z=1) – fair coin: – optimally biased coin: Bionetics 2010

Stages for ALL Baseball Propose/Oppose/Provide/Solve – based on fair coin – optimally biased coin correctly optimize polynomials – correctly eliminate noise relations – correctly implement weights – … 77Bionetics 2010

References Karl Popper, Conjectures and Refutations, London: Routledge (1963). Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge-building communities. The Journal of the Learning Sciences, 3(3), Renaissance: Tartaglia and Fior challenge (1535). Bionetics

Conclusions To address a computational problem domain X: – “map it to second life”: define a scientific community game for X on the web: SCG(X) – let the game SCG(X) run a few times and choose the winner; use strongest unrefuted claims. Benefits – Evaluates fairly, frequently, constructively and dynamically. Encourages retrieval of state-of-the-art know-how, integration and discovery. – Challenges humans, drives innovation, both competitive and collaborative. – Avatars point humans to what needs attention in problem solution / software. Bionetics

Conclusions Broad applicability, e.g., SCG(X) provides a learning process for any constructive domain. Benefits – Social Engineering: makes it fun through game. – Fair: Only hard work makes you win. – Engage a large community on one domain X. Bionetics

Thank You Bionetics

Title The Scientific Community Game: Education and Innovation Through Survival in a Virtual World of Claims 82Bionetics 2010

Abstract The Scientific Community Game (SCG) is a generic game for constructive domains where claims are defined by interactive protocols. As a starter, this includes mathematical claims containing alternating quantifiers but also non-mathematical claims involving the interaction between two parties. Scholars in SCG propose and oppose claims. Opposition means refutation or, strengthening followed by refutation. The winning scholars are good at proposing strong, un-refutable claims and at spotting refutable claims of other scholars. Scholars collaborate through competition. Applications include teaching constructive topics such as calculus and algorithms. An especially interesting version of SCG is Avatar SCG where the scholars are implemented in software. Avatar SCG is a web application implementing competitions between hundreds of avatars spread over the web. – Applications of Avatar SCG include: distributed software development for computational problems distributed knowledge maintenance and integration for computational problems teaching software development skills 83Bionetics 2010

Extra Bionetics

1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems, April Rome, Italy experimental analysis of algorithms 85Bionetics 2010

Formal: Pair HSR Alice claims ({(25,2)},9/25) {(25,2)}: set of problems 9/25: quality Refutation Protocol: – Bob refutes: only one problem: (25,2) – Alice: solves problem by providing decision tree t. – predicate: t is a correct decision tree for (25,2) of depth 9. 86Bionetics 2010

Domain Problem: Set Solution: Set valid: relation(Problem, Solution) quality: function(Problem, Solution)->[0..1] 87Bionetics 2010

Claim(Domain) Problems: Powerset(Domain.Problem) q: Quality = [0,1] r: Resource = N + = positive integer (optional) Alice claims to have a technique to solve problems in Problems with at least quality q and using at most resources r. 88Bionetics 2010

Implied Protocol of Claim(Domain) Alice claims (problems,q,r), Bob refutes Bob provides problem prob in Claim.Problems. Alice solves problem prob providing sol in Domain.Solution. check: valid(prob,sol) and quality(prob,sol)>=q and sol.resource<=r. sol.resource returns Alice’ resource consumption to solve problem prob. 89Bionetics 2010

Benefit of a game SCG-Avatar(Claim(Domain)) Knowledge discovery and evaluation – If a claim was attacked 1000 times and refuted only twice, it is a reasonable candidate for truth. – Depends on strength of avatars: Can they defend true claims? Can they refute wrong claims? 90Bionetics 2010

Game kinds 2-player game – used in tournament (full round robin or Swiss style) n-player game 91Bionetics 2010

Data produced by a game SCG-Avatar(Claim(Domain)) Ranking of avatars History: data exchanged through refutation protocols, claims proposed and strengthened A claim strengthened must be opposed by original proposer. Data mining of history 92Bionetics 2010

Two modes Teaching – give warning if true claim is refuted false claim is supported Research – don’t know the true and false claims 93Bionetics 2010

Reflection 2 Claim: For all NPO optimization problem P, there exists an SCG-Avatar game G: – better than putting 20 people into a room – learn more (give them a test) – have more fun Refutation protocol: 94Bionetics 2010

Reflection 1 For all constructive domains X, there exists a SCG game G=SCG(X): – if there is at least one good scholar, the participating scholars compared to when they cooperate in a non-structured way: create more knowledge about X using G, given the same amount of time, because they stay focused on X. have more fun thanks to the competition and collaboration. 95Bionetics 2010

Reflection 3 For all challenging constructive domain X teaching tasks, there exists an SCG family game G for X – students learn more 96Bionetics 2010

Reflection Software Development Software Development Process based on SCG 97Bionetics 2010

The Traditional Approach Solver A Static Benchmark Solver B Solver C Team A Team B Team C Parameterized by the domain. Software: Solving HSR Problem: construct decision tree of min. depth measure how close to minimum HSR(9,2)=4 HSR(25,2)=7 Ranking 98Bionetics 2010

The Bio-Inspired Approach Team A Solver A prop-opp A Team C Solver C prop-opp C Team B Solver B prop-opp B Virtual World (Game) Ranking Parameterized by the domain. Avatar A Avatar C Avatar B Dynamic Benchmark 99Bionetics 2010

A Virtual World Avatar’s View Administrator Avatar Opponents’ communication, Feedback Claims, Problems, Solutions Results Problems: Benchmark output Solutions: Software output Claims: statements about algorithms 100Bionetics 2010

What Scholars think about! If I propose claim C, what is the probability that – C is successfully refuted – C is successfully strengthened If I try to refute claim C, what is the probability that I will fail. If I try to strengthen claim C, what is the probability that I will fail? 101Bionetics 2010

Best response dynamics Nash Equilibria 102Bionetics 2010

Highest Safe Rung You are doing stress-testing on various models of glass jars to determine the height from which they can be dropped and still not break. The setup for this experiment, on a particular type of jar, is as follows. Bionetics

Highest Safe Rung Only two identical bottles to determine highest safe rung Alice Bob 104Bionetics 2010 You have a ladder with n rungs, and you want to find the highest rung from which you can drop a copy of the jar and not have it break. We call this the highest safe rung. You have a fixed ``budget'' of k > 0 jars.

Highest Safe Rung Only two identical bottles to determine highest safe rung HSR(9,2) ≤ 4 I doubt it: refutation attempt! Alice Bob Alice constructs decision tree T of depth 4 and gives it to Bob. He checks whether T is correct. Bob wins if he finds a flaw. 105Bionetics 2010

x yz yes no u highest safe rung Highest Safe Rung Decision Tree HSR(9,2)=5 106Bionetics 2010

Finding solution for HSR(n,2) Approximate min x in [0,n] (n/x) + x Exact – MaxRungs(x,y) =MaxRungs(x-1,y-1)+MaxRungs(x-1,y) – MaxRungs(x, 2) = x + MaxRungs(x – 1, 2) – MaxRungs(0, 2) = 1 – Applied to HSR(9,2) MaxRungs(3,2) = 7 < 9 MaxRungs(4,2) = 11 > 9 107Bionetics 2010 Keith Levin CS 4800 Fall 2010 MaxRungs(x,y) = the largest number of rungs we can test with y jars and at most x experiments. breaks at rootdoes not break at root

x yz yes no u highest safe rung, leaf Highest Safe Rung Decision Tree HSR(4,2)=3 (2 y (1 y h 0 h 1) n (4 y (3 y h 2 n h 3) n h 4)) Properties of decision tree: 1. at most two yes from root to any leaf. 2. longest root-leaf path has 3 edges. 3. each rung 1..n appears exactly once as internal node of the tree. 4. each rung 0..n appears exactly once as a leaf. root 108Bionetics 2010

x yz yes no u root 109Bionetics 2010

x yz yes no u 110Bionetics 2010

Swiss Tournament 1.round-robin 2.Swiss-style 3.elimination 1.single 2.double 111Bionetics 2010

The small player can win unexpectedly. 112Bionetics 2010

Elimination Tournament 113Bionetics 2010

Claim involving Experiment Claim ExperimentalTechnique(X,Y,q,r) I claim, given raw materials x in X, I can produce product y in Y of quality q and using resources r. 114Bionetics 2010

Why Scientific Community Game … motives in academic publishing: – desire for recognition and respect from the people one regards as peers, – desire to have impact (on conclusions being reached, on the development of the discipline, etc.), and – desire to participate in significant knowledge- building discourse. e.g., Scardamalia, M., & Bereiter, C. (1994) Bionetics

Recognition in SCG Scholars build their reputation by proposing and opposing claims, by defending their own claims and refuting or strengthening the claims of others. The higher their reputation, the more recognition. Bionetics

Impact in SCG second-order environment – what one scholar does in adapting changes the environment so that others must readapt. Developing novel techniques to find superior solutions challenges others to catch up. Bionetics

Knowledge-Building Discourse in SCG communication or debate. Refutation protocol defines the structure of the debate and who wins. Claims are defined through a refutation protocol. Knowledge-building: – claims that have been defended predominantly are candidates for truth Bionetics

Bereiter & Scardamaglia Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge-building communities. The Journal of the Learning Sciences, 3(3), Bionetics

Discourse We have roughly divided characteristics for knowledge-building discourse into three categories: – focus on problems and depth of understanding; – decentralized, open knowledge environments for collective understanding; and – productive interaction within broadly conceived knowledge-building communities. Scardamalia, M., & Bereiter, C. (1994) Bionetics

SCG Equilibrium reputations of scholars are stable the ranking of the scholars is invariant from tournament to tournament the science does not progress; bugs are not fixed, no new ideas are introduced example: All scholars are perfect: they propose optimal claims C(ps,q) that can neither be strengthened nor refuted. Bionetics

Claims and Refutation Protocol Alice claims: I have a program that solves inputs in domain X with quality Q and resources R. – AliceClaim(X,Q,R) Bob is critical. He prepares an input in X and gives it to Alice who applies her program. Bob refutes AliceClaim(X,Q,R) iff Alice achieves R. – Refutation protocol Bionetics

State of Avatar SCG Domain is hard-wired to Constraint Satisfaction Problems One Master student worked on making it generic but work is not complete. Bionetics