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Modelling Innovation – some options from probabilistic to radical

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A talk on the various kinds of innovation based on Margret Boden's types of creativity . Given at the European Academy, Ahrweiler, Germany 31st May 2017.

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Modelling Innovation – some options from probabilistic to radical

  1. 1. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 1 Modelling Innovation – some options from probabilistic to radical Bruce Edmonds Centre for Policy Modelling Manchester Metropolitan University
  2. 2. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 2 The problem Whilst there are many simulations/models of the spread or uptake of innovations… ...the process of innovation itself is generally not modelled
  3. 3. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 3 Talk Outline 1.  Kinds of innovation (derived from Boden, M. (2004) The creative mind: myths and mechanisms, Routledge) 2.  Three examples of modelling exploratory innovation 3.  Some thoughts about how to approach modelling transformative innovation
  4. 4. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 4 Innovation 0: Probibilistic •  When an unlikely event occurs (from a known distribution) Examples: –  two people who went to school together happen to meet in a departure lounge 20 years later –  A spore of fungus happens to infect a petri dish with a bacterial culture on it •  Not really innovation in a meaningful sense •  But it may trigger an innovation (of another kind) •  However, this is how innovation is represented in many simulations!
  5. 5. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 5 Innovation 1: Combinatorial •  When there are a number of possible ‘components’ and you find the combination of them (that does something) Examples: –  The right cut, size, colour and material for a t-shirt –  Choosing the options for a new kind of family car that is both attractive yet cheap enough to sell well •  This is hard when there are a large number of possibilities and when the number of acceptable solutions is low •  One can systematically compare solutions and maybe find an optimal combination
  6. 6. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 6 Innovation 2: Exploratory •  Where the process of discovery is path-dependent and the paths branch in complicated ways Examples: –  Finding the right genome (for some purpose) using a sequence of mutations and sexual recombinations –  Discovering how to synthesize a chemical •  This is closer to pure research – one might not know the outcome before one gets there •  Not possible to optimize, this is more a case of discovering something new (or a new process) •  Might be useful in a new way, or be a new kind
  7. 7. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 7 Innovation 3: Transformational •  When something changes the way we think about things – changes the landscape of discovery •  Examples: –  When Newton connected the movement of everyday objects and the planets via his laws of motion –  A new understanding of a relationship with someone when you discover something about their past •  Adds a new ‘dimension’ into the search for solutions, or changes the paths for exploration •  Something humans are quite good at, but this can be misleading – just because you can think of something in a new way does not make it so
  8. 8. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 8 Personal vs. Historical Innovation Just because something is new for an individual does not mean it counts as an innovation for society For it to count as a historical innovation: 1.  It has not to be commonly known or adopted already 2.  It is recognized as a particular kind of thing 3.  And judged as an innovation by the ‘field’ of people that judges that kind of thing (Kahl, CH. (2012). Creativity is more than a trait – It's a relation, Doctoral thesis, University of Hamburg). It may be that something is not immediately recognised as an innovation but may be so later due to the impact of the innovation or the field changes etc.
  9. 9. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 9 Two Examples of Modelling Exploratory Innovation 1.  A model of mathematical discovery and scientific publishing 2.  A model of making things In both: •  Knowledge is structured in complex ways •  How to “get to” the desirable structures is difficult to predict before you do, but there are clues in the intermediate stages (i.e. the search space is hard but not random) •  Items have a dual use: as ends in themselves, but also as tools to help make new items or make items more efficiently •  There are naturally “gateway” discoveries that the means to obtaining many other targets
  10. 10. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 10 Mathematical Discovery and Scientific Publishing Example 1
  11. 11. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 11 The test-bed problem •  The theories are those of classical propositional logic with connectives: ¬, ∧, ∨, →, ↔, T, F •  formulated as a “Hilbert System” with: –  14 axioms –  1 rule, Modus Ponens (MP) (explained shortly) •  110 designated “target theories” taken from textbooks •  New theories developed by taking applying MP to to existing theories •  Makes for a fairly tough problem - space of theorems is more than exponential in size
  12. 12. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 12 Agent-1 Agent-2 Structure of the Simulation The Journal The Axioms MP MP
  13. 13. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 13 Action of the MP inference rule yyxx →→→ ))(( )()(( aaaa →→→ BA → (Major Premise) A (Minor Premise) )( aa → B (Inference)
  14. 14. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 14 Agents •  Agents have two (limited) stores, for knowledge (minor) and techniques (major) •  Each iteration each agent: 1.  Decides what new items of knowledge to add to its private stores from the published set, also which to drop (both major and minor). 2.  Decides which major premise and what set of minor premises it will try with the MP rule and add any results to its (minor) store. 3.  Decides which of its private knowledge (that is not already public) it will submit to the journal •  Agents may “panic” if they have not discovered anything within a certain number of iterations and replace their knowledge (minor or major)
  15. 15. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 15 The Journal (the Journal of Artificial Sentences and Successful Syllogisms) •  The journal is the public repository of knowledge (accessible to all) •  Each iteration the journal: 1.  Makes a short-list of submissions that meet basic criteria (e.g. novelty, number of vars.) 2.  Ranks the short-list using a weighted score (in this case, shortening, shortness, past success of submitter, number of variables) 3.  Chooses from the ranked short-list (e.g. top N, randomly, probabilistically etc.)
  16. 16. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 16 The Experiment •  20 agents over 50 iterations •  Each agent stores 4 major and 27 minor premises as its current knowledge and submit all unpublished formulas they find •  1 journal, selecting for (in descending order) shortening; shortness; prestige; num vars. •  Vary the number of formula the journal publishes each iteration from 1…10 •  Results are averages over 25 independent runs for each setting
  17. 17. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 17 Example output from a run … Iteration 3 agent 3 found '->' ('->' A ('->' B C)) ('->' B ('->' A C)) agent 3 found '->' ('->' A ('->' ('->' B C) D)) ('->' ('->' B C) ('->' A D)) agent 6 found '->' ('->' A ('->' B B)) ('->' A ('->' A ('->' B B))) agent 6 found '->' ('->' A ('->' A B)) ('->' A B) agent 6 found '->' ('->' A B) ('->' ('->' B A) ('->' A B)) agent 17 found '->' ('->' A ('->' A B)) ('->' A B) agent 19 found '->' ('->' A B) ('->' ('->' C A) ('->' C B)) agent 19 found '->' ('->' A B) ('->' ('->' C ('->' ('->' A B) D)) ('->' C D)) Iteration 4 agent 7 found '->' ('->' A B) ('->' ('->' ('->' A B) C) C) agent 7 found '->' A ('->' ('->' A B) B) agent 13 found '->' ('->' A ('¬' A)) ('¬' A) agent 15 found '->' ('->' A ('¬' A)) ('¬' A) Iteration 5 Iteration 6 …
  18. 18. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 18 Number of formulas in public domain 0 100 200 300 400 500 600 0 10 20 30 40 50iteration totalnumberformulafound njp=1 njp=2 njp=3 njp=4 njp=5 njp=6 njp=7 njp=8 njp=9 njp=10
  19. 19. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 19 Number of targets found 10 10.5 11 11.5 12 0 10 20 30 40 50iteration totalnumbertargetsfound njp=10 njp=9 njp=8 njp=7 njp=6 njp=5 njp=4 njp=3 njp=2 njp=1
  20. 20. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 20 Total number found by agents (also num. submitted for publication) 0 20 40 60 80 100 120 140 160 180 0 10 20 30 40 50iteration totalnumberformulasubmitted njp=1 njp=2 njp=3 njp=4 njp=5 njp=6 njp=7 njp=8 njp=9 njp=10
  21. 21. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 21 (Average) spread (the SD) of numbers of formulas found by agents 0 1 2 3 4 0 10 20 30 40 50iteration sdofnumbersagentsfound njp=1 njp=2 njp=3 njp=4 njp=5 njp=6 njp=7 njp=8 njp=9 njp=10
  22. 22. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 22 Number found by agents (a single run, njp=2) 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 Iteration Numberfoundbyagents
  23. 23. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 23 Number found by agents (a single run, njp=10) 0 20 40 60 80 100 120 140 160 0 10 20 30 40 50 Iteration Numberfoundbyagents
  24. 24. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 24 Some issues that could be investigated in this test-bed include: •  Is any norm on methods for discovering new knowledge is counterproductive? (Feyerabend) •  What is the effect of the framework (within which knowledge is expressed) on the structure of new knowledge? (Kuhn) •  When and how do social processes act to increase the reliability of knowledge collectively produced (or otherwise)? (Merton, Popper) •  Is it helpful to have an inviolate core of knowledge/techniques that is not open to revision? (Lakatos)
  25. 25. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 25 A Model of Making Example 2
  26. 26. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 26 The String MakerWorld •  Things in this model are strings, e.g. ‘ACC&BA’ •  They are made form a finite number of ‘elements’ {A, B, C…} and the two special symbols: {&, >} •  Only certain strings can be extracted from the environment (randomly determined at the start). All other strings have to be made from these. •  Only certain target strings can have inherent value (randomly determined at the start). These can be ‘used’ to get that value •  Strings can be joined/split by hand at & but to get any other kind of longer string you have to use a tool (another string with “>” in it that can change strings)
  27. 27. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 27 Simple Example Say an agent was in the following situation: Available in environment: A; A>; AA; AB; B>; BA; BB; A&A; A&B; AAA; AB>BA Has use value to agent: AB; A&B; AAA; AAB; ABA; B&A; BBA; BBB; A&AA Possible sequences of actions by agent: •  Get A&B then immediately use it •  Get A and BA then join these to make A&BA •  Get A&B, split this into A and B, then join these to make B&A and use this •  Get AB use tool AB>BA on it to make BA, use it
  28. 28. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 28 Rationale behind String MakerWorld •  Simplest world that allows the complexity of making to be explicitly represented •  Working out how to make valuable strings is hard, which gives value to good plans (and hence motivation for trading/sharing plans) •  Control over which resources each agent has access to can add heterogeneity in production •  Control over the target strings each agent can directly use can add heterogeneity of need •  Heterogeneity of resources and needs gives motivation for the trade/sharing of objects
  29. 29. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 29 The Model •  Agents are patches but can interact with others in any pattern they choose/learn •  Things are explicitly tracked with their own properties (which matter structurally) Agents are implemented as patches Object and its string owned by an agent Some objects are complex, this one soft- joined from smaller parts Some objects are simple, this one composed of a single “element” This object is a tool, in this case adding a soft join into the string (allowing it to be maybe separated later) The arrow indicates a sale/ transfer of an object from one agent to another
  30. 30. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 30 Plans •  Plans (the sequence of actions needed to make particular things) are separate from the things •  Agents sometimes do things experimentally (ATM at random) to see what they can make •  Agents remember how they made things in terms of plans – the actions necessary to get any particular outcome •  Agents remember the better value plans and preferentially execute those again •  These plans could be sent/shared/licensed between agents
  31. 31. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 31 Some example plans learnt by an agent value 3.25: realise [BAA split-right [B&BAA get]] value 1.5: sell [B get] (patch 0 0) value 1.25: realise [BAA split-right [B&BAA split-right [B&B&BAA join [B split-left [B&BAA get]] [B&BAA get]]]] value 1.25: sell [B split-left [B&BAA get]] (patch 2 0) value -1: join-random value -1.5: B split-left [B&BAA get] value -2: get-random •  Note that alternative plans to make the same things might be remembered, but with different costs •  Plans can be arbitrarily complex, thought each action has a small cost associated with it, so more complex plans will tend to have lower values (unless they result in a more valuable result) •  Agents prefer to re-use plans with higher value
  32. 32. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 32 The (current) main simulation loop Continually (each tick), agent: Considers a number of plans (including the default random ones) with a bias towards more valuable ones: Until one works: Assess next plan to see if it would work If so, do plan! If new, compile and remember plan If have too many plans in memory, maybe forget one (with a bias towards the less valuable ones)
  33. 33. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 33 Number of things made in 10 different runs 0 20 40 60 80 100 120 140 160 0 23 46 69 92 115 138 161 184 207 230 253 276 299 322 345 368 391 414 437 460 483 1 2 3 4 5 6 7 8 9
  34. 34. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 34 Number of different things made in the 10 runs 0 5 10 15 20 25 30 0 22 44 66 88 110 132 154 176 198 220 242 264 286 308 330 352 374 396 418 440 462 484 1 2 3 4 5 6 7 8 9
  35. 35. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 35 Average number of tools found in 10 runs 0 1 2 3 4 5 6 0 21 42 63 84 105 126 147 168 189 210 231 252 273 294 315 336 357 378 399 420 441 462 483 1 2 3 4 5 6 7 8 9
  36. 36. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 36 Average String length in the 10 runs 0 5 10 15 20 25 30 0 21 42 63 84 105 126 147 168 189 210 231 252 273 294 315 336 357 378 399 420 441 462 483 1 2 3 4 5 6 7 8 9
  37. 37. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 37 Average Number of things for sale in 10 runs 0 5 10 15 20 25 0 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340 357 374 391 408 425 442 459 476 493 1 2 3 4 5 6 7 8 9 10
  38. 38. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 38 Average Maximum Plan Value in the 10 runs -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 336 352 368 384 400 416 432 448 464 480 496
  39. 39. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 39 Average Wealth in the 10 runs 0 200 400 600 800 1000 1200 1400 0 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360 378 396 414 432 450 468 486 1 2 3 4 5 6 7 8 9 10
  40. 40. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 40 Standard Deviation of Wealth in the 10 runs 0 100 200 300 400 500 600 700 800 0 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320 336 352 368 384 400 416 432 448 464 480 496 1 2 3 4 5 6 7 8 9 10
  41. 41. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 41 Issues we might explore… …include: •  Changing the heterogeneity of needs, from everybody has similar needs, to all different •  Explore the conditions under which more centralised manufacturing or markets emerge •  Explore the impact of introducing new technology (something equivalent to 3D printers) •  Looking at how the structure of communication (for plans or selling/sharing items) effects things •  Maybe even wilder topics, e.g. –  what if all objects contain their own plans –  or come with tools to disassemble/reassemble/fix it –  How might the norms of agents impact on the outcomes
  42. 42. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 42 Towards Modelling Transformative Innovation •  In order to represent transformational modelling one needs to be able to change the way agents view what they are doing •  This means they have to a)  HAVE a view of what they are doing b)  use this to make representations of their world c)  then use these for discovery (e.g. exploratory discovery) d)  sometimes be able to change their view •  In other words a Model of Modelling itself
  43. 43. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 43 A language of representation model1 model2 model3 Goals to evaluate success of models Actions Perceptions Some of what Model of Modelling would involve A world sufficiently complex to make this complex machinery worthwhile A language of representation model1 model2 model3 Goals to evaluate success of models Actions Perceptions
  44. 44. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 44 Conclusions •  Modelling more sophisticated kinds of innovation is possible within agent-based simulation •  At the moment these models are quite abstract, but there is no reason why these kinds of approaches should not be applied to modelling innovation within firms and universities •  A better understanding of the creativity that occurs could help us know how to encourage and/or direct it •  Simpler models of innovation are almost certainly insufficient to do this
  45. 45. Modelling Innovation - some options from probabilistic to radicals, Bruce Edmonds, European Academy, May 2017. slide 45 The End! Bruce Edmonds: http://bruce.edmonds.name Centre for Policy Modelling: http://cfpm.org The slides will be available at: http://slideshare.net/BruceEdmonds

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