1. On Disciplinary Fragmentation and Scientific Progress Stefano Balietti, Michael Mäs, and Dirk Helbing ETH Zurich, Chair of Sociology in particular Modeling and Simulations Social Simulation Conference – Barcelona, 05-09-2014 ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation

2. Research Questions  Why are some disciplines more fragmented into conflicting schools of thoughts than others ?  Why do disciplinary fragmentation and limited scientific progress seem to correlate ?

3. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification

4. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification Isaac Newton (1642 - 1727) Unified celestial and terrestrial forces with the law of gravity.

5. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification

6. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification James Maxwell (1831 – 1879) Unified electricity and magnetism in one single force called electromagnetism.

7. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification

8. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification Albert Einstein (1879 - 1955) Unified the Newtonian theory of gravitation and his special relativity with the theory of general relativity.

9. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification

10. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Physics: a Path of Unification Steven Weinberg (1933) Unified, on a subatomic level, the strong force, and the weak force, and the electromagnetic force in once single model called the Standard Model.

11. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation The Social Science Archipelago

12. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation The Social Science Archipelago  Science is composed of an archipelago of typically smallish and highly cohesive communities (Liljeros 2010).  High between-, low within-group variance.  Different social norms apply to different communities.

13. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation in Social Sciences H. Gintis @ Game Theory and Society Zurich, 2011. “Analytical Foundation of Sociological Game Theory” With the sole exception of economics, the social sciences are still missing a core theory that everybody acknowledges. De Langhe R (2009) Mainstream economics: Searching where the light is. Journal of Post Keynesian Economics 32: 137–150.

14. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Research Questions  Why are some disciplines more fragmented into conflicting schools of thoughts than others ?  Why do disciplinary fragmentation and limited scientific progress seem to correlate ?

15. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Research Questions  Why are some disciplines more fragmented into conflicting schools of thoughts than others ?  Why do disciplinary fragmentation and limited scientific progress seem to correlate ?

16. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation References  Vicsek et Al. (1995) “Novel type of phase transition in a system of Self-Driven particles”. Physical Review Letters 75: 1226–1229  Hegselmann R., Krause U. (2006) “Truth and cognitive division of labour: First steps towards a computer aided social epistemology.” Journal of Artificial Societies and Social Simulation 9: 1–28.

17. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Description  Scientists explore a 2-dimensional epistemic space of possible answers to a research question  The movement represents the approach  The position represents the current view  Simultaneously exposed to 3 forces:  Attraction towards the ground truth  Social influence of related opinions  Randomness (Noise)

18. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Formal Model

19. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Formal Model

20. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Formal Model

21. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Formal Model Position NoiseAngular Noise

22. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model parameters  Ground Truth – Strength of attraction τ  Social Influence:  Radius of interaction R  Strength of social influence α  Noise:  Intensity position noise ε  Intensity angular noise σ

23. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Ideal-Typical Model Outcomes

24. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Ideal-Typical Model Outcomes

25. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Ideal-Typical Model Outcomes

26. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Ideal-Typical Model Outcomes

27. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Ideal-Typical Model Outcomes

28. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Agents move randomly in the epistemic space

29. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Agents enter each other interaction areas

30. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Agents approaches are updated by social influence

31. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained New approach is weighted average of own approach and average approach within interaction radius

32. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained New approach has a new direction and intensity

33. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Approach is updated immediately

34. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Update of approaches continues for other agents

35. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained B and C are both within A's interaction radius

36. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained A's approach was reduced by social influence

37. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Approach is updated immediately

38. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Also B's velocity vector is reduced by social influence

39. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Approach is updated immediately

40. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained B and A form a cluster, C leaves interaction areas

41. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Approaches become increasingly more similar

42. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Ground truth is now introduced

43. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Agents are pulled back towards the ground truth...

44. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained … until the velocity of the approaches equals the distance from ground truth

45. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Position noise is now introduced

46. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Perturbs the relative position of agents in the cluster

47. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained but on average the distance from truth stay the same

48. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Angular noise is now introduced

49. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Perturbs the direction of agents' approaches

50. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Model Dynamics Explained Social influence reduce differences in approaches and agents move closer to ground truth

51. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Structural Variables  Strong signal from ground truth (++)  Large interaction radius (++)  Angular noise (++)  Strong social influence (+)  Fragmentation (-)  Clustering (-)

52. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Correlation Fragmentation and Scientific Progress

53. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Structural Variables Social interactions leads to clusters Clusters move agents closer to truth Angular noise keeps agents continuously slightly mis-aligned Diversity of approaches is preserved

54. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Structural Variables Social interactions leads to clusters Clusters move agents closer to truth Angular noise keeps agents continuously slightly mis-aligned Diversity of approaches is preserved Social interactions and peer disagreement are two key mechanisms to promote progress

55. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation

57. Simulation Experiment 2  Randomly assigned agents to c clusters  Clusters were placed equally spaced on a circle of radius d with the ground truth in the center  Varied c to manipulate the degree of fragmentation  Measured time necessary to form consensus on the ground truth (75% within radius 0.05 units)  Varied d to manipulated the degree of progress  Measured the average number of clusters at consensus share 50%

58. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

59. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

60. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

61. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

62. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

63. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

64. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

65. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

66. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Simulation Experiment 2

67. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation on Progress Fragmentation hampers scientific progress

68. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Progress on Fragmentation Scientific progress has no effect on fragmentation

69. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation and Progress  Fragmentation slows down scientific progress  Progress does not have an effect on fragmentation

70. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation and Progress  Fragmentation slows down scientific progress  Progress does not have an effect on fragmentation  Both structural variables and fragmentation affect scientific progress

71. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation and Progress  Fragmentation slows down scientific progress  Progress does not have an effect on fragmentation  Both structural variables and fragmentation affect scientific progress  It might be that the structural variables only affect fragmentation, that in turn slows down progress

72. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Fragmentation and Progress  Fragmentation slows down scientific progress  Progress does not have an effect on fragmentation  Both structural variables and fragmentation affect scientific progress  It might be that the structural variables only affect fragmentation, that in turn slows down progress  To test this hypothesis we performed Baron and Kenny (1986) mediation analysis

73. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Mediation Analysis Baron and Kenny (1986)  Step 1: Regress progress on structural variables (R, σ, and τ )  Step 2: Regress fragmentation on structural variables (R, σ, and τ )  Step 3: Regress progress on fragmentation and structural variables (R, σ, and τ )  If the statistical effect is smaller in Step 3. than in Step 1. the parameter is partially mediated  If the statistical effect is even insignificant, the parameter is completely mediated

74. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Mediation Analysis Results  The effect of all structural variables on progress is at least partially mediated by fragmentation  The angular noise parameter σ is completed mediated by fragmentation.

75. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Mediation Analysis Results  The effect of all structural variables on progress is at least partially mediated by fragmentation  The angular noise parameter σ is completed mediated by fragmentation  Therefore only the length of the radius of influence R, and the strength of attraction to ground truth τ are actually responsible for the correlation between disciplinary fragmentation and scientific progress.

76. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Research Questions  Why are some disciplines more fragmented into conflicting schools of thoughts than others ?  Why do disciplinary fragmentation and limited scientific progress seem to correlate ?

77. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Research Questions  Why are some disciplines more fragmented into conflicting schools of thoughts than others ?  Why do disciplinary fragmentation and limited scientific progress seem to correlate ?

78. ETH Zürich | Stefano Balietti | sbalietti@ethz.ch | SOMS Chair of Sociology, Modeling and Simulation Thank You Very Much “On Fragmentation and Scientific Progress” Stefano Balietti, ETH Zurich – sbalietti@ethz.ch Chair of Sociology, in particular Modeling and Simulations