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MTV 11: Little Models

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This is module 11 from the course Creative Modeling for Tech Vision by David E. Goldberg, The course talks about llittle quantitative models to model particular facets of complex problems from genetic …

This is module 11 from the course Creative Modeling for Tech Vision by David E. Goldberg, The course talks about llittle quantitative models to model particular facets of complex problems from genetic algorithms to organizations.

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  • 1. Creative Modeling for Technology Visionaries Qualitative & Simplified Quantitative Modeling for Product Creation Module 11: Little Models David E. Goldberg University of Illinois at Urbana-Champaign Urbana, Illinois 61801 deg@uiuc.edu
  • 2. Want Little Quantitative Models Going quantitative, need to walk before run. Existing categories often have many analyses & models. New categories often have little understanding. Build quantitative understanding as needed. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 2
  • 3. This Module The approach of little models. Dimensional analysis. Lift coefficients & innovation numbers revisited. Turning points. Little models and data. Organizational example: deciding-doing model. Little models from elementary optimization. Will Rogers theory of models. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 3
  • 4. What is a “Model?” Low Cost/ High Cost/ High Error Low Error Unarticulated Articulated Dimensional Facetwise Equations Wisdom Qualitative Models Models of Motion Model The Modeling Spectrum Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 4
  • 5. Little Models Defined Our interest is in models that are Principled Quantitative Not equations of motion Call them little models, where “little” is a term of approbation. Little models simplified, not universal. Where do little models come from? Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 5
  • 6. Sources of Little Models Dimensional analysis (more in moment) Construction of model for single facet. Reduction of equation of motion for one or small number of facets. Incorporation of qualitative reasoning. Extremum principle. Data usage (data-influenced), but empirical fit alone not enough. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 6
  • 7. Aside on Dimensional Analysis Common in physics and engineering, but not CS. Buckingham PI theorem: n dimensional parameters, m dimensions  n – m independent dimensionless parameters. [V ] = L/T, [D ] = L, [ν ] = L2/T n = 3, m = 2, n – m = 1 R = VD/ν, the Reynolds number One difference: many CS parameters are pure numbers. Must derive time, spatial, or other scale, then renormalize. Can play the same game for GAs, AI, & AL. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 7
  • 8. Lift Coefficient Revisited λ CL = ρV A 2 2 Ratio of two forces. Lift to inertial force. Angle of attack is dimensionless. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 8
  • 9. The Race Deconstructed Have two facetwise models, but want integrated understanding. Putting models in t terms gives us an idea. Consider relative magnitudes of the two times: a dimensional argument. Consider which is favorable to innovation: a qualitative argument. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 9
  • 10. Schematic of the Race Schem atic of "The Race" t* ti 1 0.8 Market Share 0.6 0.4 0.2 0 0 5 10 15 20 25 Generations Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 10
  • 11. Consider Ratio of Two Times Define innovation number G = t*/ti G = pc pi n lnn/ lns. Want takeover time greater than innovation time or G > 1. Quantity like Reynolds number in fluids. Argument was a dimensional argument. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 11
  • 12. Another View: Turning Point t* = ln n/ ln s ti = (pc pi n)-1 Consider intersection of the two curves as function of s. Sketch. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 12
  • 13. Standing Back Key element was the juxtaposition of two functional dimensions. Lift coefficients: Lift vs. inertial forces. Race: selection vs. innovation. Simplified style of model works pair by pair. m  Theoretically, m functional dimensions    2 pairings Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 13
  • 14. 3 Roles of Data for LMs  Verify model & determine range of applicability (LMs not valid throughout domain).  Determine parameters.  Derive model (functional curve fit on dimensionless parameters). Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 14
  • 15. Interaction of Little Models & Data Relationship of data and LMs 2-way street. Little models can give idea of what data to collect. Dimensional analysis and LMs suggest appropriate or better visualization. Not purely empirical. Not purely theoretical. Back and forth. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 15
  • 16. Another Domain: Organizations Much organizational theory is qualitative and remains qualitative. Computational organizational theory dominated by busy complexity of detailed simulations. Would like simplified theories. Analogy: Current situation in orgs would be like doing finite elements or elasticity in structures before understanding beam bending. δ = PL3/3EI Small number of terms, relevant variables, qualitatively and quantitatively relevant predictions. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 16
  • 17. Simon’s Administrative Behavior Primary dichotomy is between deciding and doing. Can we use this dichotomy as first focal point for entry into organizations? Need to assume topology of decision and doing and make up little models. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 17
  • 18. How Do Teams Decide? Have a discussion amongst n participants. Present to the boss, take a vote, come to consensus. Details important, perhaps, but let’s start by assuming that time to decision goes up as size of the team n. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 18
  • 19. How Do Teams Do? n participants divide the workload amongst themselves somehow. Perhaps one workhorse does and others stand around. Perhaps they all work well and divide work equally. Perhaps there is some slacking, or perhaps there is some synergy. Start by assuming time going down inversely with n. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 19
  • 20. Deciding and Doing Model Team size: n Discussing what is to be done: T1 Total time to do the task alone: T2 Total time required for task completion: Model integration via summation. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 20
  • 21. Do the Math Take derivative of T(n) with respect to n. Set to zero. Do it. Efficient team size Optimal time: Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 21
  • 22. A Specific Case Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 22
  • 23. Dimensionless Form Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 23
  • 24. Dimensional Analysis Tames Viz Note how form simplifies under dimensional analysis. All cases collapse to a single curve. Don’t need infinite family of curves. Log transform asymptotically gives straight lines up and down. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 24
  • 25. Speedup Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 25
  • 26. Consider Turning Point Derivation Tdecide = T1n Tdo = T2/n Set equal to each other. T1n* = T2/n* Same as before: Not generally the case, but not bad approximation. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 26
  • 27. Elementary Optimization Problem EOPs involve a function of one variable, sum of increasing & decreasing function: Multiplicative form: Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 27
  • 28. Double Power-law Model Double power-law particularly useful. Arises in cases with  n    topology.   k Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 28
  • 29. Lessons of LMing Facetwise approach is fast. Requires some skill in identifying correct facets and in integrating them. Payoff in understanding is out of proportion to complexity of the effort. Do not waste time on needless parametric study. Verify expected behavior and move on. Facetwise understanding improves pedagogy and ability to explain things simply. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 29
  • 30. Will Rogers Theory of Modeling I never met a model I didn’t like. Need to relax notion of “theory” to achieve objectives. Theory is not the end goal. Theory is a means to better products, better organizations, better processes.. Want principled approach, but rigor can safely be Will Rogers (1879-1935) relaxed. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 30
  • 31. Bottom Line Deconstruct the race. Consider dimensional analysis and turning point approaches to derivation. The approach of little models. Lift coefficients & innovation numbers revisited. Little models and data. Organizational example: deciding-doing model. Little models from elementary optimization. Little models give great insight for the effort. Creative Modeling for Tech Visionaries © 2007 David E. Goldberg. All rights reserved. 31