Evolution of Modeling From Ignorance to Knowing Ali Ishaq March 22 nd, 2007

1 Copyright © 2007 Deloitte Development LLC. All rights reserved. History of Modeling from Antiquity to the Present Three Condensed Versions: 1.A Progression Towards Mathematical Sophistication 2.A Progression Towards Non-Linearity 3.A Progression Towards Complexity

2 Copyright © 2007 Deloitte Development LLC. All rights reserved. A Progression Towards Increasing Mathematical Sophistication The capricious gods The beginnings of rationality and order Greek mathematics and the rigorous world 17th Century: Pascal and Fermat 18th Century: Bernoulli and the beginnings of statistics 19th Century : Keynes and collective human behavior 20th Century : Game Theory, and stochastic models

3 Copyright © 2007 Deloitte Development LLC. All rights reserved. A Progression Towards Non-Linearity Linear models – everything in its right place Linear thinking has its limitations Non-Linear Models – everything is connected Who moved my cheese? Multivariate non-parametric models to the rescue

4 Copyright © 2007 Deloitte Development LLC. All rights reserved. A Progression Towards Complexity Rudimentary models with no common framework Simple Mathematics: a common framework and quantifies reality Complex Mathematical allows more robust models of real world phenomena Growing complexity, cybernetics, and hierarchical models Neural Networks, Connection Machines, Cellular Automata, and Genetic Algorithms Patterns within patterns – Chaos Theory

5 Copyright © 2007 Deloitte Development LLC. All rights reserved. A Progression Towards Complexity My head is bursting: expert systems and automatic rule generation Are there shape-shifting computers with a non-linear soul in your future? Complexity and the limits of computation

6 Copyright © 2007 Deloitte Development LLC. All rights reserved. The Logarithmic Growth In Computation Speed Source: Ray Kurzweil – Age of Spiritual Machines

7 Copyright © 2007 Deloitte Development LLC. All rights reserved. Speed of Change is Accelerating Paradigm shifts parallel the growth in compuatation Source: Ray Kurzweil – Age of Spiritual Machines

8 Copyright © 2007 Deloitte Development LLC. All rights reserved. The End is Near

9 Copyright © 2007 Deloitte Development LLC. All rights reserved. Looking to the Future The struggle between ‘explain-ability’ and better models Expert systems + statistical models = A better brain in the box Some sign-posts to a better future Future is self organizing, goal seeking, and adaptive Solutions less linear Solution elements are highly interdependent Solution uses the shape of the problem Solution evolves with observation

10 Copyright © 2007 Deloitte Development LLC. All rights reserved. Looking to the Future Genetic algorithms: evolving and adaptive The Hive Mind : A democracy of models Silicon + Carbon : You will be assimilated:

11 Copyright © 2007 Deloitte Development LLC. All rights reserved. Looking to the Future Human beings as parts of a bigger mind (The Matrix)

12 Copyright © 2007 Deloitte Development LLC. All rights reserved. The End "Everything should be made as simple as possible, but no simpler."- Albert Einstein

13 Copyright © 2007 Deloitte Development LLC. All rights reserved. Bibliography and Acknowledgements (or Everything I know About Modeling I Learnt From The Movies) Peter L. Bernstein - Against The Gods W. Daniel Hillis - The Connection Machine, Massachusetts Institute of Technology, September, Nigel Snoad and Terry Bossomaier - MONSTER - the Ghost in the Connection Machine: Modularity Of Neural Systems in Theoretical Evolutionary Research Anita M. Flynn and John G. Harris - Recognition Algorithms for the Connection Machine, MIT Artificial Intelligence Laboratory Thanks to my colleagues Ray Stukel, Christina Sung, and Jim Guszcza for corrections, encouragement, and friendship.

Copyright © 2007 Deloitte Development LLC. All rights reserved.