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Evolution of Modeling
From Ignorance to Knowing
Ali Ishaq
March 22nd, 2007
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
Copyright © 2007 Deloitte Development LLC. All rights reserved.
1
A Progression Towards Increasing Mathematical Sophistication
•
The capricious gods
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The beginnings of rationality and order
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Greek mathematics and the rigorous world
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17th Century: Pascal and Fermat
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18th Century: Bernoulli and the beginnings of statistics
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19th Century : Keynes and collective human behavior
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20th Century : Game Theory, and stochastic models
Copyright © 2007 Deloitte Development LLC. All rights reserved.
2
A Progression Towards Non-Linearity
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Linear models – everything in its right place
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Linear thinking has its limitations
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Non-Linear Models – everything is connected
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Who moved my cheese?
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Multivariate non-parametric models to the rescue
Copyright © 2007 Deloitte Development LLC. All rights reserved.
3
A Progression Towards Complexity
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Rudimentary models with no common framework
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Simple Mathematics: a common framework and quantifies reality
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Complex Mathematical allows more robust models of real world
phenomena
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Growing complexity, cybernetics, and hierarchical models
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Neural Networks, Connection Machines, Cellular Automata, and
Genetic Algorithms
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Patterns within patterns – Chaos Theory
Copyright © 2007 Deloitte Development LLC. All rights reserved.
4
A Progression Towards Complexity
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My head is bursting: expert systems and automatic rule generation
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Are there shape-shifting computers with a non-linear soul in your
future?
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Complexity and the limits of computation
Copyright © 2007 Deloitte Development LLC. All rights reserved.
5
The Logarithmic Growth In Computation Speed
Source: Ray Kurzweil – Age of Spiritual Machines
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6
Speed of Change is Accelerating
Paradigm shifts parallel the growth in compuatation
Source: Ray Kurzweil – Age of Spiritual Machines
Copyright © 2007 Deloitte Development LLC. All rights reserved.
7
The End is Near
Copyright © 2007 Deloitte Development LLC. All rights reserved.
8
Looking to the Future
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The struggle between ‘explain-ability’ and better models
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Expert systems + statistical models = A better brain in the box
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Some sign-posts to a better future
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Future is self organizing, goal seeking, and adaptive
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Solutions less linear
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Solution elements are highly interdependent
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Solution uses the shape of the problem
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Solution evolves with observation
Copyright © 2007 Deloitte Development LLC. All rights reserved.
9
Looking to the Future
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Genetic algorithms: evolving and adaptive
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The Hive Mind : A democracy of models
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Silicon + Carbon : You will be assimilated:
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10
Looking to the Future
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Human beings as parts of a bigger mind (The Matrix)
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11
The End
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"Everything should be made as simple as possible, but no simpler."Albert Einstein
Copyright © 2007 Deloitte Development LLC. All rights reserved.
12
Bibliography and Acknowledgements
(or Everything I know About Modeling I Learnt From The Movies)
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Peter L. Bernstein - Against The Gods
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W. Daniel Hillis - The Connection Machine, Massachusetts Institute of
Technology, September, 1981.
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Nigel Snoad and Terry Bossomaier - MONSTER - the Ghost in the
Connection Machine: Modularity Of Neural Systems in Theoretical
Evolutionary Research
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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.
13
Copyright © 2007 Deloitte Development LLC. All rights reserved.