1. THE ROLE OF MODELS IN THE CONVERGENCE OF SCIENTIFIC KNOWLEDGE Linda Weiser Friedman Zicklin School of Business, Baruch College and the Graduate Center of CUNY email: Linda_Friedman@baruch.cuny.edu Hershey H. Friedman Business Program, Department of Economics Brooklyn College, CUNY email: x.friedman@att.net

2. INTRO TO MODELS: The Blind Men and the Elephant by John Godfrey Saxe (1816-1887) The following poem was based on a fable told in India many years ago… It was six men of Indostan To learning much inclined, Who went to see the Elephant (Though all of them were blind), That each by observation Might satisfy his mind The First approached the Elephant, And happening to fall Against his broad and sturdy side, At once began to bawl: “God bless me! but the Elephant Is very like a wall!” The Second, feeling of the tusk, Cried, “Ho! what have we here So very round and smooth and sharp? To me ’tis mighty clear This wonder of an Elephant Is very like a spear!” The Third approached the animal, And happening to take The squirming trunk within his hands, Thus boldly up and spake: “I see,” quoth he, “the Elephant Is very like a snake!” The Fourth reached out an eager hand, And felt about the knee. “What most this wondrous beast is like Is mighty plain,” quoth he; “ ‘Tis clear enough the Elephant Is very like a tree!” The Fifth, who chanced to touch the ear, Said: “E’en the blindest man Can tell what this resembles most; Deny the fact who can This marvel of an Elephant Is very like a fan! The Sixth no sooner had begun About the beast to grope, Than, seizing on the swinging tail That fell within his scope, “I see,” quoth he, “the Elephant Is very like a rope!” And so these men of Indostan Disputed loud and long, Each in his own opinion Exceeding stiff and strong, Though each was partly in the right, And all were in the wrong!

3. A Model of Models?

4. Models in Architecture - blueprints House House Car Car

5. Models in Architecture – scale models Housing complex Housing complex

6. Models in Statistics Regression Model Regression Model

7. Models in Training - Man-machine simulations Flight simulator Flight simulator

8. Models in Psychology – Virtual Reality VR for Social Phobia VR for Social Phobia

9. Models for the Creation of Alternative Universes Science fiction Science fiction

10. Models in Art Garden of Earthly Delights Garden of Earthly Delights

11. Models in Art Escher’s Relativity Escher’s Relativity

12. Models in Math / Physics Einstein’s Relativity Einstein’s Relativity

13. Models in Chemistry molecule scale model molecule scale model

14. What Do All These Models Have in Common? Abstraction [Black Box] Abstraction [Black Box] Information Hiding Information Hiding A way of understanding our world A way of understanding our world

15. Definition A model is a representation of the real thing but not the thing itself A model is a representation of the real thing but not the thing itself This definition is not very articulate, but it has the advantage of being generalizable to models in many different fieldsThis definition is not very articulate, but it has the advantage of being generalizable to models in many different fields

16. Fashion Model? …a representation …a representation of the real thing but not the thing itself…

17. A Model of Models? First pass First pass

18. A Model of Models? Second pass Second pass

19. A Model of Models? Continuing … Continuing … concrete mathematicalnumerical2-dimensional3-dimensional abstract

20. A Model of Models? Continuing … Continuing … abstract alternate universe mathematicalnumerical2-dim3-dim4-dim mimetic

21. A Model of Models?

22. Discussion The So-What Question… The So-What Question… Convergence of Knowledge Convergence of Knowledge Modeling Across the Curriculum Modeling Across the Curriculum