Epistemology of Post-modern Science

1. Epistemology of Post-modern Science Ayşe Erzan “Abstraction today is no longer that of the map, the double, the mirror or the concept. Simulation is no longer that of a territory, a referential being or a substance. It is the generation by models of a real without origin or reality: a hyperreal. The territory no longer precedes the map, nor survives it. Henceforth, it is the map that precedes the territory - precession of simulacra - it is the map that engenders the territory…” Jean Baudrillard, “Le précéssion de Simulacres,” Transverses (1978) Collegium Budapest 2005

2. Outline • Myth, metaphor, scientific explanation • Mathematical modeling, pattern formation and the “formal cause” • Mass distribution in the universe • Fractal growth • Emergence of complexity and levels of description in the life sciences • Modeling evolution; simulation and simulacra • A content based network • The network, modular structure, complexity • Validation? Collegium Budapest 2005

3. Myth,metaphor, scientific theory Computer age- age of the image and analogy? Collegium Budapest 2005

4. Myth and metaphor.. • A mental /social representation : a model of a phenomenon or collection of phenomena • Providing an underlying unity • Making the observations “intelligible” • ~ theory prediction (sooth saying) / manipulation (propitiation) • Conflicting modes of explanation or metaphors allowed • “Associative” reasoning, analogy, similarity Scientific model building : a map that precedes the territory Collegium Budapest 2005

5. Newtonian mechanics -epitome / paradigm of scientific modeling • F: “force” is what we will call that, which gives rise to acceleration (thus this equation defines force) • F can be independently measured in comparison to some standard force! a priviledged mathematical representation : that which is represented, is at the same time defined by the equations • Newton’s laws of motion + “Law of Gravitation”  Kepler’s Laws F=ma Collegium Budapest 2005

6. Aristotelian “causes” as bases for explanation in modern scientific modeling • Material cause - laws of motion apply to point particles regardless of the nature of the material. Interacting small volumes  fluid mechanics. Atomic theory and quantum mechanics (chemistry, molecular biology) reduce the material cause to an “efficient cause” • Efficient cause - making a (mechanical) model of system interrelations  set of equations • Formal cause - interpret not as purely geometrical but more generally mathematical “reason” (efficient cause  formal cause) •Newtonian orbits are formal rather than efficient “causes”! (the solution of a set of differential equations) • Final cause- the fulfillment of some terminal “nature,” use or function Collegium Budapest 2005

7. Modeling complex systems • Nonlinear systems: emergence of fractal patterns in space and time; sensitive dependence on initial conditions; need for statistical descriptions • Models for the emergence of complex patterns in terms of “rules” (totally or partially literal descriptions) rather than equations; e.g., fractal growth rules. New kinds of “formal causes”? Computer application of discrete rules. Simulations. In what way do the models/patterns (simulacra) emerging from the simulations provide “efficient” or “formal causes” ? Wolfram - NKS (!) Collegium Budapest 2005

8. Galactic mass distribution in the universe Purely gestalt similarity (Mandelbrot 1988) r Lévy walk with step size distribution Fractal scaling behavior M ~ R1.5 Collegium Budapest 2005

9. Laplacian fractal growth Particles released from afar do random walk, attach when they hit cluster lightning Model building: a puzzle solving activity within “normal science” (Kuhn) Need not have a “reality” to which it refers,and indeed may “precede” it Collegium Budapest 2005

10. A priviledged representation ! Discrete growth process p= growth probability, computable at each stage from some function  Equations satisfied by  have an a priori nature, they follow from the definition of the models. Diffusion Limited Aggregation, random walkers (Witten and Sander 1981)  = particle concentration formally identical to Dielectric Breakdown, electrostatics (Niemeyer and Pietronero 1984; Pietronero, Erzan,Evertsz 1988)  = electric potential Collegium Budapest 2005

11. Rectangular geometry  = constant on wavy blue lines Biological application: Bacteria growing in Petri dish towards nutrient Fujikawa and Matsushita, 1989 Collegium Budapest 2005

12. Growth in stressed environment Collective response Ben-Jacob,Shocket, Tennenbaum, Czirok, Vicsek (1995) Collegium Budapest 2005

13. Bacteria grown under stressed conditions of low nutrient, for a long time : collective response, search for new strategies The appropriateness of the abstraction should and can be checked against experiment; more sophisticated models can be developed soft agar on hard agar Collegium Budapest 2005

14. Myth,metaphor, scientific theory - the life sciences • Wealth of phenomenological observations • Complexity at all levels Collegium Budapest 2005

15. Emergence of complexity • Spontaneous self assembly • Structures at many different scales a property of all systems sustaining a flux of energy or matter. • Observed structures in living systems: engendered by the formal rules of interaction or association OR evolutionary adaptation- natural selection ? • Difficult to decide the status of theoretical predictions Collegium Budapest 2005

16. neo-Darwinian natural selection • Self replicating system The Canon • Heredity - • provided by DNA (RNA) - the genotype • Linear code with finite alphabet • Random variations in genotype variations in phenotype • The fitter are selected (who are able to reproduce more) Genotype genomic Phenotype interactions Differentiation Heritable phenotypic variations may also occur without genetic changes. Collegium Budapest 2005

17. Mathematical models of evolution Models of self-replicating, autocatalytic systems “Artificial Life” Neural networks, evolution of genetic cognition (variability may not be so random!) (c.f., C. Fernando’s and C. Langton’s talks) Simulacra of living systems / robots / future beings ! “Exploration of the possible to be able to understand the actual” Formal analogues Linear coding of “genotype” Assumed genotype  phenotype “map” Collegium Budapest 2005

18. The Genetic Algorithm optimization procedure for systems with many variables. 1. Select according tofitness, reproduce 2. Mutate, recombine, etc. 3. Remove at random maximization of desired trait  fitness a formally necessary outcome A priviledged representation or a tautology? Collegium Budapest 2005

19. Reverse engineering v.s. Statistical approach • Fitness usually defined with respect to a function • How can new functions, organs etc. arise within this paradigm? How can a function that does not yet exist be optimized? • Phenotype tightly controlled not by single genes but the genomic network, organized in a modular way • need a discrete jump - a phase transition! reorganization of the way the “phase space” (all possible settings of the relevant traits) are explored ! A rewiring of the genetic network? Collegium Budapest 2005

20. Model of an emergent gene regulatory network • Content based • Rule for connectivity: sequence matching along linear code • Reproduces certain global properties of real genomic networks • Connectivity • Modularity • Computational architecture Collegium Budapest 2005

21. Content based networkD. Balcan, A. Erzan, A. Kabakcioglu, M. Mungan 200101012010201101000110100021100211011011110111102 Simulation and analytical results: The in- and out degree distribution distribution of number of incoming Interactions on a collection of random strings outgoinginteractions Collegium Budapest 2005

22. Genomic networks found to be “scale free”n(k)  k -  (1.1 , 1.8) Spatial-temporal complexity Collegium Budapest 2005

23. Comparison a single realisation of the model chromosome and yeast microarray experiment Gustafsson et al.(2004) Collegium Budapest 2005

24. Content based network has architecture suited for computational complexity • Modular structure • Transitivity of connectivity rule X  Y and Y  Z then X  Z  observed type of modularity computing unit Shen-Orr et al. (2002) Kashtan et al. (2004) Collegium Budapest 2005

25. Formal similarity of patterns does not necessarily indicate identity of the efficient cause • Do the regulatory segments on a genomic network really display this sequence matching? Must be checked. • Further evidence for homology of interacting protein complexes Butland et al. (2005) Collegium Budapest 2005

26. Conclusions • Scientific validation of models and simulacra as efficient and formal causes follow previously established lines • Efficient and formal causes not as tightly connected - more specific empirical checks needed • Emergent properties of complex life-systems can be explored via statistical models within the same approach • They may yield theoretical predictions • Final causes should be tamed! (See following pages for some references) Collegium Budapest 2005

27. addendum Here is a very incomplete list of source material your may find useful: [1] Baudrillard, J., (1994) Simulacra and Simulation, University of Michigan Press. [2] Gross, P.R., Levitt, N. ve Lewis, M.W., (1996) The Flight from Science and Reason, Annals of the New York Academy of Sciences, 775. [3] Prigogine, I. ve Stengers, I., (1984) Order out of Chaos, New York, Bantam Books. [4] Kuhn, T. (1962) The Structure of Scientific Revolutions, Chicago, University of Chicago Press. [5] Mandelbrot, B.B., (1982) Fractal Geometry of Nature, San Francisco, Freeman. [6] Wolfram, S., (1983) “Statistical Mechanics of Cellular Automata,” Rev. Mod. Phys. 55, 601-644. [7] http://www.stephenwolfram.com/ [8] Feyerabend, P., (1975) Against Method, N.Y., Verso;(1987) Farewell to Reason, N.Y., Verso. [9] Foucault, M., Rabinov P. Ed., (1991) The Foucault Reader: An Introduction to Foucault's Thought, Penguin Social Sciences, N.Y. [10] Kauffman, S.A., (1993) The Origins of Order, Oxford University Press, Oxford. [11]Goodwin, B., Sibatani, A., Webster G., eds.,(1989) Dynamic Structures in Biology, Edinburgh University Press. see next page for some related papers. Collegium Budapest 2005

28. Related papers L. Pietronero, A. Erzan, C. Evertsz, "Theory of Fractal Growth," Phys. Rev. Lett. 61, 861(1988) L. Pietronero, A. Erzan, C. Evertsz, "Theory of Laplacian Fractals: Diffusion Limited Aggregation and Dielectric Breakdown Model," Physica (Netherlands) A51, 207 (1988) A. Erzan, L.Pietronero and A. Vespignani, "The Fixed Scale Transformation Approach to Fractal Growth,” Rev. Mod. Phys. 67, 545 (1995). Balcan, D. and Erzan, A. “Random model for RNA interference yields scale free network,” q-bio.GN/0310027, Eur. Phys. J. B, 38, 253-260 (2004) A.H. Bilge, A. Erzan and D. Balcan, “The shift-match Number and String matching Probabilities for Binary Sequences,” q-bio.GN/0409023. M. Mungan, A. Kabakçıoğlu, D. Balcan and A. Erzan, “Analytical Solution of a Stochastic Content Based Network Model,” q-bio.MN/0406049, submitted for publication. Collegium Budapest 2005