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Genetic algorithms and the changing face of scientific theories

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An informal talk about genetic algorithms, numerical simulations and scientific discovery. March 2010, HPS, University of Leeds

An informal talk about genetic algorithms, numerical simulations and scientific discovery. March 2010, HPS, University of Leeds

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  • 1. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References Numerical Simulations and Scientific Discovery paper available at: http://papers.imuntean.net Ioan Muntean Department of Philosophy and History and Philosophy of Science University of Leeds March 9, 2010 1
  • 2. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Outline 1 Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Philosophical questions Three stances The “glorified slide rule argument” My position 2 Genetic Algorithms in Numerical Simulations (GNS) Beyond Turing Survival and chance in computer science Inductive programming (skip) Genetic numerical algorithms (GNS) 3 Philosophy of GNS What philosophy for GNS? Arguments for GNS Metaphysics of GNS GNS and mathematics GNS and invariance GNS and laws of nature Objections 4 Finis Risky conclusions Weaker conclusions 5 References 2
  • 3. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions 3
  • 4. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) 3
  • 5. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) Non-Standard: NS track the dynamical evolution of real systems (St. Hartmann). 3
  • 6. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) Non-Standard: NS track the dynamical evolution of real systems (St. Hartmann). Broad: NS is a computational model that includes the equations of a model, assumptions, corrections, interpretations, justifications, and representations (Humphreys 2004, 110). 3
  • 7. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) Non-Standard: NS track the dynamical evolution of real systems (St. Hartmann). Broad: NS is a computational model that includes the equations of a model, assumptions, corrections, interpretations, justifications, and representations (Humphreys 2004, 110). History prone NS: more fine-grained, historical distinctions are needed (E. F. Keller). 3
  • 8. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) Non-Standard: NS track the dynamical evolution of real systems (St. Hartmann). Broad: NS is a computational model that includes the equations of a model, assumptions, corrections, interpretations, justifications, and representations (Humphreys 2004, 110). History prone NS: more fine-grained, historical distinctions are needed (E. F. Keller). 3
  • 9. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Definitions Standard: “the use of a computer to build a model involving equations that we cannot solve analytically”. (P. Humphreys, E. Winsberg) Non-Standard: NS track the dynamical evolution of real systems (St. Hartmann). Broad: NS is a computational model that includes the equations of a model, assumptions, corrections, interpretations, justifications, and representations (Humphreys 2004, 110). History prone NS: more fine-grained, historical distinctions are needed (E. F. Keller). I take them as “working definitions” I agree that we need to be more philosophically nuanced 3
  • 10. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position 4
  • 11. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) 4
  • 12. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not 4
  • 13. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. 4
  • 14. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. How do NS contribute to the progress of science? Not yet, not significantly. 4
  • 15. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. How do NS contribute to the progress of science? Not yet, not significantly. Witness the philosophical importance of some scientific tools: 4
  • 16. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. How do NS contribute to the progress of science? Not yet, not significantly. Witness the philosophical importance of some scientific tools: the microscope (I. Hacking), 4
  • 17. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. How do NS contribute to the progress of science? Not yet, not significantly. Witness the philosophical importance of some scientific tools: the microscope (I. Hacking), the thermometer (H. Chang). 4
  • 18. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What are they? What is their status? Are numerical simulations similar to models? M. Morrison (2009): they have the same epistemic status) Are NS mere experiments? E. Winsberg, W. Parker: they are not Are numerical experiments mere applications or spinoffs of scientific theories? We’ll discuss this. How do NS contribute to the progress of science? Not yet, not significantly. Witness the philosophical importance of some scientific tools: the microscope (I. Hacking), the thermometer (H. Chang). Why not a philosophy of NS? 4
  • 19. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Mongrels and halfway houses E. Winsberg: NS are “mongrels” between experiments and theories and have features of both theories and of experiments, without being theories or experiments. 5
  • 20. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Mongrels and halfway houses E. Winsberg: NS are “mongrels” between experiments and theories and have features of both theories and of experiments, without being theories or experiments. S. Ulam (the father of the Monte Carlo method, late 1940s): NS are a “halfway house” between elegant theory and experimental hardware (quoted in Keller 2003, 205) 5
  • 21. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Mongrels and halfway houses E. Winsberg: NS are “mongrels” between experiments and theories and have features of both theories and of experiments, without being theories or experiments. S. Ulam (the father of the Monte Carlo method, late 1940s): NS are a “halfway house” between elegant theory and experimental hardware (quoted in Keller 2003, 205) 5
  • 22. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Mongrels and halfway houses E. Winsberg: NS are “mongrels” between experiments and theories and have features of both theories and of experiments, without being theories or experiments. S. Ulam (the father of the Monte Carlo method, late 1940s): NS are a “halfway house” between elegant theory and experimental hardware (quoted in Keller 2003, 205) 5
  • 23. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The enthusiasts 6
  • 24. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The enthusiasts It is thus reasonable to conclude that we are at the threshold of an era of new scientific methodology. In view of further technical developments in the near future, computer experts suggest that we are at present only at the very beginning of this new era. [...] computer simulation offers a new tool for science: theoretical model experiments of a scope and richness far exceeding anything available before. (Rohrlich 1990, 512,516) Galison: NS constitute a new epistemology, as a new method of extracting information from physical measurements, as well as a new metaphysics that presupposed discrete entities interacting through stochastic processes (Galison 1996, 120). 6
  • 25. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Some skeptical stances
  • 26. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Some skeptical stances 1 “Old stew in a new pot”: NS are not special for philosophy of science (Frigg and Reiss 2009; Stockler 2000). 7
  • 27. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Some skeptical stances 1 “Old stew in a new pot”: NS are not special for philosophy of science (Frigg and Reiss 2009; Stockler 2000). 2 “Wait-and-see”: We do not know what are the long-term consequences of the NS 7
  • 28. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Some skeptical stances 1 “Old stew in a new pot”: NS are not special for philosophy of science (Frigg and Reiss 2009; Stockler 2000). 2 “Wait-and-see”: We do not know what are the long-term consequences of the NS 3 “Rage against the machine”: philosophical arguments pertaining to show that: “computers are dummy” “computers cannot create” etc. 7
  • 29. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun”
  • 30. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun” My answer to 2: philosophy of science is the history of future science (so to speak). Wait what? The next Ice Age? NS are here, alive and kicking.
  • 31. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun” My answer to 2: philosophy of science is the history of future science (so to speak). Wait what? The next Ice Age? NS are here, alive and kicking.
  • 32. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun” My answer to 2: philosophy of science is the history of future science (so to speak). Wait what? The next Ice Age? NS are here, alive and kicking. I focus on 3 It’s more subtle!
  • 33. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun” My answer to 2: philosophy of science is the history of future science (so to speak). Wait what? The next Ice Age? NS are here, alive and kicking. I focus on 3 It’s more subtle! It has a respectable philosophical pedigree (Descartes, Leibniz, Kant)
  • 34. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Short answers to skeptics My answer to 1: what is a novel philosophical problem? We risk to get to “nothing new under the sun” My answer to 2: philosophy of science is the history of future science (so to speak). Wait what? The next Ice Age? NS are here, alive and kicking. I focus on 3 It’s more subtle! It has a respectable philosophical pedigree (Descartes, Leibniz, Kant) It is mathematically and scientifically challenging (see Godel, Turing, J.R. Lucas)
  • 35. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 1: “Look! This is something new”?
  • 36. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 1: “Look! This is something new”? For instance, if, rather than spilling much ink on convincing ourselves that simulations are unlike everything else, we recognize that the epistemological problems presented to us by simulations have much in common with the ones that arise in connection with models, we can take the insights we gain in both fields together and try to make progress in constructing the sought-after new epistemology. (Frigg and Reiss 2009, 611). With this, I agree
  • 37. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 1: “Look! This is something new”? For instance, if, rather than spilling much ink on convincing ourselves that simulations are unlike everything else, we recognize that the epistemological problems presented to us by simulations have much in common with the ones that arise in connection with models, we can take the insights we gain in both fields together and try to make progress in constructing the sought-after new epistemology. (Frigg and Reiss 2009, 611). With this, I agree I will try to do something similar in last section
  • 38. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 2: The Greek Chorus attitude 10
  • 39. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 2: The Greek Chorus attitude Wait and see who’s winning the battle. Do not hedge your bets too early in the game. Philosophers are like Greek chorus, they come at the end to explain the victory. 10
  • 40. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 3: NS as “glorified slide rules” claim C-1 A computer algorithm is no better than the assumptions which it was built on The Analytical Engine has no pretensions to originate anything. It can do whatever we know how to order it to perform. A letter of A. Lovelace quoted in (Hatree, 1949) An argument Computers do not think Science is a creative process that involves reason and skills Computers do not contribute to progress (or discovery) in science Computers are erring in anything, like slide rules do.
  • 41. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Stance 3: NS as “glorified slide rules” claim C-1 A computer algorithm is no better than the assumptions which it was built on The Analytical Engine has no pretensions to originate anything. It can do whatever we know how to order it to perform. A letter of A. Lovelace quoted in (Hatree, 1949) An argument Computers do not think Science is a creative process that involves reason and skills Computers do not contribute to progress (or discovery) in science Computers are erring in anything, like slide rules do.
  • 42. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Consequences of the glorified slide rules argument Demoting NS again Whenever the analytic solution is discovered, a real experiment is possible or new data is available, NS can be tossed away.
  • 43. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position Consequences of the glorified slide rules argument Demoting NS again Whenever the analytic solution is discovered, a real experiment is possible or new data is available, NS can be tossed away. Nothing that NS have achieved could not have been done by an “army of well-trained scientists working with slide rules”.
  • 44. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: 13
  • 45. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality 13
  • 46. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). 13
  • 47. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; 13
  • 48. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. 13
  • 49. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. NS are fundamentally flawed. 13
  • 50. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. NS are fundamentally flawed. computers cannot simulate the continuum quantities of physics, 13
  • 51. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. NS are fundamentally flawed. computers cannot simulate the continuum quantities of physics, there are inherent errors of digitization and, 13
  • 52. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. NS are fundamentally flawed. computers cannot simulate the continuum quantities of physics, there are inherent errors of digitization and, computer arithmetic is fundamentally limited by G¨del’s o incompleteness theorem. 13
  • 53. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position The inherently limited nature of NS NS are subordinate in their nature because they do provide novel scientific knowledge only when other, more rigorous ways of representing the real world fail: NS are unreal because unlike experiments and models, they do not latch directly onto reality NS lack materiality; Materiality, maybe the most relevant, is discussed in (Parker 2009). NS bear no causal connection to the world; NS are very brute idealizations (Parker, M. Morgan 2005-2009) etc. argue for or against some of these. NS are fundamentally flawed. computers cannot simulate the continuum quantities of physics, there are inherent errors of digitization and, computer arithmetic is fundamentally limited by G¨del’s o incompleteness theorem. Hence: mathematics can show us what “machines cannot in principle do”. 13
  • 54. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories;
  • 55. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain
  • 56. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain NS do not augment scientific knowledge.
  • 57. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain NS do not augment scientific knowledge. NS are limited predicting tools, at best, and only when a pre-existing theoretical model permits it.
  • 58. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain NS do not augment scientific knowledge. NS are limited predicting tools, at best, and only when a pre-existing theoretical model permits it. Science is about explanation/understanding/unification etc.
  • 59. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain NS do not augment scientific knowledge. NS are limited predicting tools, at best, and only when a pre-existing theoretical model permits it. Science is about explanation/understanding/unification etc.
  • 60. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position science and NS NS are not able to falsify or confirm scientific theories; NS do not explain NS do not augment scientific knowledge. NS are limited predicting tools, at best, and only when a pre-existing theoretical model permits it. Science is about explanation/understanding/unification etc. No philosophy of slide rules In philosophy of science, no country for old slide rules 14
  • 61. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position A rejoinder to the “glorified slide rules” arguments 15
  • 62. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position A rejoinder to the “glorified slide rules” arguments How do we argue against the “glorified slide rules” arguments? 1 Deny C-1: computers do help us understanding and explain because they show us how to decompose systems, separate levels and see the organization of mechanisms. (Simon 1969)
  • 63. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position A rejoinder to the “glorified slide rules” arguments How do we argue against the “glorified slide rules” arguments? 1 Deny C-1: computers do help us understanding and explain because they show us how to decompose systems, separate levels and see the organization of mechanisms. (Simon 1969) 2 Show that historically it is inaccurate (Keller, 2003): Cellular Automata (CA), Neural Networks (NN) and Genetic Algorithms (GA) are counterexamples to C2. (CA illustrate the third stage in Keller).
  • 64. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position A rejoinder to the “glorified slide rules” arguments How do we argue against the “glorified slide rules” arguments? 1 Deny C-1: computers do help us understanding and explain because they show us how to decompose systems, separate levels and see the organization of mechanisms. (Simon 1969) 2 Show that historically it is inaccurate (Keller, 2003): Cellular Automata (CA), Neural Networks (NN) and Genetic Algorithms (GA) are counterexamples to C2. (CA illustrate the third stage in Keller). 3 Quantum computing may be the “best” candidate for surpassing C-1.
  • 65. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position A rejoinder to the “glorified slide rules” arguments How do we argue against the “glorified slide rules” arguments? 1 Deny C-1: computers do help us understanding and explain because they show us how to decompose systems, separate levels and see the organization of mechanisms. (Simon 1969) 2 Show that historically it is inaccurate (Keller, 2003): Cellular Automata (CA), Neural Networks (NN) and Genetic Algorithms (GA) are counterexamples to C2. (CA illustrate the third stage in Keller). 3 Quantum computing may be the “best” candidate for surpassing C-1. Here I combine 1 and 2, but insist on the paradigm shift ` la a Keller.
  • 66. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? 16
  • 67. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. 16
  • 68. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. 16
  • 69. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) 16
  • 70. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) Some NS are able to: 16
  • 71. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) Some NS are able to: build models, 16
  • 72. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) Some NS are able to: build models, find invariants, 16
  • 73. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) Some NS are able to: build models, find invariants, discover non-trivial conserved quantities etc. 16
  • 74. Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Genetic Algorithms in Numerical Simulations (GNS) Philosophical questions Philosophy of GNS Three stances Finis The “glorified slide rule argument” References My position What do i argue for? Pace Frigg&Reiss, there is philosophical novelty in NS. Not all NS are “dumb slide rules”; Some are more interesting than others. More attention to the historical developments of NS (` la a Keller and Galison) Some NS are able to: build models, find invariants, discover non-trivial conserved quantities etc. The NS under scrutiny here are: Genetic Algorithms 16
  • 75. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Outline 1 Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Philosophical questions Three stances The “glorified slide rule argument” My position 2 Genetic Algorithms in Numerical Simulations (GNS) Beyond Turing Survival and chance in computer science Inductive programming (skip) Genetic numerical algorithms (GNS) 3 Philosophy of GNS What philosophy for GNS? Arguments for GNS Metaphysics of GNS GNS and mathematics GNS and invariance GNS and laws of nature Objections 4 Finis Risky conclusions Weaker conclusions 5 References 17
  • 76. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. 18
  • 77. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. Are all machine Turing machines? 18
  • 78. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. Are all machine Turing machines? Build machines inspired by learning, discovery, game playing, solving real-life problems, etc.
  • 79. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. Are all machine Turing machines? Build machines inspired by learning, discovery, game playing, solving real-life problems, etc. Hence adopt biomimetics
  • 80. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. Are all machine Turing machines? Build machines inspired by learning, discovery, game playing, solving real-life problems, etc. Hence adopt biomimetics 1 Go stochastic in building algorithms!
  • 81. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochasticity and NS Biomimetics Q-1: How can computers be made to do what needs to be done, without being told exactly how to do it? The “glorified slide rules” argument uses the Turing machine paradigm. Are all machine Turing machines? Build machines inspired by learning, discovery, game playing, solving real-life problems, etc. Hence adopt biomimetics 1 Go stochastic in building algorithms! 2 Go Darwinian in programming computers
  • 82. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS).
  • 83. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS). Are these solutions philosophically attractive?
  • 84. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS). Are these solutions philosophically attractive? The literature on NS ignores GA
  • 85. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS). Are these solutions philosophically attractive? The literature on NS ignores GA There are interesting discussions on CA and NN. (Keller, 2003) (Barberousse, Franceschelli, and Imbert 2007) and, more dogmatically, (Wolfram 2002).
  • 86. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS). Are these solutions philosophically attractive? The literature on NS ignores GA There are interesting discussions on CA and NN. (Keller, 2003) (Barberousse, Franceschelli, and Imbert 2007) and, more dogmatically, (Wolfram 2002). The literature on NN is well-known to philosophers: (Paul and Patricia Churchland)
  • 87. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Do philosophers talk about non-Turing machines? CA, GA and NN can go beyond what a Turing machine is able to do. So did the Monte Carlo method (first NS). Are these solutions philosophically attractive? The literature on NS ignores GA There are interesting discussions on CA and NN. (Keller, 2003) (Barberousse, Franceschelli, and Imbert 2007) and, more dogmatically, (Wolfram 2002). The literature on NN is well-known to philosophers: (Paul and Patricia Churchland) I focus here on GA and GP
  • 88. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms 20
  • 89. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948.
  • 90. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”.
  • 91. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”. Turing in Mind (1950): “the child-machine needs to be taught and surveyed. Then another child-machine tried and compared to the first etc.”
  • 92. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”. Turing in Mind (1950): “the child-machine needs to be taught and surveyed. Then another child-machine tried and compared to the first etc.” the child machine = hereditary material,
  • 93. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”. Turing in Mind (1950): “the child-machine needs to be taught and surveyed. Then another child-machine tried and compared to the first etc.” the child machine = hereditary material, the changes within it = genetic mutation and
  • 94. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”. Turing in Mind (1950): “the child-machine needs to be taught and surveyed. Then another child-machine tried and compared to the first etc.” the child machine = hereditary material, the changes within it = genetic mutation and natural selection = “judgment of the experimenter”
  • 95. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Evolution of algorithms Speculated by Turing in 1948. Based on genetic or evolutionary search by which a “combination of genes is looked for, the criterion being the survival value”. Turing in Mind (1950): “the child-machine needs to be taught and surveyed. Then another child-machine tried and compared to the first etc.” the child machine = hereditary material, the changes within it = genetic mutation and natural selection = “judgment of the experimenter” In a unpublished paper, Turing realized that such a genetic search implied randomness (Turing 1996).
  • 96. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References The 1970s and 1980s Alien (1979) Aliens (1986) Alien (1992) Alien Resurrection (1997) ABBA’s “Take a chance on me” Koza, Holland et al.: Birth of the Genetic Programming and Genetic Algorithms: 1986 to 1995 21
  • 97. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming 22
  • 98. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. 22
  • 99. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced 22
  • 100. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. 22
  • 101. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. The best competitor wins and constitutes the solutions of the problem. 22
  • 102. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. The best competitor wins and constitutes the solutions of the problem. GA are implementations of the biological evolution 22
  • 103. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. The best competitor wins and constitutes the solutions of the problem. GA are implementations of the biological evolution Optimization: searching for the best solution is based on some pre-established criteria 22
  • 104. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. The best competitor wins and constitutes the solutions of the problem. GA are implementations of the biological evolution Optimization: searching for the best solution is based on some pre-established criteria Unlike in Turing, selection occurs at the level of population, not at the level of individual algorithms. 22
  • 105. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References J. Holland’s genetic programming Starts from a given number of initial programs randomly distributed in a given space of solutions. Based on relative results, the best competitors are chosen and reproduced Offspring have some (randomly chosen) features of the predecessors. The best competitor wins and constitutes the solutions of the problem. GA are implementations of the biological evolution Optimization: searching for the best solution is based on some pre-established criteria Unlike in Turing, selection occurs at the level of population, not at the level of individual algorithms. Adaptation in Natural and Artificial Systems (1975) 22
  • 106. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Stochastic algorithms Output is manifestly stochastic. 23
  • 107. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Developments in GA Crossover takes two individuals (parents) and produces two new individuals, the offspring, 24
  • 108. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Developments in GA Crossover takes two individuals (parents) and produces two new individuals, the offspring, by swapping parts of the parents (the simplest crossover operator exchanges substrings of the parents) 24
  • 109. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Developments in GA Crossover takes two individuals (parents) and produces two new individuals, the offspring, by swapping parts of the parents (the simplest crossover operator exchanges substrings of the parents) Crossover moves the search towards those regions of the search space in which results are most likely to be found.(Tomassini 1995) 24
  • 110. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Developments in GA Crossover takes two individuals (parents) and produces two new individuals, the offspring, by swapping parts of the parents (the simplest crossover operator exchanges substrings of the parents) Crossover moves the search towards those regions of the search space in which results are most likely to be found.(Tomassini 1995) Mutation is a background redistribution of strings to prevent premature convergence to local optima. 24
  • 111. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Developments in GA Crossover takes two individuals (parents) and produces two new individuals, the offspring, by swapping parts of the parents (the simplest crossover operator exchanges substrings of the parents) Crossover moves the search towards those regions of the search space in which results are most likely to be found.(Tomassini 1995) Mutation is a background redistribution of strings to prevent premature convergence to local optima. Termination condition: when the sought-for level of optimality is reached or when all the solutions converge to one candidate 24
  • 112. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Results of GA/GP GA are able to reinvent patented inventions: the negative feedback (Black 1927)
  • 113. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Results of GA/GP GA are able to reinvent patented inventions: the negative feedback (Black 1927) are able to find algorithms in quantum computing–too complicated to be discovered by humans.
  • 114. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Results of GA/GP GA are able to reinvent patented inventions: the negative feedback (Black 1927) are able to find algorithms in quantum computing–too complicated to be discovered by humans. find patterns in the EEG before the epileptic seizure (but can’t predict it!)
  • 115. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Results of GA/GP GA are able to reinvent patented inventions: the negative feedback (Black 1927) are able to find algorithms in quantum computing–too complicated to be discovered by humans. find patterns in the EEG before the epileptic seizure (but can’t predict it!) find more interesting patterns before earthquakes (but too late and in general without impact)
  • 116. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References A simple result
  • 117. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References A simple result The algorithm takes pairs of numbers between −1 and +1 that fit perfectly the quadratic polynomial x 2 + x + 1 and a set of elementary or “desired” operators F = {+; −; ×; / } used as primitive of the symbolic regression.
  • 118. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References A simple result The algorithm takes pairs of numbers between −1 and +1 that fit perfectly the quadratic polynomial x 2 + x + 1 and a set of elementary or “desired” operators F = {+; −; ×; / } used as primitive of the symbolic regression. The initial population randomly constructed had the individuals: x + 1; x 2 + 1; 2; x and were fitted with the data based on a classical metric: the area covered by the curve represented by the competitor and the given set of data.
  • 119. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References A simple result The algorithm takes pairs of numbers between −1 and +1 that fit perfectly the quadratic polynomial x 2 + x + 1 and a set of elementary or “desired” operators F = {+; −; ×; / } used as primitive of the symbolic regression. The initial population randomly constructed had the individuals: x + 1; x 2 + 1; 2; x and were fitted with the data based on a classical metric: the area covered by the curve represented by the competitor and the given set of data. After the second generation and after applying the crossover operator, the result was as expected x 2 + x + 1.
  • 120. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GA in a snapshot 27
  • 121. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GA in a snapshot produce an initial population of individuals while termination condition not met do evaluate the fitness of all individuals select fitter individuals for reproduction produce new individuals generate a new population by inserting some new good individuals and by discarding some old/bad individuals mutate some individuals endwhile 27
  • 122. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Problems of GA GA are sensitive to the initial population. For a different set of initial population, the generation can take several iterations, but for simple enough expressions, the GA converge
  • 123. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software
  • 124. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) 29
  • 125. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS.
  • 126. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc.
  • 127. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc. Bacon had a bad reception among philosophers, despite Simon’s arguments (Simon, 1992).
  • 128. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc. Bacon had a bad reception among philosophers, despite Simon’s arguments (Simon, 1992). BACON is marred with the problem of induction, does not explain, does not help us with understanding.
  • 129. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc. Bacon had a bad reception among philosophers, despite Simon’s arguments (Simon, 1992). BACON is marred with the problem of induction, does not explain, does not help us with understanding. It’s based on a totally weak analogy.
  • 130. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc. Bacon had a bad reception among philosophers, despite Simon’s arguments (Simon, 1992). BACON is marred with the problem of induction, does not explain, does not help us with understanding. It’s based on a totally weak analogy. It threatens rationality of science
  • 131. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON, the software BACON is a software best on induction (1980s by H. Simon, P. Langley, J. Shrager, etc) Other software: OCCAM, GALILEO, HUYGENS. BACON rediscovered Kepler’s laws, Prout’s hypothesis about atomic structure, etc. Bacon had a bad reception among philosophers, despite Simon’s arguments (Simon, 1992). BACON is marred with the problem of induction, does not explain, does not help us with understanding. It’s based on a totally weak analogy. It threatens rationality of science Does not explain and help us with understanding science.
  • 132. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Planck’s discovery From: To: hν 3 U(ν) = U(ω) dω = dν 8π c3 e ω/kT −1 30
  • 133. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON against the roulette (skip) GA score better than BACON because they avoid local optima. 31
  • 134. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References BACON against the roulette (skip) GA score better than BACON because they avoid local optima. Too complicated to discuss here. 31
  • 135. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References ADAM, the robot scientist (skip) R.D. King coined this term in 2004. We accept that the knowledge automatically generated by Adam is of a modest kind. However, this knowledge is not trivial, and in the case of the genes encoding 2A2OA, it sheds light on, and perhaps solves, a 50-year-old puzzle. (King et al. 2009, 88) 32
  • 136. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References ADAM, the robot scientist (skip) R.D. King coined this term in 2004. ADAM is a new software based on inductive reasoning. It identifies genes encoding orphan enzymes in Saccharomyces cerevisiae for which the encoding gene(s) are not known We accept that the knowledge automatically generated by Adam is of a modest kind. However, this knowledge is not trivial, and in the case of the genes encoding 2A2OA, it sheds light on, and perhaps solves, a 50-year-old puzzle. (King et al. 2009, 88) 32
  • 137. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References ADAM, the robot scientist (skip) R.D. King coined this term in 2004. ADAM is a new software based on inductive reasoning. It identifies genes encoding orphan enzymes in Saccharomyces cerevisiae for which the encoding gene(s) are not known We accept that the knowledge automatically generated by Adam is of a modest kind. However, this knowledge is not trivial, and in the case of the genes encoding 2A2OA, it sheds light on, and perhaps solves, a 50-year-old puzzle. (King et al. 2009, 88) 32
  • 138. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References ADAM, the robot scientist (skip) R.D. King coined this term in 2004. ADAM is a new software based on inductive reasoning. It identifies genes encoding orphan enzymes in Saccharomyces cerevisiae for which the encoding gene(s) are not known A robot scientist automatically originates hypotheses to explain observations, devises experiments to test these hypotheses, physically runs the experiments by using laboratory robotics, interprets the results, and then repeats the cycle. We accept that the knowledge automatically generated by Adam is of a modest kind. However, this knowledge is not trivial, and in the case of the genes encoding 2A2OA, it sheds light on, and perhaps solves, a 50-year-old puzzle. (King et al. 2009, 88) 32
  • 139. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References ADAM, the robot scientist (skip) R.D. King coined this term in 2004. ADAM is a new software based on inductive reasoning. It identifies genes encoding orphan enzymes in Saccharomyces cerevisiae for which the encoding gene(s) are not known A robot scientist automatically originates hypotheses to explain observations, devises experiments to test these hypotheses, physically runs the experiments by using laboratory robotics, interprets the results, and then repeats the cycle. Limitations of Adam: the scientific knowledge “discovered” by Adam is implicit in the formulation of the problem and is therefore not novel. We accept that the knowledge automatically generated by Adam is of a modest kind. However, this knowledge is not trivial, and in the case of the genes encoding 2A2OA, it sheds light on, and perhaps solves, a 50-year-old puzzle. (King et al. 2009, 88) 32
  • 140. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS?
  • 141. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS? There are genetic numerical algorithms ( GNS)
  • 142. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS? There are genetic numerical algorithms ( GNS) Best example I know of is (Schmidt&Lipson 2009)
  • 143. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS? There are genetic numerical algorithms ( GNS) Best example I know of is (Schmidt&Lipson 2009) GNS do not output data, but symbolic representations, i.e. laws and mathematical expressions from data based on GA.
  • 144. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS? There are genetic numerical algorithms ( GNS) Best example I know of is (Schmidt&Lipson 2009) GNS do not output data, but symbolic representations, i.e. laws and mathematical expressions from data based on GA. It may have a direct impact on science in the future. (remember I started by rejecting the the wait-and-see attitude)
  • 145. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References What’s GA Got To Do With NS? There are genetic numerical algorithms ( GNS) Best example I know of is (Schmidt&Lipson 2009) GNS do not output data, but symbolic representations, i.e. laws and mathematical expressions from data based on GA. It may have a direct impact on science in the future. (remember I started by rejecting the the wait-and-see attitude) I also want to defuse blind optimism 33
  • 146. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GNS and meaningfulness
  • 147. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GNS and meaningfulness Here things are getting really exciting:
  • 148. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GNS and meaningfulness Here things are getting really exciting: These GNS can discover : Hamiltonians, Lagrangians, laws of conservation, symmetries, and other invariants.
  • 149. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References GNS and meaningfulness Here things are getting really exciting: These GNS can discover : Hamiltonians, Lagrangians, laws of conservation, symmetries, and other invariants. Based on meaningfulness and interestingness.
  • 150. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References A simple illustration of a “best expression” 35
  • 151. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Schmidt and Lipson about their result We have demonstrated the discovery of physical laws, from scratch, directly from experimentally captured data with the use of a computational search [...] detect nonlinear energy conservation laws, Newtonian force laws, geometric invariants, and system manifolds in various synthetic and physically implemented systems without prior knowledge about physics, kinematics, or geometry. The concise analytical expressions that we found are amenable to human interpretation and help to reveal the physics underlying the observed phenomenon. [...] Might this process diminish the role of future scientists? Quite the contrary: Scientists may use processes such as this to help focus on interesting phenomena more rapidly and to interpret their meaning. (Schmidt and Lipson 2009, 85) 36
  • 152. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Can BACON and ADAM compete with the roulette? (skip) difficult to compare directly.
  • 153. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Can BACON and ADAM compete with the roulette? (skip) difficult to compare directly. But GNS score better than BACON because they avoid local optima.
  • 154. Philosophy of Numerical Simulations? Beyond Turing Genetic Algorithms in Numerical Simulations (GNS) Survival and chance in computer science Philosophy of GNS Inductive programming (skip) Finis Genetic numerical algorithms (GNS) References Can BACON and ADAM compete with the roulette? (skip) difficult to compare directly. But GNS score better than BACON because they avoid local optima. Too complicated to discuss here.
  • 155. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Outline 1 Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Philosophical questions Three stances The “glorified slide rule argument” My position 2 Genetic Algorithms in Numerical Simulations (GNS) Beyond Turing Survival and chance in computer science Inductive programming (skip) Genetic numerical algorithms (GNS) 3 Philosophy of GNS What philosophy for GNS? Arguments for GNS Metaphysics of GNS GNS and mathematics GNS and invariance GNS and laws of nature Objections 4 Finis Risky conclusions Weaker conclusions 5 References 38
  • 156. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive?
  • 157. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are!
  • 158. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate:
  • 159. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery.
  • 160. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models.
  • 161. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them!
  • 162. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them! It is prima facie a bottom-up view!
  • 163. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them! It is prima facie a bottom-up view! There is literally a guesswork in GNS, but:
  • 164. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them! It is prima facie a bottom-up view! There is literally a guesswork in GNS, but: It optimizes the result based on meaning and “interestingness”
  • 165. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them! It is prima facie a bottom-up view! There is literally a guesswork in GNS, but: It optimizes the result based on meaning and “interestingness” If in science we transform data into phenomena (Woodward and Bogen), then GNS qualifies as a possible candidate together with experiments
  • 166. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Are GNS philosophically attractive? In the framework of the debate about the “philosophy of NS” they are! In GNS we simulate: the process of scientific discovery. the relation between experiments, theories and models. With GNS, we do not rely on theories, we discover them! It is prima facie a bottom-up view! There is literally a guesswork in GNS, but: It optimizes the result based on meaning and “interestingness” If in science we transform data into phenomena (Woodward and Bogen), then GNS qualifies as a possible candidate together with experiments In the context of discovery, science is, for better or worse, guesswork
  • 167. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS
  • 168. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting
  • 169. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery.
  • 170. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery. Novelty and chance may be stronger related.
  • 171. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery. Novelty and chance may be stronger related. As a biological metaphor, GNS are up to their neck in stochasticity.
  • 172. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery. Novelty and chance may be stronger related. As a biological metaphor, GNS are up to their neck in stochasticity. How is chance (as part of a search procedure) related to creativity?
  • 173. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery. Novelty and chance may be stronger related. As a biological metaphor, GNS are up to their neck in stochasticity. How is chance (as part of a search procedure) related to creativity? F. Crick “chance is the only source of true novelty” (Crick 1981, 58).
  • 174. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Creativity, Luck and Chance in GNS In the context of scientific discovery, yes GNS are philosophically interesting GNS make room to chance in scientific discovery. Novelty and chance may be stronger related. As a biological metaphor, GNS are up to their neck in stochasticity. How is chance (as part of a search procedure) related to creativity? F. Crick “chance is the only source of true novelty” (Crick 1981, 58). Maybe scientific discovery is in fact closer to playing a game and hedging one’s bets.
  • 175. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections How inventive are we? 41
  • 176. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections How inventive are we? We are extremely inventive beings! Can you read this? To xllxstxatx, I cxn rxplxce xvexy txirx lextex of x sextexce xitx an x, anx yox stxll xan xanxge xo rxad xt wixh sxme xifxicxltx. Then be happy, because no Turing machine can! 41
  • 177. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections How inventive are we? We are extremely inventive beings! Can you read this? To xllxstxatx, I cxn rxplxce xvexy txirx lextex of x sextexce xitx an x, anx yox stxll xan xanxge xo rxad xt wixh sxme xifxicxltx. Then be happy, because no Turing machine can! Searching patterns and comparing them is a difficult business. 41
  • 178. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view)
  • 179. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view) Maybe the nature is stochastic/chancy (we don’t know, but we have reasons to think so) 42
  • 180. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view) Maybe the nature is stochastic/chancy (we don’t know, but we have reasons to think so) Our representation of the world should mimic it
  • 181. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view) Maybe the nature is stochastic/chancy (we don’t know, but we have reasons to think so) Our representation of the world should mimic it Then we’d better go stochastic in modeling the world
  • 182. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view) Maybe the nature is stochastic/chancy (we don’t know, but we have reasons to think so) Our representation of the world should mimic it Then we’d better go stochastic in modeling the world If the world is not stochastic, no big fuss: as humans we take chances: we are built to be stochastic (gamble, guess)
  • 183. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Stochasticism (a philosophical view) Maybe the nature is stochastic/chancy (we don’t know, but we have reasons to think so) Our representation of the world should mimic it Then we’d better go stochastic in modeling the world If the world is not stochastic, no big fuss: as humans we take chances: we are built to be stochastic (gamble, guess) We can go intuitionistic in mathematics (as opposed to Platonism, formalism,etc.)
  • 184. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Argument from stochasticity world/science The world is: deterministic non-deterministic Non-stochastic Long Live Laplace! Ooops! We are off!! Stochastic It is OK1 The best combination 1 It’s ok, it’s just a representation. Some deterministic systems are better represented by statistical models
  • 185. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS as better “epistemic enhancers” (Humphreys)
  • 186. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS as better “epistemic enhancers” (Humphreys) P. Humphreys thinks that NS in general are epistemic enhancers. 44
  • 187. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS as better “epistemic enhancers” (Humphreys) P. Humphreys thinks that NS in general are epistemic enhancers. They extend ourselves 44
  • 188. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS as better “epistemic enhancers” (Humphreys) P. Humphreys thinks that NS in general are epistemic enhancers. They extend ourselves If so, GNS pushes the limits farther than ordinary NS. 44
  • 189. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS as better “epistemic enhancers” (Humphreys) P. Humphreys thinks that NS in general are epistemic enhancers. They extend ourselves If so, GNS pushes the limits farther than ordinary NS. Pushes the limits of what is “scientifically discoverable” 44
  • 190. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint?
  • 191. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint? Think of the “unreasonable effectiveness of mathematics” argument (Steiner, Colyvain, etc) 45
  • 192. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint? Think of the “unreasonable effectiveness of mathematics” argument (Steiner, Colyvain, etc) Parenthetically, I have doubts about this argument. 45
  • 193. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint? Think of the “unreasonable effectiveness of mathematics” argument (Steiner, Colyvain, etc) Parenthetically, I have doubts about this argument. In some cases mathematics is not the driving force but the constraint. 45
  • 194. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint? Think of the “unreasonable effectiveness of mathematics” argument (Steiner, Colyvain, etc) Parenthetically, I have doubts about this argument. In some cases mathematics is not the driving force but the constraint. GNS illustrates the mathematics as “constraint”: it generates symbolic expression from data based on mathematical constraints 45
  • 195. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Mathematics as a constraint? Think of the “unreasonable effectiveness of mathematics” argument (Steiner, Colyvain, etc) Parenthetically, I have doubts about this argument. In some cases mathematics is not the driving force but the constraint. GNS illustrates the mathematics as “constraint”: it generates symbolic expression from data based on mathematical constraints First you need to decide what limits to put to your mathematics, and then GNS delivers an optimal result 45
  • 196. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability 46
  • 197. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds
  • 198. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite
  • 199. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible.
  • 200. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible. The typical way to explore possibility: change initial conditions of an experiment but keep the laws.
  • 201. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible. The typical way to explore possibility: change initial conditions of an experiment but keep the laws. Is science indeed about the possible? Maybe more about counterfactuals.
  • 202. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible. The typical way to explore possibility: change initial conditions of an experiment but keep the laws. Is science indeed about the possible? Maybe more about counterfactuals. That’s a class of nomical worlds based on physical possibilities 46
  • 203. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible. The typical way to explore possibility: change initial conditions of an experiment but keep the laws. Is science indeed about the possible? Maybe more about counterfactuals. That’s a class of nomical worlds based on physical possibilities Science teaches us that the world is richer that we can conceive with the “naked mind” (Van Fraassen)
  • 204. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Conceivability Any experiment explores possible worlds C’mon, that’s trite Science is not only about the actual, but about the possible. The typical way to explore possibility: change initial conditions of an experiment but keep the laws. Is science indeed about the possible? Maybe more about counterfactuals. That’s a class of nomical worlds based on physical possibilities Science teaches us that the world is richer that we can conceive with the “naked mind” (Van Fraassen) My argument is that NS and GNS, enhance the mind by pushing the limits of conceivability. 46
  • 205. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections What is really new? 47
  • 206. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections What is really new? Strictly speaking, data are new. 47
  • 207. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections What is really new? Strictly speaking, data are new. The way we discover it. 47
  • 208. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia 48
  • 209. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable”
  • 210. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical”
  • 211. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical”
  • 212. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable”
  • 213. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia
  • 214. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable)
  • 215. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable) My proposal: the “evolvable” (a la GNS) 48
  • 216. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable) My proposal: the “evolvable” (a la GNS) The only one that’s chancy 48
  • 217. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable) My proposal: the “evolvable” (a la GNS) The only one that’s chancy It’s natural (maybe too literally) 48
  • 218. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable) My proposal: the “evolvable” (a la GNS) The only one that’s chancy It’s natural (maybe too literally) It’s always open to re-runs (not replicable) 48
  • 219. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections GNS and possibilia The “observable” The “physical” The “logical” The “conceivable” Other less discussed possibilia The “computable” (a la Church-Turing). But is physics computable? (some systems in condensed matter physics are not NP-computable) My proposal: the “evolvable” (a la GNS) The only one that’s chancy It’s natural (maybe too literally) It’s always open to re-runs (not replicable) You can always hope for a better solution 48
  • 220. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure 49
  • 221. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: 49
  • 222. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: Newtonian spacetime has too many rest frames among the inertial frames; 49
  • 223. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: Newtonian spacetime has too many rest frames among the inertial frames; General Relativity has too many choices for the global inertial frame; 49
  • 224. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: Newtonian spacetime has too many rest frames among the inertial frames; General Relativity has too many choices for the global inertial frame; Quantum Field Theory has unitarily non-equivalent but observationally equivalent representations available; 49
  • 225. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: Newtonian spacetime has too many rest frames among the inertial frames; General Relativity has too many choices for the global inertial frame; Quantum Field Theory has unitarily non-equivalent but observationally equivalent representations available; Gauge theories provide too many solutions to the field equations which are all acceptable from an empirical point of view, etc. 49
  • 226. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The surplus mathematical structure Physics is replete with surplus mathematical structure: Newtonian spacetime has too many rest frames among the inertial frames; General Relativity has too many choices for the global inertial frame; Quantum Field Theory has unitarily non-equivalent but observationally equivalent representations available; Gauge theories provide too many solutions to the field equations which are all acceptable from an empirical point of view, etc. There are 10500 String Theories (models?) etc. 49
  • 227. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The GNS and symmetry, invariance and objectivity
  • 228. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The GNS and symmetry, invariance and objectivity Are invariance and symmetry related to objectivity? Redhead and Debs think they are not 50
  • 229. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The GNS and symmetry, invariance and objectivity Are invariance and symmetry related to objectivity? Redhead and Debs think they are not Objectivity is conventional. 50
  • 230. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections No more partial differential equations?
  • 231. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections No more partial differential equations? Laws of evolutions are based on partial differential equations: the most powerful tools in the history of science
  • 232. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS
  • 233. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature 52
  • 234. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties 52
  • 235. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. 52
  • 236. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” 52
  • 237. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: 52
  • 238. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms 52
  • 239. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms for diverse data 52
  • 240. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms for diverse data for a large range of contraints, 52
  • 241. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms for diverse data for a large range of contraints, for a large number of runs of GNS 52
  • 242. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms for diverse data for a large range of contraints, for a large number of runs of GNS converge to the same expression, then dub it “a law of nature” 52
  • 243. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections The Humeans and GNS GNS mesh well with the Mill-Ramsey-Lewis view of laws of nature MRL=laws of nature supervene on the collection of intrinsic properties Laws of nature are the best balance between strength, simplicity, expressiveness, etc. For GNS: new data, new laws. But some laws have a better stability to new data. Those are “laws of nature” Statistical and stochastic MRL: If a large population of algorithms for diverse data for a large range of contraints, for a large number of runs of GNS converge to the same expression, then dub it “a law of nature” 52
  • 244. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Advice for NS coming from GNS 53
  • 245. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Advice for NS coming from GNS Take biomimetics seriously.
  • 246. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Advice for NS coming from GNS Take biomimetics seriously. Take seriously the context of discovery.
  • 247. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Advice for NS coming from GNS Take biomimetics seriously. Take seriously the context of discovery. Naturalize philosophy of science.
  • 248. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections An argument for distributive discovery 54
  • 249. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections An argument for distributive discovery P. Humphreys suggests that the future of science belongs to the collaboration humans between computers (Humphreys 2004, 2009) 54
  • 250. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections An argument for distributive discovery P. Humphreys suggests that the future of science belongs to the collaboration humans between computers (Humphreys 2004, 2009) We need a division of labor 54
  • 251. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections An argument for distributive discovery P. Humphreys suggests that the future of science belongs to the collaboration humans between computers (Humphreys 2004, 2009) We need a division of labor This will be more evident in discovery than in justification 54
  • 252. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections An argument for distributive discovery P. Humphreys suggests that the future of science belongs to the collaboration humans between computers (Humphreys 2004, 2009) We need a division of labor This will be more evident in discovery than in justification I do not think NS score better in justification 54
  • 253. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections
  • 254. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 55
  • 255. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 55
  • 256. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 3 If the world is stochastic/chancy then we do not need to represent it by stochastic tools. 55
  • 257. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 3 If the world is stochastic/chancy then we do not need to represent it by stochastic tools. 4 You do not honor the discovery/justification distinction. 55
  • 258. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 3 If the world is stochastic/chancy then we do not need to represent it by stochastic tools. 4 You do not honor the discovery/justification distinction. 5 If nature is deterministic why should we go stochastic? (see below) 55
  • 259. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 3 If the world is stochastic/chancy then we do not need to represent it by stochastic tools. 4 You do not honor the discovery/justification distinction. 5 If nature is deterministic why should we go stochastic? (see below) 6 The “three armies” argument (see below) 55
  • 260. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Ways to retort: some objections 1 Wait-and-see (again!) GNS are not ripe to harvest. 2 GNS bring irrationality into science. Do we need it? 3 If the world is stochastic/chancy then we do not need to represent it by stochastic tools. 4 You do not honor the discovery/justification distinction. 5 If nature is deterministic why should we go stochastic? (see below) 6 The “three armies” argument (see below) 7 This is anthropomorphism in sheep clothes!(see below) 55
  • 261. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance!
  • 262. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance! Maybe at the bottom She abhors chance. 56
  • 263. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance! Maybe at the bottom She abhors chance. If so, all our models are pseudo-stochastic 56
  • 264. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance! Maybe at the bottom She abhors chance. If so, all our models are pseudo-stochastic If so, we can represent parts the world with stochastic models 56
  • 265. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance! Maybe at the bottom She abhors chance. If so, all our models are pseudo-stochastic If so, we can represent parts the world with stochastic models M. Strevens: “Not only is Nature red in tooth and claw; she is irrepresibly stochastic in her violence” (Strevens, 2009, 459) 56
  • 266. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections Back to Objection 5: Maybe Nature abhors chance! Maybe at the bottom She abhors chance. If so, all our models are pseudo-stochastic If so, we can represent parts the world with stochastic models M. Strevens: “Not only is Nature red in tooth and claw; she is irrepresibly stochastic in her violence” (Strevens, 2009, 459) models in biology have a probabilistic element. 56
  • 267. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS 57
  • 268. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS Whatever you told us, Nothing that NS have achieved could not have been done by:
  • 269. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS Whatever you told us, Nothing that NS have achieved could not have been done by: an army of well-trained scientists working with slide rules
  • 270. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS Whatever you told us, Nothing that NS have achieved could not have been done by: an army of well-trained scientists working with slide rules an army of well-trained evolutionary biologists
  • 271. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS Whatever you told us, Nothing that NS have achieved could not have been done by: an army of well-trained scientists working with slide rules an army of well-trained evolutionary biologists an army of well-trained poker dealers and gamblers
  • 272. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 6 The three armies argument against GNS Whatever you told us, Nothing that NS have achieved could not have been done by: an army of well-trained scientists working with slide rules an army of well-trained evolutionary biologists an army of well-trained poker dealers and gamblers Computers, NS are still dumb tools
  • 273. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 7: Wait: this is anthropomorhism! 58
  • 274. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 7: Wait: this is anthropomorhism! is biomimetics nothing more than anthropomorphizing? 58
  • 275. What philosophy for GNS? Philosophy of Numerical Simulations? Arguments for GNS Genetic Algorithms in Numerical Simulations (GNS) Metaphysics of GNS Philosophy of GNS GNS and mathematics Finis GNS and invariance References GNS and laws of nature Objections O 7: Wait: this is anthropomorhism! is biomimetics nothing more than anthropomorphizing? It seems the nature abhors many things 58
  • 276. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References Outline 1 Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Philosophical questions Three stances The “glorified slide rule argument” My position 2 Genetic Algorithms in Numerical Simulations (GNS) Beyond Turing Survival and chance in computer science Inductive programming (skip) Genetic numerical algorithms (GNS) 3 Philosophy of GNS What philosophy for GNS? Arguments for GNS Metaphysics of GNS GNS and mathematics GNS and invariance GNS and laws of nature Objections 4 Finis Risky conclusions Weaker conclusions 5 References 59
  • 277. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References What emerges from my analysis? 60
  • 278. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References What emerges from my analysis? Surprisingly, a less central role for mathematics in scientific discovery
  • 279. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References What emerges from my analysis? Surprisingly, a less central role for mathematics in scientific discovery More or less a bottom up image of science
  • 280. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References What emerges from my analysis? Surprisingly, a less central role for mathematics in scientific discovery More or less a bottom up image of science A new type of possibilia, the numerical possibility
  • 281. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References 61
  • 282. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References Moving from Turing to stochastic algorithms makes NS more attractive
  • 283. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References Moving from Turing to stochastic algorithms makes NS more attractive Relevance and meaning can be generated by machines
  • 284. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Risky conclusions Philosophy of GNS Weaker conclusions Finis References Moving from Turing to stochastic algorithms makes NS more attractive Relevance and meaning can be generated by machines For better, for worse, GNS are not mere glorified slide rules
  • 285. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References Outline 1 Philosophy of Numerical Simulations? What are Numerical Simulations (NS)? Philosophical questions Three stances The “glorified slide rule argument” My position 2 Genetic Algorithms in Numerical Simulations (GNS) Beyond Turing Survival and chance in computer science Inductive programming (skip) Genetic numerical algorithms (GNS) 3 Philosophy of GNS What philosophy for GNS? Arguments for GNS Metaphysics of GNS GNS and mathematics GNS and invariance GNS and laws of nature Objections 4 Finis Risky conclusions Weaker conclusions 5 References 62
  • 286. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References I Affenzeller, M., 2009. Genetic Algorithms and Genetic Programming: Modern Concepts and Practical Applications. No. v. 6 in Numerical insights. CRC Press, Boca Raton, Fla. Barberousse, A., Franceschelli, S., Imbert, C., 2007. Cellular automata, modeling, and computation. http://philsci-archive.pitt.edu/archive/00003579/. URL http://philsci-archive.pitt.edu/archive/00003579/ Callender, C., Cohen, J., 2010. Special sciences, conspiracy and the better best system account of lawhood. 63
  • 287. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References II Chaitin, G., Feb. 1995. Randomness in arithmetic and the decline and fall of reductionism in pure mathematics. Chaos, Solitons & Fractals 5 (2), 143–159. Cohen, J., Callender, C., 2009. A better best system account of lawhood. Philosophical Studies 145 (1), 1–34. Crick, F., 1981. Life Itself: Its Origin and Nature, 1ST Edition. Simon and Schuster. Davies, P. C. W., Brown, J. R., 1988. Superstrings: a theory of everything? Cambridge University Press, Cambridge U.K.; New York, book, Edited. 64
  • 288. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References III Debs, T., 2007. Objectivity, invariance, and convention : symmetry in physical science. Harvard University Press, Cambridge Mass. Floridi, L., 2008. Philosophy of computing and information : 5 questions. Automatic Press, [S.I.]. Frigg, R., Reiss, J., 2009. The philosophy of simulation: Hot new issues or same old stew? Journal for Epistemology 169 (3), 593–613. 65
  • 289. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References IV Galison, P. L., 1996. Computer simulations and the trading zone. In: Galison, P., Stump, D. J. (Eds.), The Disunity of science : boundaries, contexts, and power. Stanford University Press, Stanford Calif. Hacking, I., 1983. Representing and intervening: introductory topics in the philosophy of natural science. Cambridge University Press, Cambridge, Cambridgeshire ; New York, book, Whole. Hartmann, S., 2008. Modeling in Philosophy of Science. Ontos Verlag, Heusenstamm bei Frankfurt, book, Whole. 66
  • 290. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References V Humphreys, P., 2004. Extending ourselves: Computational science, empiricism, and scientific method. 2004. Humphreys, P., 2009. The philosophical novelty of computer simulation methods. Synthese 169 (3), 615–626. Keller, E., 2003. Models, simulation, and ’Computer experiments’. In: Radder, H. (Ed.), The Philosophy of Scientific Experimentation. University of Pittsburgh Press, pp. 198–215.
  • 291. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References VI Koza, J. R., Keane, M., Streeter, M., Mydlowec, W., Yu, J., Lanza, G. (Eds.), 2003. Genetic Programming IV: Routine Human-Competitive Machine Intelligence. Kluwer Academic Publishers, Norwell, Mass. Maddy, P., 2007. Second philosophy : a naturalistic method. Oxford University Press, Oxford ;;New York. Morrison, M., 2009. Models, measurement and computer simulation: the changing face of experimentation. Philosophical Studies 143 (1), 33–57, journal Article. 68
  • 292. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References VII Parker, W., 2009. Does matter really matter? computer simulations, experiments, and materiality. Synthese 169 (3), 483–496. Simon, H., 1969. The sciences of the artificial,. M.I.T. Press, Cambridge Mass. Simon, H. A., 1992. Scientific discovery as problem solving. International Studies in the Philosophy of Science 6 (1), 3. Simon, H. A., Langley, P. W., Bradshaw, G. L., 1981. Scientific discovery as problem solving. Synthese 47 (1), 1–27. Simonton, D. K., 2004. Creativity in Science: Chance, Logic, Genius, and Zeitgeist. Cambridge University Press, Cambridge.
  • 293. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References VIII Steiner, M. A., 1998. The applicability of mathematics as a philosophical problem. Harvard University Press, Cambridge, Mass., book, Whole. Thagard, P., 1988. Computational philosophy of science. MIT Press, Cambridge, Mass., book, Whole. Tomassini, M., 1995. A survey of genetic algorithms. Annual Reviews of Computational Physics 3, 87–118. Turing, A., 1950. Computing machine and intelligence. Mind: A Quarterly Review of Philosophy 59 (236), 433–460. Turing, A., 1996. Intelligent machinery, a heretical theory. Philosophia Mathematica 4 (3), 256–260. 70
  • 294. Philosophy of Numerical Simulations? Genetic Algorithms in Numerical Simulations (GNS) Philosophy of GNS Finis References References IX Winsberg, E., 1999. Sanctioning models: The epistemology of simulation. Science in context. 12 (2), 275. Winsberg, E., 2001. Simulations, models, and theories: Complex physical systems and their representations. Philosophy of Science 68 (3), S442–S454. Wolfram, S., 2002. A new kind of science. Wolfram Media, Champaign IL. 71