Simulations, Models, Forecasts

17 Apr 2001 12:16

Feynman's (famous, over-used, prophetic) words:

The next great awakening of human intellect may well produce a method of understanding the qualitative content of equations. Today we cannot. Today we cannot see that the water-flow equations contain such things as the barber pole structure of turbulence that one sees between rotating cylinders. Today we cannot see whether Schrödinger's equation contains frogs, musical composers, or morality --- or whether it does not.

Do simulations help attain this end at all?

Microcosms in general.
- Imagined microcosm (especially the man-state-universe analogy, on which see Needham, Tillyard; need more up-to-date sources). Farmer's idea of microcosm-macrocosm analogies arising as a way of reconciling incompatible traditions.
- Constructed microcosms.
  - Sacred buildings
  - Gardens (Islamic, and according to Eliade, Zen)
  - Maps (symbolic maps as in medieval Europe vs. representational ones as from AAA)
  - Court ritual
  - Astrology
  - Rugs? (Supposedly Christopher Alexander claims this someplace in his new book about ancient Turkish carpets)
- Why building microcosms feels good (Gelernter talks about this; so does Tuan; my adviser says its because we love to play God). Eliade's writings on repeating the Creation may be relevant.
Mechanical models
- The orrery of Archimedes.
- The Antikythera machine.
- "Heavenly Clockworks" in Europe and Asia (cf. Constructed Microcosms above).
- Observatories.
- Planetaria.
- Was it Kelvin or Maxwell who said he could not accept any theory until he had constructed a mechanical model for it? Boltzmann's article on models in the 11th ed. Encyclopedia Britannica is very good; reprinted in the English collection of his essays.
Burckhardt on growth of statistical consciousness in the Renaissance; needs of states and businesses to keep track of their affairs and (more importantly) plan for the future. [Aside: ancien regime tax-farming as a stirring warning against not planning.] Crosby's The Measure of Reality is superb but doesn't compare Europe with the rest of the world enough.
Ian Hacking on "the taming of chance" and the growth of statistical methods and ideas in the 19th century
Beniger on "control revolution" [see my review of his book by that title]
Economic planning in WWI, WWII, post-war period; the (dismal) Soviet experience
David Ricardo's "corn" economy as the first drastically simplified model of society --- or perhaps the Physiocrats? (Review the earlier history of the man-state-universe analogies.)
Of the importance of selection in the construction of models
It is an abuse to call every hypothesis, or theory, or mere notion, a model, just as it is an abuse to call everything from the most arbitrary detail of this year's haute couture to "linear Western rationalism" a "paradigm," or label a "system" everything in the world and a great deal more. The domain of hypotheses and theories is a great deal broader than that of models. Adam Smith's Wealth of Nations contains the former without limit --- consider the Invisible Hand --- but not, as for as I can recall, a single model in the way Ricardo modelled the Economy or Lorenz the weather or (as Galbraith satirically suggested in A Tenured Professor) a young economist might today model "refrigerator pricing under the assumption of perfect information." The distinction is one of detail, I suspect. With models one can "plug and chug" and get precise answers. Newton's theory was that the planets are affected (only) by an attractive force proportional to both their masses diminishing as the square of the distance between them. (It is a signal proof of the efficacy of mathematics that that ungainly sentence means just F=-GmM/r^2.) From this, we may deduce a great many consequences about their motion --- Kepler's third law, for instance, or Bertrand's theorem (every bounded orbit is closed). But none of them tells us anything specific about where a planet will be when. That requires detailed numbers, and a great deal of plugging and chugging. Kepler's laws are very general; tables of ephemeris are not. It will be seen that hypotheses approach models, the more detailed, specific and quantitative they are. Thus Smith's theory of the Invisible Hand is less of a model than Arrow and Debreu's "General Equilibrium Model" of the economy, which itself is less of a model than Wassily Leontief's input-output models.
Discuss Leontief and his models. Check out the ball-bearing story.
Geographic information systems and marketing. (See Erik Larson, The Naked Consumer, and cf. data mining)
Climate models. Global warming and other climatic catastrophes. What, if anything, can be done.
The idea that intelligence, or perhaps just understanding and explanation, is a sort of modelling or simulation. This seems to derive from Craik, looms large in cognitive science, and seems to have a natural appeal for scientists who aren't cognitivists (e.g. Monod).
Foresight and understanding; foresight as a test of understanding.
Foresight as a basic human trait. Russell on the interest rate as a measure of civilization. [Thus: civilized human beings tend to display more foresight, and powers of planning and delayed-gratification, than do uncivilized ones. Interest is a reward for delaying pleasure into the future, so the degree of civilization is inversely proportional to the prevailing rate of interest. This also works --- better, perhaps --- if interest is a compensation for uncertainty.]
Simulations as an aid to foresight; as an aid to understanding
Simulations as an aid to experiment; as a substitute for experiment. [Grab the appropriate passages from von Neumann, Pagels, Jackson, Ada Lovelace.] Contrast with the usual view of experiments --- usual at least since Claude Bernard. One problem with this is that you can make a mathematical model jump through any hoop you want, so theories backed just by models tell us about --- models.
Simulation vs. analytical theory. Extensive development of both ever since the beginnings of quantitative science. Gauss's decades spent in calculations. Development of "computing machines" as substitute for labor of human "computers". Computers lower cost of approximations as compared to analytical results. This can even lead to simply "throwing it on the computer" even when analytical results are obtainable; even, indeed, when analytical results are well-known in the literature. (Horror-stories available upon request.)
Mirror Worlds; really huge simulations --- ties back into climate modelling
Useless models and simulations. (On this, Berlinski is both excellent and scathing.)
- bad data
- bad theories; "not even wrong"
- bad model construction --- "the devil is in the details"
- bad interpretation
- A model is only as good as its worst component.
- Can be used as excuses not to, or substitutes for, dealing with the Realized World.
Twaddle about simulations.
- Reality of simulations. Usually this is just an update of Descartes' malicious demon, and no more illuminating for the technological trappings. (See the beginning of Dennett's Consciousness Explained for a good discussion of the technical difficulties faced by a Cartesian Demon.) One variant, urged by Marvin Minsky and Tipler (not people I'd expect on the same side of anything) is that a simulated person or thought is a real person or thought; Tipler at least would say, is the person simulated. This is bunkum. A simulation of me may be a person, but isn't me any more than my twin, my clone or my doppleganger is. (To begin with, I don't vanish when you unplug the Cray, but will expire messily in a few decades.)
  More pithily: no one gets wet in a simulated thunderstorm.
- Unreality of non-simulations. One Jean Baudrillard has made quite a stir by claiming that reality no longer exists, if it ever did, and all that is left are "hyper-real" simulacra, "copies of copies without originals." I am unaware of any arguments in favor of this, which I suppose is fitting. His stunningly attrocious articles saying that the Gulf War could not take place, and then that it hadn't taken place, deserve an honored place in the Museum of Intellectual Rubbish. [On these, see Christopher Norris's Uncritical Theory: Postmodernism, Intellectuals and the Gulf War ; Mr. Norris himself suffers painfully from a different strain of the French Disease.]
  It would be interesting to know if M. Baudrillard listens to weather reports.

Glossary???

The Realized World: What you can kick. Physical objects. Stolen from Walter Jon William's science fiction novel, Aristoi.

David Berlinski, On Systems Analysis
Claude Bernard, Introduction to the Study of Experimental Medicine
Jacob Burckhardt, The Civilization of the Renaissance in Italy
William Calvin
- The Cerebral Symphony
- The Ascent of Mind
Kenneth Craik, The Nature of Explanation
Alfred Crosby, The Measure of Reality: Quantification and Western Society, 1250-1600
Mircea Eliade
- Myths, Rites and Symbols
- The Forge and the Crucible
Steve Farmer, Syncretism in the West: Pico's 900 Theses (1486): The Evolution of Traditional Religious and Philosophical Systems
Steve Farmer, John B. Henderson and Peter Robinson, "Commentary Traditions and the Evolution of Premodern Religious and Philosophical Systems: A Cross-Cultural Model," paper presented at the Kolloquium zu historischen und methodologischen Aspekten der Kommentierung von Text, University of Heidelberg, July 1997; copy courtesy of Dr. Farmer
Timothy Ferris, The Mind's Sky
David Gelernter, Mirror Worlds
Christian Gouriéroux and Alain Monfort, Simulation-Based Econometric Methods [Review: By Indirection Find Direction Out]
Ian Hacking, The Taming of Chance
Heilbroner, The Worldly Philosophers --- but I must get a better source than that for the Physiocrats and Ricardo.
Paul Humphreys, "Computational Models", Philosophy of Science 69 (2002): S1--S11 [Precise of book, below]
Philip N. Johnson-Laird, The Computer and the Mind
William H. McNeill, The Pursuit of Power: Technology, Society and Armed Force since 1000 A.D.
Peter Medawar, Induction and Intuition in Scientific Thought (included in Pluto's Republic)
John H. Miller, "Active Nonlinear Tests (ANTs) of Complex Simulation Models", Management Science 44 (1998): 820--830 [JSTOR link; thanks to Will Tracy for letting me know about this paper]
Jacques Monod, Chance and Necessity
Jospeh Needham, Science and Civilisation in China
Needham et al., Heavenly Clockworks
Christopher Norris, Uncritical Theory
Alec Nove, The Economics of Feasible Socialism
Pagels, The Dreams of Reason
Theodore Porter, The Rise of Statistical Thinking
Arturo Rosenblueth and Norbert Wiener, "The Role of Models in Science", Philosophy of Science 12 (1945): 316--321 [JSTOR]
Simon, Sciences of the Artificial
Tillyard, The Elizabethan World-Picture
Toulmin, Foresight and Understanding
Yi-Fu Tuan
- Morality and Imagination
- Passing Strange and Wonderful
Tufte
- Visual Display of Quantitative Informaiton
- Visual Explanations
Weissert, Genesis of Simulation and Dynamics [OK technical history of the FPU problem, half-baked reflections on simulation-in-general]
Walter Jon Williams, Aristoi
John von Neumann, The Theory of Self-Reproducing Automata (ed. and intro. Arthur W. Burks)

Eckhart Arnold, "Tools of Toys? On Specific Challenges for Modeling and the Epistemology of Models and Computer Simulations in the Social Sciences", phil-sci/5424
Babbage, Calculating Engines
James M. Beshers (ed.), Computer Methods in the Analysis of Large-Scale Social Systems [Proceedings of a 1964 conference]
Seth Bullock, Tom Smith and Jon Bird, "Picture This: The State of the Art in Visualization for Complex Adaptive Systems", Artificial Life 12 (2006): 189--192 [Introduction to a special issue (vol. 12, no. 2) on this subject]
Mark Burgin, Walter Karplus, and Damon Liu, "Multivariant Branching Prediction, Reflection, and Retrospection," cs.CE/0110048
Dizza Bursztyn and david M. Steinberg, "Comparison of designs for computer experiments", Journal of Statistical Planning and Inference 136 (2006): 1103--1119
Concise Encyclopedia of Modelling and Simulation
Crookall and Arai (eds.), Simulation and Gaming Across Disciplines and Cultures
Manuel DeLanda, Philosophy and Simulation: The Emergence of Synthetic Reason
James A. Dewar, Assumption-Based Planning: A Tool for Reducing Avoidable Surprises
Roman Frigg, "Scientific Representation and the Semantic View of Theories", phil-sci/2926
Roman Frigg and Julia Reiss, "The Philosophy of Simulation: Hot New Issues or Same Old Stew?", phil-sci/3495
Al Globus and Eric Raible, "Fourteen Ways to Say Nothing with Scientific Visualization," Computer, July 1994, 86--88
Alyssa Goodman, "Seeing science", arxiv:0911.3349
Hall, Mapping the Next Millennium
Mary B. Hesse, Models and Analogies in Science
Frank Hindriks, "Concretization, Explanation, and Mechanisms", phil-sci/3525
Paul Humphreys
- "Computational Science and Scientific Method", Minds and Machines 5 (1995): 499--512
- Extending Ourselves: Computational Science, Empiricism, and Scientific Method
Johnson-Laird, Mental Models
Franco Landriscina, Simulation and Learning: A Model-Centered Approach
Axel Legay, Benoit Delahaye, "Statistical Model Checking: An Overview", arxiv:1005.1327 ["Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas.... [But instead one could] simulate the system for finitely many runs, and use hypothesis testing to [check for] statistical evidence for the satisfaction or violation of the specification. In this short paper, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity."]
Loic Le Gratiet and Claire Cannamela, "Kriging-based sequential design strategies using fast cross-validation techniques with extensions to multi-fidelity computer codes", arxiv:1210.6187
Aki Lehtinen and Jaakko Kuorikoski, "Computing the Perfect Model: Why Do Economists Shun Simulation", Philosophy of Science 74 (2007): 304--329 [The abstract sounds right, but more like a reason for economists to change their ideals than anything else.]
Peter Lynch, The Emergence of Numerical Weather Prediction: Richardson's Dream [Review by Brian Hayes in American Scientist]
John Mack, The Art of Small Things
Robert Mariano, Til Schuermann and Melyvn J. Weeks (eds.), Simulation-Baed Inference in Econometrics: Methods and Applications
James Mattingly and Walter Warwick, "Projectible Predicates in Analogue and Simulated Systems", phil-sci/2816 [Assuming I understand the epistemologists' jargon, they're asking how you can tell which of your simulation results also apply to reality, and which are just artifiacts. This is an excellent question, though I wonder if it's possible to say anything useful about it at that level of generality.]
William McClung, The Architecture of Paradise: Survivals of Eden and Jerusalem
William Mitchell, The Reconfigured Eye: Visual Truth in the Post-Photographic Era
Mary S. Morgan and Margaret Morrison (eds.), Models as Mediators: Perspectives on Natural and Social Science
Margaret Morrison, Reconstructing Reality: Models, Mathematics, and Simulations [Review in Notre Dame Philosophical Reviews]
David O'Sullivan George L. W. Perry, Spatial Simulation: Exploring Pattern and Process
N. Oreskes, K. Shrader-Frechette, and K. Belitz, "Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences", Science 263 (1994): 641--646
Jerome Sacks, William J. Welch, Toby J. Mitchell and Henry P. Wynn, "Design and Analysis of Computer Experiments", Statistical Science 4 (1989): 409--423
Thomas J. Santner, Brian J. Williams and William J. Note, Design and Analysis of Computer Experiments
Kimberley Anne Sawchuck, review of Mirror Worlds for CTHEORY
Joseph Schumpeter, History of Economic Analysis
Hillel Schwartz, The Culture of the Copy: Striking Likenesses, Unreasonable Facsimilies
Samuel Schiflett (eds.), Scaled Worlds: Development, Validation and Applications
Angela B. Shiflet and George W. Shiflet, Introduction to Computational Science: Modeling and Simulation for the Sciences
Jan Sprenger, "Science without (parametric) models: the case of bootstrap resampling", Synthese 180 (2011): 65--76
Barbara Maria Stafford
- Artful Science
- Good Looking
Susan G. Sterrett, "Kinds of Models", phil-sci/2363
Mikaela Sundberg, "The dynamics of coordinated comparisons: How simulationists in astrophysics, oceanography and meteorology create standards for results", Social Studies of Science 41 (2011): 107--125
James R. Thompson, Simulation: A Modeler's Approach
Adam Toon, "Models and Make-Believe", phil-sci/2805 [cf. also "Models as Make-Believe", phil-sci/3227]
Michael Weisberg, Simulation and Similarity: Using Models to Understand the World
Eric Winsberg, Science in the Age of Computer Simulation
Benjamin Woolley, Virtual Worlds: A Journey in Hype and Hyperreality