CSC 599: Computational Scientific Discovery

1. Lecture 1: Introduction to CSD and Philosophy of Science CSC 599: Computational Scientific Discovery

2. Outline • Introduction/Motivation • Writing software to extend scientific models • Science, Philosophy of Science, Computer Science • Scientific Method • Example with Meta-DENDRAL • Logical Empiricism • Goals • History • Tenets • Problems

3. We want to write software that can help scientists understand and extend scientific models by supporting prediction, explanation, visualization, consistency checking, data collection and knowledge formation. My (our?) Mission Statement

4. So ya' wanna tell a computer about science . . . Natural to ask about: • Calculation/Prediction • Explanation • Visualization • Consistency checking • Data collection • Knowledge formation Let's ask more basic questions: • What is a “computer”? • What is “science”?

5. What is a “computer”? We can convince ourselves that we know this: • Mathematical description: • Alan Turing, Alonso Church, et al • Turing mach., Push down auto., Finite state mach. • Physical description • Computing devices • Abacus (2400BC Babylon?) storage (hands + fingers)‏ • Pascal: Pascaline (1642), Leibniz: Stepped Reckoner • Programmable devices • Joseph Marie Jacquard's punch-card power loom (1801)‏ • Programmable computing devices • Babbage Analytic Engine (1837), Zuse Z3 (1941)‏ • Algorithm description • Al-Khwarizmi, Countess Lovelace Ada Byron • Donald Knuth “The Art of Computer Programming”

6. What is “science”? Is it: • A body of empirically-tested beliefs?

7. What is “science”? Or perhaps: • A body of empirically-tested beliefs? • A human activity associated building and revising such beliefs?

8. What is “science”? Or even: • A body of empirically-tested beliefs? • A human activity associated building and revising such beliefs? • A communal human activity associated building and revising such beliefs? No clear consensus!

9. Can We Really Do These Things for Science? Computer Scientists think so: • A body of empirically-tested beliefs? • Programs for handling systems of equations, sets of logic sentences, etc. • A human activity? • Heuristic based search techniques • A communal activity? • Genetic algorithms or other communal parallel search

10. Philosophers of Science (and others) might disagree . . . Modern philosophers might define science as being a social (i.e. human) enterprise

11. Our Immediate Approach Our approach is informed by three disciplines: • Philosophy of Science What do the professionals who think about how science is done for a living think? • Science What do our client scientists want? • Computer Science What can we reasonably give them?

12. "Science = logical rules"(Right?)‏ Philosophers have not (and still do not) agree about the nature of science. We can just choose the philosophy that best matches our approach. • Computer scientists like algorithms, so . . . • Try “science = application of scientific method” • Define problem • Formulate hypothesis • Test hypothesis • Analyze results • Make conclusion

13. Application of Scientific Method: Meta-DENDRAL Heuristic DENDRAL (1965-1970s): • Interprets mass spectroscopy patterns for chemists • Feigenbaum, Lederberg, Buchanan and Djerassi Has three step process: • PLAN: INPUT: molecule's mass spectrum and atoms OUTPUT: List of necessary groups (goodlist) and forbidden groups (badlist)‏ • GENERATE: Generates all molecules consistent with goodlist/badlist • TEST: Predicts fragmentation patterns of molecule

14. Whoa! What is Mass Spectroscopy? • Molecule + high-speed electron -> molecular fragments (some have positive charge)‏ • Isolate fragments by mass/charge ratio • Accelerate fragments • Pass thru electrical or magnetic field • Isolate fragments with one mass/charge • Detect them

15. Mass Spectroscopy: the Intuition • You are given a sample car, but you don't know which make/model • You smash it with a standardized slug car + high speed slug -> bumper + engine block + ... • You look at the car fragments that result “That's a Toyota bumper” “That's a Corolla engine block” (Yes its violent . . . but their just molecules!)‏

16. Finally: Meta-DENDRAL Giving exhaustive list of fragmenting rules annoys chemists • Some are implicit • Some are unknown Meta-Dendral learns splitting patterns • INTSUM: Generate specific splitting rules • RULEGEN: Generalize generated rules • RULEMOD: “Tidy” rules by specifying them not to handle negative examples, etc.

17. Meta-DENDRAL in more detail Input: • Structure of compounds • Spectrum of compounds • “Half-order” theory of what is and is not allowed in mass spectrocopy E.g. “Aromatic rings don't break” “At most 2 H's may migrate” Output: • Rule to explain each peak consistent with • The peak's m/e (“mass to charge”) ratio • The half-order theory

18. Meta-DENDRAL: RULEGEN Each INTSUM rule is very specific RULEGEN generalizes rules to try to cover more than one INTSUM rule Rules generalized by “growing” fragmentation tree • Tree made more specific according to semantic rules

19. Meta-DENDRAL: RULEMOD RULEGEN rules may cover peaks that are not observed (negative examples)‏ RULEMOD can • Merge rules • Eliminate redundancies • Make rules more specific (so don't cover negative examples)‏ • Make rules more general

20. Meta-DENDRAL vs. Scientific Method • Define problem Mass spectrum rule generation • Formulate hypothesis INTSUM + RULEGEN + RULEMOD • Test hypothesis Use rules in Heuristic DENDRAL for new cmpds • Analyze results/Make conclusions • Meta-DENDRAL rediscovered known patterns • Meta-DENDRAL found new ones, were published

21. So, science and automated discovery are compatible Let's generalize away from specifics of mass spectroscopy to a general approach • Should emphasize • Computer compatible representation • Computer compatible reasoning

22. Logical Empiricism might fit the bill Based on logic • Long tradition of theorem provers in math, A.I. • That should give us computer compatibility Austro-German beginning • Immanuel Kant (Unification of Continental Rationalists with British Empiricists)‏ • Ernst Mach and Ludwig Wittgenstein (Reductionism)‏ • Principia Mathematica (Russell and Whitehead)‏ • An attempt to derive all mathematics from axioms • Do to set theory and number theory what Euclid did for geometry • Post-First World War Vienna Circle • Reichenbach, Schlick, et al

23. Logical Empiricism Original Goals • Remove cultural considerations from science • Dismissively called “metaphysics” • Imprecise • Create lingua franca for science • Correspondence rules: map words and phrases to observations • Wanted to define “theoretical” terms (e.g. mass) in terms of things observations • Distinguish science from pseudo-science • Some were critical of Marxism and Freudian psychology as sciences

24. The Tenets of Early Logical Empiricism • Verifiability criterion of meaning • All meaningful statements if there is a finite procedure for determining if it is true or false. • Logic of discovery vs. logic of justification • The science is in justification of potential laws • which of course ought to be done by the verifiability criterion • How a scientist discovers a law may depend on “irrational” thought, but this is unimportant

25. The Tenets of Early Logical Empiricism, cont'd • Predicates for theoretical terms and predicates for observational terms • Logic usable (in principle at least) to name sensations (i.e. correspondence rules) and theoretical terms (e.g. “mass”)‏ • Science = induction • Define theoretical predicates from observational ones

26. . . . and along came Hitler Moritz Schlick Germany and Austria, assassinated 1936 (gulp!)‏ • A.J. Ayer (already was British)‏ • Karl Popper to New Zealand, then to London • Hans Reichenbach Germany to Turkey, then to UCLA • Rudolf Carnap Germany and Austria to U of Chicago • Carl Hempel Germany to Belgium, then to U. of Chicago • and so on . . .

27. Empiricism in the Anglophone World There was already an American philosophy of science (e.g. Charles Peirce)‏ but Logical Empiricism imprinted itself firmly in the UK and US • Logical Empiricism was outgrowth of Empiricism • Emphasized British Empiricists roots

28. Post-1945 Logical Empiricism Extensions of Logical Empiricism: • Dealt with Quantum Mechanics • Physicists did not given philosophers much respect • Rudolph Carnap outfitted Logical Empiricism with probability

29. Problems with Logical Empiricism • Problems with verification criterion • Ayer, Popper • Problems with reductionism • Quine • Problems with language • Quine, Maxwell and Goodman • Problems with removing science from historical context • Kuhn (next week)‏

30. Problems with Verification Criterion Recall, verification criterion: • All meaningful statements if there is a finite procedure for determining if it is true or false But some things can be verified and others not “Not all ravens are black” (Find a non-black raven)‏ “All ravens are black” (Can you really observe all ravens that were, are, and will be?)‏ Ayer's solution Strong verification: Can conclusively be establish by observation Weak verification: Experience makes it probable

31. Karl Popper and Falsification Popper went further than Ayer • Throw out verification criterion in favor of falsification • You can never prove a theory • Can you really observe all ravens to see if they are non-black? • Proper theories are in principle falsifiable • Some Marxist believe take observation X to support their Marxism, and then they take not(X) to do the same • Marxism isn't science!

32. W.V.O. Quine and Reductionism Rudolph Carnap tried to outline a “sense-datum language” for science His attempt uses concepts like “quantity q is such-and-such at <x,y,z,t>” But what is the concept “is-at”? • It's not defined . . . it's metaphysical! Pure reductionism very difficult, if not impossible

33. W.V.O. Quine and Language Distinguishing analytic from synthetic: • Consider the “analytic” statements: “No bachelor is married” “No unmarried man is married” • Convert between them we need synonyms “Bachelor == unmarried man” But where did that mapping come from? • To properly use synonyms we need salva veritate (“complete interchangability”, or substitution without loss)‏ “Necessarily all and only bachelors are unmarried men” (An analytic statement!)‏ • Synonymy needs salva veritate, needs analytics • But analytics needs synonymy Circular reasoning!

34. Grover Maxwell and the Observational-Theoretical Dichotomy Seemingly observational: “You look outside the window and observe that it's raining” But is it really devoid of theory? • Light went from rain drop to air to window to air to eye • Assumes a theory of optics Any line between “theory” and “observation” is arbitrary!

35. Goodman and Grue Something is grue if its green up until time t, and blue thereafter • If t is in the future then all emeralds are green • All emeralds are grue too! • No “rational” reason to prefer green or grue Are you happy with that? Goodman's solution: Rely on the “inertia” of language. • The concepts green and blue have been useful • The concept grue has not been useful

36. Next Week Philosophy of Science Post-Logical Empiricism • Thomas Kuhn • Imre Lakatos • Larry Laudan • Sociologies of science • Model-base philosophies Differences between CSD and Philosophy of Science What shall we conclude from all of this?