Download - CSC 599: Computational Scientific Discovery Lecture 1: Introduction to CSD and Philosophy of Science
CSC 599: Computational Scientific Discovery
Lecture 1:
Introduction to CSD and Philosophy of Science
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
My (our?) Mission Statement
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.
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”?
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”
What is “science”?
Or perhaps:0. A body of empirically-tested beliefs?1. A human activity associated building and
revising such beliefs?
What is “science”?
Or even:0. A body of empirically-tested beliefs?1. A human activity associated building and
revising such beliefs?2. A communal human activity associated
building and revising such beliefs?
No clear consensus!
Can We Really Do These Things for Science?
Computer Scientists think so:0. A body of empirically-tested beliefs?
Programs for handling systems of equations, sets of logic sentences, etc.
1. A human activity? Heuristic based search techniques
2. A communal activity? Genetic algorithms or other communal parallel
search
Philosophers of Science (and others) might disagree . . .
Modern philosophers might define science as being a social (i.e. human) enterprise
Our Immediate Approach
Our approach is informed by three disciplines:0. Philosophy of Science
What do the professionals who think about how science is done for a living think?
1. ScienceWhat do our client scientists want?
2. Computer ScienceWhat can we reasonably give them?
"Science = logical rules""Science = logical rules"(Right?)(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”
1. Define problem2. Formulate hypothesis3. Test hypothesis4. Analyze results5. Make conclusion
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:1.PLAN:
INPUT: molecule's mass spectrum and atomsOUTPUT: List of necessary groups (goodlist) and
forbidden groups (badlist)2.GENERATE:
Generates all molecules consistent with goodlist/badlist3.TEST:
Predicts fragmentation patterns of molecule
Whoa! What is Mass Spectroscopy?
1. Molecule + high-speed electron -> molecular fragments (some have positive charge)
2. Isolate fragments by mass/charge ratio1. Accelerate fragments2. Pass thru electrical or magnetic field3. Isolate fragments with one mass/charge
3. Detect them
Mass Spectroscopy: the Intuition
1. You are given a sample car, but you don't know which make/model
2. You smash it with a standardized slug
car + high speed slug -> bumper + engine block + ...
3. 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!)
Finally: Meta-DENDRAL
Giving exhaustive list of fragmenting rules annoys chemists Some are implicit Some are unknown
Meta-Dendral learns splitting patterns1. INTSUM: Generate specific splitting rules2.RULEGEN: Generalize generated rules3.RULEMOD: “Tidy” rules by specifying them not
to handle negative examples, etc.
Meta-DENDRAL in more detail
Input:1. Structure of compounds2. Spectrum of compounds3. “Half-order” theory of what is and is not allowed
in mass spectrocopyE.g. “Aromatic rings don't break” “At most 2 H's may
migrate”
Output: Rule to explain each peak consistent with
1. The peak's m/e (“mass to charge”) ratio2. The half-order theory
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
Meta-DENDRAL: RULEMOD
RULEGEN rules may cover peaks that are not observed (negative examples)
RULEMOD can1. Merge rules2. Eliminate redundancies3. Make rules more specific (so don't cover
negative examples)4. Make rules more general
Meta-DENDRAL vs. Scientific Method
1. Define problemMass spectrum rule generation
2. Formulate hypothesisINTSUM + RULEGEN + RULEMOD
3. Test hypothesisUse rules in Heuristic DENDRAL for new cmpds
4. Analyze results/Make conclusions Meta-DENDRAL rediscovered known patterns Meta-DENDRAL found new ones, were
published
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
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
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
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
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
. . . and along came Hitler
Moritz SchlickGermany and Austria, assassinated 1936 (gulp!)
A.J. Ayer(already was British)
Karl Popperto New Zealand, then to London
Hans ReichenbachGermany to Turkey, then to UCLA
Rudolf CarnapGermany and Austria to U of Chicago
Carl HempelGermany to Belgium, then to U. of Chicago
and so on . . .
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
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
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)
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 solutionStrong verification: Can conclusively be establish
by observationWeak verification: Experience makes it probable
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!
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
W.V.O. Quine and LanguageDistinguishing analytic from synthetic:
1.Consider the “analytic” statements:“No bachelor is married”“No unmarried man is married”
2.Convert between them we need synonyms“Bachelor == unmarried man”But where did that mapping come from?
3.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!)
4. Synonymy needs salva veritate, needs analytics5. But analytics needs synonymy
Circular reasoning!
Grover Maxwell and the Observational-Theoretical
DichotomySeemingly 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!
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