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”?

Is it:0. A body of empirically-tested beliefs?

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

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?