Research: Theory, Method, Practice Intro Lecture 2011 Stefan Arnborg, KTH

Courses FD3001: 7.5hp

DA2205: 3hp of 7.5

Examination: Presence on lectures with external lecturer Homework: 2 papers: DA2205: 2 from list FDD3001: 2 from list, except 1 and 2 1: Self-presentation 2: Press Release 3: Grant Application 4: Paper Analysis 5: Fraud Investigation 6: Proposal Review 7: Media Event 8: Self presentation and press release 9: Elective (must be approved by me)

Course Goals

You should be able to discuss and analyze the different value judgments that research communities recognize, in a broad area of research covering at least the CSC school of KTH, be able to evaluate research questions in these areas and relate them to principles and theories proposed in the philosophy of science and technology.

You should be able to find relevant and valid information on ethical principles guiding your conduct as researcher, and be able to apply it in your daily life as researcher.

You should be able to present your research and to plan presentations for different purposes. In these you should be able to find and communicate suitable motivations why your work leads to a better society - sustainable, bearable, robust, exciting, etc.

Course Goals

You should find it natural to present yourself, to an appropriate level of detail, as a researcher in different social contexts.

You should be able to find relevant information and procedures for financing research, fundamental and applied, and present rhetorically appropriate research plans for different financing agencies, written as well as oral and social.

Course Evaluation 2008-2010

-- Few answers to computerized survey. Please answer after course ends.

-- External lecturers very good, but more women and something on gender research requested.

-- Both course books good (but choose carefully) -- One student found advicing ‘ insufficient ’ : Let me clarify that YOU ask for advice, I am not hunting for students to advice. If you have not received answer to a mail within four days, please ask again. -- Feedback is given within a week during course (until homework deadline). After that, I must put priority on other things, so answers will be shorter and delays longer.

Norms of Academic Science: Merton 1942

• C communism (or communitarianism) • U universality: universal knowledge • D disinterestedness: no personal stakes(except honour) • O originality: NEW knowledge • S scepticism: try to falsify • Merton’s context: relation between power and scientist in dictatorships (Hitler, Stalin). Border between society and science demarcated.

Schleiermacher Odogmatisk religion WvH:s tankesmedja Christoph Markschies: Was von Humboldt noch zu lernen ist,

Berlin UP 2010

The idea of a University

“

A University is a place … whither students come from every quarter for every kind of knowledge; … a place for the communication and circulation of thought, by means of personal intercourse. … It is the place to which a thousand schools make contributions; in which the intellect may safely range and speculate. It is a place where inquiry is pushed forward, … discoveries verified and perfected, and … error exposed, by the collision of mind with mind, and knowledge with knowledge. … Mutual education, in a large sense of the word, is one of the great and incessant occupations of human society. … One generation forms another.

… We must consult the living man and listen to his living voice, … by familiar intercourse … to adjust together the claims and relations of their respective subjects of investigation. Thus is created a pure and clear atmosphere of thought, which the student also breathes.

” So wrote John Henry Newman in

The Idea of a University

in 1852.1

Post-Academic Science: Ziman 2000

• P proprietarian ( IP, business opportunity) • L local: related to local network of stakeholders • A authoritarian: hierarchical control • C commissioned (researcher is ’consultant’) • E expert: role is problem-solver • Ziman’s context: Universities are like any corporations, and output directly economically measurable. Globalization • Etzkowitz: Triple Helix: Academy/Region/Industry

Lyotard

• The post-modern condition: Commissioned work for Montreal Education authority - prophetic • Fight against concept of ’Grand Narrative ’ as opposed to complex web of ’micro-narratives’

Commodification of Knowledge

• Knowledge is a commodity like all that counts: It is produced, sold, bought and consumed in a setting where market, production efficiency, price and marketing is more relevant than whatever Humboldt and his peers thought about.

(≈ Lyotard, 1984)

• Valuable is knowledge that can be cogged into production and advising systems of society.

• Less valuable is knowledge that questions the current political thoughts about society ’ s development.

Lyotard: La condition post-moderne -rapport sur le savoir

Soyez opératoires, c’est-à-dire commensurables, ou disparaissez.

Is Praxiteles ’ work already in the marble?

NO: Structure of Science (and Truth) is the outcome of a practice Which claims can be resisted?

Which can be made?

Which allies can be brought in?

Which links resist?

Scientific truth defined in centers of calculation and verified in galleries of a community of practice extending through society as an actor network Callon, Latour ca 1985

What is Truth?

• Plato: Rationalistic, Cave simile, observations unreliable. Cf Meno.

• Aristotle: Deductive truth: What follows from true assumptions is true. Whats opposite can be deductively refuted is true. (cf proof by contradiction, statistical hypothesis tests) Aristotle: Inductive truth: What regularly obtains is true (cf statistical inference) • Peirce: What a community of scholars eventually agrees upon is Truth.

• Latour: Something is True if it cannot be resisted, tied into a network of irresistible microsociological relations between humans, ideas and material artefacts.(ANT)

Progress of Science

• Accumulation of observations, experiments and theories (Francis Bacon, Auguste Comte). Naive positivism.

• Theories are prior to observations, the latter Confirm (Carnap) or Falsify (Popper) theories. Logical Positivism • Scientific progress is revolutionary (Kuhn, Feyerabend). Paradigms, or ANYTHING GOES.

• Latour, Callon: science is a ’social’ activity connecting the research activity with an ’actor network’ linking humans and artefacts into a robust network ensuring financing, carreers and recruitment.

Kuhn: Paradigms in Science

• Normal Science: Exemplar to take after, filling in gaps, ’goldplating’ • Anomalies: Try to explain anomalies by interpretation of experiments and observations. No rejection of theory • Crisis: Anomalies are serious enough to reject theory and force a new PARADIGM.

• Typically, a new paradigm is not universally but only gradually accepted.

Feyerabend - Against Method

Science is an essentially anarchistic enterprise The only principle that does not inhibit progress is: ANYTHING GOES Hypotheses contradicting well-confirmed theories give us evidence that cannot be obtained in other ways If there is a driving force in science, it is aesthetics.

Hawthorne and Placebo

• Clients of Healers & Homeopathists, subjects in the ‘ no-intervention ’ group can also see positive changes • Is this pseudoscience?

(Kathy Sykes ’ TV programmes) • Brain ’ s reward system releases signal substances that have the same type of effect as drugs?

• Similarity with managerial methods: reorganisation, reform, events, kickoffs, and other rituals • Current fight between therapists (CBT) and psychiatrists (drugs).

This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on.

Goals in Research, sketch:

• Humanities: Understanding Phenomena • Social Sciences: Improve society • Natural Science: Predict outcome of experiments • Mathematics: 1:Solve problems prove theorems (Erdös) 2:Create Landscape in which theorems can be defined and proved (Thom).

• Engineering Science: What other sciences forgot, enabling new technology deployment.

Qualitative Research

• Margaret Mead: Best known (to American public) scientist before Einstein • Coming of Age in Samoa, ≈1925 - controversies settled or not?

• Immersion, constructing

Three Inconvenient Germans

• Karl Marx (1818-1883) Class, Organization of Production, Revolution Founder of latest state religions • Friedrich Nietzsche (1844-1900). Aesthetics revolutionized, existentialist and post-modernity icon • Sigmund Freud (1856-1938), discoverer of the unconscious

Max Weber on Marx and Nietzsche

1920: Anyone in the Social Sciences or the Humanities who claims his work independent of Nietzsche and Marx is either dishonest or incompetent

Why look at Greek science??

• Well studied and documented • Greek classicism shapes our way of seeing the world.

• Greek society cruel: Slaves, Wars, Racism,Oppression of women (i.e., like Europe) • Greek science builds on significant knowledge in China, India, Persia - most written accounts from there are however lost

Beckwith: Empires on the Silk Road

Thales -585 Anaximander 611-547 Anaximenes -502 Pythagoras 570-508 Parmenides 510 Zenon 488 Empedokles 450 Anaxagoras 500-428 Herodotos 425 Protagoras 420 Herakleitos 540-480 Demokritos 460-370 Sokrates 469-399, Antisthenes Platon 428-348 Aristarkos Aristoteles 384-322 Arkimedes -300 E Euklides Appolonius Epikureos 342-270 Selevkos Epiktetus 50-125 Poseidonius 100 Hipparkos

Theory of Evolution

• First account by Anaximandros, including sketch of natural selection • Based on mechanistic view, not Intelligent Design • Restated by Empedocles • Rejected by Aristotle as implausible.

Teleological explanation. Important paradigm shift.

Modern theory of Evolution

• Based on careful collection of supporting observations (many of which can also be found in Aristotle: Parts of animals) • Was apparently refutable by age of earth (Kelvin could not know about heating of earth by radioactivity ) and lack of understanding of genetics (Mendel ’s work had been unnoticed, despite said to have been lying on Darwin ’s desk) • Still considered somewhat daring, but only remaining ’serious’ hypothesis.

Greek Astronomy

• Relied on Eastern knowledge (Persia, India,…) • Predict eclipses (Thales, 585 BC) • Sizes of earth, moon, the zodiac to within 1% • Size of sun : Aristarkos: sun ’ s diameter 180 times that of earth -> Heliocentrism is a plausible model • Poseidonius (teacher of Cicero): Diameter of sun 9893 times that of earth (50% low, best result in antiquity!) Poseidonius also explained tidal water (sun, moon) - made possible tidal water tables

Astronomy

• Aristotle, Hipparkus and Ptolemai were geocentrists • Appolonius: Defined both conic sections (used by Kepler) and the epicycle system (used by Ptolemai).

… and in the west?

• Copernicus: Sun might be the center because of its majestic appearance? (similar to Aristarkos quantified argument) • However, predictions based on heliocentrism were inferior for a long time • It took more than 100 years before Kepler saved the heliocentric view by using Appolonius ’ conic sections instead of his epicycles. Difference is in the kinematics.

• If the heliocentricists had followed a scientific method, they should have rejected their hypothesis(Feyerabend).

Aristarchus On the Sizes and Distances of Sun and Moon

Tycho Brahe ’s system

• The moon and sun circle around earth, but planets around the sun • Absence of stellar parallax indicates geocentrism • Also convenient and safe wrt church, • Which made Brahe a looser, undeservedly because his system is ’almost right’.

Tycho Brahe: First ’Big Science’

• • • • • The construction of Uranienborg consumed a sizeable proportion of Danish State Income.

Tycho Brahe was the first (documented) ’Big Science ’ performer He had to motivate his needs by writing horoscopes for kings and their like Today ’s big scientists also have to motivate their needs by guessing about the practical use of their expensive equipment Physicists typically succeed in motivating new CERN equipment by referring to employment opportubnities and uncertain spin-offs - this does seldom work in other areas.

Atomism

• Not unique for Greek philosophers • Democrit, Leukippos suggested atomism, from observations of life cycles and chemical processes • Epikuros combined it with an ethics of ‘ no after-life ’ , explicated in one of the great antique works of literature, Lucretius ‘ De Rerum Natura ’ , On the Order of Nature.

The

‘

Dark ages

’ • Greek science and literature survived in the Byzantine and Muslim worlds, although not in a central position • Applied to rational analysis of theological problems (Ibn Rushd), medicine (Ibn Sina), social science (Ibn Khaldun).

• Grinding halt after destruction of Baghdad (1258) and conquest of Constantinople (1453) • Translated to Latin from Greek and Arabic (Plato, Aristotle) • Aristotle surpasses Plato as ‘ the Philosopher ’ , treated as semi-god rather than human.

• Scholasticism - fascinating, but not in line with course

Islamic Science

• The first islamic law schools (ca 800), e.g., in Fez, developed the academic degree system and CV concept (Doctor ’ s degree, promotion and hat) which were taken over by European Universities • Jocius of London founded ‘Collège des dix-huit’ on model of ‘madrasa’ and ‘vihâra’ • Mufti -> professor of opinion (fatwa), mostly in law, • Faqih -> Master, licenced to practice profession • Muddaris -> Doctor, licensed to teach

Islamic Scholars

• Ibn Sina (Avicenna), ca 1000, practice based medicine (antibiotics, vaccines (inoculation)).

• Ibn Rushd (Averroes), ca 1200, precursor of scholasticism, mixing ‘ axioms ’ in the form of Quran statements with observations, deriving new truth by syllogism. Saved Aristotle, clash with fundamentalism.

Ibn Khaldun (ca 1360): Muqqadimah

• Politician, social scientist, historian, economist.

• First statements of market theory, importance of stable institutions, property right, stable currency • • First scientific Marxist (without political program): Power and wealth distribution depends on how production is organized ‘ Anyone can have ideas, but only through words and language can you convince ’

Newton, (1642-1727)

1665 - Alchemy 1666 - Calculus 1667 - Fellow, Trinity College 1669 - professor 1682-4 Principia 1689 - Parlamentarian 1692 - Opticks 1696 - Royal Mint 1703 - Royal Society 1733 - Daniel and Apocalypse First modern or last ancient??

Standard view on Math Phil

• Mathematical results are certain • Mathematics is objective • Proofs are essential • Diagrams are unnecessary • Mathematics is safely founded in logic • Independent of senses • Cumulative, setbacks trivial • Computer proofs are kosher • Some exotic problems in math are unsolvable

What is a good Math result?(Bauer)

• Somewhat difficult to find • Fits into an existing paradigm (there are several), ’significant result’.

• Correct if agreed to be correct by reviewers • Most results are forgotten - if there are errors, no-one finds them • Most accepted results continue to be correct.

• However, acceptance is not proof of correctness

Exemplar paradigms in math

• Socrates in Plato ’ s Meno - arguments less formalized than ‘ modern ’ proofs. Similar methods applied, e.g., by Pythagoreans • Aristotle/Euclid: Rigor stepped up, exemplary until 1960:s • Newton, Leibniz, Maxwell, Euler, Stokes: new math rather confused, carried by community of practitioners (Wranglers) • Critizised by Bishop Berkeley: The Analyst.

• Bolzano, Weierstrass, Cauchy, Dedekind: Foundations of ‘ rigorous analysis ’ . Analysis ‘ King ’ of Math.

Cambridge Wranglers -Created the math you studied: Green, Stokes, Macauly, Routh Maxwell, Larmor, Cunningham, Dirac… -Competitive math examination aimed at ranking candidates for fellowships - -Appointments for life with no particular duties -- often awarded at age 20-25

Foundational Crises

• Hilbert last polymath: 23 centennium problems in 1900. Hilbert ’ s program.

• Russell, Whitehead: Realize logical foundation: develop all of math within logic.

• Surprise: Math and computation undecidable (Gödel, Turing). Several of Hilbert ’ s problems not solvable.

• Constructivism/Intuitionism: Only what can be ‘ intuited ’ can be real. Scientific Computation • Computational Complexity (& Algorithms) • Math ‘ educational ’ crisis: interest waning, culture disappears (Matematikdelegationen).

Zermelo-Fraenkel Set Theory with Axiom of Choice (ZFC)

• Extensionality: Two sets are the same if they have the same members.

• Empty set: There is set with no element.

• Pairing: for sets

x

and nothing else.

and

y

there is a set containing

x

and

y

, • Union: for any set

F

there is a set containing every member of every member of

F

• Infinity: There is an infinite set, eg {{},{{},{{}}},…} • Axiom (schema) of specification: For every set x and property

P

, there is a set consisting of those members of

x

satisfying

P

.

• Replacement:

Zermelo-Fraenkel Set Theory with Axiom of Choice (cont)

• Axiom of separation (definition): For every set x and property

P

, there is a set consisting of those members of

x

satisfying

P

(and only those).

• Replacement: For a function f and subset of its range x, there is a set containing the image of x, {y:y=f(z) | z  x} • Power set: For set x, there is a set consisting of the subsets of x • Regularity: Every non-empty set x contains an element y disjoint from it.

• Axiom of Choice: Given a set x of mutually disjoint non-empty sets, there is a set containing exactly one element from each member of x

Zermelo-Fraenkel Set Theory

• The safest and most accepted logical foundation of mathematics • Consistency of ZFC cannot be proven within ZFC • Consistency can be shown with forcing (Paul Cohen), as well as the independence of the Continuum Hypothesis (Hilbert ’s first problem) and other somewhat subtle things

Intuitionism/constructivism is computational

• Building on the positive integers, weaving a web of ever more sets and more functions, we get the basis structures of mathematics. Everything attaches itself to number, and every mathematical statement ultimately expresses the fact that if we perform certain computations within the set of integers, we shall get certain results. Even the most abstract mathematical statement has a computational basis. (Bishop & Bridges, 1985)

This book argues that conceptual metaphor plays a central, defining role in mathematical ideas within the cognitive unconscious from arithmetic and algebra to sets and logic to infinity in all of its forms: transfinite numbers, points at infinity, infinitesimals, and so on.

Alan Turing: Halting Theorem

First result in computational complexity: It is not possible for a computer to decide whether or not a computer computation (with unbounded memory) will terminate.

Proof by reduction: If such a method (computer program) exists, a program can be constructed which must terminate and also must not terminate

The Art of Computer Programming D.E. Knuth.

Started 1962.

Vol 1: Fundamental Algorithms, 1968 Vol 2: Seminumerical Algorithms, 1970 Vol 3: Searching and Sorting, 1973 TeX, …. Vol 4: Combinatorial Algorithms, Vol 5: Syntactical Algorithms Vol 6: Theory of Languages Vol 7: Compilers

Algorithms

• Measure performance asymptotically • Multiplication Example: as in school: • Smarter: Fourier transform, Multiplication lower bound: , since you must look at every input bit. • There is typically a (very) significant gap between lower and upper asymptotic bounds: even the lowest cost of multiplication is not known.

The Turing Machine

Unless you know its combination, 10 61 78 20 12, you must try a billion combinations Opening a combination lock is difficult

Winners of Cipher Challenge 2001

RSA cryptosystem uses that primality is easy, but factorization is difficult (Rivest, Shamir, Amir, 1971) Produce two large primes and multiply them. Produce a pair of keys (E,D).

With the product and E (public key) you can encrypt messages but you can only decrypt if you have D and the product, or know E and the factors

RSA secrets are temporary!

Year Largest prime Biggest factorization Long ago 10 digits 1957 1000 digits 1982 13400 digits 77 2005 8.7 million digits 155 digits One day your key will be factorizable!

Or, this day may be tomorrow Or yesterday for a paranoic cryptographer

With time, the chart of complexity classes has become embarrassingly complex. And it rests on unproved conjectures.

Logics of knowledge and belief Games Combinatorial optimization Feasible problems Parallelizable problems 2006: 442 classes in the complexity zoo

Zero-knowledge proofs

• Graph 3-colorability : • Given graph (V,E), known by both p(rover) and v(erifier). Only p has access to a 3-coloring  : V  {1,2,3} • In each round: p permutes colors, randomization π sends each π(i) in sealed envelope to v.

v asks for two specific adjacent vertices i,j, and p unlocks them. Now v can verify  (i)≠  (j). • v has probability ≥1/|E| to reveal a bluff in each round - if there is one

Zero-knowledge

Fundamental tool for cryptographic protocol analysis: •Key exchange and verification •Digital Cash: Anonymity, check against multiple spending … •Voting: No cheating, anonymity, no selling of votes … =? 0100100010100010001111110