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

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

2. Examination: Presence on lectures with external lecturerHomework: 2 papers: DA2205: 2 from list FDD3001: 2 from list, except 1 and 21: Self-presentation 2: Press Release 3: Grant Application4: Paper Analysis5: Fraud Investigation6: Proposal Review 7: Media Event 8: Self presentation and press release 9: Elective (must be approved by me) Courses FD3001: 7.5hpDA2205: 3hp of 7.5

3. 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.

4. 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.

5. 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.

6. 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.

8. Schleiermacher Odogmatisk religion WvH:s tankesmedja Christoph Markschies: Was von Humboldt noch zu lernen ist,Berlin UP 2010

9. 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

10. 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

12. 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’

13. 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.

14. Lyotard: La condition post-moderne-rapport sur le savoir Soyez opératoires, c’est-à-dire commensurables, ou disparaissez.

15. 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 calculationand verified in galleries of a community of practiceextending through societyas an actor network Callon, Latour ca 1985

16. 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)

17. 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 connectingthe research activity with an’actor network’ linkinghumans and artefacts into a robust network ensuring financing, carreers and recruitment.

18. 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.

19. 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. Feyerabend - Against Method

20. 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 releasessignal substances that have thesame type of effect as drugs? • Similarity with managerial methods:reorganisation, reform, events,kickoffs, and other rituals • Current fight between therapists(CBT) and psychiatrists (drugs).

21. 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.

22. 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.

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

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

25. Max Weber on Marx and Nietzsche 1920: Anyone in the Social Sciencesor the Humanities who claims his work independent of Nietzsche and Marx is either dishonest or incompetent

26. 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 - mostwritten accounts from there are however lost

27. Beckwith: Empires on the Silk Road

28. Thales -585 Anaximander 611-547 Anaximenes -502 Pythagoras 570-508 Parmenides 510- Zenon 488- Empedokles 450 Herakleitos 540-480 Anaxagoras 500-428 Herodotos 425 Protagoras 420 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 Poseidonius100 Hipparkos

29. 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.

30. 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.

31. 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

32. Astronomy • Aristotle, Hipparkus and Ptolemai were geocentrists • Appolonius: Defined both conic sections (used by Kepler) andthe 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 inferiorfor 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).

33. Aristarchus On the Sizes and Distances of Sun and Moon

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

35. 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.

36. 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.

37. 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

38. 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’ onmodel of ‘madrasa’ and ‘vihâra’ • Mufti -> professor of opinion (fatwa), mostly in law, • Faqih -> Master, licenced to practice profession • Muddaris -> Doctor, licensed to teach

39. 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.

40. 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’

41. 1665 - Alchemy 1666 - Calculus 1667 - Fellow, Trinity College1669 - professor 1682-4 Principia1689 - Parlamentarian1692 - Opticks 1696 - Royal Mint 1703 - Royal Society1733 - Daniel and Apocalypse First modern or last ancient?? Newton, (1642-1727)

42. 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

43. 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

44. 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.

45. 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

46. 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).

47. 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 y there is a set containing x and y, and nothing else. • 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:

48. 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

49. 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

50. 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)