C communism (or communitarianism)

C communism (or communitarianism)

• 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.

P proprietarian ( IP, business opportunity)

• 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

The post-modern condition: Commissioned work for Montreal Education authority - prophetic

• 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’

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)

• 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.

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

• 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)

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

• 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.

Normal Science: Exemplar to take after, filling in gaps, ’goldplating’

• 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.

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

• 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).

Humanities: Understanding Phenomena

• 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.

• Margaret Mead: Best known (to American public) scientist before Einstein

• Coming of Age in Samoa, ≈1925 - controversies settled or not?

• Immersion, constructing

Karl Marx (1818-1883) Class, Organization of Production, Revolution Founder of latest state religions

• 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

Well studied and documented

• 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

First account by Anaximandros, including sketch of natural selection

• 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.

Based on careful collection of supporting observations (many of which can also be found in Aristotle: Parts of animals)

• 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.

Relied on Eastern knowledge (Persia, India,…)

• 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

Aristotle, Hipparkus and Ptolemai were geocentrists

• 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).

The moon and sun circle around earth, but planets around the sun

• 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’.

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

• 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.

Not unique for Greek philosophers

• 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.

Greek science and literature survived in the Byzantine and Muslim worlds, although not in a central position

• 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

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

• 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

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

• 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.

Politician, social scientist, historian, economist.

• 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’

Mathematical results are certain

• 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

Somewhat difficult to find

• 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

Socrates in Plato’s Meno - arguments less formalized than ‘modern’ proofs. Similar methods applied, e.g., by Pythagoreans

• 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.

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

• 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).

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

• 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:

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).

• 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

The safest and most accepted logical foundation of mathematics

• 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

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)

• 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)

Measure performance asymptotically

• 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.

Graph 3-colorability :

• 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