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CDT 403 Research Methodology in Natural Sciences and Engineering A History of Computing: A History of Ideas Gordana Dodig-Crnkovic Department of Computer Science and Electronic Mälardalen University, Sweden 1

HISTORY OF COMPUTING • • • LEIBNIZ: LOGICAL CALCULUS BOOLE: LOGIC AS ALGEBRA FREGE: MATEMATICS AS LOGIC CANTOR: INFINITY HILBERT: PROGRAM FOR MATHEMATICS GÖDEL: END OF HILBERTS PROGRAM TURING: UNIVERSAL AUTOMATON VON NEUMAN: COMPUTER CONCEPT OF COMPUTING FUTURE COMPUTING 2

SCIENCE The whole is more than the sum of its parts. Aristotle, Metaphysica 3

SCIENCE, RESEARCH, DEVELOPMENT AND TECHNOLOGY Research Development Science Technology 4

COMPUTING Overall structure of the CC 2001 report 5

Technological advancement over the past decade – – – The World Wide Web and its applications Networking technologies, particularly those based on TCP/IP Graphics and multimedia Embedded systems Relational databases Interoperability Object-oriented programming The use of sophisticated application programmer interfaces (APIs) Human-computer interaction Software safety Security and cryptography Application domains 6

Overview of the CS Body of Knowledge – – – – Discrete Structures Programming Fundamentals Algorithms and Complexity Programming Languages Architecture and Organization Operating Systems Net-Centric Computing Human-Computer Interaction Graphics and Visual Computing Intelligent Systems Information Management Software Engineering Social and Professional Issues Computational Science and Numerical Methods 7

LEIBNIZ: LOGICAL CALCULUS Gottfried Wilhelm von Leibniz Born: 1 July 1646 in Leipzig, Saxony (now Germany) Died: 14 Nov 1716 in Hannover, Hanover (now Germany) 8

LEIBNIZ´S CALCULATING MACHINE “For it is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be relegated to anyone else if the machine were used. ” 9

LEIBNIZ´S LOGICAL CALCULUS DEFINITION 3. A is in L, or L contains A, is the same as to say that L can be made to coincide with a plurality of terms taken together of which A is one. B N = L signifies that B is in L and that B and N together compose or constitute L. The same thing holds for larger number of terms. AXIOM 1. B N = N B. POSTULATE. Any plurality of terms, as A and B, can be added to compose A B. AXIOM 2. A A = A. PROPOSITION 5. If A is in B and A = C, then C is in B. PROPOSITION 6. If C is in B and A = B, then C is in A. PROPOSITION 7. A is in A. (For A is in A A (by Definition 3). Therefore (by Proposition 6) A is in A. ) …. PROPOSITION 20. If A is in M and B is in N, then A B is in M N. 10

BOOLE: LOGIC AS ALGEBRA George Boole Born: 2 Nov 1815 in Lincoln, Lincolnshire, England Died: 8 Dec 1864 in Ballintemple, County Cork, Ireland 11

George Boole is famous because he showed that rules used in the algebra of numbers could also be applied to logic. This logic algebra, called Boolean algebra, has many properties which are similar to "regular" algebra. These rules can help us to reduce an expression to an equivalent expression that has fewer operators. 12

Properties of Boolean Operations A AND B A B A OR B A + B 13

FREGE: MATEMATICS AS LOGIC Friedrich Ludwig Gottlob Frege Born: 8 Nov 1848 in Wismar, Mecklenburg-Schwerin (now Germany) Died: 26 July 1925 in Bad Kleinen, Germany 14

The Predicate Calculus (1) In an attempt to realize Leibniz’s ideas for a language of thought and a rational calculus, Frege developed a formal notation (Begriffsschrift). He has developed the first predicate calculus: a formal system with two components: a formal language and a logic. 15

The Predicate Calculus (2) The formal language Frege designed was capable of: expressing – predicational statements of the form ‘x falls under the concept F’ and ‘x bears relation R to y’, etc. , – complex statements such as ‘it is not the case that . . . ’ and ‘if. . . then. . . ’, and – ‘quantified’ statements of the form ‘Some x is such that. . . x. . . ’ and ‘Every x is such that. . . x. . . ’. 16

The Analysis of Atomic Sentences and Quantifier Phrases Fred loves Annie. Therefore, some x is such that x loves Annie. Fred loves Annie. Therefore, some x is such that Fred loves x. Both inferences are instances of a single valid inference rule. 17

Proof As part of his predicate calculus, Frege developed a strict definition of a ‘proof’. In essence, he defined a proof to be any finite sequence of well-formed statements such that each statement in the sequence either is an axiom or follows from previous members by a valid rule of inference. 18

CANTOR: INFINITY Georg Ferdinand Ludwig Philipp Cantor Born: 3 March 1845 in St Petersburg, Russia Died: 6 Jan 1918 in Halle, Germany 19

Infinities Set of integers has an equal number of members as the set of even numbers, squares, cubes, and roots to equations! The number of points in a line segment is equal to the number of points in an infinite line, a plane and all mathematical space! The number of transcendental numbers, values such as and e that can never be the solution to any algebraic equation, were much larger than the 20 number of integers.

Hilbert described Cantor's work as: - ´. . . the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity. ´ 21

HILBERT: PROGRAM FOR MATHEMATICS David Hilbert Born: 23 Jan 1862 in Königsberg, Prussia (now Kaliningrad, Russia) Died: 14 Feb 1943 in Göttingen, Germany 22

Hilbert's program Provide a single formal system of computation capable of generating all of the true assertions of mathematics from “first principles” (first order logic and elementary set theory). Prove mathematically that this system is consistent, that is, that it contains no contradiction. This is essentially a proof of correctness. If successful, all mathematical questions could be established by mechanical computation! 23

GÖDEL: END OF HILBERTS PROGRAM Kurt Gödel Born: 28 April 1906 in Brünn, Austria-Hungary (now Brno, Czech Republic) Died: 14 Jan 1978 in Princeton, New Jersey, USA 24

Incompleteness Theorems 1931 Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme. In any axiomatic mathematical system there are propositions that cannot be proved or disproved within the axioms of the system. In particular the consistency of the axioms cannot be proved. 25

TURING: UNIVERSAL AUTOMATON Alan Mathison Turing Born: 23 June 1912 in London, England Died: 7 June 1954 in Wilmslow, Cheshire, England 26

When war was declared in 1939 Turing moved to work full-time at the Government Code and Cypher School at Bletchley Park. Together with another mathematician W G Welchman, Turing developed the Bombe, a machine based on earlier work by Polish mathematicians, which from late 1940 was decoding all messages sent by the Enigma machines of the Luftwaffe. 27

At the end of the war Turing was invited by the National Physical Laboratory in London to design a computer. His report proposing the Automatic Computing Engine (ACE) was submitted in March 1946. Turing returned to Cambridge for the academic year 1947 -48 where his interests ranged over topics far removed from computers or mathematics, in particular he studied neurology and physiology. 28

1948 Newman (professor of mathematics at the University of Manchester) offered Turing a readership there. Work was beginning on the construction of a computing machine by F C Williams and T Kilburn. The expectation was that Turing would lead the mathematical side of the work, and for a few years he continued to work, first on the design of the subroutines out of which the larger programs for such a machine are built, and then, as this kind of work became standardised, on more general problems of numerical analysis. 29

1950 Turing published Computing machinery and intelligence in Mind 1951 elected a Fellow of the Royal Society of London mainly for his work on Turing machines by 1951 working on the application of mathematical theory to biological forms. 1952 he published the first part of his theoretical study of morphogenesis, the development of pattern and form in living organisms. 30

VON NEUMAN: COMPUTER John von Neumann Born: 28 Dec 1903 in Budapest, Hungary Died: 8 Feb 1957 in Washington D. C. , USA 31

In the middle 30's, Neumann was fascinated by the problem of hydrodynamical turbulence. The phenomena described by non-linear differential equations are baffling analytically and defy even qualitative insight by present methods. Numerical work seemed to him the most promising way to obtain a feeling for the behaviour of such systems. This impelled him to study new possibilities of computation on electronic machines. . . 32

Von Neumann was one of the pioneers of computer science making significant contributions to the development of logical design. Working in automata theory was a synthesis of his early interest in logic and proof theory and his later work, during World War II and after, on large scale electronic computers. Involving a mixture of pure and applied mathematics as well as other sciences, automata theory was an ideal field for von Neumann's wide-ranging intellect. He brought to it many new insights and opened up at least two new directions of research. 33

He advanced theory of cellular automata, advocated the adoption of the bit as a measurement of computer memory, and solved problems in obtaining reliable answers from unreliable computer components. 34

Computer Science Hall of Fame Charles Babbage Julia Robinson Ada Countess of Lovelace Noam Chomsky Axel Thue Juris Hartmanis Stephen Kleene John Brzozowski 35

Computer Science Hall of Fame Richard Karp Stephen Cook Donald Knuth Sheila Greibach Manuel Blum Leonid Levin 36

References • http: //www. cs. ucsb. edu/~mturk/AHOC/schedule. html A History of Computing • http: //blip. tv/file/253405/ A History of Computing: A History of Ideas • http: //ei. cs. vt. edu/~history/TMTCTW. html The Machine That Changed the World • http: //www. alanturing. net/turing_archive/pages/Refer ence%20 Articles/Brief. Histof. Comp. html A Brief History of Computing By Jack Copeland 37

KLASSISKA VETENSKAPER I RELATION TILL ANDRA KUNSKAPSOMRÅDEN Logic & Mathematics Natural Sciences (Physics, Chemistry, Biology, …) Social Sciences (Economics, Sociology, Anthropology, …) The Humanities (Philosophy, History, Linguistics …) Kultur (religion, konst. . ) 38

CROSS DISCIPLINARY RESEARCH FIELDS Our scheme represents the classical groups of sciences. Modern sciences are stretching through several fields of our scheme. Computer science e. g. includes the field of AI that has its roots in mathematical logic and mathematics but uses physics, chemistry and biology and even has parts where medicine and psychology are very important. Examples: Environmental studies, Cognitive sciences, Cultural studies, Policy sciences, Information sciences, Women’s studies, Molecular biology, Philosophy of Computing and Information, 39 Bioinformatics, . .

CROSS DISCIPLINARY RESEARCH FIELDS Disciplinary change is a present day phenomenon. The discovery of DNA in the 1970 s was a ”cognitive revolution” which refigured traditional demarcations of physics, chemistry and biology. New fields of application arose. New discoveries, tools, and approaches change the way that research is conducted at empirical and methodological 40

WHAT IS AFTER ALL THIS THING CALLED SCIENCE The whole is more than the sum of its parts. Aristotle, Metaphysica 41

VETENSKAP vs. FORSKNING Forskning är sökande efter ny kunskap. Forskning är alltså en process. Forskningsresultat kan vara vetenskapligt relevanta. Men inte alltid! Forskning kan leda till ökade kunskaper som inte nödvändigtvis är vetenskapliga. Vetenskapen är resultat av tolkad forskning accepterat av forskarsamhällen, efter kritisk granskning och urval. http: //infovoice. se/fou/index. htm 42

SCIENCE, RESEARCH, DEVELOPMENT AND TECHNOLOGY Research Development Science TECHNOLOGY EXPANDS OUR WAYS OF THINKING ABOUT THINGS, EXPANDS OUR WAYS OF DOING THINGS. Herbert A. Simon Technology 43

POSTMODERNISMENS VETENSKAPSFIENTLIGHET From the mid 1970 s to the late 1990 s a cluster of anti-rationalist ideas became increasingly prevalent among academic sociologists in America, France and Britain. The ideas were variously known as Deconstructionism Sociology of Scientific Knowledge (SSK) Social Constructivism or Science and Technology Studies (STS). The umbrella term for these movements was Postmodernism. The famous Sokal hoax was one of the contributions in the debate, and an reaction to post-modernist views of science. 44

POSTMODERN KONST Postmodernism är en konstinriktning som kom att bli en term under 1960 -talet, men föregångare inom genren dyker upp redan under 1940 -talet. En stor del av den postmodernistiska ideologin handlar om värderelativism, d. v. s. förnekandet av fasta värden. Ofta sysselsätter sig postmodernister med att visa hur till synes motsatta ideologier eller tankesätt ofta bara är två sidor av samma mynt. Humanister har kritiserat postmodernismen för att t. ex. vilja jämställa vetenskapen med religionen, och dess vägran att erkänna några absoluta sanningar. 45

POSTMODERN KONST Den konsekventa värderelativismen har sina första moderna företrädare i form av existensialism, bl. a. Albert Camus och Jean-Paul Sartre, men också av den argentinske novellisten Jorge Luis Borges, som i sina noveller driver tankelekar och idéer nästintill bristningsgränsen. Man talar även om postmodern arkitektur. Denna typ av arkitektur var mycket populär under 1980 -talet och 1990 -talet. 46

POSTMODERNISMENS VETESKAPSFIENTLIGHET All forms of post-modernism were anti-scientific, anti-philosophical and generally highly skeptic about rationalism. The view of science as a search for truths (or approximate truths) about the world was resolutely rejected. According to postmodernists, the natural world has a small or non-existent role in the construction of scientific knowledge. Science was just another social practice, producing ``narrations'' and ``myths'' with no more validity than the myths of pre-scientific peoples. 47

POSTMODERNISMENS VETESKAPSFIENTLIGHET ``The dictum that everything that people do is 'cultural'. . . licenses the idea that every cultural critic can meaningfully analyze even the most intricate accomplishments of art and science. . It is distinctly weird to listen to pronouncements on the nature of mathematics from the lips of someone who cannot tell you what a complex number is!'' Norman Levitt, from "The flight From Science and Reason, " New York Academy of Science. Quoted from p. 183 in the October 11, 1996 Science) 48

POSTMODERNISMENS VETESKAPSFIENTLIGHET “Similarly, and ignoring some self-promoting and cynical rhetoricians, I have never met a serious social critic or historian of science who espoused anything close to a doctrine of pure relativism. The true, insightful, and fundamental statement that science, as a quintessentially human activity, must reflect a surrounding social context does not imply either that no accessible external reality exists, or that science, as a socially embedded and constructed institution, cannot achieve progressively more adequate understanding of nature's facts and mechanisms. '' Stephen J. Gould, From the article: 'Deconstructing the "Science Wars" by Reconstructing an Old Mold' in Science, Jan 14, 2000: 253 -261. 49

VETENSKAPSKRIGET – SCIENCE WARS http: //www. physics. nyu. edu/faculty/sokal/ Higher Superstition: The Academic Left and its Quarrels with Science, by biologist Paul R. Gross and mathematician Norman Levitt. http: //www. math. gatech. edu/~harrell/cult. html http: //skepdic. com/sokal. html The one culture? A conversation about science Red. Jay A Labinger & Harry Collins The University of Chicago Press A book on a theme of science wars: Beyond the Science Wars: The missing discourse about science and society Red. Ullica Segerstråle State University of New York Press After the Science Wars Keith M Ashman & Philip S Baringer, Routledge 50

VETENSKAPSKRIGET – SCIENCE WARS In early 1996 the physicist Alan Sokal created a controversy by publishing two journal articles. The first article, Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity appeared in the journal Social Text. The second article, A Physicist Experiments with Cultural Studies, appeared in the journal Lingua Franca just as issue of Social Text containing the first article came out. It revealed that the first article was in fact a hoax. 51

VETENSKAPSKRIGET – SCIENCE WARS 1996 utbröt i den amerikanska akademiska världen en kontrovers som fick stor medial uppmärksamhet och som gavs den fantasilösa beteckningen "Science Wars", vetenskapskriget. Kontroversen rörde kulturvetenskapernas behandling av naturvetenskaperna, som enligt vissa var alltför negativ eller rent av fientlig. Påstått "postmoderna" forskare anklagades för att relativisera all kunskap, den västerländska kulturen sades vara hotad av en "teoretisk röta" som spreds från Frankrike till okritiska amerikanska lärare och studenter. 52

VETENSKAPSKRIGET – SCIENCE WARS Den naturvetenskapliga forskningen, i synnerhet fysiken, var vid denna tidpunkt politiskt trängd. Kalla krigets slut hade inneburit minskade satsningar på storskaliga forskningsprojekt - bland annat beslöts 1993 att byggandet av ett gigantiskt acceleratorlaboratorium i Texas skulle avbrytas. Här finns kanske en förklaring till att naturvetenskapen nu gick till offensiv mot sina kritiker. Man sökte efter syndabockar och tyckte sig - förutom kreationister, new age-typer och andra förförare av den notoriskt obildade amerikanska allmänheten - ha funnit en grupp femtekolonnare inom universitetet, bestående 53 av kulturvetare med en vänsterpolitisk agenda.

VETENSKAPSKRIGET – SCIENCE WARS Eftersom särskilt fysiken varit nära förknippad med kapprustningen under kalla kriget kunde dispyten lätt tolkas som en konfrontation mellan en kulturkritisk vänster och en naturvetenskaplig höger. Men att en sådan politiska analys i viktiga avseenden är missledande framgick under efterspelet till den så kallade Sokalaffären. 54

VETENSKAPSKRIGET – SCIENCE WARS Den teoretiske fysikern Alan Sokal publicerade 1996 en artikel i den kulturteoretiska tidskriften Social Text där han diskuterade sambanden mellan vänsterradikal "postmodern" filosofi och kvantfysikalisk gravitationsteori. Utgivarna av Social Text förberedde ett specialnummer om vetenskapskriget och valde att där publicera Sokals uppsats. Detta visade sig vara ett misstag, milt sagt. Artikeln var en vetenskaplig camera obscura, en parodi som också innehöll en rad medvetna naturvetenskapliga absurditeter. 55

VETENSKAPSKRIGET – SCIENCE WARS Bland annat diskuterades sambanden mellan kvantfysikalisk gravitationsteori och morfogenetisk fältteori, vilket borde ha gett en stark varningssignal till redaktörerna. Biologen Rupert Sheldrakes teori om morfogenetiska fält (som förmedlar information utan att förbruka energi) stryker all etablerad naturvetenskap mothårs och uppfattas av de flesta som kätteri eller new age-inspirerat trams; den har ingenting med kvantfysik att göra och en professor i teoretisk fysik skulle inte ta i den med tång. . Sokal ville egentligen bevisa att en rad välkända filosofer och litteraturteoretiker som diskuterar naturvetenskapen befinner sig på samma parodiska nivå som hans egen artikel och tas på allvar enbart på grund av den "postmoderna" kulturvetenskapens blinda auktoritetstro. 56

VETENSKAPSKRIGET – SCIENCE WARS Detta gjorde han genom att späcka artikeln med ordagranna citat från auktoriteter som Jacques Derrida och Jacques Lacan, utvalda enbart för att de talade nonsens i naturvetenskapliga frågor. Här var poängen alltså att inte heller kulturvetarnas teoretiska husgudar begriper den naturvetenskap de ibland kritiserar och ibland försöker glänsa med. När bluffen avslöjades blev den mediala uppmärksamheten enorm. Tidskriftens försvarare gjorde ont värre genom att fara ut i anklagelser mot politiskt konservativa naturvetare, och den kända filosofen Sandra Harding gick så långt att hon utnämnde dem som hade synpunkter på den kulturteoretiska analysen av naturvetenskapen till representanter för den "antidemokratiska 57 högern".

VETENSKAPSKRIGET – SCIENCE WARS Två begrepp som har stått i centrum för diskussionen är "socialkonstruktivism" och "relativism". De används omväxlande som skällsord, retoriska tillhyggen och programförklaringar. Socialkonstruktivism betecknar en tendens att se bland annat naturvetenskapen som en kulturprodukt, till exempel genom att med antropologiska metoder analysera sambandet mellan sociala strukturer (inte minst maktstrukturer) och kunskapssystem. Relativism innebär i filosofisk mening ett ifrågasättande av föreställningen att kunskap kan vara objektiv och 58

VETENSKAPSKRIGET – SCIENCE WARS Men relativismen kan också fungera som en vetenskaplig metod, vilket kunskapssociologer gärna framhåller. Den metodiska relativismen gör inte anspråk på att lösa filosofiska problem utan används vid detaljerade fallstudier av hur vetenskaplig kunskapsproduktion faktiskt går till. Metoden innebär att man ser på vetenskapliga kontroverser som processer där utslaget inte fälls av naturen utan av mekanismer som har att göra med vetenskapens sociala system. Detta betyder inte att det inte finns någon sanning, bara att sanningen inte bryter fram självklart, av egen kraft. 59

VETENSKAPSKRIGET – SCIENCE WARS När den kände biologen Richard Dawkins säger att ingen är socialkonstruktivist i ett flygplan på 30 000 fots höjd (för där måste man lita på att de vetenskapliga teorierna bakom flygplanskonstruktionen är sanna), eller när Sokal erbjuder relativisterna att testa gravitationslagens giltighet från fönstret i hans lägenhet på tjugoförsta våningen för de ner diskussionen till en låg nivå. Den samhällsvetenskapliga och humanistiska (snarare än "postmoderna") forskning som kan betecknas som socialkonstruktivistisk förnekar inte tyngdkraftens existens eller att flygplan oftast når sin destination. Dess målsättning är att analysera vetenskaplig utveckling i relation till ett samhälle som i allt högre grad blivit en produkt av denna utveckling. Naturvetare och många andra borde ha intresse av att delta i det arbetet och inte avfärda det med glåpord. Detta även om vissa populära uppfattningar om det vetenskapliga framstegets natur då kanske 60 måste ifrågasättas.

VETENSKAPSKRIGET – SCIENCE WARS På senare tid har en rad böcker om vetenskapskriget utkommit, av vilka den bästa är vetenskapssociologen Harry Collins och kemisten Jay Labingers "The One Culture? " Där förs en sansad dialog mellan naturvetare och kulturvetare. Bland annat framför den kände fysikern Steven Weinberg ett argument som tycks tala till den metodiska relativismens nackdel. En historiker som till exempel vill förstå hur det gick till när J J Thomson vid sekelskiftet 1900 bestämde relationen mellan elektronens laddning och massa (och därmed på ett avgörande sätt bidrog till att påvisa existensen av denna elementarpartikel) har enligt Weinberg nytta av modern kunskap om dessa värden. Det visar sig nämligen att Thomson sållade bort mätningar som i själva verket låg närmare de riktiga värdena än dem han publicerade. Detta betyder enligt Weinberg att Thomson troligen lät sig påverkas av utomvetenskapliga faktorer (som lurade honom att välja fel värden), vilket borde vara en intressant historisk slutsats. 61

VETENSKAPSKRIGET – SCIENCE WARS Historikern vill bland mycket annat förstå hur Thomson resonerade när han planerade sitt experiment, byggde apparaturen, mätte och sållade bland data. Att han ofta valde "sämre" mätvärden säger oss inget om vad som eventuellt styrde hans bedömningar eftersom för honom (och oss) okända systematiska fel mycket väl kan ha förekommit. Banbrytande vetenskapliga upptäckter som Thomsons innehåller normalt stora tolkningssvårigheter och är tekniskt osäkra. Analys av sådant arbete utifrån senare tiders mer sofistikerade tekniska kunnande blir helt enkelt orättvis och skymmer den historiska förståelsen. 62

VETENSKAPSKRIGET – SCIENCE WARS De vetenskapssociologiska frontfigurerna Harry Collins och Trevor Pinch brukar säga att den metodiska relativismen är nödvändig för en demokratisk och upplyst diskussion av brännbara vetenskapliga frågor. Politiska beslutsfattare och medborgare måste ta ställning till växthuseffektens eventuella existens, kärnkraftens eventuella risker, "galna-kosjukans" eventuella överföring från kreatur till människa via hamburgare. Detta utan tillgång till enstämmig expertrådgivning utifrån etablerad sanning. I sådana lägen hjälper det att känna till något om de sociala mekanismer som verkar inom vetenskapen 63 när osäkerheten är stor, när expert står mot expert.

VETENSKAPSKRIGET – SCIENCE WARS Den metodologiska relativismen bör också kunna fungera utmärkt som ett verktyg för att mer allmänt bedöma vetenskaplig och teknisk verksamhet. Utvärdering i efterhand kan bli djupt orättvis om den görs utifrån segrarnas historieskrivning. Den bör utföras med precis den "blindhet" för naturvetenskaplig sanning som den metodiska relativismen eftersträvar. Annars blir efterklokheten vår enda klokhet. http: //www. dn. se/DNet/jsp/polopoly. jsp? d=1194&a=589 64 62

VETENSKAPSKRIGET – SCIENCE WARS “But why did I do it? I confess that I'm an unabashed Old Leftist who never quite understood how deconstruction was supposed to help the working class. And I'm a stodgy old scientist who believes, naively, that there exists an external world, that there exist objective truths about that world, and that my job is to discover some of them. --Allan Sokal “ 65

VETENSKAPSKRIGET – SCIENCE WARS “To test the prevailing intellectual standards, I decided to try a modest (though admittedly uncontrolled) experiment: Would a leading North American journal of cultural studies - whose editorial collective includes such luminaries as Fredric Jameson and Andrew Ross - publish an article liberally salted with nonsense if (a) it sounded good and (b) it flattered the editors' ideological preconceptions? “ (Sokal) 66

SCIENCE AND SOCIETY THE TRIPLE HELIX PARADIGM SOCIETY CULTURE SCIENCES & HUMANITIES 67

THE UNIVERSITY OF THE FUTURE THE TRANSFORMATION OF “IVORY TOWER” TO ENTERPRENEURIAL PARADIGM Increasingly knowledge-based societies. The triple helix model: – ACADEMIC – INDUSTRY – GOVERMENT 68

SOCIETAL ASPECTS OF SCIENCE As the 21 st century begins we must embrace the societal aspects of science as well as the applications of science and the insights science provides for foundational issues. It is necessary to bridge the increasing gap between the sciences and the humanities by promoting rational and analytical discussions of central issues of concern to scientists and other scholars, and to the public at large. 69

SOCIETAL ASPECTS OF SCIENCE SUSTAINABLE DEVELOPMENT PROJECT “If we consider Galileo alone is his cell muttering, ‘and yet it moves, ’ with the recent meeting at Kyoto–where heads of states, lobbyists, and scientists were assembled together in the same place to discuss the Earth–we measure the difference between science and research” Bruno Latour 70

THE SCIENTIFIC METHOD EXISTING THEORIES AND OBSERVATIONS HYPOTHESIS PREDICTIONS 2 3 Hypotesen Hypothesis måste must be justeras adjusted 1 Hypothesis must be redefined SELECTION AMONG COMPETING THEORIES TESTS AND NEW OBSERVATIONS 6 4 Consistency achieved EXISTING THEORY CONFIRMED The hypotetico-deductive cycle (within a new context) or NEW THEORY PUBLISHED The scientific-community cycle 5 71

SOCIETAL ASPECTS OF SCIENCE Further reading: http: //www. sciencemag. org/feature/data/150 essay. shl Essays on Science and Society Science magazine 72

ETHICAL QUESTIONS: PRECAUTIONARY PRINCIPLE (1) When an activity raises threats of harm to human health or the environment, precautionary measures should be taken even if some cause and effect relationships are not fully established scientifically. In this context the proponent of an activity, rather than the public, should bear the burden of proof. http: //www. idt. mdh. se/kurser/cd 5590/ CD 5590 Professional Ethics in Science and Engineering 73

PRECAUTIONARY PRINCIPLE (2) People have a duty to take anticipatory action to prevent harm. The burden of proof of harmlessness of a new technology, process, activity, or chemical lies with the proponents, not with the general public. 74

PRECAUTIONARY PRINCIPLE (3) Before using a new technology, process, or chemical, or starting a new activity, people have an obligation to examine "a full range of alternatives" including the alternative of doing nothing. Decisions applying the precautionary principle must be open, informed, and democratic and must include affected parties. 75

WHAT IS SCIENCE? Concentric Rinds (Concentric Space Filling/Regular Sphere Division). Maurits Cornelis Escher 76

Teknologi och Framsteg - Transport 77

Teknologi och Framsteg Beam me up Scotty next? 78

Is There Historical Progress of Science and Technology? progress • Movement, as toward a goal; advance. • Development or growth: students who show progress. • Steady improvement, as of a society or civilization: a believer in human progress. See Synonyms at development. • To advance; proceed: Work on the new building progressed at a rapid rate. • To advance toward a higher or better stage; improve steadily: as medical technology progresses. • Idiom: in progress – Going on; under way: a work in progress. 79

Is There Historical Progress of Science and Technology? Synonyms: development, evolution, progress These nouns mean a As we learn from progression from a simpler or lower to a more advanced, mature, or complex form or stage the history of science, both science and technology started from very simple form to get complex form of today – so progress&development is a historical fact. 80

IS ANY PROGRESS NECESSARILY GOOD? • Can progress be bad? • What might be the consequences of scientific progress? • What would be the alternative to the high technology society based on advanced science? • Is there any known example in history where society deliberately moved back to historical forms of living (lower technology)? 81

POSTMODERNISMEN ÄR DÖD. . . Interdisciplinarity and complexity: An evolving relationship* Postmodernismen är död. Vad kommer nu? In recent decades, the ideas of interdisciplinarity and complexity have become increasingly entwined. This convergence invites an exploration of the links and their implications. The implications include: the nature of knowledge, the structure of the university, the character of problem solving, the dialogue between science and humanities, and * Julie Thompson Klein, http: //emergence. org/ECO_site/ECO_Archive/Issue_6_12/Klein. pdf 82

EFTER POSTMODERNISMENS DÖD. . . Interdisciplinarity and Complexity • Relationships between economy, politics, law, media, and science • Emergent phenomena with nonlinear dynamics. • Effects have positive and negative feedback to causes, uncertainties continue to arise, and unexpected results occur. • ‘Reality’ is a nexus of interrelated phenomena that are not reducible to a single dimension (Goorhuis, 83

EFTER POSTMODERNISMENS DÖD. . . Interdisciplinarity and Complexity • The new discourse centers on problem- and solutionoriented research incorporating participatory approaches: – problem-oriented, – beyond disciplinarity, – practice-oriented, – participatory, and – process-oriented. 84

EFTER POSTMODERNISMENS DÖD. . . Interdisciplinarity and Complexity • Interdisciplinarity is necessitated by complexity. The nature of complex systems, provides a comprehensive rationale for interdisciplinary study, unifies the apparently divergent approaches, and offers guidance for criteria in each step of the integrative process. • The ultimate objective of any interdisciplinary inquiry becomes understanding the portion of the world modeled by a particular complex system. (William Newell) 85

Church-Turing Thesis* *Source: Stanford Encyclopaedia of Philosophy 86

A Turing machine is an abstract representation of a computing device. It is more like a computer program (software) than a computer (hardware). 87

LCMs [Logical Computing Machines: Turing’s expression for Turing machines] were first proposed by Alan Turing, in an attempt to give a mathematically precise definition of "algorithm" or "mechanical procedure". 88

• • The Church-Turing thesis concerns an effective or mechanical method in logic and mathematics. 89

• A method, M, is called ‘effective’ or ‘mechanical’ just in case: 1. M is set out in terms of a finite number of exact instructions (each instruction being expressed by means of a finite number of symbols); M will, if carried out without error, always produce the desired result in a finite number of steps; M can (in practice or in principle) be carried out by a human being unaided by any machinery except for paper and pencil; M demands no insight or ingenuity on the part of the human being carrying it out. 2. 3. 4. 90

• Turing’s thesis: LCMs [logical computing machines; TMs] can do anything that could be described as "rule of thumb" or "purely mechanical". (Turing 1948) • He adds: This is sufficiently well established that it is now agreed amongst logicians that "calculable by means of an LCM" is the correct accurate rendering of such phrases. 91

• Turing introduced this thesis in the course of arguing that the Entscheidungsproblem, or decision problem, for the predicate calculus - posed by Hilbert in 1928 was unsolvable. 92

• Church’s account of the Entscheidungsproblem • By the Entscheidungsproblem of a system of symbolic logic is here understood the problem to find an effective method by which, given any expression Q in the notation of the system, it can be determined whether or not Q is provable in the system. • 93

• The truth table test is such a method for the propositional calculus. • Turing showed that, given his thesis, there can be no such method for the predicate calculus. 94

• Turing proved formally that there is no TM which can determine, in a finite number of steps, whether or not any given formula of the predicate calculus is a theorem of the calculus. • So, given his thesis that if an effective method exists then it can be carried out by one of his machines, it follows that there is no such method to be found. 95

• Church’s thesis: A function of positive integers is effectively calculable only if recursive. 96

Misunderstandings of the Turing Thesis • Turing did not show that his machines can solve any problem that can be solved "by instructions, explicitly stated rules, or procedures" and nor did he prove that a universal Turing machine "can compute any function that any computer, with any architecture, can compute". 97

• Turing proved that his universal machine can compute any function that any Turing machine can compute; and he put forward, and advanced philosophical arguments in support of, thesis here called Turing’s thesis. 98

• A thesis concerning the extent of effective methods - procedures that a human being unaided by machinery is capable of carrying out - has no implication concerning the extent of the procedures that machines are capable of carrying out, even machines acting in accordance with ‘explicitly stated rules’. 99

• Among a machine’s repertoire of atomic operations there may be those that no human being unaided by machinery can perform. 100

• Turing introduces his machines as an idealised description of a certain human activity, the one of numerical computation, which until the advent of automatic computing machines was the occupation of many thousands of people in commerce, government, and research establishments. • 101

• Turing’s "Machines". These machines are humans who calculate. (Wittgenstein) • A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine. (Turing) 102

• The Entscheidungsproblem is the problem of finding a humanly executable procedure of a certain sort, and Turing’s aim was precisely to show that there is no such procedure in the case of predicate logic. 103

Other Models of Computation 104

Models of Computation • Turing Machines • Recursive Functions • Post Systems • Rewriting Systems 105

Turing’s Thesis A computation is mechanical if and only if it can be performed by a Turing Machine. Church’s Thesis (extended) All models of computation are equivalent. 106

Post Systems • Axioms • Productions Very similar to unrestricted grammars. 107

Theorem: A language is recursively enumerable if and only if it is generated by a Turing Machine. 108

Theorem: A language is recursively enumerable if and only if it is generated by a recursive function. 109

Post Systems Example: Unary Addition Axiom: Productions: 110

A production: 111

Post systems are good for proving mathematical statements from a set of Axioms. 112

Theorem: A language is recursively enumerable if and only if it is generated by a Post system. 113

Rewriting Systems They convert one string to another • Matrix Grammars • Markov Algorithms • Lindenmayer-Systems (L-Systems) Very similar to unrestricted grammars. 114

Matrix Grammars Example: Derivation: A set of productions is applied simultaneously. 115

116

Theorem: A language is recursively enumerable if and only if it is generated by a Matrix grammar. 117

Markov Algorithms Grammars that produce Example: Derivation: 118

In general: 119

Theorem: A language is recursively enumerable if and only if it is generated by a Markov algorithm. 120

Lindenmayer-Systems They are parallel rewriting systems Example: Derivation: 121

Lindenmayer-Systems are not general as recursively enumerable languages Extended Lindenmayer-Systems: context Theorem: A language is recursively enumerable if and only if it is generated by an Extended Lindenmayer-System. 122

L-System Example: Fibonacci numbers • Consider the following simple grammar: • • • variables : A B constants : none start: A rules: A B AB 123

• This L-system produces the following sequence of strings. . . • • Stage 0 : A Stage 1 : B Stage 2 : AB Stage 3 : BAB Stage 4 : ABBAB Stage 5 : BABABBAB Stage 6 : ABBABBAB Stage 7 : BABABBABBAB 124

• If we count the length of each string, we obtain the Fibonacci sequence of numbers : • 1 1 2 3 5 8 13 21 34. . 125

Example - Algal growth The figure shows the pattern of cell lineages found in the alga Chaetomorpha linum. To describe this pattern, we must let the symbols denote cells in different states, rather than different structures. 126

• This growth process can be generated from an axiom A and growth rules • • • A DB B C C D D E E A 127

Here is the pattern generated by this model. It matches the arrangement of cells in the original alga. • Stage 0 : A • • • Stage 1 : D B Stage 2 : E C Stage 3 : A D Stage 4 : D B E Stage 5 : E C A Stage 6 : A D D B Stage 7 : D B E E C Stage 8 : E C A A D Stage 9 : A D D B E Stage 10 : D B E E C A Stage 11 : E C A A D D B 128

Example - a compound leaf (or branch) • • • • Leaf 1 { ; Name of the l-system, "{" indicates start ; Compound leaf with alternating branches, angle 8 ; Set angle increment to (360/8)=45 degrees axiom x ; Starting character string a=n ; Change every "a" into an "n" n=o ; Likewise change "n" to "o" etc. . . o=p p=x b=e e=h h=j j=y x=F[+A(4)]Fy ; Change every "x" into "F[+A(4)]Fy" y=F[-B(4)]Fx ; Change every "y" into "F[-B(4)]Fx" [email protected] 18 [email protected] 1. 18 } ; final } indicates end 129

http: //www. xs 4 all. nl/~cvdmark/tutor. html (Cool site with animated L-systems) 130

Here is a series of forms created by slowly changing the angle parameter. lsys 00. ls Check the rest of the Gallery of L-systems: http: //home. wanadoo. nl/laurens. lapre/ 131

Plant Reception Environment Response Internal processes Response Reception A model of a horse chestnut tree inspired by the work of Chiba and Takenaka. Here branches compete for light from the sky hemisphere. Clusters of leaves cast shadows on branches further down. An apex in shade does not produce new branches. An existing branch whose leaves do not receive enough light dies and is shed from the tree. In such a manner, the competition for light controls the density of branches in the tree crowns. 132

Plant Environment Reception Response Internal processes Response Reception 133

Apropos adaptive reactive systems: "What's the color of a chameleon put onto a mirror? " -Stewart Brand (Must be possible to verify experimentally, isn’t it? ) 134

Fundamental Limits of Computation 135

Biological Computing 136

DNA Based Computing • Despite their respective complexities, biological and mathematical operations have some similarities: • The very complex structure of a living being is the result of applying simple operations to initial information encoded in a DNA sequence (genes). • All complex math problems can be reduced to simple operations like addition and subtraction. 137

• For the same reasons that DNA was presumably selected for living organisms as a genetic material, its stability and predictability in reactions, DNA strings can also be used to encode information for mathematical systems. 138

The Hamiltonian Path Problem • The objective is to find a path from start to end going through all the points only once. • This problem is difficult for conventional (serial logic) computers because they must try each path one at a time. It is like having a whole bunch of keys and trying to see which fits a lock. 139

• Conventional computers are very good at math, but poor at "key into lock" problems. DNA based computers can try all the keys at the same time (massively parallel) and thus are very good at key-into-lock problems, but much slower at simple mathematical problems like multiplication. • The Hamiltonian Path problem was chosen because every keyinto-lock problem can be solved as a Hamiltonian Path problem. 140

Solving the Hamiltonian Path Problem 1. 2. 3. 4. 5. Generate random paths through the graph. Keep only those paths that begin with the start city (A) and conclude with the end city (G). Because the graph has 7 cities, keep only those paths with 7 cities. Keep only those paths that enter all cities at least once. Any remaining paths are solutions. 141

Solving the Hamiltonian Path Problem • The key to solving the problem was using DNA to perform the five steps in the above algorithm. • These interconnecting blocks can be used to model DNA: • 142

• DNA tends to form long double helices: • • The two helices are joined by "bases", represented here by coloured blocks. Each base binds only one other specific base. In our example, we will say that each coloured block will only bind with the same colour. For example, if we only had red blocks, they would form a long chain like this: • • Any other colour will not bind with red: • • • 143

Programming with DNA • Step 1: Create a unique DNA sequence for each city A through G. For each path, for example, from A to B, create a linking piece of DNA that matches the last half of A and first half of B: • • Here the red block represents city A, while the orange block represents city B. The half-red half-orange block connecting the two other blocks represents the path from A to B. • In a test tube, all the different pieces of DNA will randomly link with each other, forming paths through the graph. 144

• Step 2: Because it is difficult to "remove" DNA from the solution, the target DNA, the DNA which started at A and ended at G was copied over and over again until the test tube contained a lot of it relative to the other random sequences. • This is essentially the same as removing all the other pieces. Imagine a sock drawer which initially contains one or two coloured socks. If you put in a hundred black socks, chances are that all you will get if you reach in is black socks! 145

• Step 3: Going by weight, the DNA sequences which were 7 "cities" long were separated from the rest. • A "sieve" was used which allows smaller pieces of DNA to pass through quickly, while larger segments are slowed down. The procedure used actually allows you to isolate the pieces which are precisely 7 cities long from any shorter or longer paths. 146

• Step 4: To ensure that the remaining sequences went through each of the cities, "sticky" pieces of DNA attached to magnets were used to separate the DNA. • The magnets were used to ensure that the target DNA remained in the test tube, while the unwanted DNA washed away. First, the magnets kept all the DNA which went through city A in the test tube, then B, then C, and D, and so on. In the end, the only DNA which remained in the tube was that which went through all seven cities. 147

• Step 5: All that was left was to sequence the DNA, revealing the path from A to B to C to D to E to F to G. 148

Advantages • The above procedure took approximately one week to perform. Although this particular problem could be solved on a piece of paper in under an hour, when the number of cities is increased to 70, the problem becomes too complex for even a supercomputer. • While a DNA computer takes much longer than a normal computer to perform each individual calculation, it performs an enormous number of operations at a time (massively parallel). 149

• DNA computers also require less energy and space than normal computers. 1000 litres of water could contain DNA with more memory than all the computers ever made, and a pound of DNA would have more computing power than all the computers ever made. 150

The Future • DNA computing is less than ten years old and for this reason, it is too early for either great optimism of great pessimism. • Early computers such as ENIAC filled entire rooms, and had to be programmed by punch cards. Since that time, computers have become much smaller and easier to use. 151

• DNA computers will become more common for solving very complex problems. • Just as DNA cloning and sequencing were once manual tasks, DNA computers will also become automated. In addition to the direct benefits of using DNA computers for performing complex computations, some of the operations of DNA computers already have, and perceivably more will be used in molecular and biochemical research. • Read more at: • http: //www. cis. udel. edu/~dna 3/DNA/dnacomp. html; http: //dna 2 z. com/dnacpu/dna. html; • • http: //www. liacs. nl/home/pier/web. Pages. DNA; http: //www. corninfo. chem. wisc. edu/writings/DNAcomputing. html; http: //www. comp. leeds. ac. uk/seth/ar 35/ 152

Quantum Computing 153

• Today: fraction of micron (10 -6 m) wide logic gates and wires on the surface of silicon chips. • Soon they will yield even smaller parts and inevitably reach a point where logic gates are so small that they are made out of only a handful of atoms. • 1 nm = 10 -9 m 154

• On the atomic scale matter obeys the rules of quantum mechanics, which are quite different from the classical rules that determine the properties of conventional logic gates. • So if computers are to become smaller in the future, new, quantum technology must replace or supplement what we have now. 155

What is quantum mechanics? • The deepest theory of physics; the framework within which all other current theories, except the general theory of relativity, are formulated. Some of its features are: • Quantisation (which means that observable quantities do not vary continuously but come in discrete chunks or 'quanta'). This is the one that makes computation, classical or quantum, possible at all. 156

• Interference (which means that the outcome of a quantum process in general depends on all the possible histories of that process). • This is the feature that makes quantum computers qualitatively more powerful than classical ones. 157

• Entanglement (Two spatially separated and non-interacting quantum systems that have interacted in the past may still have some locally inaccessible information in common – information which cannot be accessed in any experiment performed on either of them alone. ) • This is the one that makes quantum cryptography possible. 158

• The discovery that quantum physics allows fundamentally new modes of information processing has required the existing theories of computation, information and cryptography to be superseded by their quantum generalisations. 159

• Let us try to reflect a single photon off a half-silvered mirror i. e. a mirror which reflects exactly half of the light which impinges upon it, while the remaining half is transmitted directly through it. • It seems that it would be sensible to say that the photon is either in the transmitted or in the reflected beam with the same probability. 160

• Indeed, if we place two photodetectors behind the half-silvered mirror in direct lines of the two beams, the photon will be registered with the same probability either in the detector 1 or in the detector 2. • Does it really mean that after the half-silvered mirror the photon travels in either reflected or transmitted beam with the same probability 50%? • No, it does not ! In fact the photon takes `two paths at once'. 161

This can be demonstrated by recombining the two beams with the help of two fully silvered mirrors and placing another half-silvered mirror at their meeting point, with two photodectors in direct lines of the two beams. With this set up we can observe a truly amazing quantum interference phenomenon. 162

• If it were merely the case that there were a 50% chance that the photon followed one path and a 50% chance that it followed the other, then we should find a 50% probability that one of the detectors registers the photon and a 50% probability that the other one does. • However, that is not what happens. If the two possible paths are exactly equal in length, then it turns out that there is a 100% probability that the photon reaches the detector 1 and 0% probability that it reaches the other detector 2. Thus the photon is certain to strike the detector 1! 163

It seems inescapable that the photon must, in some sense, have actually travelled both routes at once for if an absorbing screen is placed in the way of either of the two routes, then it becomes equally probable that detector 1 or 2 is reached. 164

• Blocking off one of the paths actually allows detector 2 to be reached. With both routes open, the photon somehow knows that it is not permitted to reach detector 2, so it must have actually felt out both routes. • It is therefore perfectly legitimate to say that between the two half-silvered mirrors the photon took both the transmitted and the reflected paths. 165

• Using more technical language, we can say that the photon is in a coherent superposition of being in the transmitted beam and in the reflected beam. • In much the same way an atom can be prepared in a superposition of two different electronic states, and in general a quantum two state system, called a quantum bit or a qubit, can be prepared in a superposition of its two logical states 0 and 1. Thus one qubit can encode at a given moment of time both 0 and 1. 166

• In principle we know how to build a quantum computer; we can start with simple quantum logic gates and try to integrate them together into quantum circuits. • A quantum logic gate, like a classical gate, is a very simple computing device that performs one elementary quantum operation, usually on two qubits, in a given period of time. • Of course, quantum logic gates are different from their classical counterparts because they can create and perform operations on quantum superpositions. 167

• So the advantage of quantum computers arises from the way they encode a bit, the fundamental unit of information. • The state of a bit in a classical digital computer is specified by one number, 0 or 1. • An n-bit binary word in a typical computer is accordingly described by a string of n zeros and ones. 168

• A quantum bit, called a qubit, might be represented by an atom in one of two different states, which can also be denoted as 0 or 1. • Two qubits, like two classical bits, can attain four different welldefined states (0 and 0, 0 and 1, 1 and 0, or 1 and 1). 169

• But unlike classical bits, qubits can exist simultaneously as 0 and 1, with the probability for each state given by a numerical coefficient. • Describing a two-qubit quantum computer thus requires four coefficients. In general, n qubits demand 2 n numbers, which rapidly becomes a sizable set for larger values of n. 170

• For example, if n equals 50, about 1015 numbers are required to describe all the probabilities for all the possible states of the quantum machine--a number that exceeds the capacity of the largest conventional computer. • A quantum computer promises to be immensely powerful because it can be in multiple states at once (superposition) -- and because it can act on all its possible states simultaneously. • Thus, a quantum computer could naturally perform myriad operations in parallel, using only a single processing unit. 171

• The most famous example of the extra power of a quantum computer is Peter Shor's algorithm for factoring large numbers. • Factoring is an important problem in cryptography; for instance, the security of RSA public key cryptography depends on factoring being a hard problem. • Despite much research, no efficient classical factoring algorithm is known. 172

• However if we keep on putting quantum gates together into circuits we will quickly run into some serious practical problems. • The more interacting qubits are involved the harder it tends to be to engineer the interaction that would display the quantum interference. • Apart from the technical difficulties of working at single-atom and single-photon scales, one of the most important problems is that of preventing the surrounding environment from being affected by the interactions that generate quantum superpositions. 173

• The more components the more likely it is that quantum computation will spread outside the computational unit and will irreversibly dissipate useful information to the environment. • This process is called decoherence. Thus the race is to engineer sub-microscopic systems in which qubits interact only with themselves but not with the environment. 174

But, the problem is not entirely new! Remember STM? (Scanning Tuneling Microscopy ) STM was a Nobel Prize winning invention by Binning and Rohrer at IBM Zurich Laboratory in the early 1980 s 175

• Title : Quantum Corral • Media : Iron on Copper (111) 176

• Scientists discovered a new method for confining electrons to artificial structures at the nanometer length scale. • Surface state electrons on Cu(111) were confined to closed structures (corrals) defined by barriers built from Fe adatoms. T • The barriers were assembled by individually positioning Fe adatoms using the tip of a low temperature scanning tunnelling microscope (STM). A circular corral of radius 71. 3 Angstrom was constructed in this way out of 48 Fe adatoms. 177

The standing-wave patterns in the local density of states of the Cu(111) surface. These spatial oscillations are quantummechanical interference patterns caused by scattering of the twodimensional electron gas off the Fe adatoms and point defects. 178

What will quantum computers be good at? • The most important applications currently known: • Cryptography: perfectly secure communication. • Searching, especially algorithmic searching (Grover's algorithm). • Factorising large numbers very rapidly • (Shor's algorithm). • Simulating quantum-mechanical systems efficiently 179

What is Computation? • Theoretical Computer Science 317 (2004) • Burgin, M. , Super-Recursive Algorithms, Springer Monographs in Computer Science, 2005, ISBN: 0 -387 -95569 -0 • Minds and Machines (1994, 4, 4) “What is Computation? ” • Journal of Logic, Language and Information (Volume 12 No 4 2003) What is information? 180

• Theoretical Computer Science, 2004 Volume: 317 issue: 1 -3 Three aspects of super-recursive algorithms and hypercomputation or finding black swans Burgin, Klinger Hypercomputation • Toward a theory of intelligence Kugel • Algorithmic complexity of recursive and inductive algorithms Burgin • Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines Wiedermann • Experience, generations, and limits in machine learning Burgin, Klinger • Hypercomputation with quantum adiabatic processes Kieu • Super-tasks, accelerating Turing machines and uncomputability Shagrir • Natural computation and non-Turing models of computation Mac. Lennan • Continuous-time computation with restricted integration capabilities Campagnolo • The modal argument for hypercomputing minds Bringsjord, Arkoudas • Hypercomputation by definition Wells • The concept of computability Cleland • Uncomputability: the problem of induction internalized Kelly • Hypercomputation: philosophical issues Copeland 181