Sequence of Topics. 1. The Nature of Truth. 2. Biography of Alan Turing ( ) 3. The Church-Turing Thesis. 4. Interactive Computing

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2 Sequence of Topics 1. The Nature of Truth 2. Biography of Alan Turing ( ) 3. The Church-Turing Thesis 4. Interactive Computing 5. Rationalism Versus Empiricism 6. Can Machines Think? 7. Stephen Hawking (b. 1942) 8. From Physics to Computer Science 2

3 The Nature of Truth Erroneous definitions of truth have hurt society in politics, religion, and science Political failure under the French Revolution, Russian Communism, German Nazism Religious failure under Copernicus, Galileo, Darwin Scientific failure in physics (Newton), mathematics (Hilbert), computing (Turing) Physics: Newton, Einstein, quantum theory, string theory, Stephen Hawking Evolving theories expand the scope of physics, but fail to be completely true Theory of everything (TE): complete truth of discipline, no further changes necessary Einstein spent many years on TE for physics, but failed to define a true (accurate) TE String theory: attempted modern TE (1970s), failed (inaccurate) TE Stephen Hawking s final book (2010) proposes a questionable TE called M- Theory Mathematics: Hilbert (1900) proposed that all math theorems are provable by logic Gödel (1931) proved Hilbert was wrong; rejected his TE based on provability by logic Computers: Turing (1936) article shows that Turing Machines are wideranging in problem-solving but cannot solve all math problems (e.g. the halting problem). Turing excludes theory of everything for computers. Some experts claim that TMs determine a TE, but I believe they are wrong. Scientists have great scientific understanding, but cannot define a Theory of Everything No TE for physics, mathematics or computing has ever been defined; maybe it is not possible TMs are an incomplete model of computer problem-solving Computing is an incomplete model of universal problem-solving Information processing is a more complete model of computing But there is no Theory of Everything for information processing 3

4 Biography of Alan Turing ( ) Math undergraduate at King s College, Cambridge ( ). Graduated with distinction, Was made a Fellow of Kings in Attended lectures by Max Newman about logic and computing ( ) 1936 paper: On Computable Numbers with an application to the Entscheidungsproblem Princeton Institute ( ): worked with Church and Von Neumann on improved modes of computation; returned to England at end of 1938 Bletchley Park ( ): worked during World War Two on decrypting German Enigma code, thus helping to locate and sink German submarines. Was awarded OBE (Order of the British Empire) National Physical Laboratory ( ): worked on an Automatic Computing Engine (ACE) but failed because his model for ACE was too ambitious Moved to Manchester University in 1949 to join his colleague Max Newman. Introduced the Turing test to prove that computers could model humans, did research in mathematical biology, but did not redesign the ACE or build a computing machine. In 1951, Turing was prosecuted for homosexual activity, and to avoid imprisonment he agreed to take estrogen to try to counteract his sexual orientation. He committed suicide in (Britain decriminalized homosexuality by an Act of Parliament in 1967.) I never met Turing, but often discussed him with my supervisor Maurice Wilkes (designer of the EDSAC) who believed Turing was a brilliant theorist but could not build a computer because he was a weak supervisor of others. Turing s death in June 1954 occurred during the week of my Cambridge final examinations, and Wilkes informed me of his death at the time 4

5 The Church-Turing Thesis (1938) Thesis was defined during 1938 while Turing was working with Church at Princeton Church-Turing Thesis (CTT): All effective algorithms for computing mathematical functions can be computed by Turing machines or by the lambda calculus. Effective computability (as defined by Church and Turing): Turing machines, the lambda calculus, and recursive functions are three equivalent modes of effective computation The CTT was extended in the 1960s (after Turing s death) to a stronger thesis Strong Church-Turing Thesis (SCT): Turing machines can compute anything that can be computed by any computer (well beyond computable functions or algorithms) In my view, SCT is incorrect: it extends computability unnecessarily beyond computable functions and beyond algorithmic computation SCT was nevertheless widely accepted as a mathematical basis for all computation, and contributed to the high-level regard for Turing as the primary founder of the discipline of computer science. I personally believe that Turing s contribution to CS was substantial, but that his contribution has been overrated SCT was a failed attempt to create a theory of everything for computer science. Choice of mathematics as a complete basis for all computing was considered more important (especially by mathematicians) than verifying SCT s correctness 5

6 Interactive Computing Broader form of computing than TM computation. Deals with performance of services over time rather than specifying algorithms for mathematical tasks My co-authored 2007 book, Interactive Computation: The New Paradigm (18 edited chapters), published by Springer Verlag, discusses interaction. Algorithms transform inputs to outputs, perform closed actions specified in advance Inputs are specified before action begins; computation always start in same initial state Interactive systems include interfaces with the environment or with other people Interactive tasks: airline reservation, operating systems, driving home from work Driving home from work by car: This requires interaction with other cars, traffic lights, pedestrians and road workers Cannot be accomplished entirely by algorithms, requires interaction with the world Turing machines and algorithms are substantive problem-solving methods But they are limited in their ability to cover all forms of computation By contrast, interaction extends computable tasks beyond TMs. Turing understood that extended forms of computation are needed He believed in other machines beyond TMs; like choice machines or oracles Yuri Gurevich, Interactive Algorithms (article in my 2007 book). Parallel and distributed algorithms help to expand algorithms beyond the traditional model to include interaction. Goldin, Wegner: Persistent Turing Machines (PTM), extensions of TMs to dynamic input streams, persistent work-tape; the greater expressive power of PTMs over TMs has been proved by Goldin and Smolka (2004) 6

7 Rationalism versus Empiricism Rationalism: expresses tasks and actions in terms of ideas of the human mind Empiricism: uses the experience of events as a measure of the task of computation Descartes (Discourse on Method, I think therefore I am ) and Kant (Critique of Pure Reason, 1781) express rationalism. Marx and Stalin (Communism) and Hitler (Fascism) specify rationalist political beliefs Rationalist politicians can cause destructive human behaviors that accomplish bad goals Religious belief in God and the truth of biblical texts are rationalist human beliefs Rationalist politics and religion imply unchanging rather than modifiable human behavior The British philosophers Locke, Berkeley, and Hume ( ) were empiricists Locke contributed to religious toleration, control of Parliament, and American separation of Church and State. Locke contributed to differences between British and European political and religious thought Empiricism contributed to the growth and progress of the British Empire The focus on experience elevates empirical actions over mental rationalist actions Mathematicians believed that mathematics is rationalist, based on mental principles. Hilbert s rational principle was refuted by by Godel and Turing s empiricist principle. Turing machines (empiricist model) were reinterpreted by rationalist mathematicians Computer science, like politics and religion, is better modeled by empiricism British contributions to empiricism. The British Royal Society. founded in 1660, encouraged empiricist research Cavendish Lab (1880): empiricist approach to physics, improved the quality of British research 7

8 Can Machines Think? Turing proposal: If machines can respond like humans to questions, they can think. Turing believed in 1950 that machines would be able to think in a few years time Skeptical objections: Intentional skeptics: Turing machines do not exhibit awareness or understanding of ideas Specifying human behavior does not imply thinking like humans Extensional skeptics: Turing machines cannot completely simulate all physical tasks Church-Turing thesis does not imply ability to think about all physical laws Ronald Searle, an intentional skeptic: acting like a human does not express thinking Roger Penrose, extensional skeptic: The Emperor s New Mind (1991): TMs cannot think I agree with Penrose that Turing machines are physically too weak to think But in my view, interaction can better model physical and mental modes of thought Interaction observes the world empirically, instead of specifying the world s rational ideas Penrose, a platonic rationalist, excludes empiricist computation from his discussion Penrose, like other rationalists, misconceived the nature of computing, just as Hilbert, though a brilliant mathematician, misconceived the nature of mathematics 8

9 Stephen Hawking Hawking, brilliant physicist, born 1942 Undergraduate at Oxford ; graduate student at Cambridge Was Lucasian Professor at Cambridge , and retired aged 67 in 2009 (Newton was an early Lucasian Professor -- likewise for 30 years ( ) Hawking wrote A Brief History of Time (1988), and researched Black Holes and M-Theory Worked on several projects with Penrose Recent book: The Grand Design (2010), reviews physics and proposes Theory of Everything Co-author Leonard Mlodinow, a Cal Tech physicist, is author of several physics books The Grand Design is Hawking s attempt to specify a better model after his retirement Evolution: Plato, Newton, Einstein, Quantum Theory, String Theory, M-Theory Hawking believes that M-Theory can be shown to be a physical Theory of Everything I like his review of physical evolution, but I reject his claims about M-Theory Quantum Theory: uncertainty, cannot simultaneously measure both position and velocity Einstein asserted that God wants a certain universe whose laws fulfill God s intentions Einstein disagrees with quantum uncertainty, replaced by revised relativity theory 9

10 From Physics to Computer Science Quantum theory postulates a universe with millions of stars with varying behavior. Only one star (our own) is known to have a planet that supports life. Sun and Earth have special properties that support the development of life A single sun that maintains stable temperature both summer and winter Earth has Small 2% elliptical eccentricity, winter and summer weather support life. Preserves water; Goldilocks zone For 13.5 million years after the Big Bang, exploding stars distributed carbon Heavy elements like carbon were needed for human evolution These heavy elements contributed to the creation and evolution of human life Anthropic principles determine properties necessary for life Were these properties established by God to create humans? Or are there implicit laws of nature, whose specific form in our world supports life? Big Bang created life in 13.5 million years by creating the sun, the earth, and multiple exploding stars Successor to String Theory: M-Theory (Master, Miracle, or Mystery theory). 11 dimensions There is no single M-theory: multiple forms for different situations Supports many possible worlds -- including our world that encompasses humans Hawking claims M-theory supports a physical TE, but certain properties are not yet proven Many have tried and failed to create a TE; this includes Einstein, Hilbert, Turing, Hawking Surprise: creation of a TE has been attempted especially by very famous scientists Like physics, computing has no specified theory of everything Maybe attempting this task is inappropriate, and maybe it is not possible at all; our goal should be to improve our understanding of Computer Science, but in a different way 10

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Name Class Date. Ptolemy alchemy Scientific Revolution Name Class Date The Scientific Revolution Vocabulary Builder Section 1 DIRECTIONS Look up the vocabulary terms in the word bank in a dictionary. Write the dictionary definition of the word that is closest