Computers - Computers Turing machine • An...

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Unformatted text preview: Computers Turing machine • An imaginary machine o Invented by Alan Turing as a thought experiment in 1936 ! ! Turing also worked on cracking the enigma code ! o o Turing’s ideas on computing were used for cracking the enigma code ! Turing also worked on cracking the enigma code • • • • • • o ! A Turing machine can compute anything that is computable o Can uo nnything inet tan fastest most sophisticated computer can do, only it will be ! A Td ria g mach tha c he compute anything that is computable slower ! ! machine parts Turing Can do anyth ing that the fastest most sophisticated computer can do, only it will be slow ape o Endless ter o Machine that can ! F T t pnrs mato sug can tom hu e e ove ch tape ! AirsuriMg onthe ine gest chat putmans thing thamatcomputcessors – that they are y are infort is ion pro able TuringWrite hines Mac ! Can do anytsymbols on te faape t most sophisticated computer can do, only it will hing that th he t stes E ! be ring machine parts Tu slowrase symbols from the tape er o Machine instructions " pRrsonft p manipulating the t ans E e ules or s ! First ndless tao e uggest that humape are information processors – that they are Tur ngSMachtiihatscanachine i tored n the m " Machine ne Universal Turing Machine ! Turthe imach the t a or i nstructions pe o Put #ngMove ine pafrts the Turing machine on a section of the tape o Instructions in phe Turing machine are to first read the instructions from the tape, t " Endlerise a ye bols on the tape # Ws t t s m then follow the instructions " MaErase symbol from tc e tc pe o The universal tTuring ns achine han aompute anything it is instructed to compute # chin e hat ca m Modern computers are functionally equivalent to a universal Turing machine " # Move instructions M an i e the tape o They cachbn programmed with instructions for manipulating symbols o They cannot compute sinything ttatheatTpe machine cannot compute # Wrlee symbol a pulahe ghat a uring # Ru it s for man on t tin pe o All they are is faster # Etor ed ymb e mfrom e e tape # S ras s in t as s achin h o Due to things such holrandom taccess memory Turing "estMachine instructions t o First person to suggest that humans are information processors – that they are # Machines Turing Rules for manipulating the tape o Turing Srgued that brains are e uring machines because brains compute things and # a tored in the machin T anything that computes is a Turing machine • o Turing proposed that a computer could be considered to be programmed the same as a human if someone could ask it questions and it could not be distinguished from a human based on its answers Turing’s life o Most historians agree that Hitler might well have won the war if it were not for Turing o However, Turing was gay and after the war he was viewed as a security risk o He was charged with homosexuality (under the same law as Oscar Wilde), found guilty and sentenced to experimental hormone treatments o Turing, who was by all accounts shy and sensitive, was also hounded by the secret service o Turing committed suicide by eating an apple laced with cyanide Not everyone believes it was voluntary Some people also believe the apple logo is a reference to Turing • Apple denies this Turing machine program VonNeuman and Modern computers • Turing did not solve how to make the computer fast and efficient • John vonNeuman solved this problem o another super genius o Helped Turing find work while he was in the US • Invented many things • Random access memory o How modern computers work o Basic idea – store programs and data in the same system o Similar to the post office Each piece of information has its own address • Was a founder of modern economics • Also invented game theory o Which is often used as a model of human thought o Many people still believe this o vonNeuman worked for the US government (the RAND corporation) where he used game theory to argue that the US should immediately nuke the soviet union • There are many stories about vonNeuman’s unbelievable mental abilities o e.g., at parties he would invite anyone to rip a page from the telephone book and then look at it for a few moments, then anyone could ask him any question from the page and he would answer • Personality o (from wikipedia: http://en.wikipedia.org/wiki/John_von_Neumann#Computer_science) o Although von Neumann invariably wore a conservative grey flannel business suit, he enjoyed throwing large parties at his home in Princeton, occasionally twice a week.[19] Despite being a notoriously bad driver, he nonetheless enjoyed driving (frequently while reading a book)  occasioning numerous arrests as well as accidents. He once reported one of his car accidents in this way: "I was proceeding Modern Computers • Computer = information processor • Information stored in binary form o Zeros and ones o Physically manifested by switches o On and off o Example, how high can you count with 3 switches 000, 001, 010, 011, 100, 101, 110, 111 • Computers store data and alter data o Rules for altering data are stored as data o Program = a series of rules specifying how to alter the data • Most computers are serial o Change one switch at a time • Parallel processing o Throw more than one switch at a time o The problem is that things get easily out of sync and conflicts arise o Newer computers have some parallel processing But it is very limited • The brain is a massive parallel processor o So the fact that we do not understand how to build parallel computers tells us we do not understand this aspect of the brain very well The Symbol System Hypothesis • Hypothesis about the relationship between information processing and the brain • Newell and Simon (1963) • Intelligence involves manipulating symbols according to rules o A symbol is something that stands for something else • Information in the brain is symbolic o E.g., our idea of a dog is a symbol, there is no dog in your head • Symbol System Hypothesis o The purpose of the brain is to support a symbol processing system o The symbol processing system can be studied and understood separately from the physical brain down the road. The trees on the right were passing me in orderly fashion at 60 miles per hour. Suddenly one of them stepped in my path."[20] (The von Neumanns would return to Princeton at the beginning of each academic year with a new car.) o A committed hedonist, von Neumann liked to eat and drink heavily; his wife, Klara, said that he could count everything except calories. He enjoyed yiddish and "off color" humor (especially limericks) and could make very insensitive jokes (for example: "bodily violence is a displeasure done with the intention of giving pleasure").[citation needed] Von Neumann persistently gazed at the legs of young women (so much so that female secretaries at Los Alamos often covered up the exposed undersides of their desks with cardboard).[21] AI – artificial intelligence • Historically related to the symbol system hypothesis o Idea that intelligence can be studied apart from brains o Computers can be intelligent if they are programmed right • Weak AI o Some things about the brain are the same as a computer • Strong AI o A computer is a brain PDP – parallel distributed processing • Reaction against the symbol system hypothesis • Symbols do not exist as discrete physical states in the brain • Information in the brain is o Distributed Represented as a pattern across neuronal connections and firing o Parallel Activating information requires parallel activity across neurons • Neural networks o A way of making computers behave in this way • Neural models o Actual models of neural systems • Current understanding – these are different levels at which we can model the brain o Discrete symbols o Neural networks o Neural models • All of them still use symbolic information • Choice of modeling system depends on what you are modeling o Neural models Good for understanding what actual neural systems do o Neural networks Good for perception, generalization and some types of learning o Symbolic Good for higher level complex tasks Godel’s Proof: What can a computer know about itself? • Published by Kurt Godel in 1931 • Proof that a system can never fully understand itself o True for computers o True for humans • Big question o Is what we cannot know important • see Godel, Escher, Bach by Douglas Hofstader for a good read on this More from Wikipedia • • • • • Einstein often worried about his friend—and sometimes found his behavior utterly exasperating. One November day in 1952, a colleague encountered Einstein on the street, and noting his unusually perturbed expression, inquired what was wrong. "Gödel has gone completely crazy!" was the reply. "Why, what has he done now?" Einstein explained: "He voted for Eisenhower!"(i.e., Republican) Gödel died from illness related to malnutrition because he though people were trying to poison him Movement and Perception • Originally it was thought that these were easier problems • Actually very difficult • This was discovered mainly through the ongoing difficulty in creating robots that can act in the real world ...
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This note was uploaded on 12/15/2010 for the course LING LING 1001 taught by Professor Bob during the Spring '10 term at Carleton CA.

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