Changes

"It's long," s;_1id said the Knight, "but it'svery, vPry very beautiful. Everybody thathears me sing it-either it brings thetears into their eyes, or else-" "Or. else what?" said Alice, for theKnight had made a sudden pause. "Or else it doesn't, you know. Thename of the song is called 'HaddocksEyes.'" The characters in Through TheLooking Glass were in a chess game,and Lewis Carroll. , the author, wasindeed referring to the binary logic ofanother Victorian mathematician,George Boole. , in this passage. Buteven Lewis Carroll probably could nothave predicted that, thanks to Boole,chess games could be played bycomputers. Boole ·s 's contribution to logic wasdeveloping a system whereby logicalstatements could be expressed inalgebraic terms. This is done bybreaking them down to yes-no decisions decisions ("it brings tears to their eyes, orelse it doesn't"). Boole was born in 1815. , the son of ashopkeeper in Lincoln, England. Aftera meager education at a NationalSchool. , the boy struggled to teachhimself Latin and Greek and also tookc1 a commercial course. At the age of 16,he became an .:issistant assistant teacher, or

 He spent four years as an usher,teaching at two different schools. Atthe age of 20. , he opened a school of hisown and, as he was teaching mathematicsmathematics. began devoting his spare timeto studying it. Immanuel Kant. the German philosopher philosopher who died in 1804, expressed theopinion toward the end of his life thatlogic. as a subject. was complete. To comment in the form of the syllogism syllogism of classical logic, all philosophers philosophers are capable of mistakes. Kantwas a philosopher: therefore, Kantwas capable of making mistakes. Andin this case, he made one. In i854. 1854, after his mathematical publications publications had earned the self-educatedBoole a professorship, he published hismasterpiece, '''An Investigation o_f of theLaws of Thought, on which arefounded the Mathematical Theories ofLogic and Probabilities.''' He explained that he wrote the work"to investigate the fundamental lawsof those operations of the mind bywhich reasoning is performed: to giveexpression to them in the language of aCalculus. , and upon this foundation toestablish the science of Logic and construct construct its method: to make thatmethod itself the basis of a generalmethod for the application of themathematical doctrine of probabilitiesprobabilities: and, finally, to collect from thevarious elements of truth brought toview in the course of these inquiriessome probable intimations concerningthe nature and constitution of thehuman mind." Boolean algebra, despite this vastscope, can be learned by someone witha background of high school algebra. The Boolean variables are confinedto two possible values or states (Yesand No. True and False, On and Off).In the binary number system used todesign computers, the variables arerepresented as 1 and 0. Such a simplified system of notationrequires a good deal of tedious repetition. repetition, which is why many persons findprogramming tedious. It is rather as ifcommunication all took place in theform of the game "Twenty Questions"in which an object is to be guessed onlyby asking questions to which theanswer is "yes" or· ·noor "no." The computercomputer. however, often takes many morethan 20 operations. , and only the animals. animals, vegetables and minerals programmed programmed in could be "guessed." Allmathematical functions on a computer computer such as the TI99/4A are reduced toaddition-which would be a tediousway to go about it oneself, but thanksto engineering technology, can be doneon the computer more quickly thanworking them out with pencil andpaper, even with the added advantages advantages of subtraction, multiplicationand division. After publication of '''The Laws ofThought''', Boole married Mary EverestEverest, niece of the man for whom MountEverest was named. In 1857 he waselected a fellow of the Royal Society.In 1864, he died of pneumonia. Bertrand Russell and Alfred NorthWhitehead emphasized the value ofsymbolic logic for mathematicians intheir great work '''Principia Mathematica Mathematica''' (1910-1913). The practical application application of the Boolean logical patterns tothe simplicity required by an on-offswitch was first postulated by ClaudeShannon, a graduate student at theMassachusetts Institute of TechnologyTechnology, in his 1938 master's thesis. Though Jules Verne and other wri-ters writers of science fiction have proved tohave prophesied the future, it is not atall certain that some day a computerlike HAL in Stanley Kubrick's '''2001 ''' willturn on human beings and make independent independent decisions. Though reducingthe logical process to the binary function function has amazing practical applicationsapplications" making a number of "yes-no"decisions may not be . what humanbeings are doing when they are think�ing thinking logically. Hubert L. Dreyfus. in hiscontroversial book '''The Limits of Artificial Artificial Intelligence'''Intelligence. , points out that theMac Hack computer program came upwith a good move in a game of chessafter considering 26,000 possibilities in15 minutes. Dreyfus says a humanplayer can come up with an equal orbetter move in the same amount oftime, in which the human can consideronly 100-200 possible moves. Thus, hesays, human beings are doing something something besides considering alteralternatives.natives.Dreyfus cites Gestalt psychologistMax Wertheimer. who says that trialand error (a binary process) excludesthe most important aspect of problem-solving, a grasp of the essential structure structure of the problem. Interestingly. in a pamphlet writtenby Boole's wife, she records her husbandhusband's opinion that knowledge isgained from an invisible, undefinablesource-"the unconscious" -as we 11well as from direct observation. Whether the artificial intelligenceresearchers at Stanford and other places places will overcome the current limitations limitations is not for me to say. Still, it's consoling consoling to know that right now my homecomputer can't be VERY much smarter smarter than I am. Also. it's handv handy to beable to do things on it I'm not smartenough to do all by myself. "I know what you're thinkingabout," said Tweedledum: "but itisn't so. , nohow." "Contrariwise." continued continued Tweedledee, "it if was so, itmight be: and if it were so. , it would be:but as it isn't. , it ain't. That's logic."