{"id":1363,"date":"2018-08-09T10:59:55","date_gmt":"2018-08-09T04:29:55","guid":{"rendered":"http:\/\/eng.moemaka.net\/?p=1363"},"modified":"2018-08-09T10:59:55","modified_gmt":"2018-08-09T04:29:55","slug":"mathematics-behind-the-madness-of-the-cat-and-alice-by-dr-khin-maung-win-maths","status":"publish","type":"post","link":"https:\/\/moemaka.net\/eng\/2018\/08\/mathematics-behind-the-madness-of-the-cat-and-alice-by-dr-khin-maung-win-maths\/","title":{"rendered":"MATHEMATICS BEHIND THE MADNESS OF THE CAT AND ALICE by Dr Khin Maung Win (Maths)"},"content":{"rendered":"
\n
\nMATHEMATICS BEHIND THE MADNESS OF THE CAT<\/o:p><\/div>\n
\nAND ALICE by Dr Khin Maung Win (Maths)<\/o:p><\/p>\n<\/div>\n
\n<\/a><\/div>\n
\n(<\/span>http:\/\/www.specialbindings.com\/aliceinwonderlandjournal.htm)<\/span><\/span><\/div>\n
\nThe following passage is from Lewis Carrol’s ‘Alice in Wonderland’.<\/div>\n
\n<\/o:p><\/div>\n
\nThe cat said ,”We’re all mad here.I’m mad.You are mad.’<\/o:p><\/div>\n
\n”How do you know that I’m mad ?” asked Alice.<\/o:p><\/div>\n
\n”You must be  <\/span>or  <\/span>you wouldn’t have come here.”<\/o:p><\/div>\n
\nAlice didn’t think that proved it at all  <\/span>.However she went on.<\/o:p><\/div>\n
\n”And how do you know that you’re mad ?”<\/o:p><\/div>\n
\n”To begin with,a dog’s not mad.You grant that?”<\/o:p><\/div>\n
\n”I suppose so.”<\/o:p><\/div>\n
\n”Well then,you see a dog growls when it’s angry and wags its tail when it’s pleased.
\nNow,I growl when I’m pleased and wag my tail when I’m angry.Therefore I’m  <\/span>mad.”<\/div>\n
\n<\/o:p><\/div>\n
\n    <\/span>In order to give a mathematical interpretation of the conversation,
\nI shall have to recall some of the laws  <\/span>of Logic which will  <\/span>be used.
\nThey are as follows .::<\/div>\n
\n<\/o:p><\/div>\n
\n    <\/span>(1) .All statements are either true or false but never both at<\/o:p><\/div>\n
\nthe same time.<\/o:p><\/div>\n
\n     <\/span>. (2 )If a statement is not true,it is false.<\/o:p><\/div>\n
\n     <\/span>. (3)If a statement is not false, it is true.<\/o:p><\/div>\n
\n     <\/span>. (4) If two statements are joined by a conjunction ‘and’ ,then<\/o:p><\/div>\n
\nthe joined statement is true when both of the individual statements are true,
\nand false when at least one of them is false.<\/div>\n
\n<\/o:p><\/div>\n
\n  <\/span>(5)    <\/span>.If two statements are joined  <\/span>by a conjunction  <\/span>‘or’ , the joined statement is true when
\n at least one of the individual statements is true ,and false when both the individual statements are false.        <\/span><\/div>\n
\n<\/o:p><\/div>\n
\n      <\/span>Suppose  <\/span>A  <\/span>and  <\/span>B  <\/span>are two statements.Let  <\/span>‘A  <\/span>or  <\/span>B  <\/span>‘ be the joined statement of A and B.   <\/span>Suppose   <\/span>that  <\/span>‘A  <\/span>or  <\/span>B ‘   <\/span>is  <\/span>true.Then if  <\/span>A  <\/span>is false,then  <\/span>B has  <\/span>to be true  <\/span>and  <\/span>if  <\/span>B  <\/span>is false , then   <\/span>A  <\/span>has to be true.<\/p>\n<\/div>\n
\n<\/o:p><\/div>\n
\nIn other words, ‘if A is not true,B must be true and if B  <\/span>is not  <\/span>true, A  <\/span>must be true.<\/div>\n
\n<\/o:p><\/div>\n
\nIn the conversation between the cat and Alice,the last law or formula of Logic has beeen used by the cat to prove that Alice is mad,although Alice herself does not accept it.<\/p>\n<\/div>\n
\n<\/o:p><\/div>\n
\n       <\/span>To be able to give a mathematical interpretation,we shall<\/o:p><\/div>\n
\nre -write the main points of the conversation as follows.:<\/o:p><\/div>\n
\nCat   <\/span>.  <\/span>I’m  <\/span>mad.You’re  <\/span>mad.<\/o:p><\/div>\n
\nAlice  <\/span>.  <\/span>How do you know  <\/span>that  <\/span>I’m mad ?<\/o:p><\/div>\n
\nCat    <\/span>.  <\/span>You must be  <\/span>or you wouldn’t  <\/span>come  <\/span>here.<\/o:p><\/div>\n
\nThere are two statements  <\/span>namely , ‘The cat is mad.’   <\/span>and<\/o:p><\/div>\n
\n‘Alice  <\/span>is mad .’ The reason for ‘   <\/span>Alice   <\/span> <\/span>is mad’ is given by<\/o:p><\/div>\n
\n‘You must be or you wouldn’t come here.’ Re writing it mathematiclly it becomes two statements joined by ‘or’ in the following way  <\/span>.<\/div>\n
\n<\/o:p><\/p>\n<\/div>\n
\n‘Alice is mad  <\/span>or  <\/span>Alice does not come here. ‘<\/o:p><\/div>\n
\nAccording to the laws of Logic,it means that  <\/span><\/o:p><\/div>\n
\nIf the statement ‘Alice does not come here ‘ is false, then the statement ‘Alice is mad ‘must me true. ‘Alice does not come here ‘ is false means that ‘Alice comes here ‘ .<\/div>\n
\n<\/o:p><\/div>\n
\nThus it means that ‘If Alice comes here,Alice is mad.’ But Alice didn’t think that proved it at all.It means  <\/span>that Alice does not accept it as the proof.It is for the reader to<\/div>\n
\n<\/o:p><\/div>\n
\ndecide whether to accept it as the proof or not. Whether to accept or not ,
\n boils down  <\/span>to whether to accept this statement   <\/span>to be true or not .’If someone comes here ,
\nthen he or she is mad.’  <\/span>Alice does not aaccept it as true.. Do you ?<\/div>\n
\n<\/o:p><\/div>\n
\nNext,let us cconsider the reasons behind the  <\/span>statement ‘The cat is mad.’<\/o:p><\/div>\n
\nThe conversation may be  <\/span>re written mathematically as follows.<\/o:p><\/div>\n
\nA dog is not mad.  <\/span><\/o:p><\/div>\n
\nIf the dog is angry , then the dog growls.<\/o:p><\/div>\n
\nIf the dog is pleased, then the dog wags its tail.<\/o:p><\/div>\n
\nIf the cat is pleased,then the cat growls.<\/o:p><\/div>\n
\nIf the cat is angry, then the cat wags its tail.<\/o:p><\/div>\n
\nAccording  <\/span>to the given laws of Logic, there is no connection between madness, being angry ,being pleased, growling  <\/span>and wagging one’s tail.<\/div>\n
\n<\/o:p><\/div>\n
\nSo there is no valid reason ,according to the given laws of Logic,for the<\/o:p><\/div>\n
\ncat’s madness.<\/o:p><\/div>\n
\nWe have shown how we may analyse the conversation mathematically. <\/span><\/div>\n