# Knot III: Mad Mathesis explained — A Tangled Tale > Chapter companion for A Tangled Tale by Lewis Carroll. ## What happens Clara and her aunt Mad Mathesis visit the Charing Cross Metropolitan Station and engage in two train-meeting matches. The first match involves counting trains met while traveling opposite directions around a circular route; Clara loses. In the second match, they start counting only after their trains first meet, and Clara feels optimistic about winning. ## Themes in this chapter ### Competition and Achievement Clara and Mad Mathesis engage in two competitive train-meeting matches, with Clara striving to win and feeling disappointment at loss. ### Mathematical Reasoning Clara makes a 'brief mental calculation' to choose her train and expects to meet exactly half as many again as her aunt, highlighting mathematical reasoning in the contest. ### Social Critique Mad Mathesis criticizes modern norms such as wearing long trains, playing lawn-tennis, and High Schools, advocating for women to be 'meek and lowly.' ## Character check-ins ### Clara Clara is Mad Mathesis's niece, a high school student on vacation, who cautiously questions her aunt's nickname and participates in train-meeting matches. ### Mad Mathesis Mad Mathesis, Clara's aunt, is eccentric and critical of modern conventions; she proposes the train matches and speaks with undisguised aversion to High Schools. ## Key lines > I never do what sane people are expected to do nowadays. I never wear long trains, (talking of trains, that’s the Charing Cross Metropolitan Station—I’ve something to tell you about that), and I never play lawn-tennis. I can’t cook an omelette. I can’t even set a broken limb! There’s an ignoramus for you! Mad Mathesis declares she defies social expectations by avoiding long trains, lawn-tennis, cooking, and medical skills, calling herself an ignoramus. _Mad Mathesis introduces her eccentric character and sets the stage for the train-themed competition._ > Let a woman be meek and lowly! None of your High Schools for me! Mad Mathesis expresses her aversion to High Schools, advocating for traditional female humility. _Reflects Mad Mathesis's conservative views on women's education._ > The way the trains run is most peculiar. The westerly ones go round in two hours; the easterly ones take three; but they always manage to start two trains from here, opposite ways, punctually every quarter-of-an-hour. Mad Mathesis explains the circular train schedule: westerly trains take two hours, easterly three, and trains depart in opposite directions every fifteen minutes. _Provides the logistical basis for the train-meeting match._ > Let me choose my train, and I’ll engage to meet exactly half as many again as you do. Clara proposes that if she can choose her train, she will meet 50% more trains than her aunt. _Clara's mathematical confidence sets up the first match._ > Remember, we only count the trains we meet on the way. You mustn’t count the one that starts as you start, nor the one that arrives as you arrive. Mad Mathesis clarifies the counting rules: exclude the train that departs with you and the one that arrives with you. _Defines the rules for the competition._ > When we see each other, we will say ‘One!’ and so count on till we come here again. Mad Mathesis proposes a second match where counting begins only after their trains first meet. _Introduces the revised rules for the second match._ ## Links - HTML: https://www.betterreads.online/discover/a_tangled_tale_se/chapters/knot-iii-mad-mathesis - Book: https://www.betterreads.online/discover/a_tangled_tale_se - All chapters: https://www.betterreads.online/discover/a_tangled_tale_se/chapters