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Jupe's father is involved in a horse-riding circus and this is not respectablein Gradgrind's opinion. He advises Cecilia to refer to her father as a "farrier" (the person who shoes a horse) or perhaps, a "veterinary surgeon."
The lesson continues with Gradgrind's command: "Give me your definition of a horse." While Girl number twenty knows what a horse is, she is unable to define one. Another child in the class, a boy called Bitzer, easily defines the animal by means of biological classifications (quadruped, graminivorous, etc.). After this, the third gentleman steps forward. He is a government officer as well as a famous boxer and he is known for his alert belligerence. His job is to remove "fancy" and "imagination" from the minds of the children. They learn that it is nonsense to decorate a room with representations of horses because horses do not walk up and down the sides of rooms in reality.
The major theme of the chapter can be easily inferred from Dickens' description of Cecilia in the classroom. The "horses" and carpeted "flowers" are all double symbols of her femininity and youth, but most important, Cecilia represents Art in opposition to mechanization. Dickens is not arguing against education, science or progress. He is arguing against a mode of factory-style, mind-numbing, grad-grinding production that takes the fun out of life. But even worse than the loss of "fun" or "leisure," Dickens is arguing that art requires an inquisitive and desiring mind. Especially as Dickens is known to have read and enjoyed Arabian Nights in his youth, we can see a bit of autobiography in his tender treatment of Ceciliaperhaps if he had come under a Mr. M'Choakumchild, he would have proved incapable of becoming an artist.