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Partway up the stairs to Infinity, Milo realizes his climb will never end. Tired, he sits. Another boy appears, but he consists only of his own left side, or 0.58 of a person. He belongs to a typical family, and average families have 2.58 children; he’s the .58 part. Milo protests that averages are imaginary; the boy responds that they’re useful nonetheless. He gives the example of someone with no money in a group of five people, four of whom have an average of $10 each: All five members thus average $8 apiece, so the broke person now has some cash.
The .58 boy offers other examples, like a rat cornered by nine cats who, given the number of creatures involved, averages 90% cat. Milo objects that these are impossibilities, but the boy counters that even impossible things can be calculated, and sometimes they’re useful to know, like the properties of infinity. Realizing he has much to learn before he can rescue the princesses, Milo returns downstairs.
To the Mathemagician, Milo asks why some things that are correct seem nevertheless not to be right. The Mathemagician, with tears in his eyes, agrees and says it’s been that way since Rhyme and Reason were sent away. In a sudden rage, he blames King Azaz. Milo asks if the two kings might talk it out. The Mathemagician says he sent a friendly letter to Azaz, who never replied. Milo sees a copy of the letter: It’s all numbers.
Tock says they want to rescue the princesses, but the Mathemagician refuses to allow it, claiming he’ll never consent to what Azaz agrees to. Milo says that’s not true. The Mathemagician says if Milo can prove it, he’ll let them rescue the princesses. Milo argues that since neither king will do what the other wants, they’ve agreed to disagree. Defeated, the Mathemagician permits the travelers to continue on their journey. He warns them that the trek will be dangerous and that demons may try to defeat them. Another problem is even worse, but the king won’t tell them about it until after they return.
Attended by the Dodecahedron—some of his faces sad or crying—the Mathematician escorts the travelers to the edge of Digitopolis. The king gives Milo a pencil, a miniature version of the ruler’s magical walking staff, saying, “Use it well and there is nothing it cannot do for you” (201). The Dodecahedron hands Milo a bag of the sights, sounds, and words the boy has collected thus far on his journey.
Milo, Tock, and the Humbug set off along the narrow path into the mountains. As they climb, the region grows dark with a sense of impending evil. They encounter a large, very dirty bird, the Everpresent Wordsnatcher, who interrupts whatever Milo says and deliberately misinterprets the boy’s words to make them seem futile or malicious. Milo, annoyed, asks if the bird is a demon; the Wordsnatcher replies that he’s merely a visitor and that the worst he can be is a nuisance. The bird takes off; Milo, filled with questions, cries, “Wait!” but the bird shrieks, “Thirty-four pounds” (207).
They climb higher. Up ahead, leaning against a tree, is a well-dressed man with no face who addresses them cheerfully. The trio is happy to meet someone nice. The man asks if they can help him with some small tasks, and they agree. He hands Milo a pair of tweezers and asks him to move a large pile of sand. To Tock, he gives an eye dropper with which the dog must move water from one well to another. He gives the Humbug a needle with which to dig a hole into a cliff. The travelers comply; they work “hour after hour after hour after hour after hour after hour after hour after hour” (210).
The travelers continue to work for days but make almost no progress. Strangely, Milo doesn’t feel tired at all. He wonders, though, how long the tasks will take. Tock suggests he use his magic pencil to find out; Milo employs it to make some quick calculations and reckons that their work will take more than 800 years to complete. He points this out to the faceless man, suggesting that the tasks aren’t really important or necessary. The man retorts that the whole point is to waste the travelers’ time, so they fail to complete their quest.
As the Trivium reaches out to snatch them, a voice urges the trio to run. They do so, scrambling up a mountainside, and then follow the voice’s directions through a bog and into a giant pit. The voice claims it’s large and scary, but Milo uses his telescope to find that the demon is small, furry, and full of anxiety. The creature admits it’s a demon of insincerity who leads people astray.
Climbing on each other’s backs, the visitors manage to get themselves out of the pit. They walk for some time, but the land they’re on suddenly rises up, and they realize they’ve walked onto the hand of a giant. It wants to eat them, but Milo keeps asking it questions and learns that this Gelatinous Giant, despite its size, is afraid of everything and prefers to take the shape of wherever it is—in this case, the mountains—to remain unnoticed. Milo asks if the giant would like to help them rescue the princesses. The giant says he better not, sets them down, and hurries off.
Other demons, hearing the news about the visitors, begin to convene on the trio, who hurry away up the trail.
At last, they see a staircase spiraling upward from the highest peak. Above it floats the Castle in the Air. At the base is a man with thick glasses, ink-stained clothes, and a ledger. He’s the “Senses Taker,” and he requires that the visitors answer a few dozen questions before he takes their senses. The questions include name, age at birth, “[h]ow many ice-cream cones you eat in a week” (227), and numerous other pointless queries, plus several forms that each must fill out. Meanwhile, the other demons are getting closer.
The team finally finishes and starts up the stairs, but the Senses Taker lures them back with an entertaining circus performing nearby. Entranced, they stare until Milo’s sack falls from his shoulder, releasing some sounds, including laughter. This breaks the spell, and the trio realizes that the circus is an illusion. The Senses Taker says his job is to take their senses of purpose, duty, and proportion, but the sound of laughter prevents him from taking their sense of humor.
As the demons close in, the three travelers escape up the stairway. The spiral stairs have no railing; they teeter in a strong wind. Milo, Tock, and the Humbug help each other up the stairs until they break through the clouds, where a bright, sunny sky shines above the castle. They enter the building and, inside the great hall, meet the beautiful princesses—Reason, smiling serenely, and Rhyme, laughing with her eyes sparkling with joy. Milo asks them why he had to learn so many things that seem pointless; the ladies explain that everything he learns has a value that sometimes shows up much later.
The demons chop down the stairway, and the Castle drifts away. Tock, who can fly, offers to carry everyone down to the ground. The princesses climb onto Tock’s back, Milo grabs his tail, the Humbug grabs Milo’s ankles, and they leap from the Castle.
The group sails down and lands with a jolt among the mountains. Demons pursue them, and they hurry away, the princesses on Tock’s galloping back and Milo and the Humbug right behind. They rush past the “Triple Demons of Compromise” (238), who constantly agree to do what none of them wants and, therefore, never get anywhere. Another demon, “Horrible Hopping Hindsight” (238), chases them with his rear in front and eyes in back, constantly crashing but at least always knowing what he should have done. Giant, slimy snails, the “Gorgons of Hate and Malice” (238), also give chase, much faster than expected. Other demons include the Overbearing Know-it-all, the Gross Exaggeration, and the Threadbare Excuse.
Just as the demons are about to capture and devour them, the creatures stop in horror. Beyond, arrayed across a plain in the Kingdom of Wisdom, stand vast ranks of armored, mounted warriors led by Kings Azaz and the Mathemagician. With them are all the people Milo met on his journey. The vast army charges at the demons, who, terrified, escape back into the mountains.
The princesses reunite with their brothers. Azaz’s ministers proclaim that Milo, Tock, and the Humbug are “heroes of the realm” and that three days of celebration will begin at once (246). The victorious army parades through the flower-strewn kingdom, cheered by locals.
The two kings reveal to Milo’s group the one thing they were reluctant to admit before—that the rescue of the princesses was considered undoable but that “so many things are possible just as long as you don’t know they’re impossible” (247).
The parade arrives at a point midway between the two great cities, where a carnival begins. Rides, shows, and booths are quickly set up. The Mathemagician fires off exploding fireworks of multiplying numbers, their color and noise provided by Chroma and Dr. Dischord. The Soundkeeper provides laughter and music. Three nights of banqueting include delicious words and dividing dumplings. It’s the best carnival ever.
Afterward, Milo says a tearful goodbye to Tock, the Humbug, and everyone else. Promising someday to return, Milo retrieves his newly shined car and drives off. As he leaves, the boy hears the kings arguing anew about whether words or numbers are more important, and he worries that the dispute might reignite.
Up ahead is the tollbooth. Milo realizes he’s been away for several weeks; he hopes his family isn’t upset. At the tollbooth, Milo deposits a coin, drives through, and finds himself back in his bedroom. It’s 6:00 pm on the same day he left. He’s been away for one hour.
The next day, his head full of plans, Milo hurries home impatiently, planning another tollbooth trip. When he gets to his bedroom, the tollbooth is gone, replaced by a blue envelope addressed to him. Inside, a letter explains that, since Milo has completed his trip, the tollbooth must go to other kids who need it. The letter predicts that Milo will visit many more strange lands but that he will “find a way to reach them all by [him]self” (255).
Feeling sad, Milo looks out the window, seeing beautiful, scudding clouds, green shoots on trees, and a world of things to explore. His room is filled with books and toys and projects. He says, “I would like to make another trip […] but I really don’t know when I’ll have the time. There’s just so much to do right here” (256).
The final chapters detail the journey of Milo and his friends as they rescue Rhyme and Reason and return them triumphantly to the Kingdom of Wisdom. In this section, the action crescendos to a climax as the group tries desperately to escape the demons of Ignorance. They succeed, and the tension is released in a great celebration. Milo returns home with his newfound wisdom about the adventures and discoveries of everyday life.
Chapter 16 is a transitional episode: It begins in Digitopolis and ends deep in the Mountains of Ignorance. During this chapter, the Mathemagician blesses Milo’s quest to retrieve Rhyme and Reason. The ruler agrees that a strange form of “insanity” has swept the land but blames his brother, King Azaz. Milo suggests that the kings talk it out; the Mathemagician says he sent a letter to Azaz, but his brother never replied.
Milo views a copy of the letter: It’s written entirely in numbers. The Mathemagician, though brilliant with digits, is blind to letters and other ways of seeing the world. This is a lesson in empathy: If we cannot grasp other people’s viewpoints nor communicate in a language they understand, we can never reach agreements.
The Mathemagician gifts Milo with a wand that’s a miniature version of the ruler’s magical walking stave. The wand is really a pencil; it’s the author’s way of saying that the tools of education have magic all their own. With a box of words from Azaz, Alec Bings’s contribution of a telescope, and the Soundkeeper’s gift of sounds, Milo now has a bag of totems to help him on his journey. These gifts symbolize the attributes of a prepared mind: With an informed brain, Milo can overcome anything.
The search for Rhyme and Reason begins earnestly and takes up most of the book’s final chapters. To reach the rickety, spiraling stairway entrance to the Castle in the Air, Milo, Tock, and the Humbug must brave the dark and forbidding Mountains of Ignorance, where they’re beset by demons, each of which represents a temptation to which innocent minds are drawn. The days of useless work given to them by the faceless Terrible Trivium cater to their desire to procrastinate and thereby avoid the dangers that lie ahead. The Senses Taker, who delays the group’s climb up the stairway to the Castle in the Air, represents the book’s final dig at bureaucrats whose mindless rules can interfere with people’s attempts to do good things.
Other demons represent a grab-bag of assorted weaknesses that can distract people on a mission. Together, the demons form part of the book’s theme on The Pitfalls of Learning. The band escapes these beasts through sheer determination and returns to the Kingdom of Wisdom. The author thus suggests that the demons of Ignorance can be banished by a resolute conviction to leave them behind.
Rhyme and Reason, the counterparts to the words of Dictionopolis and the numbers of Digitopolis, help to reunify the kingdom and return the people to sanity. It’s the refreshed mental health of minds that, once again, understand and accept the balance between the two sides of thought, creative and logical. Thus, the theme of Rhyme, Reason, and Wisdom is finally shown not by absence but rather by the presence of these attributes. The health and happiness that return with their presence contrast with the deficiencies Milos observed and experienced from their absence in Dictionopolis and Digitopolis.
As Milo leaves the Lands Beyond, he overhears the two kings begin to argue again about which of them is the more important. The author thus issues a warning: Mental balance can be a delicate thing, and complacency may lead to renewed disruption. A mind untended often relapses into old bad habits.
Despite all the changes wrought by time and technology in today’s world, the human heart remains the same, and The Phantom Tollbooth is as relevant today as ever it was. The author, who died in 2021, saw the vast alterations in children’s lives brought about by computerized tablets and phones, but he also recognized that education and learning how to think are still essential parts of growing up. Juster noted, “Today’s world of texting and tweeting is quite a different place, but children are still the same as they've always been. They still get bored and confused, and still struggle to figure out the important questions of life” (Juster, Norton. “My Accidental Masterpiece: The Phantom Tollbooth.” NPR, 25 Oct. 2011).
Ultimately, the entire point of the tollbooth is to teach Milo that people can never be bored if they’re open to the wonders of the everyday world. A mind that sees both sides of everything has the perspective to navigate successfully through a complex world. Life gives up its secrets to those who think things through with perspective, wisdom, and an affectionate regard for everything they encounter.