of children my own age. They kill each other. Did it always used to be this way?

Clarisse represents the wonder and creativity with which children look at the world. Growing up in this dystopia, Montag probably missed out on this perspective. She is the first to ask if Montag has ever read the books he burns. She is also the first to ask if firemen used to put out fires as opposed to starting them. She initially sparks his curiosity more than any other character.

I’m not sure I would simply characterize their relationship as a father/daughter dynamic. They both learn from each other and Clarisse represents an alternative or foil to Mildred which is to say that Clarisse is, in an innocent way, a romantic infatuation as well as a platonic one. I would say that Montag learns more from her than she from him. For lack of something more definitive, I would just say that they are friends. They are so different from each other that each seems exotic to the other; as if they are from two different countries. Maybe I would use exotic friendship. The implication of exotic means foreign, different and curious.

This scene comes when Montag first meets Clarisse, and she expresses the surprising opinion (to him) that she is not afraid of him, because although most people are scared of firemen, she can see that he is just a man:

He saw himself in her eyes, suspended in two shining drops of bright water, himself dark and tiny, in fine detail, the lines about his mouth, everything there, as if her eyes were two miraculous bits of violet amber that might capture and hold him intact.
(Bradbury, Fahrenheit 451, Google Books)

By seeing himself in her eyes, Montag comes to the realization that she is correct; he is just a man, like any other man. More importantly, he is a product of society, common, ordinary; his job is just another job, no more or less important than that of anyone else. This realization starts the process that shocks him out of his complacency, and gives him the motivation to try and become a reasoning individual instead of a faithful, unthinking cog in society.

When Montag sees his own reflection in Clarisse's eyes, I think he is seeing himself through a different lens, or way of seeing things. Everything Montag perceives in his life in Bradbury's Fahrenheit 451 is based upon the propaganda he has been fed all his life, which he believes without question. With Clarisse's infuence, we see...

...the transformation of Montag from an obedient servant of the state to a questioning human being.

Clarisse provides a new point of reference so that Montag starts to question what he believes of the world, of himself, and of his place in the world—burning books, houses, and eventually, watching a woman die rather than give up her books.

When Montag meets Clarisse, they begin to discuss her ideas, which are extremely foreign to Montag. She asks questions that are often difficult or impossible for him to conceive, let along answer.

"Are you happy?" she said.

"Am I what?" he cried.

Happiness is a concept that Montag does not think about. He thinks about his job. He likes to watch things burn. He essentially remains passive, avoiding any behavior that might draw attention to him. (This is especially important later when we learn that Montag's theft of a book from the fire at 105 Elm is not his first.) At first he insists in a conversation in his brain that he is happy, but quickly realizes that he is lying to himself. Had Clarisse not asked the question, he would never have asked himself.

In their discussions, Montag notes:

How like a mirror, too, her face. Impossible; for how many people did you know that refracted your own light to you?

Clarisse is honest with Montag. This act opens his eyes.

Early on, Clarisse notices things about him when they speak of his profession. He tells her that he can never quite get rid of the smell of the kerosene they use to burn the books. Her questions get Montag to thinking:

Last night I thought about all the kerosene I've used in the past ten years.  And I thought about books.  And for the first time I realized that a man was behind each one of the books.

And in looking at the reflection of himself in Clarisse's eyes, he realizes that he doesn't see the cows in the fields or colors of the flowers as his car speeds along its way. He does not have fun: putting a yellow flower beneath his chin or catching rain on his tongue. In Clarisse, the child is still alive, full of questions—simple questions that have anything but simple answers.

As he perceives himself through Clarisse's eyes, he begins to question everything in his world. And though Clarisse is later killed in a car accident, her way of looking at the world has changed Montag. In studying himself through Clarisse's worldview, his perceptions change, and ultimately, so does his destiny. In the challenges Clarisse put to Montag, she not only allows him to start thinking for himself, but eventually the enlightenment he experiences saves his life.

I believe that this is symbolic of what happens to Montag when he meets Clarisse.  It shows how he sees his life through her eyes and that makes him change.  So he's seeing himself in her eyes (literally) but that's a metaphor or a symbol for him seeing himself (figuratively) through her eyes.

To Clarisse, Montag has sort of lost his ability to think and to perceive and to relax.  She talks to him about all the kinds of things she does and he realizes his life isn't like that.  After he sees himself through her eyes, he changes and starts to think more about himself and life.

You can say that it is after he sees himself through her eyes that he rebels.

This dystopia that Bradbury has created is built upon primal pleasures.  These pleasures are individual, and personal connections are not encouraged.  Personal relationships might lead people to want more than just 'pleasure', thus causing citizens to rebel against their society.  When Montag sees himself in Clarisse's eyes, this indicates a connection between two souls.  The eyes are, after all, the window to the soul.  To touch into the humanity is to reject the teachings of this new American society.  This foreshadows Montag's rebellion.

Guy Montag meets Clarisse within the first few pages of Fahrenheit 451. Montag is leaving work very late at night (approximately midnight), and as he walks home, he contemplates the odd feeling that he has had that someone had been on the same sidewalk as him a mere "moment before making the turn." It's a feeling that's afflicted him for the past several nights, and yet he can't make sense of it, no matter how hard he tries.

On this fateful night, however, Montag turns the corner to see a girl who seems to be propelled forward by the wind and leaves rather than moving of her own accord. She is described as having a slender and "milk-white" face with a "gentle hunger" and an expression of "pale surprise."

When Montag asks this girl if she is the new neighbor, she very oddly replies that Montag must be "the fireman," commenting that she'd "have known it with [her] eyes shut." They chit-chat about the smell of kerosene until finally she introduces herself as Clarisse McClellan.

In Fahrenheit 451 by Ray Bradbury, Montag meets Clarisse on the third page. She is unlike anyone he has ever known. While he and his wife and "friends" are automotons, doing everything as directed by the government, Clarisse and her family actually do what the men down the river do at the end of the novel: they try to remain connected to the past, remembering things that matter, things that uplift the human experience. They are not a part of the unnatural flow of the community, but keep to themselves and find comfort in each other.

Clarisse encourages Montag look at the world through her eyes—she asks him if he thinks about things, and if he is happy. Montag finds her very odd. She explains that she does not go to school: no one misses her, saying that she's not social. She disagrees and then the reader realizes that it's really because she won't "behave." She says:

But I don't think it's social to get a bunch of people together and then not let them talk, do you?

Clarisse is curious about the world. She watches people to see how they act. She listens to people everywhere, but says that they don't talk about anything. She notices blades of grass and flowers, which no one sees because no one drives slow enough to do so. They have become desensitized. In sharing all of these things, she gets Montag to think about "thinking." She pushes him to notice the world around him and to ask questions.

The purpose of Clarisse and Montag's meeting is to get him to engage more with the world around him, so he begins to notice things and ask his own questions. He becomes concerned with the apathetic way his wife lives. He questions the validity of what firemen do.

Once the first idea is planted, Montag cannot help himself—he secretly collects more and more books. He questions society's laws. Soon, he is ready to make a break from this oppressive society of which he is a part.

However, when he faces Beatty at the end, his boss brings up Clarisse to Montag, sneering at the way Montag fell under her influence.

"You weren't fooled by that little idiot's outine, were you? Flowers, butterlfies, leaes, sunsets, oh, hell! It's all in her file...A few hrass blades and the quarters of the moon. What trash. What good did she ever do with all that?"

Montag sat on the cold fender of the Dragon... "She saw everything. She didn't do anything to anyone. She just let them alone."

"Alone, hell! She chewed around you, didn't she?..."

While it would seem at first that Clarisse gave Montag a desire to ask questions and engage with the world around him rather than passivley passing the time, as Mildred did, Beatty's knowledge of Clarisse and her time spent with Montag would indicate that Montag was being watched for a long time. Beatty even admits that he knew that Montag was involved with books before they came to burn his home.

However, the fact that Beatty tells Montag about Clarisse, along with the sense the reader gets with Montag's lament, "She didn't do anything to anyone," makes the reader wonder. Can we infer that the car that hit Clarisse may not have done so accidentally? After Montag kills Beatty and runs away, he has a moment of clarity, realizing that Beatty wanted Montag to kill him. Perhaps he mentioned Clarisse as just another way to drive Montag to end Beatty's life. So that Clarisse and Montag's meeting may well have served two purposes.

Both Clarisse McClellan and Mildred Montag can be perceived as victims of their environment and the technology of their society.  Both women die prematurely in completely needless, senseless fashions: Clarisse is killed by a speeding car, and Mildred dies when her city is fire-bombed. 

Bradbury makes Clarisse's death purposefully empty and tragic to contrast her vitality and love of life.  She is truly a victim of the fast-paced lifestyle embraced by the futuristic citizens.  At the same time, Mildred's death reinforces the vapid, shallow lifestyle of her society.  The reader does not actually see Mildred's death, except through Guy Montag's imagined account as he hopes that she realizes how brainwashed and robotic her beloved television and society has made her. 

Bradbury uses both women's deaths as a warning about the dangerous acceptance of fast-paced living, mass media, and technology.