The Dot and the Line: a romance in lower mathematics. (Allowing Children to Join the Conversation)

The following blog post will explore the surprisingly complex world Norton Juster Creates as he tells the story of a line that falls hopelessly in love with a dot.  Once several of these themes have been explored, this paper will relate the attitudes of this text in relation to the enlightenment (as expressed by John Locke) and a more modern school of thought through the writing of Strasburg.  Finally, this paper will argue that this text brings a very important third party into this conversation: the child.

Norton Juster didn’t placate to young children with small words or pretty pictures as he wrote The Dot and the Line: a romance in lower mathematics.  He didn’t wonder what words young children might already know or what kinds of bunnies might capture a young audience.  He didn’t wonder if a child could relate to the line as he unveiled the yearning soul of his unrequited love.  He didn’t make it easy for someone to guess how old they should be to enjoy this book.  That is because he did not write this book for the young or even the old; he wrote it for anyone with an imagination.

From cover to cover, this tale never settles comfortably into any genre.  Some might argue that it’s simply too complex for children and all together too silly for adults.  Readers may have trouble finding the demographic for this book because Norton Juster never imagined one.  Norton Juster doesn’t imagine his audience when he writes a story; he imagines a story worth telling.  This story is just as refreshingly original as any person who has been lucky enough to pick it up off a shelf (no matter what section they find it in.)  It may not quite fit in a specific genre but neither does the reader.

Norton Juster dedicates this book to Euclid, the father of geometry.  This may seem a little strange for a picture book since Euclid has been dead for more than 2,000 years and very few children have ever heard of him.  Beneath his portrait is the caption “For Euclid, no matter what they say.”  Between the title, the dedication page, and speaking to an ancient mathematician as if they were old friends, this book hardly seems like something that might capture a child’s interests.  After all, romance and mathematics have nothing to do with each other and even less to do with children.

The reader must thumb through the covers and cupids and cherubs before they are finally confronted with the first child-like line “Once upon a time…” (Pg. 1)  This traditional fairytale beginning might give the impression of an ‘age-appropriate’ children’s book, but it won’t fool the reader for long.  At one moment this story is complex and witty and at the very next it is whimsy and nonsensical.  Every page is unique in its own way and not one of them suffers the age demographic rubric that plagues so many other picture books.

Norton Juster begins his story with some very simple drawings that seem to be at constant odds with the vocabulary throughout this book.  The illustrations are small and plain and ordinary and everything that the words are not.  The contrasts of such simple pictures and complex words adds even more visual irony to his already irony-rich pages.

While the shapes themselves may seem quite plain, their lives are anything but vanilla.  Juster breathes a surprising amount of depth into these two-dimensional characters as he draws the reader into their world.  These shapes may be small but they come to life in a big way as we discover a lovelorn line forced to watch “the wanton dot throwing her life away on a disreputable squiggle!”  (back cover)

Limiting his artwork to basic shapes also develops a common element to this story that most fairytales could not.  This story does not limit love and courage to the brave and powerful.  The line may seem simple and underwhelming but his love is just the opposite.  This simple use of art shows us how love is not a phenomenon reserved for the aristocrats; it is felt for and by everyman.  One does not need to be a prince or princess to feel the complexities of love and depression and pain and happiness; one simply needs to be alive.  Much like Euclid’s lessons in mathematics, the rule of love is written and proven all around us.

The main characters in this book are a line, a dot and a squiggle.  Bringing special attention to each character by introducing them one at a time, these pages beg the reader to ask why each of these specific shapes were chosen.  Lines extend forever, dots represent a point within that line and a squiggle is nothing more than chaos.  Much like his book, each of these shapes are simple yet endlessly complex beneath his pen.

Perhaps the most powerful shape in this story is not the one Norton Juster has drawn but the one he has created through his words.  The love triangle begins on page nine as we witness the dot throwing herself into the arms of a squiggle.  The line walks away in the rain, lonely and yearning for the dot who has given herself into the throes of chaos.

His friends, a grey cluster of lines, cross the gutter of a two-page spread to reach the lonely line but their advice falls hapless as their lovelorn friend.  Ironically, they fault the dot for the very characteristics they themselves possess.  These two-dimensional lines claim the dot “…lacks depth.”  These multiple straight lines argue dots are the ones who all “…look alike anyway.”  Lightly drawn in shades of grey, these lines, much like their advice, fade into the page.  The solid black line may be feeling down but he does not lose what defines him.  He shows little interests in their consolation as he pushes himself as far away as the page will allow him to go.

Yearning for the dot, the desperate line begins to imagine himself as something more than the shortest distance from point A to B.  Drawing the world around him (quite literally on pages 22-23) he tries to create something out of himself but he fails to make any real or lasting changes.

For the next several pages we see the line imagining himself as a great leader in history, law and world affairs but he never bends.  This brief retreat into self-deception falls flat for several reasons.  First, he does not appear like the strong, bold line he claims to be on any of these pages.  Instead of adding something valuable to the artwork, the long white streak takes something away.  Secondly, what the reader would perceive to be the line’s imagination hardly proves original.  The credits to the real artists are listed before the story even begins.  Once reading these it is easy to see how the line has simply superimposed himself upon other people’s ideas.  Thirdly, the rusty-orange background of these pages are much different than the strong contrasts of black, white and read found throughout the rest of the book.  These pale colors, white lines and copied artwork illustrate the line’s half-hearted attempt to make any real changes in his life.

Imagination may fill him with a sense of pride for a moment but we can see this inflation does not last very long as he floats back down to reality.  In fact, he comes down so far down that the entire line can bee seen lying at the bottom of the page.  This is the first and only time we see the line without at least one end stretching beyond the pages.  Shapeless and losing his direction, he has become no better than the squiggle.  Desperation and loneliness have consumed him.  Even the placement of the text emphasizes a large, empty space above the sagging line.  He has not just given up on love, but himself as well.

The world he imagines is not original, the change is not real and every attempt the line has made to fill the void of his unrequited love has failed him.  His friends cannot cheer him up and his brief retreat into self-delusion has left him feeling even worse than before.  Reflecting back on these famous works of art may have made him feel better but it didn’t change who he really was.  If he wanted to win the dot he would have to do a lot more than look back into history, he would have to go out and make some of his own.

Suddenly, inspiration hits.  The line decides he isn’t just going to make something for himself; he is going to make something out of himself.  He picks himself up off the floor, straightens his back and then does something amazing.  He bends, not just once but several times.  The line begins to twist and turn over and over and becomes so excited he hardly thinks of which direction he is going.  This aimless excitement is also illustrated within the awkwardness of the text.  For the first time the words become hard to read and seemingly traveling in every direction the line is bending.

He is so excited he can make an angle that he begins to twist and turn without thinking of where he’s going.  Simply changing direction for the sake of change becomes more important than the direction he chooses.  Tossing his sense and inhibitions to the side, he has become nothing more than the squiggle with sharper angles.  Realizing his mistake, he tells himself, “Freedom is not a license for chaos…” and quickly resolves to use his talents more responsibly.  Learning he can bend is important but bending is not what defines him.  His decision to become more than just a line and more than just a squiggle and more than just himself is what makes this line unique.

He is clearly excited with this new talent but it does not distract him from the dot for which he longs.  He may have discovered the hidden power of a simple line but that is not enough.   He needs a point, a place, a reason to belong.  Lines may go on forever but this one is not interested in going anywhere without his dot.

With newfound confidence, he finally confronts the love of his life and wayward squiggle who has stolen her.  This is the only page where all three characters are drawn together but there is no fight or argument that breaks out between them.  In fact, the line never says a single word to any character throughout this entire book.  From beginning to end, the only times the line speaks is to himself but that doesn’t stop him from winning over the dot in the end.

By this point in the story, we see the dot has become hopelessly entangled within the dark lines of the squiggle.  This does nothing to dismay the line as he begins to woo her with his amazing shapes and angles.  Instead of the pale background he once imagined, the pages turn deep, dark and black as he brings the dot into his world.

The dot is thoroughly overwhelmed but she seems to have learned a lesson about her emotions.  Instead of jumping right into this new charmer’s arms, she gives the squiggle one last chance to prove himself.  The squiggle tries to win her back but he has no direction to pull her.  He has no direction at all.  The chaos may have been exciting but there was nothing constructive, productive or sensible about the squiggle.  Looking back on her mistake, she begins to grow, quite literally.  The dot grows larger and larger until she grows so big that she can no longer be fully captured on the page and pushes the squiggle completely off of it.

The line wins her over by becoming something more than he was born into and the dot has outgrown her past.  They aren’t just crashing into each other like the dot and the squiggle once did, but forming something together.  Making an exclamation mark, we can see the line finally has a point of origin, a beginning, and a future that stretches beyond the page.

The last words wrap this story quite neatly with a new twist on an old moral, “To the vector belong the spoils.”  One should take special care to notice this new twist on an old moral.  Norton Juster has changes the word ‘victor’ into ‘vector.’ Vector is a phrase of geometry that describes a shift or direction of movement in the relationship of two points.  Substituting this one vowel completely changes the meaning, just as making one angle can completely change a line.

Reading this moral much more carefully, we can see Norton Juster does not find victory nearly as important as the ability to change and adjust and discover a completely new and original direction.  This line did not win the love of the dot by relying on the past (as he briefly turned to in the history of art) but by redefining his future.  He did not give up structure and sensibility like the squiggle (as he was first tempted to when he began creating angles) but dedicated himself to learning and deeper understanding.  He did not win the dot over by picking a fight with the squiggle and winning, he simply demonstrated a better use of his talents.

This book was published in 1963 and many could argue that this squiggle represents the free love movement of that era.  The line is structured and traditional and has clear direction but the dot is not interested.  She is caught up in the excitement of the squiggle and jumps right into the chaos as she gives into his every whim.  The dot, the new generation seeking it identity, is calling for something different and it is this cry that ultimately challenges the line to bend.

Others may argue this is a much smaller story about a young and easily swayed girl looking for excitement.  She finds what she thinks is romance in the squiggle but soon discovers he isn’t capable of providing any long-term security.  Realizing the squiggle is no good for her, she comes to her senses and falls back on the more traditional roles and lines.

Still others may say this is a story of challenge and change.  The lesson in this story could be that greater and more productive things can come from challenging authority than abandoning it completely.  This could be a lesson of using skills wisely or not abandoning your convictions as the line was tempted to do.  Still yet, this story can teach the values of finding the potential in oneself or just as importantly, the potential in others.  This line never truly discovers who he is till he first discovers the beauty in the dot.  Norton Juster could be telling us how we will never find ourselves until we learn to see others.

One might get a fuller understanding of this story if they read this book cover to cover.  This includes the jacket, the dedication page, the author’s note and the very back cover.  On the front cover we see cupid aiming his arrow at the dot.  The dot is no more than an inch from the tip of the arrow and its destiny seems all but decided until we open the book and see the dot bouncing away unscathed.  The ball continues to bounce over two more cherubs, the title page and right into the arms of the squiggle on page nine.  We see cupid one more time, still aiming his arrow but with no dot in sight.  The reader may be inclined to think the dot has gotten away, especially when s/he turns the page to only see the dotted path where the dot has been.  Turning the page one more time, we see this dotted line bounce across a third and fourth page until the arrow finally strikes.

This could illustrate how fate is waiting for us all and no matter how far we run or think we are getting away, the arrow is always on us.  Norton Juster seems to be describing that there is always a greater force right above us with a much more perfect timing than our own.  If the dot fell in love with the line in the beginning of this book he never would have struggled or discovered himself.

There are a lot of lessons, big words and even bigger ideas in this tiny little book.  There is also a lot of irony written and drawn into these pages, much of which, many young children probably wouldn’t understand without some explanation.  Unfortunately for this younger audience, many adults have already decided books like these simply weren’t meant for them.  Too many people are afraid to give kids a book that might not fully grasp upon first reading.

Many people approach children with a series of graded literacy by providing and replacing books as their understanding grows.  Paying very little attention to the child as an individual, they are often grouped into reading comprehension levels according to age.  Second graders should read these books, then stop reading them as soon as they graduate and begin reading third-grader books the following September.  Too many teachers, too many schools and far too many parents have standardized reading and completely robbed the process of all creativity.

Writing down to this perceived notion of the child, too many picture books are targeting children with small words instead of great literature.  The goal should not consist of giving children a book they can completely understand and move on from, but one which makes them investigate the big words and ask questions and have an evolving understanding as they grow and possibly re-read the book instead of simply tossing it to the side when they are done.  Unfortunately, this has become the practice of many.  Authors and publisher alike have been content to write down to this perceived notion of ‘the child’ and nothing has ever dared them to introduce big words.  Somewhere along the line, publishers have decided that children simply don’t like learning big words and publish their books with a filter that catches anything a child might not fully grasp upon first glance.

Luckily, there have been a few authors like Norton Juster who decided that picture books are more than just a primer for children to read until they are ready for real literature.  I read The Dot and the Line as a child and if someone asked what I remembered most, it was the big words.  I loved, and still love, this book because it is so unique and original and brimming with irony and double meanings.  I read much more into this book now than I did as a child but that is exactly what this book has taught me: there is always more to read.

Too many adults have decided that children are simple people and must have simple worlds with simple words and simple books.  There are no small and simple children and any attempt to define their literature as such betrays them.  Most of the books we put in their hands do nothing but confine their growing and exploring minds.  Not even the authors and illustrators themselves can claim to fully understand every intrinsic meaning of the books they have written.

Children are not simple creatures and the books we give them should not treat them this way.  Just because a few deeper meanings or some quiet humor might be over their heads is no excuse to keep the book out of their reach.  Not even adults can claim a full understanding of every book they read; keeping children from these books for the same reason bears no logic.  Instead of writing down to children, we should teach them that books are more than just words and pictures are more than just images.  We should teach them books don’t end at the last page and there is more meaning to these words than a dictionary can explain.

One might reflect back on the dedication page as they finish reading this short tale.  Perhaps dedicating this book to the father of geometry wasn’t so strange after all.  Norton Juster wanted to add something to all the rules and theories and laws of mathematics, something that Euclid left out of the equation.  The world isn’t just black and white; there is a bright red dot that changes everything.  There is a lesson, a romance in lower mathematics to be learned after all.  Love, much like the rules of math, is written and proven all around us, and is that yearning that causes the straight line to bend and squiggles to be tossed aside.

Norton Juster has created quite a big world with these simple geometric shapes and one doesn’t need to be an adult to visit.  One doesn’t even need to read the same story or come to the same conclusions or take the same metaphors from this story to enjoy reading it.  A young child may read something different than an adult but that doesn’t make it wrong or any less important.  Norton Juster doesn’t discriminate or try to define the child.  His tale is quirky, his words are big and his audience is everyone.

John Locke would suggest that books like these serve no purpose in rasing the child.  He claims that they  ”…should be shewn what to do, and by reiterated actions be fashion’d beforehand into the practice of what is fit and becoming.  ”(Locke, Sect. 67). In Locke’s ideal world, this line would never have found his potential by breaking free of conformity.  In fact, this variation from conformity would be nothing less than a squandering of said potential.  John Locke does not believe that a child (or in this case a line) should grow up to be anything that they are feeling inside of them, rather they should become a reflection of the world around them.

Luckily, more modern ideas have emerged since this so-called age of enlightenment.  Strasburg suggests “ children should be empowered to take control of their own media experiences, negotiating and learning along the way,” (Strasburger, 10). He would be happy to watch the line find his potential and create all sorts of wonderful shapes and images as he searches deep inside himself for a meaning that the rest of the world could not teach him.  Strasburg would have children find themselves through self exploration while Locke would simply persuade them to arrive at the final destination he has chosen for them.  Norton Juster does something a little different than either of these men proposes.  He does not discuss the life of children with fellow adults.  He creates a world for imagination; a world that welcomes both children and adults into the same conversation.

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