two of the project's apartment buildings.” Later, when she is Gitl and living in a rural village, she sees that “the moon hung ripely between two heavy gray clouds.” The similarimagery of the moon hanging between two objects represents how the world is the same, even at the time of the horrors of the Holocaust and in modern day New Rochelle.

Numbers play a key role as symbols that represent individual Jews who were killed or survived the camps and the aggregate of six million. The brand on Grandpa Will’s arm, the tattoo that Hannah writes on her own arm in ink, the book's title and her trying to tell the others when she is transported back in time are all representative of the unimaginable numbers of people killed.

"No, Rabbi, six million in Poland and Germany and Holland and France and ... "
"My child, such a number."

Some allusions in The Devil's Arithmetic include one that is introduced in the very title of the book and is repeated throughout the story. It is the allusion to the Nazi’s arithmetic—or systematic extinguishment of the Jewish people. The Nazis try to strip people of their individuality and humanity and convert them to numbers tattooed on their arms. Hence the word "Arithmetic" in the book's title. The "Devil" in the title is an allusion to the Nazis.

This allusion is repeated in several places. The first time is when Hannah recalls something that occurred years earlier with Grandpa Will who has "strange fits, showing off the tattoo on his left arm and screaming in both English and Yiddish." When Hannah uses a ballpoint pen to create a tattoo on her own arm, it is also an allusion to the dream when Hannah becomes Chaya. Not surprisingly, Hannah's tattoo causes Grandpa Will much pain as he recollects his experiences in the death camps.

At the family seder, Grandpa Will's comment about what his sister Eva "would have given for a little glass of watered wine" is an allusion to the terrible conditions the Jews endured in the camps. The Nazis starved them, and they were constantly hungry and thirsty.

In the dream sequence, when Hannah/Chaya meets Fayge, Fayge says,

We are going to be such friends, you and I. Best friends. Life will be good to us forever and ever, I know.

Sadly, this is an allusion to the horrors about to come very shortly. The reader understands that life is not going to be good to them at all. Once they see the Nazis at the shul, the phrase "malach ha-mavis" is repeated, the Angel of Death.

Another important allusion is that of Hannah's Hebrew name: Chaya, life. At the camp, Gitl tells her:

You are a name, not a number. Never forget that name, whatever they tell you here. You will always be Chaya—life—to me. You are my brother's child. You are my blood.

Despite the intention of the Nazis to wipe out her people and the Angel of Death or malach ha-mavis, another allusion used throughout the book, Hannah is alive and represents their continuity. Life is something that she must remember when she remembers the six million. There are allusions to this throughout the book.

An allusion is a casual reference to a well-known place,story, book, historical event or work of art.  There are many literary and Biblical allusions in The Devil's Arithmetic.

When Hannah first meets Rachel and the girls at the wedding, she tells them stories  and totally entertains them.  The stories she tells them are current day movies, stories, and books. 

"Stories seems to tumble out of Hannah's mouth, reruns of all the movies and  books she could think of.  She told the girls about Yentl and then about Conan the Barbarian with equal vigor; about Star Wars, which confused them; and Fiddler on the Roof, which did not.  She told them the plot of Little Women in ten minutes, a miracle of compression, especially since her book report had been seven typed pages." (pg 50)

These are literary allusions since they are about movies and books.  Jane Yolan is alluding to literary works that she feels the reader will know and make a connection.  Another literary allusion is

"'So let me tell you about the Wizard of Oz' she said.  She couldn't remember which was the movie and which was the book.  Shrugging her shoulders. she began a strange mixture of the two, speeding along until the line 'Gosh, Toto, this sure doesn't look like Kansas." (pg 51)

This makes a literary allusion by not only giving the title of the book and movie but also by giving a famous, well-known line from the story.

An illusion that comes from Jewish mythology and deals with God is the story of Lilith's Cave.  According to mythology, when God first made man and woman, he made Adam and Lilith.  Adam wanted to govern Lilith, and she rebelled, leaving Adam and taking residence with the demons. She told the angel that God sent to get her that she was going to kill all the children. The entrance to the gas chambers was called "Lilith's Cave" in the book as an allusion to this myth. God then made Eve for Adam.  Fayge tells Hannah,

"Your words will fly up to heaven and call down the Angel of Death, Lilith's bridegroom, with his poisoned sword." (pg 67)

When Reuven is taken to the gas chamber, Hannah gets upset and feels that all humans are monsters for letting the Holocaust happen, Rivka tells her,

"God is letting it happen....But there is a reason.  We cannot see it yet.  Like the binding of Issac." (pg 142)

This is a Biblical allusion to the story of Abraham and Issac.  God told Abraham to sacrifice his only son to him, and Abraham went as far as binding his son to the sacrificial altar until an Angel of God stops him.  God had a reason for his request, and Rivka believes that God has a reason for what is happening to them. Rivka also says,

"You want to be a hero, like Joshua at Jericho, like Samson against the Philistines." (pg  142)

Again, these are Biblical allusions. Joshua, following God's orders, destroyed the city of Jericho and led his people into the Promised Land.  Samson, to whom God had given unbelievable strength, was betrayed by Delilah and captured by the Philistines, who cut out his eyes and made him work for them.  He pulled down the pillars around the Philistines, killing them and himself.

Finally, there is an allusion to a Yiddish proverb.  I do not know what it means, but it says,

"Afile brenen un bruin.... even if you should be burned and roasted.  Here that is not a proverb to be spoken aloud." (pg 143)

Certainly it is fascinating question to think about why any novel was given the name that it bears. There are two places in the novel that refer directly to the "devil's arithmetic" which explore why this concept is so important to the novel as a whole. Firstly, at the beginning of Chapter 16, Hannah/Chaya comments on her life in camp, talking about how each day that she remains alive is a cause for triumph:

Part of her revolted against the insanity of the rules. Part of her was grateful. In a world of chaos, any guidelines helped. And she knew that each day she remained alive, she remained alive. One plus one plus one. The Devil's arithmetic, Gitl called it.

Note how the title here is used to reinforce the desperate battle for survival that the Jews were engaged in, where every single day that they survived was a battle won and success.

In Chapter 17, the devil's arithmetic is given a different meaning as Hannah/Chaya desperately awaits for news of the escape plan from Gitl:

The days' routines were as before, the only change being the constant redness of the sky as train-loads of nameless zugangi were shipped along the rails of death. Still the camp seemed curiously lightened because of it, as if everyone knew that as long as others were processed, they would not be. A simple bit of mathematics, like subtraction, where one taken away from the top line becomes one added on to the bottom. The Devil's arithmetic.

Note here how the survival this phrase refers to explores how the deaths of the nameless Jews means life for the Jews working in the camp. It seems harsh that the Jews in the camp are able to be "lighthearted" for such a reason, and yet we must remember that the holocaust was an exceptional situation where the desperate struggle for survival changed the order of ethics and morals.

Arguably the most important symbol in The Devil's Arithmetic is that of the swallow. Hannah notices the swallows outside the concentration camp flying, singing, and hunting for insects. The birds are behaving normally, completely impervious to what is going on in the human world.

Although there is no freedom inside the camp, there is still plenty outside in nature. For nature, as represented by the swallow, is free, irrespective of the unimaginable evil that is being wrought upon this part of the world by the Nazis.

It's notable that when Hannah returns home to the present, she and her family's talk and laughter at the dinner table are described as dipping and soaring about them like swallows would be soaring in the air around the camp. This is an indication of just how free they are, especially by comparison with their ancestors.

Another important symbol in the story is that of Hannah's front door. Initially, it remains firmly closed, representing Hannah's closed-minded view of religion and general ignorance about her Jewish faith. But once the door opens, she's given a portal into another world: the world of her ancestors. Here, she will learn to appreciate the religious and cultural traditions of those who came before her. That being the case, the open door represents a greater degree of openness on Hannah's part to her Jewish faith.

There are many symbols throughout the novel, The Devil's Arithmetic, especially ones that come from Jewish traditions and folklore. For example, the Jewish people refer to the gas chamber/crematorium as Lilith's Cave, which comes from an old Jewish story about a female demon named Lilith who lures people into her cave when they look at themselves in the mirror. According to Jewish folklore, Lilith was Adam's first wife before Eve who would not be obedient to him. Lilith's Cave therefore represents hell and death for the Jews, as once they go into the gas chambers, they're never coming back. Another example is how the Nazis in command are referred to as Angels of Death or Dark Angels, because they would come for the "Chosen" or the Jews they had chosen to kill in the gas chambers that day.

However, in my opinion, the most poignant symbols are the sparrows that Hannah sees singing, flying, and diving for insects in the trees around the concentration camp. They are particularly powerful because Hannah notices them while the Jews are suffering inside the camp. They represent the idea that nature continues in spite of human evil, as the birds still sing happily as if nothing is happening. They represent the "freedom" right outside the walls and fences of the camp, which is so close and natural, yet unattainable. Hannah seems to watch them with envy because they are free to do as they will. When Hannah finally escapes the "dream" and returns to the present time where she is having a traditional dinner with her family, the author writes: "the talk and laughter at the table dipped and soared about them like swallows" ( Yolen 163). This symbolizes that Hannah and her family are free.

Some symbols in this novel are the door, the fever, and the time-slip itself. First, the door represents Hannah's views on religion. At first, Hannah has a closed-minded view of religion, which is symbolized by the closed door. However, when she opens the door to Elijah, she also opens her heart to her family and their religion.

Next, the fever symbolizes the confusion which Hannah faces when she first arrives in the village following the time-slip. The fever gives Hannah's neighbors and fellow villagers a reason for her strange questions when she first arrives, which allows the story to continue without revealing to the villagers the fact that Hannah truly is from the future.

Finally, the time-slip itself represents the passing on of knowledge from survivors to future generations, as it allows Hannah to gain knowledge of the Holocaust. There were many survivors of this event (though many more who did not survive), and their passing on of knowledge has allowed the story of the Holocaust to be remembered. In this novel, the time-slip itself symbolizes the passing on of that knowledge.

In my mind, the closet door is probably the most important symbol in Yolen's work.  The closet door is what Hannah must go towards to welcome Elijah during Passover Dinner.  The closet door is the portal by which Hannah must enter the past and become Chaya.  Given the fact that Hannah did not have much care for her heritage and ethnicity at the outset of the novel, the closet door represents a particular symbol that represents Hannah's moment where she is both active teenager who is concerned with traditionally adolescent aims, but also the instant where she becomes instantly connected with her identity.  The closet door is what allows the story in Yolen's work to develop.