"You always were the best rememberer I ever saw. We used to make a game of it. Tell you a line to memorize, or a song. Didn't matter how much time had passed, you'd have the whole thing in your mouth. Made your parents proud." (3.43)
In terms of memorizing things, Isabel is kind of a child prodigy. Jenny's recollection of her perfect memory, even as a child, foreshadows the way this gift will aid Isabel in her quest for freedom.
"Two words: 'ad astra.' It's Latin; it means 'to the stars.' Will you be able to remember it?"
"I never forget a thing, sir." (16.93-94)
Here's the payoff for that description of Isabel's child prodigy memory: She really doesn't forget anything. If you're going to be a spy at age thirteen, it only helps to be one who can remember stuff on cue. Especially secret passwords.
[Lady Seymour] paused in the doorway. "You miss your parents terribly, don't you?"
"While you lay in the fever, you spoke of them with great affection, as it they were in the room with us." (24.34-36)
In the midst of the aftermath of her branding, Isabel finds herself completely alone. Even as she lies partly unconscious in her fever, she still draws on the memory of her parents to comfort her.
I preferred the chores that took me out of the kitchen, for it was there the bees tricked me into seeing Ruth's ghost playing on the floor, churning butter, or counting out kernels of corn. When her voice whispered to me, I caught fire again, from my toes to my face, and I burned slow, like damp wood. (25.9)
Memory can help Isabel, but it can also hurt her. In the weeks after Ruth is sent away, she finds herself haunted by her sister, surrounded by reminders that she's gone. Not only that, but Ruth's absence reminds Isabel of the ordeal she went through with the trial and branding, and she can still feel the loss and the burning.
Christmas at home had meant eating Momma's bread pudding with maple syrup and nutmeg, and reading the Gospel of Matthew out loud whilst Ruth played in Momma's lap. I was miles away from celebrating like that. I tried to bury the remembery, but it kept floating to the top of my mind like a cork in a stormy sea, and foolish tears spilled over. (38.5)
Isabel's thoughts of Christmas with Momma and Ruth are another instance where her perfect memory inflicts pain. She's lost them both, and for the first time ever, she's spending this emotionally loaded holiday alone. It's also a cool example of Isabel's unique voice in the novel—there's something lyrical about "remembery" that fits her character more than the word memory would.
It took some convincing to explain my mission, but I spoke polite and firm and held out the bread pudding, and the children snuck out in their nightclothes and just about dove into the bowl. The mother took the basket and said, "Thank you," and then "Thank you again," and then "Thank you most, most kindly," and they went back inside.
I hummed a carol as I walked away, finally feeling at peace. (38.51-52)
Ultimately, memories of her past Christmases with family persuade Isabel to celebrate this year by doing an act of kindness for someone else. She bakes Momma's bread pudding, but rather than indulge herself by stuffing her face with it, she takes it to a Loyalist family in the district that suffered the worst damage from the fire. While she can't recreate her memories from the past, she can still give others the feeling of warmth and comfort she associates with them.
I dried my face. Why was I thinking of Ruth? I'd worked hard to pack her away from my mind, along with the thoughts of Momma and Poppa and the life Ruth and I were promised. Didn't help to ponder things that were forever gone. It only made a body restless and fill up with bees all wanting to sting something. (41.38)
Isabel's flawless memory becomes so much of a curse in the time after Ruth's departure that she actually wills herself to forget her family. Obviously, though, it's not quite that easy. No matter how painful the loss is, it's impossible for her to forget the family that has brought her through the pain of slavery.
Momma said we had to fight the evil inside us by overcoming it with goodness. She said it was a hard thing to do, but it made us worthy. (43.22)
Memory also plays a role in helping Isabel decide how to handle hard situations. Shortly after she recalls this lesson from Momma, she chooses to overcome Madam Lockton's evil intent for her through the goodness of protecting the Patriots by throwing Captain Farrar's note in the fire.
When Ruth and I slept down here, the far corner of the cellar went muddy in a heavy rain. Maybe the damp had eaten at the boards […] I sat back and put my feet on each board in turn and pushed. The third board I tried gave way a little. So did the next two. (43.69-70)
Isabel's memory is so amazing that it helps her break out of the potato bin. Specifically, her attention to detail and ability to remember even the smallest thing she notices give her the ability to escape.
I closed my eyes and thought of home; the smell of fresh-cut hay and the taste of raspberries. Robins chasing bugs in the bean patch. Setting worms to work at the base of the corn plants. Showing Ruth what was weed and what was flower…
I opened my eyes, dipped the quill, and wrote out my true name. (43.99-100)
Memory ultimately triumphs as one of Isabel's most important skills. Where it once caused Isabel great pain and reminded her of loss, her memory of home eventually empowers her to give herself a new identity: a free person named Isabel Gardener.