"I could dig the hole! I could dig the hole! LET ME DIG THE HOLE! Please."
The Steam Shovel Operator says this to the Clown as the Clown digs a grave for Mary. The Operator wants to use his invention to quickly dig the massive grave, but the Clown ignores him as he knows that digging the grave shovel by shovel allows him to never forget what happened that day.
"But not me. I eat peanuts. Stops it all from blurrin' together. All them colored boys led out to the yard must blur togethert something' fierce, 'cause noboy ever talks aobut how they hung colored boys in Erwin. They just talk about how they hung an elephant. Damdest thing. Damdest thing.
Peanut?"
The Hungry Townsperson says this to the audience at the end of the play. He says he eats peanuts to help him remember, that elephants' brains are like traps. That all the peanuts the animal eats may be the reason for their long memories. His statement digs into the theme of how people so soon forget the horrors perpetrated upon human beings. They're capable of remembering Mary the elephant's horrible hanging, but sooner forget or bury the brutal hangings of young black men.
"And we can do anything we dream of. Anything at all."
The Marshal here is talking about America, how in America you can do anything you dream of; that killing Mary is the realization of a dream come true. That the impossible has become possible. It is the horror of the misinterpretation of progress which allows the expense of humanity.