Stead

One night, after Stead had gone on for an ailing lead, a stagehand's daughter named Bit asked how she managed to seem like a completely different person.

"I didn't become someone else," said Stead. "There was an empty place in the play — a spot marked for the lead. I stepped into that spot and did what it needed. The play didn't change. Only the person filling the place did." Bit turned this over. "So the play had a hole shaped like a person," she said, "and you fit yourself into it, and it worked out to a whole play again." "A hole shaped like a person," Stead repeated, delighted. "Exactly that." That night she wrote inside her script: A PLACE HELD OPEN. Step in, do what the place needs — and do it EVERY time the place appears — and the whole thing works out.

After that Stead saw held-open places everywhere — a seat kept for a guest, a blank on a form waiting for a name, a gap in a wall where any stone of the right size would do.

A year later the EquationQuest academy, forever trying to explain what the mysterious letter x actually is, heard of a theatre understudy who "stepped into a held-open place and made the whole thing work out." The master wrote to her. Stead, who had spent enough evenings in the wings, accepted.

The board, Stead found, was a stage full of held-open places, each marked not with a chalk cross but with a letter. She wrote: 2x + 1.

"A play with a place held open," she said, and tapped the x. "This x is not a number yet. It is a mark on the stage — a variable, a spot waiting for someone to step in. The play can't finish until the place is filled. Now — suppose I tell you that today, x is 5." She wrote x = 5 to one side. "Then I do what an understudy does: I step 5 into the place where x stood." She wrote it slowly: 2x + 1 becomes 2(5) + 1. "And notice I put the 5 in brackets — because 2x always meant two times x, so stepping the value in keeps the multiplication the part called for. Two times five, then plus one: 10 + 1 = 11. The letter is gone; the 5 stands in its stead; the scary symbol became a plain number the instant something stepped in."

"So x was never really a mystery," said Bit's cousin in the front row. "It was just a place waiting for a value." "A place waiting for a value," said Stead. "That's the whole of substitution. And here's the discipline that makes it faithful: the same value fills every copy of the same letter. If an expression is x² + x and today x is 5, then both x's become five — 25 + 5 = 30. You don't get to make one of them a different number. A place held open means the same player, wherever it appears."