Each doubling outweighs the past

Write the series down. Two is more than one. Four is more than one plus two. Eight is more than one plus two plus four. Sixteen is more than everything before it.

That is not a coincidence. If you keep doubling, each new step is greater than the sum of all the steps that came before. The newest square is not a topping. It is most of the pile.

Go back to the chessboard. The first square of the second half already beats the entire first half. The second half of the board is not “the rest of the wheat.” It is almost all of the wheat.

If a climb is doubling, the loud week is not a small extra. It is larger than every quiet week you already lived through, added together.

The tempting mistake is to treat the last doubling as one more similar piece, because it is only “one step.” One step in this rule is not one brick. It is a new pile.

That is what lets you look at a finish line from the other direction.