You imagine yourself at sixty-five. The face is yours, older. The voice is yours, lower. You can picture this person clearly. You're saving for him. You're planning around him. You're working hard now so he can have ease later. He doesn't exist. You've never met him. The person at sixty-five will be a stranger, partly shaped by what you're doing now and partly by everything you can't predict. The image you have of him is a fiction you treat as a fact.
K's observation about continuity: the continuous person you imagine yourself to be is the source of most fear. The continuous person is what dies. The continuous person needs to be defended. The continuous person carries grudges, makes promises, fears the future, regrets the past. Take the continuous person away and most of the heavy machinery of fear loses its subject. There's no one for the fear to be about.
Continuity is constructed every morning. You wake up. The mind retrieves the autobiography. Today's you links to yesterday's you and projects to tomorrow's you. The link feels seamless. It isn't. The linking is the work of memory plus narrative. The actual person now isn't identical to the one who fell asleep last night. The continuity is a story you tell, every morning, that lets you keep being the same person. Useful for some purposes. Catastrophic for others.
When the story of continuity briefly drops, the experience is sometimes called waking up. Not the literal kind. Something else. A morning when the autobiography doesn't resume. The body is in the bed. There's breath. There's light through the curtain. The full I am Susan, and I have these problems, and these plans, and these worries — that whole package hasn't loaded yet. The few seconds before it loads are some of the lightest seconds people experience. Then the package loads, and the day proceeds, and the package becomes invisible again.
Continuity is the illusion that makes the fragment fearable. Drop the belief in tomorrow's you and most of the fear about tomorrow's you goes. K wasn't saying you shouldn't plan. He was saying: notice that the planner is constructing the planned-for, and the construction is what generates the fear of failure of the plan. The fear belongs to the fiction.