In The Courage to Create, Rollo May shares a story from Jules Henri Poincaré, writing in his autobiography. In it, Poincaré describes many long days trying to sort out some mathematical question and finding no solution. When he finally becomes overwhelmed with failure, he skips town and goes to the beach. There, while walking, he has a sudden epiphany about the math that had previously escaped him. Of the experience, Poincaré writes:

Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to be incontestable, and traces of it would be found in other cases where it is less evident. Often when one works at a hard question, nothing good is accomplished at the first attack. Then one takes a rest, longer or shorter, and sits down anew to the work. During the first half-hour, as before, nothing is found, and then all of a sudden the decisive idea presents itself to the mind. It might be said that the conscious work has been more fruitful because it has been interrupted and the rest has given back to the mind its force and freshness.

May, The Courage to Create, page 64

And yet, it’s not rest alone that made the idea arrive, but the oscillation of effort and rest. Poincaré continues:

These sudden inspirations…never happen except after some days of voluntary effort which has appeared absolutely fruitless and whence nothing good seems to have come, where the way taken seems totally astray. These efforts have not been as sterile as one thinks; they have set agoing the unconscious machine and without them it would not have moved and would have produced nothing.

May, The Courage to Create, page 65

Just as importantly, the rest has certain characteristics. Here is May:

I propose that in our day this alternation...requires the capacity for the constructive use of solitude. It requires that we be able to retire from a world that is “too much with us,” that we be able to be quiet, that we let the solitude work for us and in us.

May, The Courage to Create, page 66

This brings to mind a note from The Burnout Society by Byung-Chul Han, who asserts that:

Today we live in a world that is very poor in interruption; “betweens” and “between-time” are lacking. Acceleration is abolishing all intervals.

Han, The Burnout Society, page 22

Poincaré’s epiphany required the interval, the between time, the suspension of expectation and structure. It wasn’t enough that he worked long and hard at a problem; it wasn’t enough that he took some time to rest; it was necessary, also, for him to go to the sea, to walk along the bluff—to welcome solitude and to let it do its work.

Without the interval, there is no solitude; without solitude, the unconscious machine sputters and gasps. Over time, I fear that the gears begin to rust, and it becomes harder to start it up again. But not impossible. Never impossible.