Depth

I'm pretty sure self-serenity is pretty universal description of a deep wise person.

A Buddhist response

Excerpt from: the Bala-pandita Sutta: The Fool & the Wise Person
translated from the Pali by
Thanissaro Bhikkhu
? 1998-2009

Dialog between the Buddha and monks.

"So what difference, what distinction, what distinguishing factor is there between the wise person and the fool?" [asks the Buddha]

"For us, lord, the teachings have the Blessed One as their root, their guide, & their arbitrator. It would be good if the Blessed One himself would explicate the meaning of this statement. Having heard it from the Blessed One, the monks will remember it."

"In that case, monks, listen & pay close attention. I will speak."

"As you say, lord," the monks responded.

The Blessed One said, "The ignorance with which the fool is obstructed, the craving with which he is conjoined, through which this body results: that ignorance has not been abandoned by the fool; that craving has not been destroyed. Why is that? The fool has not practiced the holy life for the right ending of stress. Therefore, at the break-up of the body, he is headed for a [new] body. Headed for a body, he is not entirely freed from birth, aging, death, sorrow, lamentation, pain, distress, & despair. I tell you, he is not entirely freed from stress & suffering.

"The ignorance with which the wise person is obstructed, the craving with which he is conjoined, through which this body results: that ignorance has been abandoned by the wise person; that craving has been destroyed. Why is that? The wise person has practiced the holy life for the right ending of stress. Therefore, at the break-up of the body, he is not headed for a [new] body. Not headed for a body, he is entirely freed from birth, aging, death, sorrow, lamentation, pain, distress, & despair. He is, I tell you, entirely freed from stress & suffering."

From Access to Insight

In early Judaism, there is the Judgment of Solomon, which through story illustrates wisdom. I would interpret this story as wisdom being the ability to find that one thing that clearly differentiates the two.