to fix full attention on something: to look at it closely or think it over carefully
TranslatabilityApproximateCertaintySettled
This verb joins careful looking with careful thinking. The plain word behind it means "to perceive with the mind, understand" (νοέω); the prefix pins that attention onto one thing, so the word means to take a good, deliberate look and take it in.
Sometimes the attention is with the eyes: Moses turning aside to study the burning bush, a man peering at his own face in a mirror, sailors making out a bay in the distance, or a person eyeing the speck in someone else's eye. Sometimes it turns inward to reflection: Jesus telling his hearers to "consider" the ravens and the lilies until the lesson lands, or the letter to the Hebrews urging readers to keep their eyes on Jesus and to think hard about how to spur one another on. The same verb can also mean noticing what is really going on, as when Jesus saw through a trick question.
It is stronger than a passing glance. Where the ordinary word for looking (βλέπω) can be momentary, this verb points to attention that stays on its object until understanding follows.
Nuances
1ato look closely at something, observing it with fixed attention
here the looking has turned into seeing through something to what is really going onLuk 20:23
Both
both name coming to notice what is actually thereLuk 20:23
Only perceive
"perceive" can sound like a passive impression, while this verb is active, deliberate attention
How katanoeō differs from similar Greek words
βλέπωthe ordinary word for seeing or looking, without the fixed, studying attention this verb carries.
θεωρέωto watch or behold, often as an onlooker taking in a sight; this verb adds the mental grasp that turns looking into understanding.
νοέωthe plain verb for perceiving with the mind and understanding; this compound aims that mental perception at a specific object and adds the act of looking at it.
Reaches down to plain noticing: simply catching sight of or spotting something, with no careful study implied. The sailors just make out a bay with a beach.Act 27:39
Can be a purely inward act of weighing a fact in the mind, with no looking involved at all. Abraham reckons the deadness of his own body when he thinks about God's promise.Rom 4:19
Ranges into perceiving what someone is really up to, seeing through an intention rather than an object. Jesus discerns the trap behind his opponents' question.Luk 20:23
Both
Both name deliberate, attentive consideration that goes past passive sight, fixing the mind on something to take it in and learn from it.Heb 13:7Heb 10:24
Looks something over closely and in full, examining it carefully rather than glancing at it. In Athens Paul does not merely see the altars but scrutinizes the objects of worship as he moves through the city.Act 17:23
Reviews the whole course of something already completed, taking its measure by looking back over it. It is used for reflecting on how the lives of past leaders turned out.Heb 13:7
Turns up most often in the negative, for what a person fails to notice about himself while spotting the same fault in someone else.Mat 7:3Luk 6:41
Names the mind working out what is really going on, so it can be rendered "perceive" where there is nothing for the eyes to rest on, such as a hidden motive or a plain fact a man must face about himself.Luk 20:23Rom 4:19
Asks for attention held long enough to change the one paying it, which is also why it fits the man who takes a good look at himself and then walks off and forgets.Heb 3:1Heb 10:24Jas 1:23Jas 1:24
Reports the moment of making something out and recognizing what it is, whether a strange sight up close or a stretch of coastline at a distance.Act 7:31Act 27:39
Both
Both point a listener at something in the world so that he learns from it, and the two Gospel forms of the same saying about God's care use one word each for the birds.Mat 6:26Luk 12:24
Both describe eyes fixed on something actually present and taking it in, whether a crowd still staring at the sky or a man peering at what has just come down in front of him.Act 1:11Act 11:6
Covers plain eyesight, the bare ability to see anything at all, so it is the word used when sight is lost or restored.Mrk 8:25Act 22:11
Describes one person's eyes settling on another at a decisive moment, where the look itself does the work of the scene and no words are needed to explain it.Mrk 10:21Luk 22:61Mrk 14:67
Marks the pause before a hard saying: the speaker fixes his eyes on the people in front of him and only then speaks.Mat 19:26Mrk 10:27Luk 20:17Jhn 1:42
katanoeō in the other biblical languages
בִּיןHebrew“to understand”the Hebrew verb for discerning or understanding; it covers the reflective side of this word but not its careful looking.
נָבַטHebrew“to look”the Hebrew verb for looking intently or gazing; it covers the attentive-looking side but not the reflection.
What scholars say about katanoeō
κατανοέω is the intensive compound of νοέω "to perceive, understand," the κατα- prefix directing the perception fully onto its object (BDAG; LSJ). BDAG groups the New Testament uses under two heads: observing something perceptible to the senses (Mt 7:3;Lk 6:41; 12:24, 27; Acts 7:31-32; 11:6; 27:39; Ro 4:19; Js 1:23-24) and considering or contemplating (Heb 3:1; 10:24), with Lk 20:23 shading into discernment. Behm, treating the whole νοέω word-group in TDNT, notes the movement in these compounds from sense perception toward reflective understanding. The lexica agree on the range, and there is no significant dispute over the meaning.
Sources
BDAG, s.v. κατανοέωlexicon
LSJ, s.v. κατανοέωlexicon
J. Behm, "νοέω κτλ.," in Theological Dictionary of the New Testament, vol. 4theological-dictionary