muse +

(Latin: musum, "muzzle, snout"; Old French muser "to meditate, to ponder", perhaps literally "to go around with one's nose in the air" from muse "muzzle, snout")

amuse, amuses, amused, amusing (verb forms)
1. To divert the attention of someone from serious business by anything trifling, ludicrous, or entertaining.
2. To divert or to please with anything light or cheerful.
3. To amuse someone with an anecdote, by telling him or her a story; to amuse oneself with a puzzle, with, by, or in sketching; to be amused with a toy or whimsical person, by telling a story about an incident.
4. To cause (time) to pass pleasantly, to entertain agreeably; to "beguile", to while away the time, to enliven.
5. Etymology: from Middle French (1400-1600) amuser, "divert, cause to muse;" from à, "at, to" + muser, "ponder, stare fixedly".

The current meaning "divert, entertain" did not emerge into usage until the 17th century, and the most common application of the verb in the 17th and 18th centuries was to "deceive, cheat". Such meanings seem to have developed from an earlier "bewilder, puzzle", and pointed back to an original sense of "make someone stare open-mouthed". This is thought to link with the probable source of muser, namely muse, an "animal's mouth", from medieval Latin musum from which the English word muzzle came.

Everyone should keep in mind that there is no connection with this muse and the mythological muse from which music and museum are derived.

The sense of "divert from serious business, tickle the fancy of" is recorded from 1631, but through the 18th century, the primary meaning was "deceive, cheat" by first occupying the attention of a person, or people.

—Based on information from John Ayoto and Webster's Word Histories
amusement (s), amusements (pl) (noun forms)
1. The pleasurable occupation of one's attention, or diversion of the mind (from serious duties, etc.).
2. Passing from an idle time-wasting diversion, or entertainment.
3. Recreation, relaxation, the pleasurable action upon the mind of anything light and cheerful.
4. Pleasant excitement of the risible faculty by anything droll or grotesque, tickling of the fancy.
5. Anything which lightly and pleasantly diverts the attention, or beguiles the time; a pastime, a play, a game, or a form of recreation.
amuser (s), amusers (pl) (noun forms)
1. Someone who provides diversion; a diverter, an entertainer.
2. In the past, someone who put people in a muse; that which arrests or distracts attention; especially, with trifling or insignificant things.
3. Someone who trifles with people's attention or expectations; a trifler, deceiver, a cheat.
amusive (adjective)
1. Affording pleasing entertainment.
2. Engaging the attention, interesting.
3. Tickling the fancy or exciting laughter.
bemuse, bemuses, bemused, bemusing (verb forms)
1. To make utterly confused or muddled, as with intoxicating liquor.
2. To cause to be emotionally confused or to put into a stupid stare, to stupefy: "Since she usually appeared to have an opinion about everything, her silence on this particular subject bemused him."
3. To cause someone to be preoccupied or lost in thought: "The news about his ex-wife getting married again bemused him."

"Since he thought of himself to be an ordinary student, he was bemused by all of the attention that he was getting from the class."

bemusedly (adverb)
In a bemused or bewildered manner or condition.
bemusement (s), bemusements (pl) (noun forms)
In a bemused condition or confusion resulting from failure to understand: "She smiled with bemusement when he made the remark about her dress."
muse (s), muses (pl) (noun forms)
1. Someone who causes another person to have ideas about creating a work of art; or who inspires an artist, writer, etc.: "The writer lost his muse when his wife left him."
2. Someone or something that provides the enthusiasm and determination for an artist, poet, musician, etc. to create something artistic: "When an artist pleonastically asked her husband if she should paint a still life or a portrait, or both of them on the same canvas; his response was, 'Are you trying to amuse your muse with redundancy?' "

—Inspired by the "Garfield" cartoon strip by Jim Davis; May 3, 2011;
as seen in The Global Edition of the New York Times, page 15.
muse, mused, muses, musing (verb forms)
1. To be absorbed in one's thoughts; to engage in meditation: "She was musing about what might have been if she had finished her education."
2. To consider or to say thoughtfully: "She mused that it might take longer to drive than to walk."
3. To think about something in a deep and serious, or dreamy, and abstracted way: "He mused about the possibility of changing jobs."
4. To say something in a thoughtful or a questioning way: "I think we could sell our house, she mused; but then where would we move to?"
5. To gaze at someone or something thoughtfully or abstractedly: "She was musing what her new-born son would grow up to be."
6. Etymology: from Old French muser, "to meditate", and perhaps literally "to go around with one's nose in the air", from muse, "muzzle, snout", from medieval Latin musum source of the English word muzzle.

Muse comes with the meanings of "ponder, meditate," and implies focused attention, but it suggests a less intellectual purpose.

It often implies absorption and a languid turning over of a topic as if in a dream or in some kind of remembrance.

museful (adjective; musefully (adverb)
1. Deeply thoughtful; pensive.
2. Meditative; thoughtfully silent.
muzzle, muzzler (noun);
1. The projecting part of an animal's face, made up of its nose and jaws.
2. A device that is strapped over the nose and jaws of an animal to prevent it from opening its mouth, e.g. to bite, bark, or eat.
3. The front open end of the barrel of a firearm.
4. Something that is meant to prevent free expression; such as, to muzzle the press when reporting on a military operation.
5. Transitive verb forms: (past and past participle muzzled, present participle muzzling, 3rd person present singular muzzles):
6. To put a muzzle over the nose and jaws of an animal.
7. To prevent a person or group from publicly expressing their views or opinions.
8. To roll up and secure a sail.
9. Etymology: from Middle English mosel, from Old French musel, from Medieval Latin musellum, diminutive of musum, "muzzle, snout".
muzzle, muzzles, muzzled, muzzling (verb forms)
1. Something that is meant to prevent free expression; such as, to muzzle the press when reporting on a military operation.
2. Placing a muzzle over the nose and jaws of an animal; such as, a dog to keep it from biting someone: "Our dog has a tendency to bite strangers who walk near him, so he needs to be muzzled; in fact, we muzzle him whenever we take him out for a walk."
3. To prevent a person or group from publicly expressing their views or opinions: "The company tried to muzzle its employees by forbidding them to speak to the press about the accident."
4. To roll up and to secure a sail on a boat.
overmuse, overmuses, overmused, overmusing (verb forms)
1. To overcome with bewilderment: "The tornado was so severe and shocking, that many people were simply overmused."
2. To muse too much; to become weary or to bewilder oneself by excessive meditation: "Sometimes she overmuses herself and doesn't know what is going on."
unamused (adjective)
Not amused; not considered entertaining nor amusing: "No matter how much he tried to entertain her with jokes, she was still unamused and upset about her son going into the military."