【Ponder】 , 【meditate】 ,  【muse】 ,  【ruminate】  can mean to consider or examine something attentively, seriously, and with more or less deliberation.

【Ponder】  characteristically retains its original implication of weighing and usually suggests consideration of a problem from all angles or of a thing in all its relations in order that nothing important will escape one; unlike weigh in a related sense (see CONSIDER 1 ) it does not usually suggest a balancing that leads to a conclusion.

【Meditate】  adds to  【ponder】 an implication of a definite directing or focusing of one’s thought; in intransitive use, especially, it more often suggests an effort to understand the thing so considered in all its aspects, relations, or values than an effort to work out a definite problem. In transitive use  【meditate】  implies such deep consideration of a plan or project that it approaches intend or purpose in meaning.

【Muse】  comes close to  【meditate】 in implying focused attention but it suggests a less intellectual aim; often it implies absorption and a languid turning over of a topic as if in a dream, a fancy, or a remembrance.

【Ruminate】  implies a going over the same problem, the same subject, or the same object of meditation again and again; it may be used in place of any of these words, but it does not carry as strong a suggestion of weighing as  【ponder】 , of concentrated attention as  【meditate】 , or of absorption as  【muse】 , and it more often implies such processes as reasoning or speculation.