What does it mean to think carefully about something, or to ponder?

To think carefully about something or to ponder is best captured by the term "cogitate." This word implies a deep and considered process of thinking, often involving reflection and deliberation. When someone cogitates, they are not just fleetingly considering an idea; instead, they are engaging in a thoughtful examination of it, weighing different aspects and possibly contemplating consequences or complexities.

The word "decide," while related to making a conclusion after consideration, lacks the depth of thought implied in pondering. Similarly, "speculate" often refers to forming theories or conjectures without firm evidence, which can suggest a more uncertain or superficial form of thinking. "Discuss" involves talking about an idea with others, which can facilitate deeper thought but doesn't inherently emphasize the individual contemplation that the term "cogitate" does. Thus, cogitating is the most accurate term for processes of careful and profound thought.