Curled-up dimensions refer to spatial dimensions that are compactified to such a small scale that they become difficult to detect, akin to how a two-dimensional being might perceive a three-dimensional space. This concept is often illustrated using examples from classic video games, where moving off one edge of the screen leads to reappearing on the opposite side, suggesting a non-traditional geometry. The discussion highlights that while string theory proposes these curled dimensions, it lacks empirical evidence to support its claims, making it more of a mathematical philosophy than a confirmed scientific theory. Participants also explore the implications of living in such dimensions, including potential ways to detect them, such as observing the behavior of light beams in motion. Ultimately, the conversation raises questions about the nature of dimensions and their interactions, emphasizing the speculative nature of these ideas in theoretical physics.