Final answer:
In 'The Time Machine', the Time Traveller mentions a sphinx to foreshadow danger, connecting to its role in both Greek mythology and Egyptian culture as a guardian and herald of peril.
Step-by-step explanation:
In The Time Machine, the Time Traveller repeatedly mentions a sphinx because it foreshadows danger. This symbolism ties into the Greek mythology of Oedipus and the Sphinx, wherein the creature asked travelers riddles that, if unanswered, would lead to their demise. Furthermore, within Egyptian art and culture, the sphinx is a fixture often found guarding tombs and temples, such as those at Karnak and alongside the pyramids, suggesting a protective yet perilous role. The sphinx in H.G. Wells' narrative alludes to both its mythological and historical significance, serving as a harbinger of the challenges and threats the Time Traveller will face in the future world.