The Arch lays the fertile ground – or foundation – to St.Louis and gives birth to the rest of the nation, symbolized by the symbols of fertility on the Arch grounds.
The Sphinx alludes towards the mind ascending to take dominion over the processes of life, disorder, and destruction being overcome. It represents equilibrium or the balance of all forces of nature, it also intimates illusion and like the Sphinx of Oedipus sits ready to destroy all incapable of answering it’s riddle. The whole sphere of Nature as man knows it is but a shadow of reality. The Sphinx is the keeper of the gates of mystery, illusion itself is the keeper of reality and illusion destroys itself when we give the right answer to life’s riddles. Though there is only one, the Sphinx of Egypt guarding the Giza complex, looking East, watching the sunrise, these two sphinxes sit back to back watching the sunrise and sunset as if they’re the keepers of this illusion we call reality (crowning the Wheel of Fortune). These sit just like the Sphinx on the Wheel of Fortune card in Tarot crowning the wheel declaring the entire wheel itself is an illusion.
Credit for the large majority of the interpretation goes to Yolanda M. Robinson and Manly P. Hall