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I.e., in order to wade into it, or perhaps to swim through it, thus braving the seemingly fathomless deep: possibly a symbolic indication of the fear which a human being may feel when his own search after truth forces him to abandon the warm, soothing security of his erstwhile social and mental environment, and to venture into the - as yet - unknown realm of the spirit.
I.e., not a dangerous, bottomless deep, as it appeared at first glance, but, rather, the firm, glass-clear light of truth: and with her perception of the ever-existing difference between appearance and reality, the Queen of Sheba comes to the end of her spiritual journey.
Bilqis, having been received with honour on her arrival, and having accepted the transformation of her throne, placed presumably in an outer building of the Palace, is asked to enter the great Palace itself. Its floor was made of slabs of smooth polished glass, that glistened like water. She thought it was water, and tucked up her clothes to pass through it, showing her bare feet and ankles. This was a very undignified position for a woman, especially one of the position of a Queen. Solomon immediately told her the real facts, when she felt grateful, and joined herself with Solomon in praising Allah.
A gentle leader points out the truth. Instead of resenting it, the new entrant is grateful; acknowledges his own mistake freely and frankly; and heartily joins with the Teacher in the worship of Allah, the Source of all truth and knowledge.