in this Sentence what does fathom mean?
There was a tiny dance
of melody in the air, her Seashell was tamped in her ear again and she was listening
to far people in far places, her eyes wide and staring at the fathoms of blackness
above her in the ceiling.
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mysteries, known depth
Or endless abyss
It's a reference to an obsolete unit of length, the fathom, which is 6 feet long. Fathoms were used for quite a long time (and in some cases still today) to measure the depth of bodies of water by sailors. It's a natural unit, because you measure the depth of water by tossing in a line with a weight on the end, letting it hit the bottom, then hauling it up and seeing how much line went out. When you are hauling the line in, you can easily measure how many multiples you haul in of the amount of line that fits between your outstretched arms. The distance between outstretched arms of a grown man is about 6 feet. Hence it's easy to measure out line in multiples of 6 feet, or fathoms.
Because of the critical importance of sailing and navigation to England in the16th through 19th centuries, a fair amount of nautical English found its way into common usage. "Fathom" was one of those words. Since when you talk about the depth of the ocean, your intuition suggests something very deep -- as well as dark and mysterious, holding strange surprises, possibly not very nice surprises -- a depth measured in fathoms has come to have the connotation of a murky and unknown depth. That's the sense in which "fathoms" is used in your passage.