I have The Lettermen version of the song Windmills of Your Mind and I absolutely love it. I believe it is the best version I've ever heard of this song. It makes the interpretation easier to understand. What makes the song so difficult to interpret is that the song is meant to be felt, not just heard. Listen the to Lettermen version while you have your eyes closed and let your mind go with the imagery of the words. By the third stanza or paragraph, you will understand the song through your feelings. It opens up like a flower.
Here is my interpretation: The song is meant to convey the feelings of the singer as he grapples with the almost overwhelming emotional confusion brought on by the ending of a brief, but intense love affair.
As his mind races back to the beginning of their relationship, the first stanza describes the intoxicating joy of their passionate love (possibly a "first" love) with the "circle in a spiral" and "a wheel within a wheel" and the roller-coaster-like effect of new love "never ending or beginning on an ever-spinning reel". The joy of the relationship and how fast it grew is also conveyed with "snowball on a mountain" and "carnival balloon". And "a carousel that's turning rings around the moon" signifies the giddly heights of his affection and joy.
The repeating line "like a clock whose hands are sweeping past the minutes of its face" represents how fast time flew while in their relationship.
"And the world is like an apple whirling silently in space" represents the purity of their world and of their relationship.
This paragraph represents the feelings of despair as the realization of the relationship's ending sinks in.
Using imagery that expresses feeling hopelessly lost "Like a tunnel that you follow to a tunnel of its own, down a hollow to a cavern where the sun has never shown"
The nightmare feeling of her leaving him is expressed as "Like a door that keeps revolving in a half forgotten dream" and he feels the loneliness of her rejection with the line "or the ripples from a pebble someone tosses in a stream".
The repeating lines of "Like the clock whose hands are sweeping past the minutes of its face, And the world is like an apple whirling silently in space" are used here to describe the slowing of time as the relationship winds down and the solitary apple is now represents the feeling of sadness of being alone.
This paragraph brings us to the singer's present consciousness (signified by "Keys that jingle in your pocket") as he continues to relive his memories in search for answers.
"Words that jangle in your head" represent how distracted he is now.
"Why did summer go so quickly" represents the possible timespan of their affair.
"Was it something that you said?" represents the natural questioning we go through after a breakup.
"Lovers walk along a shore and leave their footprints in the sand" represents his romantic illusions of their relationship and, like footprints in the sand, how fleeting their relationship seemed.
"Is the sound of distant drumming just the fingers of your hand?" again, represents his inability to focus through his sadness or to even be aware of his surroundings.
"Pictures hanging in a hallway, and the fragment of a song, Half-remembered names and faces, but to whom do they belong?" probably represent the various artifacts of their relationship, including photos of the friends they made while they were a couple. "To whom do they belong?" could be questioning if these people are now HER friends or HIS friends. "Half remembered names and faces" indicates just how much he was emotionally invested in the relationship; to the point where everyone else was just in the background.
"When you knew that it was over, you were suddenly aware that the autumn leaves were turning to the color of her hair." I cannot do justice to this line, but it probably means that everything beautiful now reminds him of his lost love.
This paragraph is a repeat of of the "circle in a spiral" imagery which is to indicate that his sorrow continues as he tries to recover from a broken heart.
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