Lucy in the Sky with Diamonds

My parents and I got into a debate over the meaning of this song. I say (like alomst everyone else) that this song is about LSD. My parents say that it is just a song about a girl.

Here are the lyrics, decide for yourself:

Lucy in the Sky with Diamonds

Picture yourself in a boat on a river
With tangerine trees and marmalade skies.
Somebody calls you, you answer quite slowly,
A girl with caleidoscope eyes.

Cellophane flowers of yellow and green
Towering over your head.
Look for the girl with the sun in her eyes
And she's gone.

Follow her down to a bridge by the fountain
Where rocking horse people eat marshmallow pies.
Everyone smiles as you drift past the flowers
That grow so incredibly high.

Newspaper taxis appear on the shore
Waiting to take you away
Climb in the back with your head in the clouds
And you're gone.

Picture yourself on a train in a station
With plasticine porters with looking glass ties,
Suddenly someone is there at the turnstile,
The girl with caleidoscope eyes.

[Ref:] Lucy in the sky with diamonds
Lucy in the sky with diamonds
Lucy in the sky with diamonds, ah, ah