a scarf short of a sandwich

People are strange, sang The Doors,
And they was bang on, Mom, don't ya think?
Ill mental health for one in four
And we all just gotta hope the floor
Doesn't open up -
To assist us in our will to sink.

And the sane are few and far between
If they exist?
I'm doubtful Doctor, that many minds
Live in a 'normal' realm,
It rarely seems to be
Something we can outwit.

Drug induced or genetically anxious?
Panic attacks or a lifelong madness lived?
In which beside yourself, you sit,
Trying to make the pieces fit
On the jumbled jigsaw puzzle
(That's your brain).

Does anyone really float
Through life on a hardy boat oblivious
To all kinds of mental delirium?
Staid, placid, steady away,
Impervious to the madness
That surrounds their steadfast steed?

And "Why do you wear that
Thing on your head?" I said, intrigued,
"For protection of course",
"But protection from what, my friend?"
"Exotic birds and stuff",
And the next time I saw him

He'd shed this scarf,
I don't know what this means.