"Thirteen Ways of Looking at a Blackbird"

I know a lot of people had mixed feelings about this poem, and in way I do too. It's definitely strange. I think I like it, but I'm not really sure why.

This is the way I look at it:

Thirteen ways of looking at a blackbird --> thirteen(+) ways of looking at this poem --> thirteen(+) ways of looking at anything
But all of these ways are connected by some thread; all of these potential meanings make up a whole and are all part of the same thing.

No matter who you are, where you are in the world, etc., you're looking at something that someone else has seen. Your experience of it may be different, but there's at least some element that is the same.
I'm not sure if that's what Stevens meant, but I see a lot of symbols of unity and cyclicality throughout this poem:

"A man and a woman and a blackbird 
Are one."  

... 

"But I know, too,That the blackbird is involved
In what I know." 

... 

"When the blackbird flew out of sight,
It marked the edge
Of one of many circles." 

... 

"The river is moving.
The blackbird must be flying."

 

All of these images give me the sense that everything is connected. Stevens gives us thirteen different snapshots to demonstrate the multiplicity of perception and experience, but keeps returning to this theme of cohesion.
The verse that says, "The blackbird whirled in the autumn winds./It was a small part of the pantomime" is what first drew me to this idea. "Pantomime" is an interesting choice of words - it places the blackbird in the context of a theatrical performance, which is something in which several different elements are orchestrated to contribute to an overall effect. No matter what you choose to focus on - the acting, the costumes, the lights - and how you experience it, everyone in the audience is seeing the same play.

These are the ideas that stood out to me, but this is probably just one of the many ways to interpret this poem.