Terrence J. Rynne, a professor of Peace Studies at Marquette University has an interesting interpretation of the Eucharist (last supper).

Using the Sermon of the Mount interpretation of nonviolence and the oneness of all humans he has a different concept of what the words mean -

"Do this in memory of me" - Do this action, this sacrifice, in memory of me. When you do this action, you make me really present again under the species of bread and wine. The Second Vatican Council considered it to be a celebration of a meal whose purpose is to form a community in Jesus' name. All the participants could communicate with one another as in a family meal.

It also takes on the meaning that the community meal is a way that you really become a community that supports one another.
 
Finally, it has taken on the meaning of "Do this way of acting that I have shown you. Do this way of resisting evil and returning good for evil that I lived and taught. Do it even if it is hard and stirs up resistance. Do it filled with love, because you know that you are loved."

"Do this in memory of me" could also have to do with the specialness of the supper. The last supper was the passover supper. It was a time for the jews to remember the blood of the lamb that caused death to pass by their door in egypt and to remember God's unfailing love and faithfulness. By saying "do this in rememberance of me" he could be calling himself the sacrificial lamb, which is pointed out at other points in new and old testament; and the do this is remember him everytime you eat.

For me, the difference is the perspective.  One is one my actions.  The other is on His actions.  (And no, I don't consider them to be two different perspectives of the same thing.)  In the first, I am trying to do what he did.  In the later, I admit that I could never do what he did, and remember, with love and appreciation, that he did it for me.

Because the one cross I can not carry is the cross he carried for the sins of the world.  Yes, I can love as he loved.  Heal as he healed.  Teach as he taught.  And together as the Body of Christ (note: one body) we can do more than he did.  But I honestly believe that only he could "give his life as a ransom for many".  I needed "a bridge" to God.  He supplied that "bridge".  I want to remember that.  Respect that.  And even point the direction out to others so they can find the "bridge".  But the one thing I can't do is be the "bridge".

But thanks for pointing out that verse.  Love the research.  And it is an important verse for us to remember.  And I don't disagree that the Communion should remind us that as Christ Followers we have to be willing to give our bodies and, if necessary, shed our blood in service of others.  So it is a great perspective.  I just don't want to make my sacrifice the equivalent (specifically chosen word) of his.

If you don't mind, I'd like to argue semantics. I beleive that not only can we, but we are called to be the bridge. As a body we are called to make the kingdom of heaven reign here on earth. We are called to be the intercessors for those who don't know Christ. I beleive that we are the bridge between the nonbeleivers and Jesus/God.


Now, I will agree with the tearer of the sin veil. We can not bear the sins of this world and wash them clean. But, in part, that is because that was already done by Jesus and there is nothing left ofr us to do in that area.

And this too is a valid interpretation. 

But can you accept that the others also make sense for those who interpret them as such?