"So, you might say that each piece of a hologram stores information about the whole image, but from its own viewing angle. No two pieces will give you a view that is exactly the same."
-Holographic Studio's FAQ
So here's what I'm thinking. Can a piece of Torah be taken out of context, and still be properly understood? If so, how far and how much of the "context" can be removed while retaining meaning? To illustrate this, consider the binding of Issac. If cut small enough the story is:
"Abraham, sacrifice your son to me and I shall bless you."
"Ok; I'll do it!"
But this is not the correct message of the story. Broadening our viewpoint, we see the "conclusion", with Abraham finding the ram to sacrifice in Issac's place. The meaning of the story is changed, is outright reversed in fact. But is that the end of the story?
Widen our view still farther; Abraham spares Issac, but Issac promptly leaves home and never sees his mother alive again. This represents a further changing of the story. It now can be seen as a parable about a father's overzealous religious devotion fracturing his family, chasing his son away and possibly hastening his wife's death. Is this the entire story?
Pulling our lens back further, we see earlier events as well. Abraham previously argued with HaShem to save the cities of Sodom and Gomorrah. So now we see someone with the chutzpah to argue for the life of strangers, but not to argue for his own son. How does that change our story?
Then of course there are the ripples of these events. The death of Lot's wife and the incest of his daughters follow from this moment, and that leads in turn to the birth of Jesus.
My point is this: does a single verse of Torah retain its meaning independent of the rest, or can it only be seen as a part of the whole? The discussion of holograms cited above continues by comparing "breaking" a hologram into pieces to viewing a room through slits in a curtain. Each view of the room potentially shows you the whole room, but only from a certain point of view; one slit shows a painting, but another shows just the frame.
When we consider the laws about widows and orphans, we only see "the frame" of Kashrut. They occupy the same "room", but few views allow us to see both fully.
So, fine. That's well and good. If you can't go inside the room to see the whole thing at once, then multiple viewpoints are good. They help you understand the whole in a sort of intellectual triangulation.
But too small a viewpoint is no good. Imagine viewing the same room through just a pinhole; you might only see a single chair, not nearly enough information to make deductions about the room's inhabitants. Multiple pinholes might show a chair, a table, and a lamp; more information, true, and it might tell us about the occupant's design sensibilities, but we still know almost nothing about the room as a whole.
This is what happens when people use a single line of Torah, a single pinpoint view, to make decisions. Does "no homosexuality" override the general context of "be kind to people"? Does our dominion over nature override the general context of Tikkun Olam?