Big enormous question, Molly.  Where to begin?  I'm not even a mathematician.

But this quote from the Guernica thread riled me a little:

But I agree that something has dramatically changed in art. It seems that in our time, as of very recently, the artist no longer feels addressed, called upon to bear witness. Of course, art is still about the expression of  individual consciousness, but this is importantly different. Somehow the proliferation of technology to capture images, to store them, to record, to substitute for memory has -- prematurely of course -- made art's function as a witness seem obsolete. "Can you describe this?" No one would ask this question in our time.  They would record it digitally from every possible angle.

I ask the artists, is this true?  Do you not feel compelled to bear witness?  Someone explain this for me.  Describe it.
Can it be that there will be no more paintings or music or poetry because of advances in technology?  Or am I reading this wrong?

And the final question:

How would you describe the nature of scientific creativity? Has it changed since the nineteenth century? Has it changed appreciably since the introduction of computing machines -- whether Turing machines or their more modern counterparts?

I cannot address the nature of scientific creativity, it's far beyond my capabilities.
I'm not a scientist but from my feeble observations of it, it seems that science has turned more inward than outward.
No more Saturn rockets.
iPods and Chip Implants instead.  Tiny machines that can extend our minds and memories and our consciousness.  It seems to be going into the tiny realms which in actuality are not tiny at all, they are foundational to the existence of all that is, where a rocket is not.  Even the large Hadron Collider is looking for the ultra small particle that made us--or something like that.

And an observation regarding the vampires:  There's always been a fascination with the things that are not quite human and yet are.
Mr. Spock,  Data the Robot, The Terminator, The Shadow.  Things that stand off to the periphery looking like we do but remaining aloof.  There's a yearning for something more perfect and less hobbled by emotion and desire.

Maybe when humans are all cyber-beings we really won't have any need for art or whimsical representation of anything.
But did anyone see the movie Equilibrium?

Hmmm, much to think about.
First, about the "art as a witness" quote, my reading of it (especially in the context of the original post) was really primarily as a lament -- "many people choose recording everything over the difficult process of distilling it into a memory you can then carry. Something crucial is being lost here." Even though the act of interpretation and distillation is still possible, it has a different urgency. If Picasso hadn't painted Guernica, a lot of people would have never been exposed to anything like a visual, emotional account of the event. If CNN had been there, Picasso could have still done the painting, but he wouldn't have had the pressure of "it's up to you to distill this incomprehensible, overwhelming event into something which later generations can actually see and remember." If the person you love can be photographed, you can draw their portrait for many reasons, but it loses its status as a functional act, a necessary way to remember.  It's like what refrigeration, or for that matter vacuum packing, has done for vegetables. No need to rush in and savor the tomato off the vine on this one perfect day... when you get around to it, it will be there. The relation to time is different. Probably a lot of other things change, too, as a result.

And doubtless these same sorts of things will affect science. I remember once reading that the proper way to do an archaeological dig is to excavate half the remaining site, the idea being that in the process of digging a lot of information is destroyed (what soil went where, for instance) and no matter how good your tools are, there's probably something they can't pick up on; so out of courtesy to the future you're supposed to leave a bit of the place intact for future advances and future instruments. So there you have creativity defering to the mechanistic!

Linda, your insight about the large and small (inner and outer) is wonderful. Molly, I wonder whether this has in some way to do with the kinds of fundamental questions you described, atoms almost, thinking and rethinking foundations?

Thinking back to the nineteenth century, it's hard to imagine how much has happened in science -- geology, cosmology, physics, evolution, not to mention biology, chemistry and mathematics -- there's that movement inwards again. Is there a meaningful way in which we are able to distinguish "mechanistic" thinking from "creative" thinking along the way? Certainly there's a big industry in computer-aided theorem proving and theorem checking. I'd expect many people have an intuitive feeling for what creativity is in this context, but how to articulate it?

A couple of really tiny comments.
I think the question of whether mathematics in general is a creative process is a very interesting one. What does discovery mean, compared to aesthetic creation. What happens when computers prove theorems and not people. For example, what's called the four color problem was famously proved by a computer rather than a person., by going through all the options. Yes, a person programmed it to check, but no one can check if the program made a mistake. It's a tough question.

Linda mentions: "Even the large Hadron Collider is looking for the ultra small particle that made us--or something like that."
Something which amused me in the development of cinema is how in the 50s-70s they created these tiny models to seemingly recreate huge things. For example filming a tiny model of a starship which would look huge on screen.
In the 80s and 90s the roles were almost reversed, where the bat-plane (for Batman 2) was I think larger than the one in the movie. The models started to get huge.