This is a follow-up to an intriguing question last year about tension in string theory.
What are the strings in string theory composed of?
I am serious. Strings made of matter are complex objects that require a highly specific form of long-chain inter-atomic bonding (mostly carbon based) that would be difficult to implement if the physics parameters of our universe were tweaked even a tiny bit. That bonding gets even more complicated when you add in elasticity. The vibration modes of a real string are the non-obvious emergent outcome of a complex interplay of mass, angular momentum, various conservation laws, and convenient linearities inherent in of our form of spacetime.
In short, a matter-based vibrating real string is the outcome of the interplay of most of the more important physics rules of our universe. Its composition -- what is is made of -- is particularly complex. Real strings are composed out of a statistically unlikely form of long-chain bonding, which in turn depend on the rather unlikely properties that emerge from highly complex multiparticle entities called atoms.
So how does string theory handle all of this? What are the strings in string theory made of, and what is it about this substance that makes string-theories simple in comparison to the emergent and non-obvious complexities required to produce string-like vibrations in real, matter-based strings?
Addendum 2012-12-28 (all new as of 2012-12-29):
OK, I'm trying to go back to my original question after some apt complaints that my addendum yesterday had morphed it into an entirely new question. But I don't want to trash the great responses that addendum produced, so I'm trying to walk the razor's edge by creating an entirely new addendum that I hope expands on the intent of my question without changing it in any fundamental way. Here goes:
The simplest answer to my question is that strings are pure mathematical abstractions, and so need no further explanation. All of the initial answers were variants of that answer. I truly did not expect that to happen!
While such answers are sincere and certainly well-intended, I suspect that most people reading my original question will find them a bit disappointing and almost certainly not terribly insightful. They will be hoping for more, and here's why.
While most of modern mathematical physics arguably is derived from materials analogies, early wave analogies tended towards placing waves within homogeneous and isotropic "water like" or "air like" media, e.g. the aether of the late 1800s.
Over time and with no small amount of insight, these early analogies were transformed into sets of equations that increasingly removed the need for physical media analogies. The history of Maxwell's equations and then SR is a gorgeous example. That one nicely demonstrates the remarkable progress of the associated physics theories away from using physical media, and towards more universal mathematical constructs. In those cases I understand immediately why the outcomes are considered "fundamental." After all, they started out with clunky material-science analogies, and then managed over time to strip away the encumbering analogies, leaving for us shiny little nuggets of pure math that to this day are gorgeous to behold.
Now in the more recent case of string theory, here's where I think the rub is for most of us who are not immersed in it on a daily basis: The very word "string" invokes the image of a vibrating entity that is a good deal more complicated and specific than some isotropic wave medium. For one thing the word string invokes (perhaps incorrectly) an image of an object localized in space. That is, the vibrations are taking place not within some isotropic field located throughout space, but within some entity located in some very specific region of space. Strings in string theory also seem to possess a rather complicated and certainly non-trivial suite materials-like properties such as length, rigidity, tension, and I'm sure others (e.g. some analog of angular momentum?).
So, again trying to keep to my original question:
Can someone explain what a string in string theory is made of in a way that provides some insight into why such an unusually object-like "medium of vibration" was selected as the basis for building all of the surrounding mathematics of string theory?
From one excellent comment (you know who you are!), I can even give an example of the kind of answer I was hoping for. Paraphrasing, the comment was this:
"Strings vibrate in ways that are immediately reminiscent of the harmonic oscillators that have proven so useful analytically in wave and quantum theory."
Now I like that style of answer a lot! For one thing, anyone who has read Feynman's section on such oscillators in his lectures will immediately get the idea. Based on that, my own understanding of the origins of strings has now shifted to something far more specific and "connectable" to historical physics, which is this:
Making tuning forks smaller and smaller has been been shown repeatedly in the history of physics to provide an exceptionally powerful analytical method for analyzing how various types of vibrations propagate and interact. So, why not take this idea to the logical limit and make space itself into what amounts to a huge field of very small, tuning-fork-like harmonic oscillators?
Now that I can at least understand as an argument for why strings "resonated" well with a lot of physicists as an interesting approach to unifying physics.