The main difficulties in giving an accurate and brief statement of what physics is for someone who's never seen anything like it are (1) that physics is a very big subject and (2) that your stipulation about the audience seems to be intended to assume they don't know any mathematics to speak of either.
Are you claiming that DI is a hugely varied subject like physics? (If so: How is that even possible, given how recent it apparently is?)
Are you claiming that DI depends on a large and conceptually very difficult substrate, as physics does with mathematics? (If so: What is that substrate?)
If the answers are both "no", then I'll adjust your question to fix those two mismatches, and attempt to give a brief summary of (not all of physics, but) Newtonian particle mechanics for (not someone completely ignorant of mathematics, but) someone who has college-level mathematics but has somehow managed not to hear that it can be applied to understanding the physical world.
"This is a theory about the motion of small rigid objects such as rocks. The same theory can actually handle large objects by considering them as aggregates of smaller ones, but for the moment we'll only consider objects that are very small. So, suppose we have a bunch of small objects. At any instant we can describe the state of the universe by saying (1) where these objects are -- we specify this by giving three coordinates for each object -- and (2) how fast and in what direction each object is moving -- we specify this by another set of three coordinates, which collectively we call the velocity. And the only other thing there is to know about each object is its mass, a single positive number that in some sense describes how much of it there is; it's closely related to how heavy it feels when you hold it.
"Now the basic rules are as follows. First: the derivative of position with respect to time is the velocity. Second: the derivative of velocity with respect to time, which we call the acceleration, is completely determined by a set of rules that care only about the positions, velocities, and masses of the objects. (As long as they don't actually crash into one another. We'll talk about that in a moment.)
"Third: the rule for finding the acceleration is as follows. The acceleration of each object is a sum of vectors, one for each other object. What's happening here is that all the objects are pulling on one another; objects with more mass pull harder. More precisely, the formula goes like this: the acceleration of an object with mass m is the sum over all the other objects of Mr/|r|^3 where r is the vector from our object to the other object and M is the mass of the other object. So the further away the other object is, the less effect it has; in practice this means we can mostly ignore objects very far away.
"Here's an exercise, to give you a feeling for what the theory lets you do. Define the momentum of an object to be the mass times the velocity. Then prove that the sum of all the momenta in the system never changes.
"This system takes some getting used to, although basically it's just fairly elementary mathematics. Let me mention a few of the things that follow from it. We just saw a "conservation law": the total momentum is constant. There are a whole lot of other conservation laws, and in many cases one can make detailed predictions using only those. If you have one object whose mass is very large and all other nearby objects have much smaller mass and don't get too close to one another, then you can pretend that the first object stays fixed in place, and that the others' motions are affected only by it, and in that case it turns out that their paths are always conic sections. In particular, our solar system is like this, and the planets move in near-perfect ellipses. If you do the calculations more carefully, taking into account the planets' influence on one another, you can get very accurate results, and in fact someone once found a previously unknown planet by noticing that another already known planet wasn't moving quite as expected and working out where another planet would have to be to produce the observed deviations.
"That'll do for now. If you want a more difficult challenge, try to prove the statement I made about conic sections."
...Okay, that is honestly an impressively rapid bit of writing in its own unusual context (as a summary of newtonian particle mechanics to someone who had college math but had somehow never heard about physics, like you said.)
But my original analogy was never meant to be expanded, because it was never an argument by analogy in the first place, as I told Jem
[NOTE: This was a discussion post asking if anyone would mind giving feedback on a very rough draft in progress.
If you are downvoting it because you do not want to see discussion posts asking for feedback like this, then by all means, that's a valid use of a downvote.
But if you are downvoting it in order to express your opinion of the quality of the draft, I urge you to reconsider]
This is another work in progress coming at the DI issue from a somewhat different direction. It's contained in the comments of the original, and I'm posting this to ask for more wonderful beta-reader critics to tell me if it's a step in the right direction. (It's still very informal writing, but it's the ideas I'm dealing with now.)
And about what I'm looking for in the LW audience, someone asked me in a private message:
And I said:
Well, that's the major part of what I want that's important here. I also had to add:
But that's not important here (except to disclose that is where I'm coming from). LWers would first have to understand DI to fully grasp that. And I am significantly less certain of my current beliefs about those 'strategic twists' (although still pretty certain), and LWers proficient in DI would be the best to evaluate the ideas.