The case for the humanities is easy:

- Science is about
**how the physical world works**. - Engineering is about
**how to get the physical world to do what you want**. - The humanities are about
**deciding what you want in the first place**.

**A metaphor**

Say life is about finding the shortest path through a graph. Science tells you what the edges of the graph are -- what nodes are connected to what other nodes. Engineering gives you a shortest-path algorithm (say, Dijkstra's). The humanities tell you what node to find the shortest path *to*

.
**A control-theoretic perspective:**

More generally, the world has a state *x(t)*, and science gives us the transition model -- the function *f* such that,

dx/dt = f(x,u)

where *u(t)* is our control input to the world at time *t*. This is Newton's Theory of Universal Gravitation, or Einstein's Theory of General Relativity, or whatever.

Engineering is about the following problem: Given a functional *V* that takes a state trajectory and returns a cost for that trajectory (this summarizes our opinion about what we want and what we do not want), solve (or approximately solve) the following optimization problem:

minu V(x)
s.t.
dx/dt = f(x,u)
x(0) = x0

In other words: Having decided what I want (*V*), and having figured out how the universe will react to my actions (*f*), figure out how to make the universe do what I want.

The humanities are about deciding what functional *V* to use. Science can't give it to you: It's an input to this whole thing.

The above formulation can be tweaked a little -- for instance, there is no uncertainty involved -- but it captures the gist of things.