What is the big idea with algorithms?
dmlorenzetti: To understand why algorithms are important, and how they are used, it might help for you to give up your mental model, described in your original question, of the link between physics and algorithms.  They are not both attempts to represent some set of quantities.  Rather, think in terms of physics as stating the equations (describing how the values relate to one another), and algorithms as methods for solving the equations (calculating the values).So for example, physics describes the answer to "where will this spacecraft be five years from now?" while to compute a numerical answer you need to apply some particular algorithm (like a differential-equation solver).Most of the algorithms in "Nutshell" are what you might call core-level methods of figuring things out.  For example, the book describes different sorting algorithms.  From your question, you sound more interested in what kinds of problems demand sorting (for example).  For that, you might try a bigger-picture book, for example Steven Skiena's "Algorithm Design Manual."  It goes into less detail about actual implementation, and more detail about what the algorithms do for you, and when you might apply them.