Type $\sim$ Minimal Polynomial & Orbit In Model Theory by Wilfrid Hodges, he gives an intuition of what a type is in the following way:

"One can think of types as a common generalisation of two
  well-known mathematical notions: the notion of a minimal polynomial in
  the field theory, and the notion of an orbit in permutation group
  theory."

I would be appreciated if someone help me understand the connection and the intuition behind those... 
 A: For the minimal polynomial analogy, consider an arbitrary algebraically closed field $K$, considered as a structure in the language of ring theory. Then for any $A\subseteq K$ and any $\alpha\in K$ algebraic over (the subfield generated by) $A$, the type of $\alpha$ over $A$ is uniquely determined by the minimal polynomial of $\alpha$ over (the subfield generated by) $A$, and the other way around: the irreducible monic polynomials are in natural, bijective correspondence with isolated types. The only type which does not correspond to a monic polynomial is that of an element transcendent over (the subfield generated by) $A$, as such an element has no minimal polynomial. All such elements have the same type.
For the orbit analogy, consider an arbitrary model $M$ and a subset $A$ of $M$. Consider the group $G=\operatorname{Aut}(M/A)$ of automorphisms of $M$ which fix $A$ pointwise. Then all elements in an orbit of $G$ have the same type over $A$. The converse is not always true, but for any $A$ we can find a larger model $M'\succeq M$ such that orbits of $\operatorname{Aut}(M'/A)$ correspond exactly to types over $A$.
