We argue that if an organizing principle exists it must have to do with the linear connectivity of the monomers since this feature is what distinguishes polymers from all other materials. We then compare a linear polymer threading a pore in a membrane (PTM) with an equal number of unconnected monomers which are also allowed to transit through a pore in a membrane. The crucial difference between the two cases is that the connected monomers are distinguishable from one another by virtue of their location along the polymer chain whereas the disconnected monomers are indistinguishable. Because of this, the disconnected monomers obey the ideal gas laws while the connected monomers undergo a first-order thermodynamic phase transition! Four other phase transitions occurring in isolated linear polymer molecules are known. They are the helix to random coil (HR) transitions in biological polymers, surface adsorption (SA), polymer collapse (C), and a model of polymerization (P). These five kinds of transitions can be coupled to one another resulting in a sizable number of exactly solvable minimal models of phase transitions. There are also five classes of phase transitions in many polymers systems. The coupling of these 10 classes of transitions to each-other results in a plethora of phases. These in turn provide the basis for the many polymer structures observed in the world about us. (c) 2006 Wiley Periodicals, Inc.