How Thinking Putty Works
The complicated version for the Chemistry Professors out there...
Some of the behaviors we listed are an example of a dilatant compound, where the viscosity (i.e. the resistance to flow) increases faster than the strain rate. Although not common, some materials do exhibit dilatant behavior (concentrated aqueous corn starch suspensions -- read: Oobleck).
However on its own, this is not enough to explain the behavior of Thinking Putty. In fact there are two mechanisms (and hence two characteristic time scales) at work.
The high molecular weight of the primary ingredient PDMS (Poly Dimethyl Siloxane) has a characteristic polymeric relaxation time, defined by the time that a random walk allows the chain to relax from a stretched state through thermal vibrations.
However due to the Boric acid (the fourth ingredient by weight), there are also transient Boron mediated crosslinks (and you thought I was kidding about the Chemistry Professor bit) arising from associating Boron linkages. These act to give the Thinking Putty a behavior more like an elastic solid than a liquid.
However since these crosslinks are dynamic, the material is not permanently locked in place and can consequently flow under the correct conditions. Therefore at longer time scales, the Thinking Putty behaves like a high molecular weight polymeric fluid. (Still here? Wow, you must be really interested!)
Over very short time scales the putty behaves like a crosslinked elastic solid, shattering like a ceramic on impact. QED.