The problem I see with Kirznerian “surprise,” as Kirzner elaborates on in his “Entrepreneurial Discovery and the Competitive Market Process,” (1997, pp. 71-2) is that his exposition of the nature of surprise makes the process of entrepreneurial discovery rather mystical, dependent on some inscrutable quality called “alertness.”
Yes, people do not search the neoclassical way. But people do search in other ways: they try to find new perspectives with which to look at old problems, they purposefully take risks to jolt themselves and their thinking out of their comfort zone, they divide their knowledge with new people and experts, they go to school to learn more about an area they believe will be fruitful to their entrepreneurial search, and so on.
Kirzner was right in that the neoclassical approach to understanding how entrepreneurs made profits from arbitrage was likely incorrect, as it presumed a calculable equilibrium that was within reach given enough search. (Fixed points of this sort are generally incalculable in complex social systems.) But by stripping individuals of all possible deliberative heuristics of search, Kirzner missed an opportunity to talk about how entrepreneurs choose which heuristics to use in which contexts and what kinds of social institutions might have emerged to support this process of choice.
I think Kirznerian surprise can still go through as a viable idea if we entertain the idea that a surprising solution is thoroughly outside an entrepreneur’s expectations — they cannot assign a probability to its existence because they are unable to conceive of it, and thus they have no reliable, methodical way of searching for a surprising solution. A surprising solution is an utter novelty, but a useful novelty, for an entrepreneur’s ends. There may be no methodical way to produce useful novelty, or to even know when you should be trying to produce useful novelty, because you have no way of calculating whether your ends are better furthered by the employment of any particular novelty because you cannot conceive of it.