Premise:
In the future, mankind manages to perfect psychology (here meaning a "unified" social science, a mathematical theory that predicts action) to the extent that using mathematics, a particular scientist is able to anticipate the deterioration of the galactic empire, and constructs an elaborate plan using these calculations to shorten the ensuing dark age from 30,000 years to only 1000.

Sci-fi stuff/technological assumptions:
Warp/Hyperspace travel (every piece of space fiction written in the modern age needs this, because the size of the galaxy is relatively common knowledge, and faster-than-light is thus essential)

Powerful technology, but not really computers. Calculations are made by hand, and while advanced computers are described, they have very specific and linear functions. Although this is the same universe in which intelligent robots were created by men (i, robot), they no longer exist.

Psychohistory, the tool used to predict human action, exists as a reliable predictor of the actions of mass quantities of humans (billions), but not the actions of humans on an individual scale. Asimovs conception of social stipulates that the actions of humans are "random", and cannot by mapped reliably on an individual level (although this capability is developed later in the series).

My response:
Considering when these books were written, one can hardly fault Asimov for not anticipating the rapid proliferation, and personalization, of computers (as well as the rapidly decreasing size). The idea that human behavior is unpredictable or "random" on an individual scale is romantic, but probably wrong.
My contention (and the contention of modern psychology, predicated on neuroscientific research) is that human actions depend on a physical organ, and that organ responds in particular ways to particular stimuli. Therefore it is likely, that given a sufficiently powerful computer and sufficiently sensitive equipment, human behavior could be mapped and modelled on a computer. This (despite the topic of the thread) is not science fiction: practically every new issue of Scientific American or Nature plays into this "futurist" idea (read: fuels my confirmation bias). Given current trends, I find the development of these computers and these processes almost unavoidable during my lifetime (unless I am to meet some unforseen early end, and I assure you all that I'm currently hiding on a bunker in the rocky mountains, riding out the storm).