This allows him to predict planetary + galactic scale events, including a surprising and imminent regression of humanity into a new Dark Age.
There’s a smarter treatment of the idea in the John C. Wright’s “Count to the Eschaton” series.
Do you not the know the Second Foundation?
In fact, that mathematics turns out to be much more widely applicable than mere Psychohistory, since it applies to all systems of all types and purposes, not just human societies. A small system like a web server is simple enough that you or I can confidently predict its eventual failure; the hardware simply doesn’t last forever so eventually a disk will fail or a capacitor will pop or whatever. But the company running the web server is a much more complex system that is much harder to predict. Does the company fail if it pivots to a different market and turns off the web server? Or if the cleaning lady unplugs it once a week to vacuum? If you want that particular web server, or the pages it serves, to last forever then you really have to design that corporation well. You don't want it to divert from the plans you gave it when the market changes and there is more profit to be made elsewhere. In fact to keep that web server running over the long term you really might have to design the society around it so that the situation _doesn’t_ change too much. Society will keep changing as fads come and go and people are born and die, but you want it to always orbit a chaotic attractor of your choosing in the phase space of possible societies.
The series takes this idea to its logical extreme, giving the main characters access to and control over larger and larger systems until they are controlling vast galactic superclusters. The degree to which the many myriad intelligences, human and otherwise, in those vast systems can carry out the main character’s purposes over deep time depends on how well the rules they have devised work and how well those intelligences understand and implement them.
To be fair, the Foundation series it takes literally centuries for events to play out.
A lot of self-interested motives would not be well served by that timeframe.
The premise was that even being aware of the impending collapse was not enough to stop it.