Hmm, it's interesting that you found yourself disappointed by Asimov's treatment of chaos. I can't help but suspect that you may have missed something when you first read it. I know I certainly did. Actually, Asimov's treatment of chaos is what sold me on hard scifi. Here are some of the high points that directly address your concerns:
1) The "thermodynamic" explanation of psychohistory (small, unpredictable actions "average out" in some sense) was bullshit even inside Asimov's fictional universe. It was merely an excuse that Seldon used to get the Foundation placed where he wanted it so that #2 could happen. The fact that the characters in-universe continued to buy in to the deception could have confused you (it certainly confused me). In my final analysis I consider this a stroke a brilliance on Asimov's part, even if it was introduced retroactively (I don't remember if this was the case).
2) Seldon's plan didn't rely on precise predictions of any kind (broad or narrow). He simply had to ensure that the set of probable broad predictions led to the next attractor state (Seldon crisis) so that intervening chaotic deviations could be neglected for the purposes of computing the subsequent ~50 years. For instance, the metaphorical pebble-in-the-shoe-that-loses-the-war would be handled by ensuring that both outcomes of the war led to the next Seldon crisis. In fact, this is the very subject of the 2nd book in the series.
3) The "random events such as mutation" that you suspect would spoil Seldon's predictions form the driving force behind the plot of the 3rd, 4th, and 5th books in the series. While Seldon's solution can hardly be considered elegant, it was somewhat effective and more believable than a great many things I'd be willing to suspend disbelief over. It makes for good reading in any case.
Your conclusion that psychohistory was more of a "what if" than a serious proposal holds true but I still think you haven't given Asimov enough credit for subtlety in addressing the chaos problem.
I'm listening to the series now. One of the oddities which struck me is how psychohistory could predict the microminiaturization of nuclear power cells. Nuclear power had been known for about 15,000 years, but only in the last 200 hundred was there a specific need by a resource-poor planet to figure out how to make those things, and so they did. Yet it was essential that those power plants exist in order to power the trade goods and the personal shields.
Sure, the Empire thinks in terms of large scale, but there's always a need for small, energy dense power systems. I can't figure out why they didn't exist already. And even if they didn't exist already, I don't see how psychohistory could have predicted that it would exist.
While on the other hand it makes the prediction that nothing will replace the standard jump technology for interstellar travel. If there were a way to go from Terminus to Trantor in, say, 1 jump instead of many, or if they could be done much faster, then the dynamics of the civilizations would also change in quite unexpected ways. There would be no "edge" of the galaxy, for example, since every planet would have about the same travel time to the other.
How can psychohistory make that prediction? More importantly, by the end of the original series, the "Lens had performed a near-revolution in interstellar travel", making hyperspace travel much faster. How could psychohistory predict that it would exist, much less when it would arise?
Either one of these - the lack of small nuclear power sources, or earlier creation of the Lens - would make big changes in the Foundation. And big enough changes that there's no way it would get to the same sort of semi-stable attractor as the alternative.
I think the answer is that Seldon probably knew that Psychohistory only works within fairly specific parameters. If something like the Lens were discovered then the assumptions underlying his predictions would be come invalid, therefore he simply had to hope that something like the lens would not be discovered.
As for miniaturised atomics, it's quite possible that the only reasons they hadn't been discovered already were sociological in nature - regulatory rules put in place at the behest of incumbent monopolies to protect vested interests. Seldon may have been able to plot the curve of atomic tech development up to the point the regulations killed further development, and then assumed that with the destruction of those vested interests along with the empire, tech development would continue on it's previous trajectory.
This is getting too close to describing how making the Kessel Run in less than twelve parsecs is meaningful.
The introduction is quite clear that the mathematics is understandable by other mathematicians. The commentary from the Encyclopedia Galactica (116th edition, published about 1020 years after Sheldon's death) describes "Seldon found the field little more than a set of vague axioms; he left it a profound statistical science." Gaal, by the end of a day of collaboration, was able to accept that its predictions were valid. It's hard to imagine that Seldon managed to hide the uncertainties in his work, given that others would be looking for precisely those uncertainties.
The justification in the series was that need drove development of micro atomic power units. Terminus is described as a metal-poor planet which needs to import just about everything. (Which then makes me wonder how there's enough minerals in the soil to provide the food needed for humans to survive. Do they even import the zinc needed to prevent zinc deficiency?)
But atomics weren't the only power source. Trantor uses only geothermal power because it's cheaper than atomics. So it isn't like there's a complete power monopoly. In addition, the personal shield would be quite the coup. Given "the known probability of Imperial assassination", there's a strong inventive for the Emperor and others to push for a personal shield, and a matching power source.
So you have the strange case where out of the million inhabited planets, only one retained atomic power and the rest fell into "barbarism." 200 years in the new era, fully 1/4 of the population was no longer under Imperial control, and yet all the rest of the people stopped understanding how nuclear power worked. That speaks to a very rote-based education system. But then how did the people of Terminus manage to not only remember it but advance on it?
It just doesn't make sense. Of course, in book it's all a fraud. The Second Foundation, full of psychics, and of course the robots, are working behind the scenes to keep everything on track. I think that's a cop-out, and I found it very hard to accept the later books in the series.
And of course in real life it's a SF version of the fall of the Roman Empire, and as that's the history that we (as Western readers) know best, the parallels feel comfortable. Had it been based on the Incan or Mongol empires, there would be a completely different sense of inevitability.
Thinking on this further just now, one of the biggest concepts of the series is how the tiny Foundation had to survive purely by out-thinking and out-maneveuring the larger Empire who had more people, resources, etc.
Fundamentally - no pun intended - isn't this what we do for a living?
By the numbers, our startups are in the same position. Our competitors have 100x the revenue, cash on hand, employees, partnerships, patents etc, etc. According to the spreadsheets, they win.
Instead, lack of resources becomes hunger and creativity. Lack of people becomes a lack of bureaucracy and results in flexibility. When you have very little, "losing everything" isn't scary.
Challenging the Empire just got to be a little more fun. ;)
I just want to express my support for any personal perspective that demonstrates and encourages reading of Isaac Asimov, especially my favorite series. Perspective win.
Personally, I tend to think of it as hindsight before the fact.
When people look back at major events like WWI, WWII, the fall of Berlin Wall, and eventually the Soviet Union, most of the signs were there. There were subtle "vibrations" appearing in the system and major rattling in the system. It's only after the fact that everyone says "oh yes, given A, B, and C, it was obvious."
I think about Seldon's psychohistory less as predicting the future and more of simply identifying A, B, and C before the "obvious" event occurs. Throw in the Second Foundation's tweaking and it seems plausible.
I'm sure you're right, but many of my SF reading friends bought into the concept of psychohistory hook line and sinker, which got me into lots of arguments. It's those disagreements with other fans of the book which coloured my perception of it, I'm sure unfairly.
1) The "thermodynamic" explanation of psychohistory (small, unpredictable actions "average out" in some sense) was bullshit even inside Asimov's fictional universe. It was merely an excuse that Seldon used to get the Foundation placed where he wanted it so that #2 could happen. The fact that the characters in-universe continued to buy in to the deception could have confused you (it certainly confused me). In my final analysis I consider this a stroke a brilliance on Asimov's part, even if it was introduced retroactively (I don't remember if this was the case).
2) Seldon's plan didn't rely on precise predictions of any kind (broad or narrow). He simply had to ensure that the set of probable broad predictions led to the next attractor state (Seldon crisis) so that intervening chaotic deviations could be neglected for the purposes of computing the subsequent ~50 years. For instance, the metaphorical pebble-in-the-shoe-that-loses-the-war would be handled by ensuring that both outcomes of the war led to the next Seldon crisis. In fact, this is the very subject of the 2nd book in the series.
3) The "random events such as mutation" that you suspect would spoil Seldon's predictions form the driving force behind the plot of the 3rd, 4th, and 5th books in the series. While Seldon's solution can hardly be considered elegant, it was somewhat effective and more believable than a great many things I'd be willing to suspend disbelief over. It makes for good reading in any case.
Your conclusion that psychohistory was more of a "what if" than a serious proposal holds true but I still think you haven't given Asimov enough credit for subtlety in addressing the chaos problem.