A link on HN yesterday that talks about critical points and phase transitions:

* A mathematician explains what Foundation gets right about predicting the future (spoiler: critical points!): https://www.sciof.fi/a-mathematician-explains-psychohistory/

And if you're still interested, there's a more in-depth explanation with mathematical formulas and all. Even if I understood only 10-20% of what Ken Wilson was talking about, he gives a lucid motivation for why critical points are important and why they can be found in practice using renormalization groups, and not computer simulations:

* Ken Wilson's Nobel Prize lecture: https://www.nobelprize.org/uploads/2018/06/wilson-lecture-2....