Why the fuck does this even freak her out as much as it does, it's not like she was actually using the possibility of in principle predicting the future from the present on the atomic level for anything
but the possibility was an asymptote to strive towards
It sounds like most things still happen for reasons most of the time in most universes and the metanarrative is on her side about wanting to avoid the exceptions
she liked living in a cosmos built on a foundation of math stronger than any stone
There could still be regularities, randomness drawn from a knowable distribution, usable for probabilistic predictions, there could still be something it would mean to understand how everything worked.
but what if there isn't
Gödel proved that no system can prove its own consistency, but this did not destroy the usefulness of logical systems. Just because there are places you can't reach from any given set of axioms and rules of inference, doesn't mean that there are no places you can reach. A physical system that evolves according to known rules can be pushed into an unreachable state by interference from a source of randomness--and then it will keep evolving from that new state according to its rules. And it remains possible in principle to say what will happen in the absence of randomness, and therefore to detect randomness when it happens and return to making predictions based on new observations after it passes.
Is that enough to carry on with and stay sane? It's going to have to be. Whatever is true is already so, finding out about it doesn't make it worse.
She still has mathematics itself, and the experimental method. As long as a mind can look at the chaos and observe that it is chaos there is still order. There are dragons in the cornerstones of the world and they cannot be slain but they cannot devour everything.