The lapse here is not math, but rather spending lots of attention on abstract thought disconnected from any kind of reality check. Of course, there’s nothing inherently wrong with speculating sans evidence about the future, it’s generally a harmless hobby. In the best case it makes for fun SF novels. Convincing yourself, still without direct evidence, that your speculation reflects truth implies that something has gone off the rails in the reasoning process, however.

Using statistical analysis to understand real causal relationships in areas we have real data about is damn hard, and even plenty of people who are highly trained as statisticians screw up all the time. Academic fields like comparative politics (to take an example I spent a fair amount of time studying) are rife with poor conclusions drawn from bad analysis. The LessWrong folks are hardly unique in applying logic poorly. But they do tend to tackle more speculative questions and convince themselves more firmly of their conclusions (at least, such is my impression as an outsider).