[isotropy]

Fusion: Turbulence, plus Naiver-Stokes was known to be hard, plus adding in EM fields, plus the exothermic state change of the nuclei fusing introduces discontinuous jumps in the free energy.

Collatz: if you replace 1 and 3 with arbitrary parameters, Conway showed that this class of problems is undecidable, so any particular instance could be arbitrarily hard.

[feoren]

Genuinely great responses. I'm not sure "it can be generalized to an undecidable problem" really explains why it's hard though, as the 5n + 1 problem is very easy (to prove false) and generalizes just the same. And all good points about Fusion, but my point was that it took some time (months, at the very least) for them to realize that's what was spoiling their machines. Remember that this is all a counterexample to the statement that "If you can't easily explain why something is difficult, then it's incidental complexity" -- meaning all the difficulty you are encountering is your fault (and therefore the actual problem must be easy, and you must be stupid.) That's literally what TFA says.

[isotropy]

> I'm not sure "it can be generalized to an undecidable problem" really explains why it's hard....

Hah! I agree with this. :)