> The halting problem is thus decidable for non-infinite systems. That's only true in the most boring way possible, i.e. because every system must eventually h

> The halting problem is thus decidable for non-infinite systems. That's only true in the most boring way possible, i.e. because every system must eventually halt in a universe where the laws of thermodynamics hold. If you replace "halts" with "halts in a reasonable amount of time" (for whatever value you consider reasonable), you'll find that the same diagonalisation argument shows that no algorithm can decide in a reasonable amount of time whether some arbitrary program halts in a reasonable amount of time.