A good example for demonstrating the computational role of a world-model is a "street map".
A map permits you to compare
distances and choose routes without
actually driving through the same city before. More importantly, a map allows you to circumvent unanticipated obstacles (say a street closed for construction) without having to buy a new map, in which the obstacle is marked.
Likewise, it enables the city planner to
assess what effect a local change would
have on the traffic pattern in the city
prior to implementing that change.
To appreciate this feature, imagine that, instead
of a map, your GPS gives you a left-right-forward instructions at every corner, so that
you arrive at your destination optimally.
Theoretically, this GPS system should be as good as a map. Yet most drivers prefer having both, GPS and a road map. Why? Suppose you hit a street closed for construction. The GPS provides you almost no help to get out of the predicament. The map, on the other hand guides you wisely toward finding an alternate route around the blocked street.
Note that this advantage of maps to handle unanticipated changes only works when the changes are local, that is, road construction in one street leaves all other streets in tact. The map is useless if the construction transforms a large number of streets all over the city.
The GPS system can be improved, of course, to emulate this capability of a map, by storing a right-left-forward instruction for each and every possible street closure event. But this would necessitate a substantial increase in storage space.
We should use this metaphor when we seek ways of testing whether a system has a model of the world or not.
I should add that I touched on this dilemma in this interview
ucla.in/3L91Yvt and I plan to elaborate in an upcoming paper. ML folks are not concerned with this dilemma because they haven't seen how the "world model" trick works for humans, some have never seen a world model.