I like the theory in your spoiler tag, and I know the nuke was thrown as a "won't be practical or desirable for Parson alone" thing.
BUT, no offense, the kind of thinking in most of that post is exactly the kind of thinking that leads to serious documentaries about molecule-sized tractors.
It's a different world, people!
For one thing, there is no entropy in Erfworld. Assuming the rest of physics works (huh?), you are capable of producing 100% efficiency engines, and -shocker- heatpumps of any ratio you care to name. You could have a simple gadget that could pump out all the heat off a desert into a city and just cost you the energy of a gentle whisper.
But with entropy chucked out, chances are everything else is back to square zero. It would be rather disappointing to see Erfworld do steam-engines, since Erfworld also has a cheap portalling technology, which in our Universe is only glimpsed in the acid trips of string theorists.
Sorry for the rant. Anyway, yes, maybe this once you were looking for nails for your hammer of knowledge
Well, I am not sure that entropy doesn't exist in Erfworld. The first law of thermodynamics works just fine with magic, its just another added term (pick a side of the equation). I would argue that at the beginning of each turn the magic of Erfworld 'resets' everyone by adding 'energy' (magic) to the system. We can't derive the first law from any other equation, so altering the basic assumptions of the universe just changes the equations you have to use.
I imagine Erfworld as a string of pearls universe- each 'hex' is a separate universe, governed closely by the same laws, with certain transition points to other nearby universes. This helps answer why those arrows just stick on the hex boundry- they can not translate through the transition for whatever reason, but there is no violation of F=ma or conservation of energy, their energy simply contributes to whatever energy state is at the boundary, which is an infinite or nearly so sink AND source surrounding the hex.
This can be extended to explain why City hexes have special rules compared to say a desert hex. While most of the baseline rules are the same, these pocket universes have some modifications, no problem.
So, with case 1) Entropy doesn't exist, the energy balance can be maintained by the infinite source/sinks at the boundaries, Time (rate of change) can vary across hexes based on the observer (or lack there of), but you still can't get much out of a infinite heat pump without finding out what the rules are on translating that energy across the hex boundary.
Case 2) Entropy exists local to a hex, but again your energy is modified by the transition point to accommodate your new universe. There are certain global energy pools (based on your Side- either from the Capital hex or your Overlord) without which you either cease to exist or are frozen at a entropy point- in time, until another observer arrives to start things up again. But you still have access to chemical reactions (still gotta breathe, eat, sleep, and poop) and so much of what we know from our world is familiar and useful.
But you take a guy like Parson. Sizemore is describing the scientific method, a way of learning about the world that is pretty efficient but not necessarily obvious (look how long it took our world to figure it out). If I am in a string of pearls universe, the questions that I start to ask are- what /are/ the physics that govern this place? Make an experiment regarding your infinite heat pump, measure the entropy, and compare.
If you are a mathamancer, you spend some juice and derive the new equations. Maybe a lot of juice. Lather rinse and repeat, gaining greater and greater understanding of your world. Parson gets it for free with the bracer... if he can ask the right questions. Hence my curiosity at his education level.
Then comes the tricky part- going from theory to practice. I inserted a "then a miracle occurs" item for that. In our world, translation without acceleration is either impossible or energy prohibitive. In Erfworld, moving between hexes is a translation without acceleration, and the energy cost is one movement point. If you can manipulate your "hex" value to a new one using advanced mathemancy and a macguffin, you can effectively teleport- which we already know is possible to some degree using portals to the magic kingdom- and not use movement points. Scary stuff, and a tactical/strategic genius would cheerfully sacrifice a given limb for such an advantage. Maybe you could use it to move at Night, as Parson wanted to do so long ago, despite having zero movement points. The Tools' apprehension at our way of doing war (When do your units heal? When do you plan?) might presage the terror others might feel when introduced to real time combat.
The more I think about our weapons of war, the less I think they are going to be what is needed to 'break' war. All of them just represent killing more people more efficiently from a greater range. But hell, 90% of the people in Erfworld barely qualify as people, at least according to the dominate social structure in place. Who cares if you slaughter a few thousand/million bats anyway? Pop some more.
Thats all just speculation on how to break the world into peace. My main point was that its not the knowledge of our equations, necessarily, that gives power, but a way of thinking about your surroundings and then manipulating them. Training in math or the sciences (or logic even) helps mold a way of thinking that leads to such discoveries, ideally. Couple that with instant easy calculations (through mathemancy or the bracer, an Artifact that _I_ would sacrifice a limb for!) and you are really cooking. Add on the ability the ability to control the result, and gunpowder, NBC weapons, or whatever else becomes kind of a side show really. And killing people faster longer harder is a pretty low end use for such power, frankly. Control theory applies to any system where you can define the inputs and observe the outputs after all. Black boxing the brain is even being attempted. You start working your way up the magical food chain using those methods, who knows where you end up.