Why is a physical simulation so determinedly different than a mental one? I understand that physical props are useful for immediate representation like pictures instead of words, but why couldn't the professor have used a map, drawn or mental?
Because a map is an abstraction. The physical simulation, while obviously still an incomplete representation, is far, far closer to the actual reality than stick figures on a white board. Not all simulations are created equally of course. Some are far more detailed than others. The more detailed a simulation is, the closer it comes to actually being what is modeled. It's not a case of either/or, but rather a spectrum from reality to completely abstract.
If skill challenges are simulations, how can they be shared narrations, while combat simulations are not?
The skill challenge is a simulation. You are attempting to simulate an event using rules other than the combat ones. Those rules allow the player, with the DM's permission, to affect minor changes to the scenery.
One does not preclude the other. The player must still succeed in the skill challenge or fail as the case may be. However, the parameters of the situation are not entirely in the hands of the DM.
The very definitions of the words Simulation or Model include "incomplete representation of". That doesn't change these into "shared narrational authority resolution" systems. A Player wandering the desert in the Outdoor Survival system (our OD&D system) could not say, "there is a ruined tower here my PC scrambles up." Nor is the determination of reality a "Stake" where the dice are used to adjudicate who gets to be "King of Determining the World". The DM isn't allowed to do this, why would someone playing a PC in that world be able to? The DM has to base the existence of said tower or chandelier on his knowledge of what the world may hold or use whatever system is in place to determine such. If you want to include said determination into a Skill Challenge dice roll, you've changed role-players into role-players plus world creators.
So, only the things you've written down before the game starts may be used? No DM may ever extemporize any details of the setting during play? That's ridiculous. DM's do it all the time. DM's are allowed to determine what is or is not in their world every second of the day. And, while changing an existing detail without justification is bad DMing, adding something certainly isn't. I may not say that there is a badger hole in the hill, but, it's not unreasonable to think that there might be one there.
Does it really matter who places that badger hole?
This doesn't work for most folks as the challenge stops being "beating your opponents as your character" into "beating your opponents by halfway wishing the world into existence to win."
I'm not de-legitimizing this for those who want it. But it is absolutely a different thing than role-playing. At best, it's a hybrid of playing the PC and God. Nor could you play both at the same time. Either you are playing a role or you are telling a story. The only exception In character is telling the story of your PCs personality by Imrov Acting.
This is a completely false assertion. The old 007 game back in the 80's had a hero point mechanic where you as the player could spend a hero point to add in setting elements that were in keeping with the genre. The game actually ENCOURAGED players to do so.
Trying to tell me that I'm suddenly not role playing simply because I have limited authorial control over setting elements that are not detailed by the GM is laughable.
This is the difference between people jumping up from the table shouting, "WE KICKED YOUR BUTT!!" to "That was a good story we made."
Again with the entirely false assertion. Do you allow players to make backgrounds for their characters? Why? You are allowing them to have limited authorial control over the setting, therefore they are no longer role playing. Heck, do you allow them to choose their race or class? How is that any different? If I choose to play an elf, I am affecting the setting. Thus, I must not be roleplaying?
It is my assertion success is as important to role-players as it is to wargamers and cardsharks. I think most every RPG company gets this when they strive for balance in their rulesets. It's not about appeasing complaining players who can't stand having a PC with less influence in any given situation) It's because they intuitively know that power to win is important in "games". IMO, it is as true for DDM as it is for simulations with scopes broad enough to be called RPGs/D&D.
But, even with limited authorial control, you still have success. At no point can you say, "I win" as a player. You might, at best, be able to give yourself a chance of winning, but, that's entirely up the DM and still not a guaranteed success.