Fitts's law (often cited as Fitts' law) is a model of human movement primarily used in human–computer interaction and ergonomics that predicts that the time required to rapidly move to a target area is a function of the distance to the target and the size of the target
How does that do anything but confirm the GP's point, that it's dumb to place a menu bar potentially thousands of pixels away from the window it applies to?
Because Fitts's law relates both the target size and the target distance to the speed and accuracy of hitting the target. Not just the target distance. You can move the mouse very quickly to cover the large distance, without worrying about the accuracy, thus reducing the negative contribution of the distance, because the target size is practically infinite. The target area of the menu bar at the top of the screen extends infinitely up above the screen, because when your mouse hits the edge, it stops moving and stays in the target. Try it yourself. It's EXTREMELY easy to move the cursor to the top of the screen, no matter how far away it is. The distance doesn't matter, because the target size overwhelms it. That's what is meant by the "Mile High Menu Bar" -- calling it a mile high is an understatement!
This is also why pie menus have improved time and error rates over linear menus: linear menu targets are very small, and increasing distances away from the cursor, but the pie menu items all start out adjacent to the cursor, and extend all the way out to the screen edge, so you can trade off increased distance of movement for increased target size. The target area of the pie-slice shaped wedges get wider and wider as you move out further away from the menu center. (I don't mean they dynamically change size as you move, I mean that as you move out, you're in a much larger part of the slice. So with a four-item pie menu, each target area gets about 1/4 of the screen real estate, and you can keep moving the mouse even further when you hit the edge and still be in the same target slice.) Pie menus also minimize the distance, but around the center, the targets are at their smallest, but you can always move out further to get more "leverage" and directional accuracy.
> How does that do anything but confirm the GP's point, that it's dumb to place a menu bar potentially thousands of pixels away from the window it applies to?
That menu bar is effectively a billion pixels tall. You can throw the mouse pointer to the top of the screen and only concentrate on accurate horizontal positioning, since the mouse will not leave the top edge.
Putting the menu bar at the top sells out the distance side of the function to dramatically increase the target size.
So now that you've thrown the mouse to that easy to find top of the screen mile high menu bar, and completed your mouse action, don't you now have to find your teeny weeny window over in some far off portion of the screen and move that mouse back into the window you're actually working in?
That is correct. And one of the largest consistent complaints by new OS X (and prior to that MacOS) users in terms of usability problems.
On multiple monitors, the menu can be 1 or more monitors away from your app window. It might not just be up at the top of the screen, it might be up at the top of 1 screen over and two up.
How does that do anything but confirm the GP's point, that it's dumb to place a menu bar potentially thousands of pixels away from the window it applies to?