Not if they talked to a competent topologist. Working with high-dimensional things is part and parcel of linear algebra, too.
Indeed.
To the extent that a higher dimensional object is disjoint from the "flatland" space, it is the equivalent of not existing at all (to the flatlander, that is, since he can only perceive that which is part of his flat space). On the other hand, to the extent that a higher dimensional object DOES interact with the "flatland" space, it is perceived BY THE FLATLANDERS as the projection of the higher dimensional object onto the lower dimensional "flatland" space, i.e., it is percieved as a flat object, like any other in "flatland."
To illustrate the point consider a cone suspended above a flat plane ("flatland"). If the cone does not intersect the plane, the "flatlanders" have no idea there is such a thing, as it can't intereact with their "Universe" as long as it not "in" their "Universe," which is equivalent to and indistinguishable from it not exiting at all, from their point of view.
If, however, we thrust the cone thru the plane such that the cone's axis is orthogonal to the plane, a circle of expanding diameter is formed on the plane, coincident with the cone being "sliced" by the plane. If we incline the axis intersection of the cone slightly, an expanding ellipse is formed in the plane, instead of a circle. Increasing the angle of intersection even more such that the plane never cuts completely across the cone, a parabola will be formed in the plane, and if the cone intersects the plane with its axis parallel to the plane, one branch of an hyperbola will be created by the intersection.
Note that in every case where the cone interacts with the plane of "flatland," the object formed by this projection of the cone onto the plane is an ordinary "flatland" object (point, circle, ellipse, parabola, hyperbola). [Note: they are perceived as the foregoing geometric shapes ONLY if we view the flat space form a point external to the space. To the "flatlander," all "flatland" objects appear as points or lines that "block" various paths within "flatland".]
There is NOTHING "magical" or "mysterious" or "supernatural" about what they would see when a higher dimensional object interacts with their lower dimensional space. The "flatlanders" would just see more points and lines, just as they always do (as "flatlanders" can't "look down" on their own space.)
Not that anyone asked.....
Not if they talked to a competent topologist.
Please. There's no topology in a flatland...it's FLAT. If it had topology, it would be three-dimensional, wouldn't it?
If you cheat in solving dilemmas, and subsequently convince yourself that you have solved it, where does that leave you? Perhaps in the same place as scientists who realize there must be additional mass at the outer layers of the galaxy, but cannot account for it?
Judging by the answers I get on these threads to difficult questions, I am starting to formulate a theory that the most intellectual-seeming among us are those who invent the most clever ways of avoiding the questions.