And they say that it feels that solution would be more difficult to find if it squishes things into a line compared to if it is squished into a plane. But it seems to me that it should be opposite. A plane has an infinite number of lines so it seems that the chances should be higher not lower. Am I missing something here?
The idea is that an even larger number of points from the 3-D object are all squished into a single point in the 1-D case. If you wanted to go backwards from a point on the line to all the points in 3-D space that had been squished into it, you have a ton of options (this is why there is no inverse).
It’s true in the 2D case as well that lots of points from the 3-D object have all been squished into a single point, but the 1D case is even more extreme.