As many commenters noted in the original discussion (https://news.ycombinator.com/item?id=7513182) if you increase the number of dimensions you can increase the number of lines that can be perpendicular to one another. How a person would "draw" in such a space is merely a question of semantics.
You can certainly draw a kitten with a line. Just not a straight line. This definitely complicates the perpendicularity requirement, but I suppose that if every line is identical (they all draw kittens), then it can be done.
Finally, color is just a question of lighting. You can draw red lines with green ink. Just draw the lines in one color setting (where the ink is green) and display the lines to the client with different lighting where the lines are red. The fact that the lines must be drawn with red, green, and transparent ink complicates the lighting setup, but it can be done.
The inflation of the red balloon should be trivial but could be delegated to a less technical member of his staff if necessary.
I certainly don't envy him the task, but Anderson should quit with the excuses and get to it.