And now, a diversion
Anyone who wants to take a topological visualization test, now is your chance
At an early stage of my PhD dissertation, I studied intelligence tests. My specific interest was the spatial visualization component of those tests, because such tests were supposedly very good at predicting aptitude in various professions related to the one I was studying, computer graphics.
I gave my students a battery of tests at the beginning of several school years to see how well their test scores predicted their later performance in school. The results did not correlate well. However, I noticed that the paper visualization tests I used, and almost all of the ones available, were designed to test a person’s ability to mentally rotate a 3D object.
This skill is useful for airplane pilots and other professions where rotation in space is a necessary skill. In computer graphics, all 3D applications and video games do this for you. This trains students to be so good at it that almost all of my students aced the tests with perfect or near-perfect scores. That is why the results couldn’t be used to compare with a much wider range of performance in class on real world problems.
I decided to make a new type of spatial visualization test for which mental rotation was irrelevant. Instead, it focused on topology. Topology is the way things are connected to each other. Topological awareness is a very valuable skill to have in computer graphics, and I knew from experience that many professional CG artists had a hard time with it. Only the best had strong topological awareness.
The image at the top of this post is one of the tests I made. The idea was to scramble the configuration of pips on each die, and then present two views with the aim of determining which of a group of three views matched that die. In total, five sides of each die were shown, leaving one face hidden. This forced test takers to visualize the topology of each die, rather than using logic to determine the answer.
This test proved to be very difficult but very accurate. When I gave it to the programming and art teachers, all of the art teachers passed and none of the programming teachers passed. One programming teacher, who I think can fairly be described as a genius, gave up on the test after 45 minutes. Another, who was famous as a game developer, gave up after well over an hour, declaring “This is impossible!”
Meanwhile, my best art teacher got a perfect score in less than 5 minutes. None of the art teachers took more than 10 minutes to finish. None of the programmers took less than half an hour, some much longer.
So here’s your chance to test yourselves on one sheet of the test. I originally intended to make it a 5 page test, but after the results from the programming team, decided to limit it to one page. It made it easier for artists, but I didn’t want to be responsible for the way programmers reacted to a 5 page test.
I’ll post the answer key later. Post your answers in the comments.
And here is the easier version of the test:
I flunk, as I don't even comprehend the instructions! Ha! But this topological test doesn't reveal to me anything I didn't already know about my poor grasp of all things 3D. Another Ha!
Ok. My answer before I read comments.
B, E, D, A, C
I'm sure we're all honest here. But to notate my answer... I realized as a programmer, I would have given up and spent hours debating. As a Puzzle, I did things differently. I'm not an artist by any means and like to believe I can think a bit in 3D.
That being said, my answers could be entirely wrong and you can say so. They weren't guesses though! So, I can be proud of that at least!
-Mo