Necker Cube Redux

Looking at the necker cube again, I noticed something cool. There is actually a plausible 3D shape in the drawing; a kind of trapezoial looking structure. Treat the middle rectangle as the top (blackened in the image attached). Treat the trapezoids which share the sides of the center rectangle as side of the 3D figure. Do the same to the triangles which meet at top-left and bottom-right corners.

What do you see?

Maybe I'm juts making this up though...I need to stop staring at this thing and actually study for my finals...

This Spinning Ballerina and Other Curiosities About Our Perception

This is an old optical illusion, which had been erroneously associated with a right brain vs. left brain test. But for the past few days I can't help but constantly think about it and the implications the results have. Here is the image of the spinning dancer:

Of course, the phenomena involved is the same as that of the Necker Cube:

The astute observer notes that our brain is attempting to make sense of visual information before us that is lacking in very crucuial information. In this case, both the cube and the dancer are two-dimensional objects with no real cues on the depth of the object being presented. However, our brains process the given image three-dimensionally since they seem very familiar to us already.

We have all seen cubes before. We expect cubes to have a specific length, width, and height that are equivalent. The necker cube seemingly has such proportions, but it has no means of biasing our interpretation of the three-dimensionality. The front of the cube cube can be either the lower-left square or the upper-right square. Instead of viewing the image for what it is, several rectangles that either share sides or bisect one another, our brain interprets the shape into something familiar.

This is what is happening with the dancer. the dancer does not exist. It is a two-dimensional piece of art that moves. It is really an assimulation of pixels of various shades of grey and black changing with time. You can literally sit here and determine the trajectory of various pixels over time, and consider the motion as oscillatory.

But our brains aren't programed to initial think of the dancer as a collection of composite pixels. We see an image. The initial guess is that of a dancer, and the collective motion of the pixels gives rise to a spinning dancer. But which way is the dancer truly spinning? Due to the lack of specific cues in the image, the dancer can spin either way for an observer. The image possesses an instability due to lack of information, and our brain simply choses a direction of spin.

You can stare at the image and get the spinner to spin either clockwise or counter-clockwise. That is a fun feat. But the real power comes from seeing the motion of the pixels themselves. That is, instead of seeing a dancer that is spinning, you are observing instead the oscillatory motion of the collection of pixels. To do this, you need to consciously trick your brain.

First, stare at the extended foot. When it reaches the extremum on one side of the image, try and follow the foot as if it is returning the way you saw it spin. You may not be successful at first, but keep trying. You should be able to finally achieve the interesting feat of seeing the image for what it truly is.

All images that possess the multistable perceptual phenomena have a real shape and then the percieved shape. The Necker cube is really a collection of two-dimensional shapes. The dancer is really pixels in motion across a screen. But our minds didn't evolve under conditions of being astute geometrists or graphic designers. It evolved under the necessity to process information and to make assumptions. In real environments, such assumptions have utility, such as maintaining survival. In highly contrived environments, such as those available to us through the means of technology, we can manipulate these perceptions and see where the assumptions are created.

This is what has amused me for the past few days. What do you think?

An Update

I almost forgot I had this blog.

A little background story for those unfamiliar with who I am. I am a first year graduate student at the University of Illinois in Urbana-Champaign. As a first-year, your goals are to (1) pass classes, (2) teach undergraduates, and (3) find a research group. Actually, the most important one is the last one, but the others need to be accomplished as well.

Objectives (1) and (2) are easy to do, especially when the course you teach is general chemistry and the courses you are enrolled in you have taken as an undergraduate before. In my case, I just had to brush up some more on chemical equilibria[1] and with being a physics undergraduate I have already suffered through enough mechanics (classical, quantum, and statistical) to last me awhile. It is that pesky (3) that is seemingly difficult.

This is the step/level I am stuck on. I came here for several specific reasons, most of which seem to have gone by the wayside due to circumstances beyond my control. I have a couple of options left for me, but they are closing fast. Objective (3) has kept me the busiest. I don't burn the midnight oil on my homework or on grading quizzes. I've been burning it to try and figure out what my next move is.

I came here to do chemistry, but if push comes to shove, I may have to defect to another department/program altogether. Perhaps a masters in mathematical physics would open more doors for me? The future is a blank slate ready to be written on.

-------------
Notes:
[1] Actually, the correct term would be to "dumb down". Apparently, chemical activities are not taught on the freshmen level...

Chemists have a sense of humor

Science is a human endeavor, and so humor tends to be intertwined amongst the seriousness. This webpage with various silly-named compounds is a prime example. I might buy the book for my desk to keep me smiling throughout the day.