Spinning clockwise or anticlockwise?
On 15 December, Professor Ian Stewart from Warwick University gave a riveting explanation to the mathematics behind visual illusions, at Oxford University. From the equations as to why a dancer spinning in one direction only can be seen rotating both clockwise and anticlockwise at the same time, to the theory behind the notorious ‘Is it a duck or a rabbit?’ photograph.
The evening began with Professor Stewart projecting the ‘Spinning Dancer Illusion’. At once, the audience became rather uncertain as to why we were watching a figure spin repeatedly over and over, until a few voices called out rather contradictory statements. From some it was ‘She’s spinning anticlockwise, what is so significant about this?’ yet others proclaimed, ‘No actually you’re incorrect, she is turning clockwise’. This is where the confusion began. How can one image be interpreted in two opposing ways? Well, in this case the illusion is ambiguous. The eyes see the same information, but with two options of interpretation the observer switches them fairly randomly, so in fact one is able to see both possible interpretations, depending on which part of the dancer is being focused on.
Other examples of ambiguous cases include the ‘Necker Cube’ and ‘My wife and my Mother-in-Law’ , where an old woman’s face can be seen simultaneously to the side profile of a young woman. Again, whichever is seen is due to interpretation. This idea is used to also explain Fraser’s Spiral. This is a spiral which appears to be moving on a still image, yet there are no movements and even more mind-blowing there are only circles, not twisting spirals. Upon this declaration the audience immediately became rather hesitant as to whether or not to fully believe this. Amused by our confusion, Professor Stewart traced around the lines of the circles and the observers all together gasped in astonishment.
We were also introduced to the idea of seemingly impossible visuals, including ‘Impossible Elephant’ where the animal does not appear to have a set number of feet and ‘Impossible Escher’ where stairs are said to be going both upwards and downwards.
The third type of visual illusions shown were those involving rivalry images. The information of such is presented to each eye separately, whilst conflicting each other, leading to no coherent interpretation. To demonstrate we were shown the ‘Monkey Text Experiment’. One picture of a monkey and one picture of writing are mixed together to make two collages, containing both sections of the monkey and sections of the text. When shown to an observer however, one either sees only the monkey or only the text. The brain amazingly fixes the broken image to put the pieces together, revealing a previously unseen display. It was completely astonishing! From this, scientists are hoping to predict new phenomena!
To explain such a complex structure in a matter of lines, the cause of illusions is a result of what is known as the ‘Wilson Network’ - a neural network model for high decision-making. Certain nerve cells are trained to recognise certain colours and between each are inhibitory connections. If one, for example, was to be shown an ambiguous image, where the two interpretations were either a red or green image, it would all depend on where the eye looks first. If red was looked at first, this nerve cell would become a lot more active and would tell the other colour nerve cells to shut down, thus explaining why the green would no longer be seen. This explains the ‘Monkey Test Experiment’.
There are also two types of networks, ‘Model Independent’ (where typical types of behaviour are expected) and ‘Dependent’ (relying on specific models). Referring back to the Rabbit and Duck, Ian Stewart taught that this involves two cells and one column, known as simple rivalry, where it is Model Dependent and the most important variable is the rate at which a neuron fires. An equation behind it is: G= gain function [G (z)] = 0 for z is less than or equal to 0. The cell with the largest activity variable wins.
With the John Rimel Graph it shows the flips between interpretations are sometimes not regular which leads to impossible images being seen. There is an equilibrium which loses stability and throws off a limit cycle and the network oscillates between two possible choices. For the in-phase X2 (t) = X1(t) - the network can’t distinguish the images perceived.
Out-of-phase X2(t) = X1 (t+T/Z) where T=Time period.
Z2 Symmetry dX1/dt = f(X1,X2) dX2/dt = f(X2,X1)
Professor Stewart then explained how the brain swaps levels based on patterns of oscillations that are not ruled out by inhibitory connections.
The session was concluded with the ‘Poston Cube’ shown, at first seeming to have three perspectives, but arguably possessing four - a fascinating concept.
After a completely mesmerising lecture, everyone hurried out to buy one of his books and get it signed by such an incredible and intelligent man!
Annabelle Simmonds (Sydenham High School)
