Hebrew U: How we can do math without knowing

Many high school and college students would prefer to forget the mathematics they have learned, because they found it so difficult and even traumatic.

But now, according to a team of Hebrew University psychologists, it is possible to solve multi-step math problems and even read words and phrases subliminally without being aware of them.

The study was published this week in the US by Dr. Ran Hassin and his graduate students Asael Sklar, Ariel Goldstein, Nir Levy and Roi Mandel, as well as Dr. Anat Maril.

The results, they said, pose a challenge to existing theories of unconscious processes that maintain that reading and solving math problems – two major examples of complex, rulebased operations – require consciousness.

Their new findings, they stated, call for “a significant update of our view of conscious and unconscious processes.”

The metaphor for unconscious recognition is “a brain reading under the water’s surface.” The team conducted a series of experiments in which they showed that multiple-word verbal expressions can be processed outside conscious awareness and that multi-step math equations can be solved unconsciously.

All experiments used a new technique called “continuous flash suppression” (CFS) to make stimuli in the brain “invisible” for relatively long durations.

The results showed that novel word combinations, in the form of expressions that contain violations of semantic rules, become conscious before expressions that do not contain semantic violations. In addition, they found that the more negative a verbal expression, the more quickly it becomes conscious, and that subliminal arithmetic equations prepare for their results.

In CFS, one eye is exposed to a series of rapidly changing images, while the other is simultaneously exposed to a constant image. The rapid changes in the one eye dominate consciousness, so that the image presented to the other eye is not experienced consciously. Using this technique, more than 270 Hebrew University students were exposed to sentences and arithmetic problems.

In one set of experiments using this technique, participants were asked to pronounce numbers that appeared on a computer’s screen. These numbers were preceded with unconscious arithmetic equations. The results of the experiments showed that participants could more quickly pronounce the conscious number if it had been the result of the unconscious equation.

In another set of experiments reported in the paper, participants were non-consciously exposed to a number of short verbal expressions that remained on screen until participants could say that they saw them. In the meantime, the other eye was exposed to the rapidly flashing images. The results showed that negative verbal expressions (such as “human trafficking”) or unusual phrases (such as “the bench ate a zebra”) became conscious to the viewers before more positive expressions (such as “ironed shirt”) and more logical phrases (“the lion ate a zebra”). “These results show that the humans can perform complex, rule-based operations unconsciously, contrary to existing models of consciousness and the unconscious,” the researchers said.

“Therefore,” said Hassin, “current theories of the unconscious processes and human consciousness need to be revised. These revisions would bring us closer to solving one of the biggest scientific mysteries of the 21st century: What are the functions of human consciousness?”