Hebrew U: How we can do math without knowing
It is possible to solve math problems and even read words and phrases subliminally without being aware of them.
Economy Photo: Courtesy
Many high school and college students would prefer to forget the mathematics
they have learned, because they found it so difficult and even
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
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
Their new findings, they stated, call for “a significant
update of our view of conscious and unconscious processes.”
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.
used a new technique called “continuous flash suppression” (CFS) to make stimuli
in the brain “invisible” for relatively long durations.
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
“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?”