The following is a description of an experiment conducted by Michael S. Gazanniga and Joseph E. LeDoux.  I shall quote from descriptions appearing in two books:  Michael S. Gazanniga and Joseph E. LeDoux, The Integrated Mind, New York: Plenum, 1978, and Michael S. Gazzinga, The Social Brain: Discovering the Networks of the Mind, New York: Basic Books, 1985.

Two problems are presented simultaneously, one to the talking lef brain and one to the non-talking right brain.  The answers for each problem are available in full view in front of the patient.

... a basic mental mechanism common to us all.  We feel that the conscious verbal self is not always privy to the origin of our actions, and when it observes the person behaving for unknown reasons, it attributes causes to the action as if it knows, but in fact it does not.  It is as if the verbal self looks out and sees what the person is doing, and from that knowledge it interprets a reality.

The "chicken claw" experiment was performed by Michael S. Gazziniga and Joseph E. LeDoux using patient P. S., who underwent a full callosal surgery (cutting of the corpus callosum, interconnecting LB and RB) to control seizures.  As elaborated in the second book cited above:
 

...the experiment requires each hemisphere to solve a simple conceptual problem.  A distinct picture is lateralized to one hemisphere: in this case, the left sees a picture of a claw.  At the same time the right hemisphere sees a picture of a snow scene.  Placed in front of the patient are a series of cards that serve as possible answers to the implicit questions of what goes with what.  The correct answer for the left hemisphere is a chicken.  The answer for the right hemisphere is a shovel.

After the two pictures are flashed to each half-brain, the subjects are required to point to the answers.  A typical response is that of P.S., who pointed to the chicken with his right hand [controlled by the left brain] and the shovel with the left [controlled by the right brain].  After his response we asked him, "Paul, why did you do that?"  Paul looked up, and without a moment's hesitation said from his left hemisphere, "Oh, that's easy.  The chicken claw goes with the chicken and you need a shovel to clean out the chicken coop."

It is hard to describe the spell-binding power of seeing such things.

My interpretation is that the normal brain is organized into modular-processing systems, hundreds of them or maybe thousands, and that these modules can usually express themselves only through real action, not through verbal communication.

Again, from the first book:

... a basic mental mechanism common to us all.  We feel that the conscious verbal self is not always privy to the origin of our actions, and when it observes the person behaving for unknown reasons, it attributes causes to the action as if it knows, but in fact it does not.  It is as if the verbal self looks out and sees what the person is doing, and from that knowledge it interprets a reality.