RESEARCH MATHEMATICS AND THE UNCONSCIOUS

It was Monday morning in a class of first-graders in one of those many countries, into which Germany had been dissected following the Thirty-years War. The time was probably the late seventeen hundreds. The teacher had no intention of teaching the class because he wanted to read his Sunday newspaper, which he had not been able to because his kids had been all over him during the weekend. He wanted to be left alone now, and therefore gave the class some busy work: "Add the first one hundred numbers."

The task was this:

1   +   2   +   3   +   ....  +   50   +   51  +   ....  +   98   +   99   +   100.

He thought that he would have hours before someone got the first result in. He was wrong. After about two  minutes, a six-year-old came up to him with the result: 5 050.

A way to achieve this may be reconstructed like this:

Let us assume that we have to do the following addition:

7 + 36 + 13. We may do it quickly by rearranging the order: First plus last plus second: 7 + 13 = 20, plus 36 equals 56.

Let us tackle now the addition of all numbers up to 100:

1  +  100  =   101

2  +   99   =   101

3  +   98   =   101

...........................

50 +  51   =  101

So, the sum is 50 x 101, which is equal to 5 050.

(Question: What is 1+2+3+.......+141 ? You will find the answer on the page ANSWERS, Problem 1.)

Several decades later, this unusual boy (Gauss) had become one of the most famous mathematicians of his time. And more than 200 hundred years later, another famous mathematician (Jacques Hadamard) wrote about the grown-up Gauss:

Thus Gauss, referring to an arithmetical theorem which had unsuccessfully tried to prove for years, writes: "Finally, two days ago, I succeeded, not on account of my painful efforts, but by the grace of God. Like a sudden flash of lightning, the riddle happened to be solved. I myself cannot say what was the conducting thread which connected what I previously knew with what made my success possible."

Can you imagine the magnitude of this problem--the problem, which the clever little six-year had to solve several decades later? And the solution happened without any conscious effort.

Hadamard's book--although containing a testimonial letter by professor Einstein--is largely unknown to both mathematicians and psychologists. Let me give you a very condensed summary:

• The unconscious can be a highly cognitive problem-solving "machine." It operates without effort.
• The effort is used in the initial phase of giving the unconscious a clear understanding of the problem it has to work on.

It is highly unlikely that you will have fully understood the consequences of these statements, so let me go a little deeper into the situation.

The first consequence is that psychological ideas about the unconscious--such as those by Freud and Jung--are wrong. They do not believe that the unconscious is able to solve highly cognitive problems. I chose mathematics because it is the most "brainy" subject.

The second consequence is that you have to stay with the problem far longer than is normally done. That is the conscious work--and it has to be extensive--until you are really sure that you have gotten what you want to solve. The solution then happens all by itself. No effort needed.

However, if we deal with psychological problems, we run into another issue: Psychologists normally work with theories. These theories mold their formulation and perception of the problem the client is facing. Change the theory, and you change the perception of the problem. Now, we have shown above, that the unconscious is quite intelligent. This means that the client's unconscious will recognize if the formulation and perception of the problem is not adequate and refuse the input. An effective therapist has to be able to formulate and perceive the problem in a realistic, objective, and very detailed way, which is accepted by the unconscious.