I am a retired lawyer. I look for puzzles to entertain myself and cluster theory is among one of the things I use to distract and intrigue myself.

I tell people all the time that I never have had an original thought in my life so my task is to find amusement and distraction in the original thoughts of others.

I borrowed some equations from Pierre de Fermat, a 16th century mathematician lawyer, and Albert Einstein who developed the theory of relativity and merely added to them.

I had very poor marks (50s) in high school math, but I used to get in the 90th percentile range on provincial standardized tests. On these tests I just guessed at the one that looked right.

In 2004, I was having a creative period of mania and came up with what I call cluster theory. I haven't been able to duplicate the exact form of the equations due to my lack of knowledge of an equation editor so it probably easier if I just describe the function of the main equation.

I was working on a project that had in theory a number of components that looked like clusters. As a distraction I looked on the internet for the mathematician Fermat. He had an equation that required the input of two prime numbers {a} and {p}.

As I worked the equation, it appeared that the purpose was a numerical machine for prime numbers.

The shape of this equation included corkscrews and I likened it to an elaborate birdhouse with spirals not unlike the clusters that I had been working on.

It is my opinion that the inputs into this prime number machine are like stem cells; fundamental forces in science. The inputs are forced into the machine and result in the building blocks of our universe.

It is from these two fundamental forces that all things spring whether it be physics, chemistry, or the social sciences. These two fundamental forces are in simple terms marketing and group dynamics.

I worked out the various mathematical variations all night and by morning I wanted to tell the world to stop working on these equations and concentrate on something else. By then everyone knew I was manic and I landed in the hospital. My mathematical proofs were thrown in the garbage.

In the hospital over the next number of weeks, I worked out the equations on a white board to see if they were accurate. To me they worked out. They were more shapes than numbers. I didn't care that other people didn't understand, I wanted to find my own proof.

Every essay I ever did in university was written in one sitting. I would read what was needed and write the essay without changes. After the essay was finished I would remember very little about the details of the subject, usually only the theme.

It is the same with my equations. I can't even start to duplicate the math that went into solving them but I know what the answers are. The answers are shown in terms would be understandable to most people. It is how I remember the shape of the equations.

I did a History Degree with a number of courses in the History of Science so even though I wasn't in the scientific profession I did have some exposure to the evolution of thought in the sciences.

There were three books that I referred to while attempting to articulate this theory:

A Brief History of Time by Stephen Hawking

The Elegant Universe by Brian Greene

Physics Demystified A self teaching guide

I would venture to say that John Steinbeck, John Milton, Stephen King and every other author I have ever read has had much to do with the way I view the "math." in cluster theory.

My equation shows that there is a variable in every instance.

x = uncertainty (you change something just by observing it)

[e=mc²] + x= a

a must be prime

p must be prime

[e=mc²] + x = prime

[e=mc²] + x = a

e = energy

c = speed of light

m = mass

a = group dynamics

p = vector

I sum it up as such......

energy equals mass times the speed of light squared

T times the speed of light squared equals mass times the speed of light squared

T= mass

T= thought

mass plus thought equals matter

matter is neither created nor destroyed

thought times the speed of light squared

equals mass times the speed of light squared

equals energy

In case any body cares, there are as many dimensions as there are prime numbers. Each of them is unique, just like us.

The four forces that would represent the fundamental forces as outlined in Cluster Theory can be explained in my terms as Group Dynamics, Supply, Marketing and Demand each of them having an inverse relationship in concert yet when acting together they are none the less equal to each other for having that relationship.

Peter E. O'Neill