Creativity: through the eye of an elephant gun

My creativity comes from connecting big problems with math.  I start out tackling a huge problem where I think I can get some traction.  In the problem space I spend many years reading all that I can and trying to fully understand the core essential problem.

My first such effort was studying why software didn't work -- -- why it wasn't rigorously tested, why it had errors, and why it was unmaintainable.  I spent over two years doing this and doing nothing else.  In parallel with the problem domain I search for mathematical results that in some way is connected to the problem and would provide some traction.  In the case of software I published a graph theoretic complexity measure after two such years -- -- it became a national standard.

I have spent five years studying the AIDS genome.  This resulted in an AIDS characterization as a mathematical group that would explain the underlying mechanism for the production of AIDS mutations.

Recently I have spent about 18 months studying software security threats and viruses.  This resulted in a algebraic reduction technique that I am in the process of publishing.  I also presented this technique to a software audience in Paris on March 9.

The beginning of this process is a bit schizophrenic being emerged in parallel problem spaces and mathematical spaces.  As the process continues I try to whittle down the problem space to both it's essence and something that's tractable.  At the same time I consider various mathematical models that have underlying simplicity and rigor and look in some way connected. Typically there are very many connections but a breakthrough has to provide a fresh new insight and map onto something operational that solves the problem.

The underlying process is a duality between working very hard and then letting go.  It's like interval training for an athlete --- run full blast, walk for a while, run full blast....  And then when I let go and all is quiet it announces itself.

 It's also an emotional roller coaster -- -- when I find a mathematical connection it's euphoric -- -- when I then find it has no operational use I feel like I'm wasting my life.  Very often after the biggest disappointments and the accompanying depression will be followed by a huge result, wherein I refine the focus and what I thought was an obstacle leads me to the truth.

Here's what drives me.  Rather than science I feel like this is a quest for an underlying truth -- -- wherein I can characterize a big problem with mathematical rigor and get a breakthrough result.  It feels like Columbus on the high seas discovering a new continent  --- the truth was always there, the excitement is finding it.

My next step is to go out and tell the world --- always to the practitioners never to the academics.  The practitioners know what works, the academics certify the math after the fact.  The reinforcement I got lecturing about software complexity gave me the confidence and momentum to build a successful company.

In short I look for big messy expensive problems being addressed with anemic slingshots -- -- and  lug in my elephant gun.

My creative spark in writing poetry is quite different -- -- I aim at the big elephant in the room.  Poetry lets me address the unaddressable in a light way.

Considering Opposites

One of the most fun things about mathematics is the surprising appearance from time to time of truths that are counter-intuitive. The existence of different orders of infinity, for example, or the impossibility of a set that contains all sets. Perhaps it is examples like these that make me wary that my own thinking may be ruling out viable possibilities. And thus, I sometimes generate new thoughts by considering a favorite truth and prodding myself to "Consider the opposite." As a result, I may discover one of my thoughts to be wrong--or, what is more exciting, a pair of opposite truths.

I like these lines from Robert Frost:

"We dance around the ring and suppose,
but the Secret sits in the middle and knows."

Creativity:Truth is Beauty and Beauty is Truth

Truth is Beauty and Beauty is Truth.

This phrase is my key to Creativity. My approach to creative discovery is to follow the mathematics. Galileo said the Book of the Universe is written in the language of mathematics

When I create something, from Math and Physics to Religion, it is a search for Beauty. For example, Maxwell’s Equations, the most famous equations in science, I found to be not symmetric and not Beautiful. This observation led me to investigate where these equations came from and led me to William Rowan Hamilton’s Quaternion Mathematics. Hamilton had developed Quaternions as a means to rotate mathematically a line in space. In the process he invented the concept of vectors.. He started with three vectors:

I, J and K

paralleling space directions. He worked with these for 15 years without success, Then he found that he needed to add a scalar number 1 to make the rotation work.

Quaternion = 1 + I + J + K

The three vectors and one scalar (real number) created Quaternions, a four dimensional space. This was a correct four dimensional space, 60 years before Einstein’s Relativity Theory.


Maxwell used Hamilton’s Quaternion vectors for his equations and went on to make the greatest prediction in the history of science, that Light is a form of Electricity.

Hamilton also invented vector calculus creating a three dimensional vector derivative,

Del= Id/dx + Jd/dy + Kd/dz

Hamilton‘s Vector Derivative, was mathematically incomplete being only a vector not a Quaternion Derivative. I added a scalar derivative to create a Quaternion Derivative:

X= d/dr +Del= d/dr + Id/dx + Jd/dy + Kd/dz = d/cdt + Del

This is a simple addition but with this I can derive mathematically, Maxwell’s Equation as a simple Quaternion Derivative:

0 = XE = (d/dr + Del) (Es + Ev) = (dEs/dr - Del.Ev) + ( dEv/dr + Del Es + DelxEv)

Maxwell’s Equations are written as four Equations involving two scalar fields and two vector fields. The Quaternions contain both the scalar and a the vector field. That is what Hamilton discovered , that mathematics and Nature require both a scalar and a vector field in general. In addition, Maxwell’s Equations has two different fields (E and B)where Quaternions show that the only one field is present. The difference is that in Maxwell's time there was no idea of Four dimensional space. Space and time were separate and the time derivative and space derivative are called different names, Electric fields and Magnetic fields. The reason there is always an electric field accompanying the magnetic field is because there is only one field.


Many years later I was looking for a way to present the reality of Quaternions in science. I looked to the Heavens where Hubble's pictures are Beautiful. Hubble's Redshift is the foundation of the Expanding Universe. Hubble himself, did not believe that his Redshift indicated an expanding Universe. Hubble believed the Redshift is “an hitherto unknown principle of Nature”. Hubble was right.

Investigating Newton’s and Einstein’s Gravity Theories, and applying Quaternions to Newton‘s Law of Gravity, the Universe is stable not expanding. Hubble is correct.. I derived mathematically the redshift. The Redshift indicates the balance force to the gravity contraction, needing No "Dark Energy, or No Cosmological Constant".

Space is not curved as Einstein's General Relativity Theory holds, Light is attracted by Gravity and Einstein's Deflection is Newtonian,

Tan deflection= y/Rs = .5gt^2/Rs = .5gRs/c^2 = 8.1666E-6 and deflection = 1.68'

Simplicity is another mark of Beauty!

Truth is Beauty and Beauty is Truth!

Nuff said.

Looking Within to Look Beyond

I have been thinking about the creative process as looking within in order to look beyond. Here's a poem about that.

Night on the Deck

I spend it silently churning,

sweeping the dark around me,

baring myself to the inexpressible

that is hovering nearby as
the stars are dying and becoming.
I stay for hours wrapped outside

of myself, until I hear a single cricket

and then less then a cricket, and then

I listen in on the infinite smallness

where the poem not written by me

finally begins its clear, fragile song.