Despite what some people think, the genetic code did not evolve. It has been unchanged for billions of years. I call it the generic code. Why? Because the code even preceded biological life. There is another kind of lifeform that preceded the emergence of biological life. This prebiological lifeform is none other than the universe we live in. It is an ancient idea: the universe is a living entity. However, there is a difference. Unlike biological lifeforms, the generic material for the universe is not distinct from the material it manages. The genetic and the ordinary all seem to be the same stuff.

If this perspective is accepted, then the four-letter alphabet that encodes biological life should also map to the subatomic particles of matter. The result should be a “periodic table” for subatomic particles.

I am writing this all up. This post is an excerpt. A sneak preview of such a periodic table can be explored in my online database.

Metaphysical First Principles

The problem introduced in this section was admirably described in the short lead in to a conference entitled Metaphysical Principles soon to be held at the College de France in Paris. The problematic is simply rolled out as:

Metaphysics has traditionally been conceived, if no longer as the “science”, at least as the study of “first principles”.

A terse enumeration of what is often meant by “first principles” followed. The role of the Principle of Non-Contradiction gets a mention and Leibniz’s favourite term “Sufficient Reason” is slipped in. Also listed is the circular problem of establishing the grounding of metaphysics as well as handling the metaphysics of the grounding. Then there is the relationship between metaphysics and the axiomatic: metaphysical axioms anyone? In brief, if metaphysics is to advance, what kind of principles are involved? Are the principles formal or just intuitive?

This project claims to provide answers to these questions in the only definitive way possible; viz., by reverting back to the age-old original project of developing metaphysics as a full-blown science in its own right. Given the nature of the endeavour, this is an all-or-nothing project. There can be no half measures.

Leibniz’s Dream

It was Leibniz that clearly laid out the task ahead when he declared his dream of a simple universal unifying science. The new approach with its accompanying algebra based on “only a few letters” and a radically simplifying geometry would greatly ease the cognitive burden of fundamentally explaining how and why Nature actually work. In his words:

If it were completed in the way in which I think of it, one could carry out the description of a machine, no matter how complicated, in characters which would be merely the letters of the alphabet, and so provide the mind with a method of knowing the machine and all its parts, their motion and use, distinctly and easily without the use of any figures or models and without the need of imagination. Yet the figure would inevitably be present to the mind whenever one wishes to interpret the characters. One could also give exact descriptions of natural things by means of it, such, for example, as the structure of plants and animals. (Leibniz)

Like many of his time, and previous times for that matter, Leibniz believed that not only were the existence of plants and animals explicable in terms of some kind of life-principle. The universe itself was also a living organism based on the very same principle. Newton was of similar mind. He even imagined that the “veins” he saw in the rockface of mines he visited were the veins of planet earth as a living and breathing biosphere. The philosopher Spinoza added a theological twist to the living universe version: the universe was a pantheist living god. For Leibniz, biological  lifeforms and the cosmic lifeform were based on the same life principle.

Geometry without number

The science envisaged by Leibniz not only would involve a universal and simplifying algebra, he famously claimed that its semantics would be explained in the form of an equally universal and simplifying geometry without number that he called analysis situs.

Leibniz’s analysis situs dream geometry was to rest in limbo until Leibniz’s bicentennial celebration. A mathematical competition was organised with a prize to whoever could solve Leibnitz’s problem of a geometry without number.  At first there were no entrants. Mobius eventually enticed Herman Grassmann to enter. Grassmann obliged as even though he had not developed a geometry without number he had developed a geometry without coordinates. He was subsequently awarded the prize. A key aspect of his geometry was his notion of a geometric outer product construct which lead to an algebra. Hamilton and Cayley extended the approach to a universal geometric product. In modern times, David Hestenes refined the system and called the result Geometric Algebra (GA) which is how it is known today.

Also inspired by Grassmann. Heaviside and Gibbs independently developed a simple vector and matrix approach to geometry which became linear algebra. In its most generalised abstract form it becomes Algebraic Geometry ( AG).

We thus have two distinctly different geometries, GA and AG, If you are a stalwart of FORTRAN programming you are more than likely an AG, linear algebra fan. On the other hand. If you are into Object Oriented programming and like simplicity, power, and elegance in your geometry then you will be an advocate of GA. I personally like to refer to these two geometric takes on the world as using left or right side rationality. GA is right side, AG is left side. These are the two takes on the geometry of reality, one synthetic, the other analytic.

Most advanced computer graphics in virtual reality and advanced games, employ GA. Most physicists tend to find that AG, linear algebra is sufficient as they are mainly interested in sheer number crunching.

Is Geometric Algebra the answer to Leibniz’s dream?

Is Geometric Algebra the answer to Leibniz’s dream? When used as Conformal Geometric Algebra (CGA) David Hestenes thinks so. So does Hongbo Li who specialises in developing incredibly hyper-simple proofs for geometric theorems only made possible through CGA.

However, what is ignored in these claims is the even bigger picture painted by Leibniz. This mathematical geometry is to provide the algebra of all the natural forms of Nature. In other words, the project should explain the inner workings of the genetic code and unravel its semantics.  Genetic engineering should be more than cut and splice. That works but one should know why before messing around with Nature. And one should also be able to explain the inner workings of matter in the quantum mechanics domain, perhaps with the same four-letter code!

Such a big picture enterprise is the one undertaken in this project.

Biological and Pre-biological lifeforms

What Leibniz’s dream adds to the equation is a glimpse of how this “life principle” might look like once rendered into a formal tractable form. He imagined that it was expressible in a geometric algebra of only a few letters. We now know that all Biological lifeforms are organised around the same code, the genetic code, and certainly based on “only a few letters,” namely four. We know that the algebra is expressed at the molecular level through the DNA genetic material. The genetic material is separate from the functional material making up the body of the organism. Because the genetic and functional matter are separate in biological organisms, I will refer to them as bi-orgs.

A common misunderstanding is that the genetic code was the subject of evolution. Like everything biological, it just evolved. But there is absolutely no evidence that the genetic code evolved. All evidence is to the contrary as it seems certain that the genetic code has remained unchanged over billions of years. Some explain it as a great “historic accident” appearing fully formed at the same time as the emergence of biological life.

However, if the universe hosting these bi-org lifeforms is based on the same life principle, then it too should be based on the same code. Like all living creatures the universe should “have its own DNA,” so to speak. If so, where is it? Where is our universe’s genetic code? The fact is that no one has found the universe’s DNA. No matter how hard the physicists look, they only see the same old molecules and particles. The evidence is pretty compelling. This suggests two possibilities. The first hypothesis is that Leibniz was wrong. Putting aside biological matter, the universe is simple a great conglomerate of inanimate stuff. It’s all just dead Cartesian matter. The second hypothesis is that the matter is self-managed Leibniz style matter subject to some kind of life principle . In this case the genetic matter and the managed matter are “mixed” and in superposition in some way. The genetic and the managed matter will all appear as being the same stuff. Our universe, as such an organism would not be a bi-org, but a mono-org where the genetic and the managed appear to be one.

Genetic versus Generic code

Thus, does our universe consist of dead Cartesian stuff or living, self-managed Leibnizian stuff? I argue for the latter explanation. To me, the universe is a living mono-org organism. In which case the form of elementary particles for the mono-org should be expressible in perhaps exactly the same four-letter code as for bi-orgs. Bi-orgs express divergence of the genetic and managed, mono-orgs express a more primitive pre-divergence form. Such an hypothesis raises the challenge of matching the genetic code common for all bi-orgs to the subatomic particles making up biological matter.

The “periodic table” of pre-biological matter

After considerable time and effort, I have come up with what I believe to be such a match. The result is my version of a “periodic table” for the sub-atomic particles of physics. The table includes all the known together with the as yet to be discovered, unknowns. Many and perhaps all of the latter may not be directly detectable, but their existence can be imputed by my non-empiricist methodology.

The methodology is based on pure reason dedicated to the age-old ontological question of “What is?” Resolving this question in a tractable and coherent way naturally leads to an ontology formalised algebraically by what I call the generic code. The genetic code is one such instance of its application applicable to biorgs. The methodology is easier to understand in its application to mono-orgs as we can intuitively discern the function of the entities emerging from of our enumerative ontology.