There is no construct in science more fundamental than gender. The ancients knew this but the moderns have long since forgotten it.
This post will explore the epistemological and ontological potential of gender in providing a unifying foundation for science and mathematics. In this respect, the structure of the French language provides a first glimpse of the relationship between knowledge and gender. French tends to explain concepts in terms of oppositions, often expressed across opposing genders. For example, French for knowledge is the feminine term la connaissance. The natural corresponding opposition in French is the masculine le savoir. Someone with a lot of specialised connaissance or knowledge is a connasseur. The most extreme kind of connaisseur.is the legendary idiot savant, the one who can digest the contents of the Yellow Pages in one sitting. On the opposite side of the fence is the savant of the non-idiot kind. The most gifted savant of all time was the equally legendary Socrates who had no reliable knowledge whatsoever as expressed in his Confession of Ignorance. However, he knew that fact with absolute certainty, a mark of the true savant. It is quite ironic that the Socratic Confession of Ignorance provides the key principle in developing algebra capable of integrating pure ignorance with pure certitude in a tractable manner, as we shall see.
Including axiomatic mathematics, all of the traditional modern day sciences are of the ordinary, common sense, analytic, fact-based, “connaissance” style of scholarship. These sciences are all well known as deductionist, abstract, atomist, and dualist. Employing the metaphor of the biological brain, we will refer to these sciences as instances of the left side scientific paradigm. The position we take in this paper is that left side paradigm is totally unsuited to provide a foundational science. Any unifying foundational science must be based on savoir, not connaissance. The savoir kind of scholarship we refer to as right side science. Our first task will be to explain the central role of gender in right side science.
Different natural languages implement gender in various grammatical ways. For example, Tagalog of the Philippines is remarkable for its complete absence of grammatical gender Even personal pronouns are neuter and so do not explicitly expose the sexual gender of the respondent. At the other end of spectrum is Jingulu, an Aboriginal language of Australia that has four genders. It is also interesting to note that Jingulu, like other Aboriginal languages, does not categorically distinguish nouns from adjectives, they all collapse into a broader category of nominals. In this paper we introduce the study of a code like language where even the categorical distinction between nominal and verb. and any other grammatical category, all such distinctions evaporate. The syntax becomes so generic that it virtually disappears. We call this language the generic code. We propose this language as the calculus for right side science. All natural languages are left side languages. There is only one right side language, the generic code. We will show how the semantics of this generic code can be reverse engineered from generic principles. With great trepidation, we also claim that this reverse engineered language provides the semantic foundations of the biological genetic code. In other words, the genetic code is an instance of a totally universal, generic code. This generic code is not subject to evolution. It must be in place right from the very beginnings of whatever might start to begin. We will show that the most salient feature of this generic cum genetic code is that, like Jingulu, the language is based on four genders.
Before attempting to tackle the problem of developing a generic language, we must look at the generic problem domain in which it is to operate. Generic language is to provide the calculus for a generic science. What is the nature of such a science?
This is a rough draft of a section of the paper I am writing.
In this paper we develop the foundations of a qualitatively different kind of science to any of the traditional sciences. Aristotle provided a good characterisation of these two kinds of science – the sciences of the particular versus an all-embracing universal science. According to Aristotle, the entities studied by traditional sciences all must possess a determined genus. Traditional science becomes the study of the attributes and species of the genus. The other kind of science can be characterised as being bereft of any determine genus whatsoever. Aristotle interpreted it as the science of Being, or to be more precise, Being qua Being. During the Middle Ages, Saint Thomas Aquinas continued in the Aristotelian tradition, as Jean Grondin writes
It is interesting how Being founds the universality of Thomas’s inquiry. These universal principles, he points out. cannot he grasped by any particular science because they always study a determined genus … Only a science of Being can account for the universal principles common and prior to all the other sciences. Thus there is a science of universal principles that is the master of all the other sciences. (Grondin, 2004)
Over more than two millennia, there have been many attempts to develop such a science and render it into a tractable form. The task has proved so allusive that the prevalent modern consensus is that developing such a science is impossible. In this paper, we intend to refute this position by providing the foundations of such a science.
For discursive convenience, we will refer to Aristotle’s traditional forms of knowledge as left side science. On the other hand, the universal science that operates without a determined genus will be referred to as right side science. Left side sciences are based on generalisations where the degree of abstraction depends on location in a species, genus tree structure. All traditional sciences are based on abstraction. The task of this paper is to tackle the ancient problem of developing the foundations of a tractable right side science. Because such a science can have no determined genus, the science cannot be founded on any tree structuring of knowledge, so characteristic of the left side. There can be no abstraction hierarchy. The science must be abstraction free. If such a science is possible, this right side science must provide a viable alternative to abstraction. The alternative to the abstract is not the concrete as the concrete itself is an abstraction, albeit a zero-order abstraction. Instead, we need something universal. We propose that the epistemological alternative to the abstract is the generic. Right side science must replace abstract generalisation thinking with a form of thinking which is generic and universal. As we shall see, right side science takes the other path towards knowledge, not by generalisations and abstraction but by understanding the universal and generic nature of reality – the universalisation of one single unifying principle. A key sticking point, of course, will be – and always has been – the task of grappling with what constitutes the unifying principle.
We note in passing that universals can arise in a left science; the universal structures of mathematical Category Theory are a good example. However, these are not true universals but primarily abstract generalisations about universals, the generalisation qua universal, so to speak. In brief, universals treated abstractly, or treated as abstractions, are false universals. In order to study the universal, free of the pollution of abstraction, a totally separate science is called for. The epistemological scientific brain must have two hemispheres of operation – abstraction of the contingent does not mix with the universality of the generic.
Immanuel Kant provided another characterisation of the difference between the two kinds of science. Kant characterised the traditional sciences as depending on a priori knowledge. In a modern context, such a priori structure could take the form of empirically determined facts for empirical sciences or sets of axioms for mathematics. The measurements or the axioms constitute the a priori knowledge without which left side scientific knowledge is impossible. Kant characterised the other kind of science as that which produces knowledge without relying on any a priori knowledge. We will call this the Kantian Condition. The Kantian condition effectively stipulates that right side science must produce knowledge without appealing to any a priori knowledge whatsoever, relying on pure reason alone – whatever pure reason might turn out to be. We will return to the Kantian condition later. For the moment we look for a more tractable handle on this most slippery of all forms of knowledge.
We note that we have introduced a handedness convention into our description of the two kinds of science. According to our convention, there is left side science and there is right side science. In so doing we have surreptitiously introduced another possible characterisations of the difference between left and right side science. As it turns out, right side science is permeated through and through with handedness whilst left side science is not. In fact, as is well known, traditional left side science is so non-handed that even its laws of physics are equally valid even if one reveres the direction of time.
In the case of the empirical left side sciences, we can identify science as an empirical activity carried out in controlled confines such as a laboratory. On the other hand, the universal right side science knows no such limitations – it must be the science of Nature’s organisms at work left to their own accord, unrestrained by any a priorist scenario. We now come to an incredible discovery, first reported by Pasteur. Working with organic substances, certain chemical processes carried out in the laboratory produce amino acids. The result is always a 50-50 mix of left and right handed amino acids. Pasteur observed that this was not the case when living organisms produce the amino acids. Biosynthesis produces amino acids for the synthesis of protein. All of these amino acids, without exception, are left handed. All proteins produced from such amino acids are also left handed… Similarly, the D-amino acids that are involved in the biosynthesis of D-sugars all turn out to be right handed. In short, the organisation of biological life seems to be dominated through and through by handedness.
Evolution critics exploit this fact to attack the primeval soup hypothesis for the spontaneous creation of life. The critics argue that it is not enough to start with a soup of amino acids to build the proteins necessary to kick start life as all the amino acids have to be left handed. The presence of one single amino acid molecule of the wrong handedness in a sequence is enough to upset the applecart irretrievably.
Some writers (Mason, 1991) (McManus, 2002) suggest that this mysterious homochirality of amino acids, proteins, and sugars in living organic material can be explained by physical asymmetries at the level of sub-atomic particles. From this perspective, the asymmetries in Nature would sweep right across the sub-atomic world, up the scale through chemistry to biochemistry, and onto the macro world of Nature’s complex biological organisms continuing right up to Homo Sapiens. Handedness would be everywhere and at all scales. A noble universal principle would seem to be at play here, the problem is to understand it.
There have been many attempts to explain the asymmetries in Nature’s handedness enigma. A constant refrain by many writers, McManus included, is that biological asymmetries, even lateralisation of the brain, must somehow provide a favourable functional advantage in Evolution. Evolution results in the functional advantage being coded into specific genes for the various asymmetries.
We simply remark that all of the various theories proposed for biological asymmetries over the years are made from the traditional left side scientific paradigm: biological asymmetries are caused. The left-handedness of all proteins is somehow caused by the left-handedness of all left-handed amino acids, which in turn are caused by violation of parity of the subatomic level. In the search for a first principle explanation, the old problem of Aristotle’s infinite regress raises its head. What explains parity violation? For Aristotle the buck stopped at his Unmoved Mover. The genetic explanation of biological asymmetries appears more straightforward. Asymmetries are caused by being coded. Specific codings evolved through the mutation randomness and selection processes of Evolution. Once again there is are causal sequences stretching back in time to some sort of primordial chance event kicked off by Pure Chance Incarnate, or some kind of Aristotelian Dice less Dice-Thrower.
The right side scientific paradigm takes a radically different perspective. Instead of getting carried away with an ever-changing world caught up in the grip of the ephemeral hazard dominated dynamics of Evolutionism, right side science must home in on more solid turf. We do not have to look very far, the story starts becoming tractable with the genetic code. The genetic code is a universal language that codes all living beings from viruses and microbes right up to homo sapiens, with practically no variation. As a language, one must admit that the code has the biggest user base in the Cosmos. All beings without exception, implement and organise themselves with this universal body language. And here is the most amazing fact. The genetic code is the same language that coded primordial single cell life forms back in the Achaean Age 3.5 billion years ago. With Evolution, everything changes. With the genetic code, nothing changes.
In this paper, we argue that handedness and other asymmetries that abound in the biological world can be explained in terms of the structure of the genetic code. Granted, the specificity of any particular handedness of an organism may be sequenced in its genome. However, the most fundamental aspects of handedness are structurally built into the genetic code itself – into the structure of the language. In other words, handedness is a fundamental structural feature of the language semantics.
Such a claim goes against the prevailing view of molecular biology. According to the Central Dogma of molecular biology, first enunciated by Crick, the genetic code is merely the starting point of a one way linear information flow of sequenced information. A sequence of DNA transcribes an mRNA sequence, which transcribes an amino acid sequence, which translates to the sequential structuring of a protein. The Central Dogma essentially states that the semantics of the genetic code is synonymous with that of a one-way transcription/translation system. Ultimately, the meaning of a DNA sequence becomes is nothing more than the protein to which it so deterministically and faithfully translates. Languages with this “labelling” semantics we refer to as having zero-order. semantics. The Central Dogma essentially declares that the genetic code has zero order semantics.
In this paper, we will reverse engineer the genetic code from first principles and call it the generic code. The code will be shown to have semantics expressed as a form of geometric algebra of generic forms. Unlike present day “left side science” geometry, Generic Geometry will be shown to be fundamentally handed. However, the nature of its asymmetries flows much deeper than mere handedness. We employ the most asymmetrical construct of them all – gender. Our task is to show that the genetic code is nothing less than the calculus of gender. It is this calculus that we propose as the elementary calculus of right side science, the calculus that philosophers from. Aristotle to Kant and Hegel had so long aspired. In the process we are obliged to take a fresh look at the science and logic of the ancient Stoics and goes right back to Empedocles. The universality of this calculus seems to know no bounds. At the end of this paper, we indicate how the gender calculus relates, not just to articulating the forms and shapes of biological life forms, but even to generic forms of the elementary particles of physics.
The Leibniz Vision
Another characterisation of left side science is that it is dualist through and through. The inherent dualism between abstract theory and its object is just one example. On the other hand, right side science must be non-dualist. One consequence of a non-dualist perspective on reality is that there can be no absolute dichotomy between “live stuff” and “dead stuff.” All that exists, in order to exist, must be subject to the same organisational principles. Non-dualism implies that even the universe is a living entity.
The idea that the universe is a living entity is not new. The history of Western philosophy provides a good example with the Stoics. It was also a popular idea during the Enlightenment entertained by both Newton and Leibniz, not to mention Spinoza. Newton even imagined the Earth as a living, breathing biosphere like entity. He thought that the veins of rock visible in underground mines were part of the terrestrial circulatory system of earthly vapours. Leibniz took a more modern approach and it is his vision that provides a clear beacon of what we intend to achieve in this work.
Leibniz saw the possibility of a new science based on geometry without number. The geometry would be based on a fundamental algebra of a few letters applicable right across the biological and non-biological domains. In the following passage, with astonishing insight, he states the problem:
If it were completed in the way in which we 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)
Leibniz claimed that there should be a universal language for coding the structure of “natural things.” We now know that Leibniz was correct. There is indeed such a universal language, the genetic code. If the physical universe we live in is also a “natural thing” then it should also be subject to the dictates of this same universal code. That is the story spelt out in this work.
Leibniz claimed that even more important than the descriptive powers of the algebra, was the explanatory power and the simplicity involved. He argued that traditional explanations were too complicated. Scientific progress becomes blocked unless we can find a simpler way of explaining things. He used the example of explaining a rainbow:
Finally, we have no hope that we can get very far in physics until we have found some such method of abridgment to lighten its burden of imagination. For example, we see what a series of geometrical reasoning is necessary merely to explain the rainbow, one of the simplest effects of nature.
Leibniz called for a simple and simplifying algebra for geometric reasoning. The simplification and demystification for which Leibniz yearned, calls out for an alternative “operational” approach to geometry and science in general. Operational approaches ease the “burden of imagination.” For example, the engineer Heaviside introduced the operational calculus for solving differential equations. Solving and understanding a system in terms of differential equations, doing it the “old way” in the time domain, is an onerous task, as any student knows. Heaviside found that by simply replacing differentials with complex number valued variables the problem can be reduced to the simple algebra of complex variables in the frequency domain. There is much less “burden of imagination” in the frequency domain. The problem with traditional science is that left side reasoning is essentially diachronic in nature. Instead of this “hard way” of explaining science in the diachronic epistemological hemisphere, the right side science must be anchored in the synchronic. The right side epistemology must be fundamentally operational in nature. As a result, this will bring about enormous and sometimes astonishing simplifications to scientific explanations.
Read more: Gender and the Genetic Code