This is just a catchy title. All the Greek texts I have show that Euclid's nalytical sequence stops at the Seemeioon, and the notion prior to that is the Gramme. However it is anecdotal that Euclid spent time with the string makers and rope and net makers in Egypt, and so had a proprioceptive notion of gramme based on string, and that of point based on a sharp pin or pointed stake nailed into yhe ground.
The notion of a good line naturally arises from the tussle and tension with a rope as one struggles to pull it taught against internal and external " forces".
In addition the curvature and flexibility of string to mark out groundworks and survey sectors is crucial to the fluidity that Euclid attaches to the notion of segmenting a piece of string. A single piece of string can mark all the boundaries of any form/ idea tha a man may have, and so a string may measure the very magnitudes of space that involve region and boundary. String is the ultimate quantifier, the most elemental tool for bounding ideas and form that man can devise. That it should be abstracted to the process of drawing a line or marking, is not just an analogy, it is a staking of "power" onto gramme, so that it may encompass the space between the inner subjective process and the outer external , objective procedures.
I will show how string, in the form of Gramme has shaped our very notions of synthesis.
When I analyse a gramme I come down to 2 pragmatisms: a mark made by heaping things together in a flowing sequence; a mark made by removing or displacing things through or by a flowing sequence.
The notion of sequence , common to both , distinguishes a gramme from a Seemeioon, not by action or activity or even motion, but by the nature of that motion perceived spatially. Even in the auditory sense , a gramme is perceivable only by spatial stereophonic distinction.
In a similar sense the heaping action, when motionless leads to a spatial difference in scale , a visual difference in density and intensity, and an auditory difference in intensity, et, for we must not forget the other sensory mesh distinctions. Already a gramme is a complex experiential phenomenon, but we apprehend it through subjective processing experiences that mirror the sequences inherent within it.
It is not that I have a line faculty, but that I have a series of faculties that distinguish a line. By this I mean, that my internal processes, by sequencing and bracketing actions of a finite nature re-produce an external sequence that distinguishes itself as a uniquely identifiable encoding , this encoding experience, and the recognisable code it evokes I , by some other mechanism call and recognise by naming — a gramme.
Similarly for all named objects or vocabularised experiences.
Thus without much philosophy I evoke from experiences a model of the world consisting in these encoded experiences and the language mechanisms that are used to name them.
If I look beyond this combined process, I must envisage a minimum of 2 faculties engaged in this process. But then I realise that looking beyond what I am focused upon in active engagement of understanding opens up an endless looking beyond process. This is the experience of conjugation, as it reveals that the focus region is only a factor or part of a greater region(Shunya), and that in fact that egion has a multiple form structure.
It has long been perceived that an onion layer structure is a powerful analogy of this experience, but it took Benoit Mandelbrot to give it the Latin derived name Fractal.
Iteration and it's cousin recursive ness had also long been appreciated, but due to complexity, the human tendency to simplify went counter to this everywhere apparent cyclical nature of our experience. This is not universally true, as some cultures had been given insight by their deepest thinkers. But apart from general pragmatics, much of this knowledge was again simplified into cultural belief systems.
The iterative nature of looking beyond was explored by a few who developed an "esoteric" language to encode it. By this we mean they did not use everyday speech, and yet the mythology and magic that has derived from this simplest of human acts of creating a distinct language to describe experiences is a study in itself.
Conjugation is therefore a dynamic fractal concept, in which Shunya is factorised into multiple forms that aggregate continuously, but which determine each other by scale, by disposition and by factorisation. The final consequence is the dual relation between count and formf, and eventually ratio count and form which tied together logos and arithmos in Napier's remarkable analysis.
Thus the tenuous complexity of our apprehension of Shunya is documented through our languages our histories and our cultures. The "confusion " of encodings reflects the individual uniqueness of each encoder. That we have agreed a workable consensus does not remove these idesyncracies. It requires a fluid and adept mind to navigate these intricacies. Millennia of human experience and reworking and rewording of these cultural consensus eas has resulted in a particularly smooth version of the languages and techniques , but it requires a schooled and tutored mind to navigate the knowledge in its most pragmatic, utilitarian form
Euclid was such a mind. But he was one of many throughout history east and west. Why Euclid has become so universal is because of a confluence of such minds in the greek empire, which both established a successful encoding of the human philosophical processes involved, as well as demonstrating its utility to a wide imperial urine! This was magic on he grandest scale, and presented with Kairos!
This, above all is one of the fundamental skills of mind that is necessary to explain he Greek success. For the doctrine of Kairos meant that fractal iteration was made into an imperial policy through the Greek gymnasium. Every communication had to be scrutinised for Kairos. Thus this rhetorical style ensured that the hearts and minds of those who received communications were respected, because all communications were tailored to the audience, so that every audience might understand in their own language, using their own idioms and in line with their own cultures.
For Euclid's Stoikeioon this meant offering a course in philosophy all could apprehend at the level of Academy. For this we have to add the genius of Plato, who travelled the world to find the most fundamental teachers and schools of thought, and then using his teacher's (Socrates') own methods to inculcate, indoctrinate and to hypnagogically suggest these ideas into the minds of his Students. That this may be Machiavellian is not questioned, but it may also be termed Musean. For Pythagoras believed and taught , and his school followed these principles, tht the Muses were responsible for inspiring the next generation of leaders and cultural executives whom the gods wanted to guide the destiny of mankind.
Thus, the dual strictures of Academia derive from Platoes interpretation of the strict almost monastic commune like systems of the Pythagorean school in Italy.
Socrates had a theory of Form/Idea. The presentation of it was in these Kohanic riddles. These presentations Plato developed into engaging plays, songs, debates, theatre. This was consistent with the way of the Muses. They inspired those who were ready to receive their instruction. Alongside this form of engagement, there was the serious study of conventional, consensus methods to provide Kohans for the students. Many would pass through without inspiration, but receive a damn good education, but the few would be inspired by the Muses and completely revolutionise the courses, curricula nd the teaching materials.
Thus we have a system that encourages conformity while lauding the non conformist, which maintains old confusing ideas while at the same time encouraging thorough revision and redaction. It is this tension between the two corses of action that have kept Academia as it is. Every so often, academia has to be pruned to the ground, to give all the new shoots a chance to really grow. Thus stability and Musean or Machievellian revolution is part and parcel of Academia.
Thus it is a thing to note how amazingly successful Euclidean philosophy has been! The reason is Kairos, and the subject of subjective processing of spatial interaction. The fact that it has been misunderstood, misapplied, falsely denigrated all adds to its fundamental subject matter being of universal importance, because our subjective process has not changed over the course of so long a time, ven though our subjective perceptions or interpretations have varied wildly.
Again and again. The muses inspire us to pay attention to our subjective processing of everyday activities, actions and events. Of these, for process of rope making seems an unlikely fundamental, but let us consider the fundamental actions of the craft , and why it then has universal applicability.
After years of analysis and meditation I found myself looking at a simple piece of scrawl. It said -1,- i, 1, i scribbled inside a wonky circle. In that moment I saw conjugates. Conjugates brought adjugates swimming in to view. Thus in this scrawl was the essential notion of conjugating Shunya into its adjugate factors, and that this was as factorisation that could be written as conjuncted labels of each adjugates but how this really differentiated into so called multiplication and addition I did not immediately recognise…..
The essence of our interaction with space, that is Shunya, I have "termed" the Logos Kairos Sunthemata Sumbols Summetria Resonse, each term having a significance and a terminological effect on the processing description. When we came to a consensus on systematic syllabaries and from them writing scripts and alphabets we allowed individual experience to be recorded in a medium that survived the moment and the memory of it. This was truly "spell" making, and reading it back aloud spell casting and spell binding! Now , with the whole act regarded as literacy, the magic of this technological breakthrough called symbolic language is no longer awe inspiring, except in the hands ofe certain Awe-thorns and skilled practitioners and rhetoricians. The Greek movement to public education took away this priestly power, the power of sorceres and Shamans and witches ans wizards, and taught a wider public the pragmatic uses of symbolic marks and consensus.
It took millennia to record the oral rituals and communications of many cultures in this format, but once it was done, the great libraries provided the enterprising individual magical access to knowledges both in ones own language and in that of others, skills recorded awkwardly and requiring a teacher or master to interpret, but recorded nonetheless. The common or lingua franca of many imperial systems led to the gradual collection and dissemination of the world's knowledges, the wisdom of the world. For the first time an individual coluld be "educated" in knowledges even if impractical in daily living!
We find that historically, many philosophers had a trade, or the religious or mythological culture set them up to receive contributions from the social groups amongst whom they moved. Some were warriors who took what they needed from others to survive, because the core need of all animates is to survive, that is the imperative on which all else is built. This fundamental imperative takes our lofty minds down to the microbial scale. Here we find all the laws that govern our lives and behaviours in direct empirical demonstration. Here we come to grasp that even beyond this scale there is a smaller scale of chemical interactions. And the onion layers keep coming, because beyond the chemical is the electro-physical scale, a nd this scale we call the quantum scale. Thus we find that we are deeply enmeshed in an interaction with space that synthesises to the level of conscious experience we have.
How this synthesis really works is a fractal analytical quest, but because it is fractal, it can be modelled to lesser degrees of similarity, to lower scales of exactitude, approximately and good enough to enable us to devise real mechanical magic; mechanisms that not only mimic organic structures and behaviours, but which also demonstrate internal imaginations and machinations.
Our processes called thinking involve complex, meshed networks in conjuncting, shunting, adjugating and synthesising their " recorde, encoded, or stored" information. In this way subjective processes occur and thoughts and knowledge is developed into ideas and notions, all of which are tautologically and iteratively processed to produce a fractal state of mind. This state of mind is the one piece we call consciousness perched on top a mountain of unconscious fractal processes..