Shunya is the foundational concept of Manipume, and it is twinned(dual-ed) with the experience of Shunya that i as a related conception, have of shunya.
Tautologically,reflexively i am a part of shunya and it is a part of me, and my internal experience of shunya is a part of shunya as Shunya is the essence of my internal experience, and my internal/external experience is a part of shunya even as shunya is so divided by my essential experience. But the division of my experience of shunya is my distinction of the differences in Shunya, even as the experience of the differnces is part of Shunya, and these different experiences are of differing magnitudes and are of fractal structure , even as they are part of shunya.
That magnitudes of difference are part of Shunya i have no other way of "knowing" except by a process of comparison of these divisions, which process is a compound conjunction of a process of division and a process of comparison. And to this i and i alone must give my assent, and accept it as it seems to me.
Thus even my internal processes are a part of shunya because i accept that this is the case.
Thus the magnitudes of experience in shunya that i also experience internally , that is within me as a part of shunya, form a complete and irreducible tautology. From this basis i begin my reasoning., my comparing, and therefore by another name my ratioing, and in the wider context of shunya my proportioning of the magnitudes within shunya, that is my experience of them, and my assent to them and my acceptance of them.
That it may be otherwise stated is tautologically allowed,and that it may all be a tissue of phantasms is also allowed, Thus what i accept is of my own choosing,as it seems "good" or of value and use to me.
That i fundamentally dual my experience with my accepted notion of the status of shunya, is a fundamental psychological experience within Shunya by which i judge and make comparison, how i distinguish whatever it may be that is dual-ed, whethr it be internal or within the wider shunya, by what i accept from due process. The fractal structure therefore of Shunya is dual-ed by the fractal structure within me.
If i want to distinguish a concept which i may call number, let it be defined as the comparison of any pair of magnitudes, and let a pair be defined as the number two while a distinct magnitude is defined as one. Thus i may say that any pair of ones is 2 and ant such pair are tautologically a pair of the same magnitude, that the magnitude is dual-ed, that there is a multiple magnitude, that distinct magnitudes which are pair-able in this way imply some other distinction to distinguish them, and that other distinction must form part of the greater magnitude to which the then lesser magnitudes belong; and that the nature of their duality is some common magnitude that I have in experiencing them, despite this other distinction.
This common experience borne of experiencing 2 distinct magnitudes is of course now a distinct magnitude, and tautologically entitled to be called one.
Thus by this convoluted process i may now refer to two distinct magnitudes as one or dual or the same or equal, by this one common experience.
God forbid that i should now call a pair of distinct magnitudes one, having just defined them as two! Yet seemingly this is what we are led to do. Thus we distinguish this one by the term "ratio", which in short means one arrived at by a tautological process of wordsmithing and comparison, that is by the Logos!
Therefore we have the defined one which is a magnitude i experience directly and the logos 1 which i arrive at in a process of reasoned comparison and wordsmithing. Thus our reasoning has ever been convoluted, tautological and psychologically abjurious.
Thank god we can "define away" some of the mental torture if we be willing to just accept the final conclusion of such processes, and no wonder the simple refusal to do such a consensual thing gives rise to an otherwise incomprehensible ire!
That ishould ever want to call such an arch construction a Natural number is only understandable should the adjective refer to the direct and natural experience i call magnitude which underpins the entire "logoi of the process.
Are Principles he same as Axioms? i mean to say that is there a common experience which is the same in both referents, by which i may rationalise duality, equality and similarity, even congruence? Indeed there is for the very same is also termed "fundamental, elemental, foundational,axiomatic, the main structural relation".
What is to be said of all this terminology? that too many needless boks have been written, reiterating, repeating and otherwise copying and mimicking the very same notion? that redundancy has gone mad? Or rather is arrogant analysis missing the plain fractal structure of being?
It is rather that each "individual" has a unique experience of Shuynya, requiring that unique experience to define its individuality, and yet individual within a greater society, without which individuation is meaningless. But this individuation is a process that occurs within larger societies all of which are within a larger context called shunya, by me, with the very same or similar goal of individuation!. Thus the fractal nature of individuation is defined and distinguished, and recognised by meat any scale size.
Thus complex forms which on analysisi show simple relations endlessly repeated seemingly redundantly, which very ewdundancy in abaysis caused us to discard its significance, and even in arrogance to promoe this simplification as elegance, meant that we threw out the one synthetic principle that recombines all so called elegant notions ,and fits them to the inelegant whole? That is the complex whole.
thus, having pursued analysis to absurd ends, we absurdly rejected the redundant repetition that necessarily entails in synthesis, favouring instead elegant ,but ideal forms by magnification and simple conjunction or combination.
Thus it was that Newton, in revisiting the principles of Euclid in the dynamical setting, found it necessary to carefully lay out how one might synthesise and indeed compound these "elegances" to do real and useful descriptive work in building real and dynamic forms. His compounding method is the fundaments of vector algebra, a system more fully explained by Grassmann, and his method of fluxions is a fractal algorithm utilising this vector algebra. That it took the arrival of Benoit Mandelbrots insight and termonology to draw out this fundamental synthetic principle of structure and construction from Newtons conception, is a mark of the subtlety of Newtons' thinking.
What is called the Calculus is not at all the same as the method of fluxions, for there is no single comparable idea that encompasses both.The best that i may firly say, in the spirit of Mandelbrot,is that they are"almost similar"; and that or me is a very satisfying outcome for Newon and Mandelbrot.
the divisional structure of analysis and the fractal structure of synthesis is therefore fundamental to Manipume. The Newtonian redaction of Euclid to the dynamic situation, which was ever there in Euclid, but put to a different purpose, is the basis of principles or axioms in Manipume, along with the foundational revisions of conceptions by Hamilton and Grassmann, and some of my own speculations on spaciometry and fractality, abd process algebra, which applies generally to divisional analysis and fractal combinatoric synthetis.
Newtons revision of the notions of Duality and their extension i find deeply fundamental, regarding the praise of his sagacity to be just and not at all hyperbolic. In that he chose to base all his reasoning on unity through duality rather than to fall into the mistake of equality in zero(?) is a subtle distinction missed by the many, but a fundamental Platonic notion advanced by aristotle.