To find a fractal geometry at the foundation of mathematics is the last thing i would have formerly expected.
This means that ar are the fundamental forms, that dynamic ar are the foundational reality, that motion sequents are the description of our interaction with space, that spaciometry is our entire visual knowledge of reality, and it is not enough. We have to include dynamic intensities of all descriptions to begin to describe the experiential continuum of ceaseless, endless motion.
And that motion is not "chaotic". It is not merely complex. It is convoluted, iterated and relative in such away that you and i can make sense of it as a fractal, fractured, contiguous geometry with the utmost
beauty,fragility,sensibility and ephenerality, and yet it also seems so permanent.
The attributes we give to space reflect the infinite possibilities of relations between moving intensities called by me ars. And amongst those possibilities are quantum probabilities of extremes among the general equilibrial systems.
From the ars with our interaction the dynamics produce condensation and evaporation of "matter", sublimation in the extreme to condensation in the extreme with stability existing in the vast range between these poles.
From this dynamic, dangerous reality comes the dance and song of life, the rhythm of existence, the evolution of evaporation from condensation, and the devolution of possibility into probability into reality of eventfulness.
And our response? our answer is to sing and dance. And our song is the count of naming, the naming of countings, the countless cries of recognition of the similarites, the congruencies, the summetrias, the endless flow of invariants, the tensors of existence, all inspiringly and wonderfully ar-ranged at every level in a kaleidoscope of pattern, colour, meaning, interaction and sensationalism.
To number is to respond to the fractal nature of your experiential continuum, to recognise the glorious discontinuities that lie cheek by jowl with each other and yet move smoothly one against the other,most of the time, but then sometimes they explode!
This is Shunya from which we all come by trochoidal motions and to which we all return by trochoidal motions, from which trigonometric relations have infinite meaning, and to which all trigonometric ratios refer, From which equivalence classes of every kind stream forth in a wild fractal dance and to which every infinite class makes its end in ceaseless motion.
Dynamic shunya is at the white hot foundation of mathematics and all things, and our response is to measure in rhythms of song and dance and countings.
Manipome-ar is about celebrating that in this wild dance of life there are so many things that remain invariant summetrias! That is what i dedicate Manipume-ar to: the celebration of dynamic magnitudes and their dance with invariant relations between every ar that has them.