Why revisit the notion of computation which mathematicians have been doing for centuries and which is formally characterized as what a mathematician does with her pencil and paper. A pretty straightforward precedent laden view. But is an arbitrarily expressive mathematician with pencil and paper really the essence of computation or might there be a be a deeper more comprehensive accounting of computation that encompasses the mathematician with her pencil and paper as well as much more?
“Second, though, I also want to make evident just how much such a transformation costs. Politics, creativity, ambiguity, irreverence—none of these can be grafted at a later stage, onto a silent steel core, or even poured, like life-giving water, over inherently desiccated foundations. The whole story has to be turned upside down.” *
*Smith, Brian Cantwell, On the Origin of Objects. Cambridge, MA: MIT Press, 1996. p x
The journey of the upside down story commences with the discovery that the conventional primitives of computation, Boolean logic and stepwise sequentiality are not, in themselves, expressively primitive but require extrinsic expressional assistance. It is further realized that this extrinsic assistance is delivered by arbitrarily capable humans in the works who can make anything work including insufficiently expressive primitivities (Chapter 1).
In Chapter 2 a most primitive primitivity is proposed; a counterpoint of sameness and differentness with differentnesses spontaneously interacting and changing. Understanding that humans must be removed from consideration it is further proposed that the primitivities behave entirely on their own expressional merits in a computation universe containing only the behaving primtivities and nothing more. Exploring the evolution of computation within this computation universe the journey discovers:
an accounting of computation in which primitive behaviors compose to greater expressivity on their own intrinsic expressional merits in no need of extrinsic intervention and with no discontinuity in form of expression.
a context of timeful computation, in contrast to a context of timeless mathematics, in which time is a fully vested citizen of expression in contrast to an imposed mandate,
a context of spontaneously, dependently and concurrently flowing wavefronts of transition in contrast to a context of explicitly controlled sequential steps of state update,
a context in which determined sequence emerges from dependent concurrency in contrast to a context in which dependent concurrency emerges from determined sequence,
a context providing a common characterization of disparate forms of computation whether in a biological cell, in a digital computer or in a mathematician’s thoughts encompassing the real as well as the abstract, the biological as well as the logical, how nature computes as well as how humans compute,
a context within which familiar forms of computation, Boolean logic with its time interval place value number with its arithmetic and sequential interpretation with its notions of sequence control and state update emerge through considerations quite different from those of their historic development.
The journey is an evolving document and will be periodically updated as topics mature sufficiently to be presented.
A journey through Computation: Natural and Human updated 7-24-26 .
Dependency language Updated 6-2-26 to include the derivation of place value number and its arithmetic in terms of the language.
Experience the Flow of Flow Computation
Youtube Video demonstrating and explaining spontaneously flowing wavefronts of transition. Download movie file and single step it to more clearly see the behavior. To play the demonstration interactively on Snap!. Download ringG.xml.zip file and unzip. Go to run Snap!. Drag ringG.xml file onto the Snap! page.
The Gears and Levers of the Flowing Ring
Youtube video presenting the ring structures and behaviors of flow computation. Play movie. Download the spreadsheet files.
iHeart radio interview
The Life Changes show interview on iHeart radio.