The page is 221, the chapter is titled 'Closing', the book is 'emergence', John H. Holland.
Despite having that book for a year and more, I can not recall visiting that page before, since as usual my mind gets stuck amidst its paragraphs, hooks, each sentence a potential hook that drags along via imperceptible tags thoughts and ideas, already stored in my brain.
Talking about mathematics and mathematicians, abound by rigor, as what is needed to organise a purposeful assault in elucidating emergence, and as it is mentioned
"This recapitulation extracts its points from the context that supplies much of their. Meaning is less dependent on contextual remarks when there is an overarching theory, but our exploration has not yet progressed that far."
to generalize from the contextual points and provide the laws that are applicable in each and every case that emergence appears.
Each paragraph, the whole page, the whole book as such, is rigor itself. A prime example of rigor giving the concept of mathematics another dimension. Unseen laws, no different in substance from the axioms and theorems of a mathematical body of knowledge, used to construct meaningful approaches towards understanding emergence.
Which signifies the importance in providing clear-cut definitions for a firm or a firmer grasp of reality. Precision engineered, skillfully forged surgical tools for lucid concepts so other individuals usefully to employ and enhance their understanding of emergence, individually and collectively.
As John H. Holland admits
"... but I'd have to employ a more intricate formal apparatus to express them."
He, himself skillfully applying rigor in his approach, makes certain that the message he wants to pass on is clear and unambiguous.
I am not rigorous myself, I do not have that quality, my mind flies from nest to nest and in its way it gathers up bits and pieces here and there, leaving or letting or allowing emergence itself to do its bit. What I mean is, to assemble all these thoughts into my mind into a coherent structure, to associate all these disparate notions into something meaningful.
In my lack of rigor, I see emergence as being universal in its application, ubiquitous, everywhere, in every realm imagined. A trait passed on by its parent, chaos itself, chaos that spawn emergence.
In page 231 John H. Holland hints
"It is possible, at this point, to discern some of the obstacles between our present position and a better understanding of emergence, and I will describe them here. There is one larger issue, however, that I will avoid. It may be that the parts of the universe that we can understand in a scientific sense-the parts of the universe that we describe via laws (axioms, equations)-constitute a small fragment of the whole."
"If that is so, then there may aspects of emergence we cannot understand scientifically."
The question arises. If we can not understand them scientifically what other way is left? Can we understand a phenomenon in any other way but by science?
Without going into the many interpretations such a line of thought might lead to, as it is not necessary to fathom in and get lost in procedure and miss the goal, what it comes out of that, what is needed is, multiplicity of perspective.
Multiplicity of perspective amply provided by the multitude of individuals around us, each one a unit, and I emphasize that. One of the units that inhabit this earth, with its own unique hallmark as any unit possess. Providing a unique perspective, its very own angle of observation of the states the world presents itself to each and every one of us.
Armed with the tools that John H. Holland and all other individuals rigorously involved in this search produce, then each and every individual to offer its unique perspective in attacking the issue and enhancing our understanding for something that affects all aspects of our lives.
Enriching its armory of concepts and ideas, the tools to employ to enhance its understanding of the going-ons in the world.