Pieces, Subsets and Subops
Out of Reduction
Philosophic and mathematical analytic frame for reductionism happened to be enunciated by Descartes. Differential or derivable calculus created by Newton and Leibniz turned the mathematical foundation of reductionism during the eighteen century. Assumption was that infinite small parts could go regularly in operations (derivations and integration) and be managed in smooth, unique and continuous ways. This helped to step down or up in dimensions. Also it was necessary that object could be pictured by non material summarizing point(s).
To remind, very briefly that you can, by derivation, pass from a volume to area (dimension 3 to 2) and from there to line (dimension 2 to 1) and by integration at the reverse. Sort of heuristic solving, like making a complex object a simple point, made a concept, sometimes without dimension. Like an argument defined for every purpose - but then far from reality and with all a series of reductive assumptions ignoring anything around or within; be them neighbors, environment or various mixtures, natural confusion and metastable dynamic equilibrium. We have gone too far in these reductions. Paradigm recruited surepticiously for ignoring, smoothing for refuting real contradictions and balances. Reduction ignored transitions, make improper discontinuities were they often do not exist or prescribe continuity at will of human mistakes, then absolving themselves from any responsibility.
The paradigm of reductionnism, behaved as if its conceptual objects could explain anything pointed to; put in tiny parts and simply operated ("better than any "weak culture practice of low civilization). It overqualified any dominating, imperialist, colonialist, hegemonic social systems labels, meanwhile have also been able to large scale engineering technological devices and harmfull tools.
Philosophic paradigm was necesarry. For experimental sciences it was important to get out abstracts that could be only dogmatic labels, such as theological ones. Controversies at these times where uncheckable, biased controlled and heretics were burned or controversies, todays seen as childish, led to wars. Since the fields of real concern: physics principles (cosmology - the one of Copernicus & Kepler; optics - that of Descartes - mechanics - of Newton), experimental reproducible devices modelled by a mathematical system of equations (Galileo's heuristic) all were in great need of freedom or at least: flexibility and proteccion. But the paradigm of scientific reduction also used same sort of tools (weapons, coaction, invasion) redesigns while developping others looking-like disqualifications.
Laic paradigms do not mean that any religion is improper to scientific issues. Neither that as individual many believers contributed well by their efforts to sciences. Neither that any monotheism could get more reasonable views on exact sciences and, last but not least, that science could not inspire new forms of spiriturally (this to whom may feel concerned).
Reductionism, which could have been not indispensable in other scientific histories, was obtained at the cost of non essential inconvenients at that time. But latelly it turned also the major problems of end of past century. Partitions (apple pie cuts ) within systems can impossibly be perfect and all parts equal. Ergodic motion (pure randomness), which founded statistics was an implication of this paradigm but turned an ambiguous one.
Think Simple and Mind Complex
At first because of natural exact science aims and necessary progresses into scientific corpus (density, concentration focus are useful too): it was not necessary to move things together with contradiccions if they could be experimentally separated. Many formal contradictions were not consistently existing yet. It took a long time for "institutions of knowledge" to care a bit more scientific completeness; for example the gap between inductive formal axiomatic methods and deductions of experimental devices. They can play with mirror's effects when complex, but enough coincidence they had in essential principles of physics, universal to all. Empirism was interpretative and even proper 1st order logic axiomatic method neither deductive logics of experiments were existing (first started end of XIXth century theory of sets culminated its basic mid first half of XXth). Aristotles' system also had to be revised. Devices were simple and robustly reproducible. As a result, artifact, effect filters and other difficulties where uncontrolled, ignored or reduced to statistics' noise.
Modern days problems and complexities turned progressively essential for many reasons. Balances did show that linear relations of reductions were not satisfying; even in reduced models weirdness appeared. Enormous development of good formalism reached dead-end effects. Many logical impossibilities turned demonstrated within perfect formal systems. Perfect inductive formal systems, without considering that they are still poorly applied and wrongly used in common human issues, but, even when well specified, did not fill the expectations put on them. While their pedagogy and proper diffusion are not made honnestly and still obstruct communication or information while inflating non legitimate manipulations (not to see that only neoliberals CFO lie on their statments, many make it somehow unconsciously: "it's not them").
Intermediate or complicated systems of units shown not to be properly explained by partition(s) and parts. Intermediate multiples states or varieties in definitions are not to be ignored. For example quantic mechanics provided better explanations in simple things of physics and qualified its mechanics in the debates of fundamental physics. But now, at the light of how systems should be thermodynamically be thought: open and intermediate, almost irreversible and dynamic since they are open and relate with environment. Out profane esoteric explanations, like spiritual, holistic all generally "wholistic - willistic", there is a need to rethink logical frames to evidence more fruitfully interfaces, balances, confusion and mixtures simulations, previous to decision and to position conceptual observers (analysis and informal active witnesses) at the margins where heterogeneity and diversity could express.
Complex notions as well as objective phenomena have appeared to be essentiel to our understanding. Meanwhile most basic ones like: entropy (virtual concept of thermodynamic information: essential to physics), operators cutting the continuity (Dirac's function), particle-wave systemic relations (from de Broglie), irreversibility of systems (Prigogine) and time and so on ... should be part of the intuitive ressources used by complex management and distribute cautious and cares in societies to balance better traditional ways of leadership, social roles rigid definitions, oversimplifications, fast unique track to labels. Processes of democratic definitions, appropriations need to incorporate more properly essential and care more common operations.
Mind Simple Complex
More practically we have to join in mind sort of blurred pieces that could help us in disturbing our explorations (short ranged by proximity). But it is not as a principle to ignore tools of reduction or simplification. For some examples of reductions and simple parts:
- Partition: Mind the complete cut of non overlapping pieces, like virtual drawer of square compartments. Well in the minimum conditions of selection at random (in a as wholistic as practical set of drawers and compartments) with enough units of part in each compartments, to obtain representativity of your sample, respect to proceeding population. Think it like a tree leaves = square compartment with instructions in each. Mind amso alternative forms of branching, their logic advantage or disadvantage, like the ones explored in botany.
- Graphs: Find in book of theory of graphs and/or special algebra (Lie's or Clifford for those used in fundamental physics) and the sort of families, classified according properties. Indeed their nodes, links oriented or not are for not being ambiguous. There are different forms, some are trees, others are hypergraphs. Think about if since a mainframe (which may eventually be pure if calling a more fundamental system), and that they could be influenced, blurred, filled partly in the interstices by criteria, mediated by marginal functions or interface and never empty environments, which can occasionaly turn significant (while not very appearent in averages).
- Nodes: they can be weighted, even in the theory of graphs or developped in empirical methods (as in PERT or GANTT programming and schedulling). Mind them as they are, in theory of graphs but think also if they can be subunits: subset with the properties of set or other contributing to overall-unit. Complex ones or part of a systems respect to which they assume a role, on which they depend and eventually some similar systemic frame looking like the larger one: Nature mimics too (only humans pretend to reinvent hot water all the time).
- Nexus or links: when they are weighted, quite often by time (delays of executions) they are homogeneous. Matrix calculus applies in regular theory of graphs with hard constraints (linearity-normality): multivariate normality. But, think alternatives to optimum purity (eigenvalues on main diagonal, other cells of unclean triangular matrix - not filled with zeros). Mind to analyze purity or impurity: systemic reality of autocorrelated matrix.
- Equals intervals: observe that many simple processes consider intervalles better as equals . Try to find structure (by structural analysis), irregularities and discrepancies or discontinuities in empirical distributions of results over irregular intervalles of scales (as using kinds of multiple scaled signal analysis methods - wavelets and fractals ones).
- Processes, by the middle or by the extrema in a wise way, considering practical limits and objective (phenomenologic evidence) to humans' "windows". Arithmetic processes proceed alternativelly by the middle, lower or higher value of interval, applied to areas that smallest, averaged and/or barycentric point or highest area.
Think Complex but not Too
For some examples of complexities introduced as abstracts you have to think like if:
- Patterns & Designs stay for a while, not for long, as far as they are not contradicted by evidence or anticipated by humane will.
- Cuts & Confusions not complete, produce overlaps, correlations, thickness, uncomplete separations.
- Residual may be circumstantially meaningful.
- Mixing & Replicators: consider ordered and unordered processes. Pictures could be picked from fluid dynamics as convolutions, whirlwinds, variety of fluid regimes (perfect fluid, elastic, turbulent).
- Approach by probable kinds of pattern in given area of regimes (generally explored by phase-diagrams graphs).
- Smooth but strange bifurcations, like strange attractors. To imagine such kind of patterns, locally very empirically impossible to fix precisely, with some explosive or regressive transitions impossible to predict. Like when abruptly or changing their mainplane and directions of trajectories. There are patterns of bifurcations (pitchforks, and so on) which are standards. Just well drawed on a scheme can avoid managing lengthy formulations.
- Self-similar patterns as Fractals and Constructals, looking like the same be the scale level micro or macro. Care about discernability and scale. It is very probable that nature may reproduce them as facilities of complexity, meaning that some pattern can be essentiel and exist whatever the scale. They are helpful to explore compartment(s) non deterministic details.
- Think that the pathways to complexity may be not so impossible: Nature experiment and locally waste a lot, it is not just linear, mono or bivariates. Consider volumes not just 2 sectors economy, nor just the always same winnner and the loosers of everything.
- Analogies, functions, involutions / evolutions: since much of what you decide, design, assign and so on, is arbitrary and will have the legitimacy of social actors and the feedback of responsibility. You can have creativity and imagination in the management of yours affairs. But invention is not so spontaneous. Analogy will be an important ressource: think of something (but do it), a mechanism (but make it safe), an inspiring scheme or picture (but share it), design a device (but test it), this is innovation. The testing, thorough, systemic review, synthesis and rigorous development will distant it from the original idea, close it to your application and specifications. This in our opinion gives you lot of freedom respect to non consistent academism or dogmatic prohibition; but listen their explanations while care more essentiel principles (rather just "management principles"), no blind respect for any explanations: engineers are often biased by their own paradigms. They are often social efficient but not so effective.
Scale(s) and Complexity
Between simple and complex issues, you should mind in various ways. Properly following simple formalism is like what is already praticed in exact sciences. Listen doubts, seek conditions of pure application (they are the real constraints) and do not take theoretical statments for definitive best pure theorem applied to complex things. As in mirrors logical effect of theoretical formal sciences as mathematics and logics, cautiously consider constraints and conditions; care "easy calculus" of derivations and integration. Infinite calculus is only good at few applied things (enough regular in the wide or small with huge mix of equal meaning properties. Even if ignored by soft sciences which does not stop their experts to give results from wrong assumptions and myspecified models.
Complexity may expresses as universal patterns, but, intuitivelly local definitions and specifications make comprehension more easy with complexity. You may have some use and lessons but should not insist if away from original specifications. Model with large scale can still have some utility for virtual simulations of few phenomena (non human), but do they deserve so many waste of brain drain and diversion? Complexity, where we switch to uncommensuratedness, is enough basic for disqualify any soft theory. So, it may be interesting to find cultural ways for appropriation of scientific concepts in transfert of essential knowledge. Forms or patterns should be adapted and be respecified, eventually into another use for appropriation.
Same is the problem to interpret history in the terms of another time. You may interpret, but often not pretend it the view or value prevailing at that time. This applies from one culture to another: care not to interpretate since only your own. Indeed complexity tends to relativize plenty of lessons of historical time and cultural space. Adapt and translate olicognographic frames preventivelly has also the sense to relay responsibility.
See as a whole or in a "wholistic way" is another "essential" of complexity. May be a frame not too reduced could be better than the one short judgment since which, all things are deduced. Soft definitions are not universal they are more tautological truisms (quite intelligent). Consider sort of complex scale, with complicated shape joining different levels. Somehow these levels are positionned by the registers of development of methods. But the highest levels, could have been disconnected, by humans from material ground. This may have had an interest to discriminate overgeneralizing interpretations. From zooanthropomorphism of utilitarism and neodarwinism horrendous policies have jumpep on eugenic stupidities.
Ground sort of problems at the minimum covering 2 or 3 levels of complexity. Say for example a technological ground, engineering program and social criteria inclusion: Minimum of 2 levels of scale and the 3rd part of the problem. This inspires our sort of complex modelling program. For example: project - materialist constraints - conceptual criteria - social or ecological issue. Also the reason why to suggest micro/macro, micro (complex subparts) / meso (set the complex unit) / macro (the environment somewhere also a meso unit), and so on.
Complex scale should have local irregularities, windows of validity, short life liability, overlaps, blurredness, fuzzyness or thickness, periodicity, cyclicity (regularities too) and you try to mind a piece of it, position the design a collective model, catch some complexity (ground - program - criteria). Trying to avoid the excess of the mexican vaquero sombrero (it may be good for giving some shadow also to your horse when going to the feria, but not exactly the best way to mind a soft social science, instead you would like to be seen as a "loco en el desierto, guapo en la plaza".
Subcomplex Pieces
We have mentionned some of few tips and tricks you could try to find in the patterns with the "eyes of the believer". Increasingly popular are the patterns of simple complexity (cellular automata "New Kind of Science", strange attractors, standard of bifurcations, fractal pictures and so on. What could still be needed is profane explanations, if they can help to think about patterns and practical uses.
May be the visual stimuli could help in catching the attention of cognitive potential. But since most rhethoretic and dialectic have consisted to use and abuse the demonstrative appearance of verbal conviction and elegant wrritings: it could be, we experienced it, quite difficult to make understand that most of language included inflated non consistancy inspiring wrong "real politic" cynnical behaviors or human madness and this do turn sadly increasingly objective. Some, artists may have been pleasant and eventually the expression of human genius, but other, supposed to be more politically serious, and correct have been disastrous.
Olicognographs are of a kind of tool we suggest to articulate logical geometric frames, graphism of key concepts and collective intelligence of citizens' cognition; preserving some liberty in definitions anf specifications. They do not invent much; only trying to suggest frames that could fit to some circumstances, suggesting to adapt them almost always. Include common sense evidences or discuss during the process of reframing, adaptation and appropriation.
Practical life is analysis and many tips have been invented to help thinking. Popular says have often good economic wisdom, still undervalued because economists or formalist have not provided them with logical formula. But we are arriving to that. Other concepts are philosophic or concept. System of conjunctions is well known to sequence the identification of concept: when, where, what, how, why. Other have been the invents of rhethoric or dialectic, such as thesis - antithesis - synthesis.
If intermediate separations can have been conceived - between special algebra, techniques of limited design, contains and contained; deductions and hopes to be universal - not much attention has been paid to systemics explorations, especially when not part of a purified logical system. This because set theory have in fact given the formal tools to purified logical systems of assumptions. With a catalogue of pure properties it would be easier to examine the specified formal problem and identify the properties that apply or wanted to be. Dictionnary of concepts have appeared, yet not as we could like.
A proposal of olicognography considers - on one side - the ideographic pattern, as a puzzle of pieces, minded in a simple complex way, moving via geometric commeasurable logical pieces, with intentions. Where partial algebra could stick and - on other side - qualitative and quantitative specification to similar situations, but inducing to (re)explore the democratic consensus and recruit more scientific knowledge adaptating the frames.
Practically it means that when using a piece of 3, 4 or 5 "cardinals" I have a functional intention. Labels disposed so, seek essence, which can be quite scientific on one side or be motivated, if more of the kind of "social softness" (including social interpretation of otherwise scientifc concepts) a democratic specification, close to manageable fields of application.
Despite our purpose is essential, communal, empirical and profane we care more you show, in the drawing or the scheme what you think and you mind it to implement it. It is to imagine also that we can intent to copy and classify, more analogically than scientifically, all the tricks and tips that could sign our balance between unsafe and unsure objects. Whatever they are, implicit or explicit, written or oral, visual or, may be in the future auditive, treated as label, disposed as filters or as preliminaries waiting a more ideographic-conceptual ideogramm (way for some lexicographic specification: - mind that standards exist and pieces are somehow polyvalent or multiple purposed. Complexity, yes but interestingly manageable (of what would stay is just wait the end of time). Calling these aids as you like: subsets, subsystems of dimensions, subops, structuring subpieces, systems of filters, concepts of influence, and so on.
Basic could be: energy/ information/ matter; quality/quantity/time/space; structure/summary/funcion, structure/complexity/simplified; politics/social/technologic; politics/social/economics; before/constraints/criteria/after, intern/interface/extern, micro/meso/macro
You have a puzzle to make with your communities, a building consistent game of humane economic values, key words and modular pieces of complexity with enough frame made popular ...
