Friday, April 18, 2014

Part 6 -- How Humanity Saved the Biosphere. The Dialectic of Nature.








To My Readers,



Below is the sixth part of my multi-part re-rendition, in this blog, of a rare, classic text, written by an anonymous collective author, one which -- very early-on, in the 1970s -- '''smelled a rat [smelled the 'Rocke-Nazi' rat -- in my opinion, the biggest, rottenest rat in all of human [pre-]history to-date -- the most rabid, the most massively "ambitious" mass torturers, and mass murderers, in all of human history, who make the bloody Vlad The Impaler pale to an infinitesimal in comparison] in the "Global Warming", "People Are Pollution" rap''', and circulated, in <<samizdat>> fashion, a rather comprehensive warning to humanity about this new "eu"-genocidal ploy, which remained scarcely-known until years later, when an updated version of this text became available on the world wide web.


The internet version of this text is entitled --

Crises by Nature:  How Humanity Saved the Biosphere   



For the Resumption of Humanity's Ascent, and, with it -- and by means of it -- the Regeneration of Our Planetary Biosphere,

M. Milankovitch












Crises by Nature
 How Humanity Saved The Biosphere

by
Capitalist Crisis Studies
[with modifications by M. Milankovitch]
Table of Contents







VI  - The Dialectic of Nature

To what extent does this pattern of natural-historical development constitute a “dialectic” of the biosphere, a dialectic of Nature?
My answera1 is as follows: a ‘dialectic’ is present in whatever we can express by a ‘reflexive’ sentence; it is present wherever we have a formula containing a ‘subject-[verb-]object identical’. 
A process which we need to model, in natural language, by a sentence of the following shape is a dialectical process:
( name of entity )            ( acts on, changes (in some way) )        ( itself )subject                                        verb                                        object
The verb here should be a concrete verb, denoting a definite action or operation, not a form of the so-called verb “to be”, or other such passive constructions.

By this criterion, we have a ‘dialectic of Nature’ whenever we have a process which can be modeled in accordance with the general form --
Nature (acts upon) Nature.

-- and, in so doing, as an inherent, inescapable, non-repetitive result of this [apparent] repetition --


Nature (changes) itself.


In fact, the three instances we have explored above, of the Heterotrophic, Photosynthetic, and Fossil-Fuel based stages of the biosphere respectively, all belong to the general model --
The Biosphere reproduces itself.
  
-- and, in doing so, also, as an ineluctable consequence of this [ostensive] mere self-maintenance --

The Biosphere transforms itself, qualitatively and ontologically.


We can further clarify such models if we recognize that the activity denoted by the verb should not be conceived as external to the subject in question, here the biosphere, but, rather, as an inherent part of that agent’s nature; as essential to and inseparable from its existence and its nature. 

That is, we should incorporate the activity of the subject with its substance, conceiving it as a process-entity. 

Then the verb is absorbed into the noun [or vice-versa].

The term “the biosphere”, denoting the subject and object of the clauses above, would then symbolize both the “thing” biosphere and the behavior characteristic of a biosphere, by a single term.

The conceptual separation between object and event, being and becoming, enforced in our grammar, is, therein, rejected.


In mathematical terms, “the Biosphere” now symbolizes a process, an “operation” — a very complex one — and, in a move characteristic of mathematical symbolization, we are going to replace the string of ‘phonograms’ “Biosphere” by the ‘phonogram-become-ideogram’ “B”. 

The symbol “B” refers to the biosphere by denoting its idea, whereas the word ‘meta-symbol’ made up out of multiple phonetic character-symbols, “B i o s p h e r e”, refers to the biosphere by representing the sound of its word.


Our sentence above then condenses to B “of” B, B(B), B·B, BB or simply B2, in terms of this ‘ideographic translation’ of the phonogramic sentence-model. 

Since the verb is absorbed into B (into "both" Bs), there need be no symbol between the first occurrence of B and the second. 

The “action” of our sentence is presented simply by the operation of the ‘operator’ B upon itself, B(B) = BB = B2.


 
The application or activation of an operation, call it f, upon another operation, call it x, is conventionally denoted simply by their juxtaposition:  fx = f(x) = f·x. 

The leftmost symbol is called the “operator” (function) in such cases, and the rightmost is called the “operand” (argument).

 
Notice that “multiplication” in this generalized sense does not always mean the operation that we call “times”, but rather, it means the mutual activation upon one-another of whatever operation is represented by the “function” and “argument”, “operator” and “operand” symbols involved in the expression. 

In this generalization, the formula 5×6 = 30 is actually a redundant form. 
The notation 5(6) = 30 would do just as well. 

In this case, juxtaposition does mean the operation “times” — the 5 counts the 6 five times, and then sums the resulting five sixes, giving 30 as the “product” — but this is only due to these specific symbols', the 5's and the 6's, involvement, i.e., to the general nature of the operation denoted by both these two ordinary numerals, which is the operation of counting. 

But this is not true for operators in general, for the “multiplication” of symbols which represent operations other than counting — for example, for the operation written i (= ), which denotes the operation of 90° counterclockwise circular rotation in an instance of two-dimensional Cartesian number-space interpreted as the “Complex Plane”  (5i·6i = -30  +30).


In this perspective, a dialectical process is one, in whose ‘mathematical’ (ideographic) representation, operator and operand are composed of the same symbol. 

In function language: a dialectic is represented by a ‘function of itself’, also called a “[self-]reflexive function”.c53 

In the notation of an operator ideography, examples of what such functions look like would include --
f(f), B(B), fx(fx), f(f(f)), and fx(fx(fx) which might also be written f 2, B2, (fx)2, f 3, and (fx)3 respectively.a2


The form a ‘subject-[verb-]object identical’ takes on in the notation of an operational ideography — an ideography of operations (a symbolic logic of verbs or of ‘noun-verbs’, instead of a, crypto-Parmenidean, symbolic logic of nouns alone) — is that of a self-function, a self-operation. 


In current mathematical discourse, such a subject-[verb-]object identical, or self-operation, is often called a “nonlinear term”. 


The “nonlinear term”, i.e., the self-operating generic unknown-function-value, is the form in which “self-reflexive function[-value]s”, i.e., self-operating operators, typically crop up within contemporary mathematics, especially within its domain of "dynamical integrodifferential equations".


A nonlinear term in such an equation is a ‘self-product’ term which contains the unknown function or operation for which that equation is meant to be “solved”. 


That is, in that, nonlinear, term, the generic value of the unknown function occurs in a form “multiplied” against itself, or against another of the equation’s’ unknown function generic values, some number of times or, as is usually said, it occurs in a “power”, or with an “exponent”, or with a “degree”, greater than (or less than) 1 -- with a “degree” greater than 1 in “absolute value”.c54  


Only terms with no “power”, i.e., of degreea3 1, or unity, in that generic value of the unknown operation(s), i.e., terms without self-reflexiveness, are called “linear terms”.


A simple example of a “time-varying” or “dynamical” nonlinear term occurs in the “dynamical” differential equation --


d(x(t))/dt   =   d(xt)/dt   =   ax(t)2  


-- wherein --


 x(t)2   =   x(t) . x(t)   =   xt(xt)

 
This equation asserts that the instantaneous rate of change (“differential”) of the generic function-value, denoted by x(t), with respect to the differential of t(ime), denoted dt, is proportional, by a purely-quantitative factor denoted by a, to a second degree of x(t), that is, to the two-fold self-operation of the generic function-value, denoted by x(t), of that function-unknown, denoted by x, for the generic value of the time variable, denoted by t, i.e., to the operation of the ‘compound operator’, denoted by xt, upon itself.p4 


Any equation containing a “nonlinear term” in the unknown is said to be a “nonlinear equation”. 


In particular, a “differential equation” — an equation involving the operation of differentiation, denoted by d — which also includes a “nonlinear term” involving its function-unknown, is said to be a “nonlinear differential equation”.  


By way of contrast, the differential equation dy(t)/dt  =  cy(t), in which only the first power, or simple presence, of the function-unknown, y(t), occurs, is a linear differential equation, whose asymptotic solution, e.g., for c = -1, is a single point, a “fixed point attractor” or “equilibrium”, ‘crypto-Parmenideanically’ unvarying in its value for all values of the time-variable, t -- e.g., ostensively, for all eternity, although the actual trajectory, or the actual trajectories, that ever-approach to this “fixed point attractor”, “take forever to get there” -- take “until” t = infinity, i.e., “until” a “time” which never can, and which never does, arrive, to asymptotically “arrive” at that equilibrium.  



In this linearity domain of [pseudo-]dynamics, it is all very Platonian. And therefore also very Parmenidean, in terms of the solutions / “attractors” themselves:   the “transcendental”, “perfect”, “immutable”, “eternally unchanging” solutions/“attractors” reside in a realm that forever transcends the imperfect, lower, physical, mutable, ever-changing, dynamical, sensuous world; the solutions/“attractors” reside in a realm of perfection and changelessness which that sensuous lower world can only ever approach, and approximate, but which it can never touch.   


Indeed, in this case, that equilibrium attractor, ‘point of changelessness’, or ‘point of no further change’ is none-other than the value 0 itself.  Parmenides would be pleased!






We see that our dialectical sentence-models, [self-]reflexive sentences when expressed in phonogramic writing, take the form, in ideographic writing, of nonlinear equations, containing terms such as B2 — a term of “second degree” or a “quadratically nonlinear” term. 


If our sentence had described the effect of the product of B with B on itself, we would have had B2(B2) = B4,  instead — a “quartically nonlinear” term, and so on.

 

In fact, we can formulate our Biosphere model as a dynamical nonlinear differential equation.a4  


We can because the sentence-model is precisely about how B operates upon B to produce the transformation of B, i.e., about how B changes B as a process of time. 


The basic form of the “differential coefficient”, presently written usually ‘d/dt’ denotes the operation of measuring the “instantaneous” ratio of operation-change to clock-change. 


That is, the ‘dynamical differentiation operation’, denoted by d/dt, applied to another operation, e.g., to an unknown “dynamical” function, or, i.e., to a “dynamical” function-unknown, stands for the measurement of the “instantaneous rate of change with respect to time” of that other operation. 


The differential operation is actually a [hyper]number, albeit of a non-counting type.c55 


The occurrence of the “dynamical” differential operation symbol, “d/dt”, in an equation renders that equation a ‘dynamical’ “differential equation”, typically describing the “dynamics” or “law of motion” of a “dynamical system”.



Applied to our ‘Biosphere operation’, B, this operation, called “dynamical differentiation”, or “differentiation with respect to time”, would yield an equation containing a nonlinear term in (at least) B2. 


Why? 


Because the self-change-making process of the Biosphere is symbolized B(B) = B2.



Therefore, the time rate of change of B would, in part at least, be proportional to B2:


d/dt(B)   =   .... aB2 .... + ....



The above would be, because it contains at least one term of degree >1 in the unknown operation B, a “nonlinear differential equation”. 



To “solve” this equation would mean to be able to write another equation of the form -- 


 ‘B = ....(t)....’ 


-- which would constitute the mathematical definition of B, for all time t.


That is, this solution-equation would define B universally and explicitly in terms of other, more basic, operations, for every given moment of time, generically denoted by t.





The explicit version of B, spelled-out on the right-hand side of that solution-equation, and revealing the ‘internal anatomy’ -- as it were hidden from view ‘inside’ the univocal symbol B, on the left-hand side of that same solution-equation -- should be a rather intricate affair, if our B2 is to represent an at all realistic specification of the “dynamical system” of the Biosphere as a state spacea5 trajectory, the “flow” or “vector field” or “landscape” of whose “state-space” would represent the multi-dimensional “Biosphere [self-]operation”. 


Our symbol ‘B’ represents, in fact, a ramified “system of operations”a6, onethat would have to be expressed in terms of a multitudinous composition of more fundamental ideographical “verbs”, or “noun-verbs” — i.e., of “operations” ,of  “[hyper-]numbers”, of “functions”.


We have simply used “B” to stand for our ‘[self-]operational, dialectical model’ of the Biosphere. 


We have not displayed here any of its detailed content in ideographic symbolic form, although this entire study is about that content as formulated in a different, non-ideographic, narrative manner. 


A ‘manifold’ operation like B would ordinarily resolve itself into a ‘product’ of many other operations combined.  


B would ‘factor out’ into a very long string of other operators, or into an inhomogeneous polynomial “sum” of such strings, that is, into a many-elemented “n-tuple” (“vector”), or even into an n-dimensional, perhaps ‘tensorial’ array of such strings. 



Furthermore, there is no guarantee — in fact, very little likelihood — that B could be “decomposed” into currently formulated operations, i.e., in terms of presently recognized kinds of [hyper-]numbers, or of “known functions” --

 
“As has been abundantly observed in preceding pages of this work, the solution of many types of nonlinear equations in a closed analytical form is not possible. The range of available functions is much too limited and many equations are intractable to the usual devices of analysis. In fact, most nonlinear equations define new functions, whose properties have not been explored nor for which tables exist.” c56




Be that as it may, we have found an intuitive link between dialectical processes and nonlinear (integro-)differential equations, allowing us to clarify what we mean by a “dialectic of Nature”. 


In fact, the inefficacy of contemporary [capitalist-epoch-mentality-infused] mathematics with respect to “nonlinear” processes is to be expected and predicted, from a Marxian perspective, in view of the ideological and anti-dialectical -- atomistic and reductionist — conceptual premises, conscious and unconscious, from which that mathematics has developed. 


The problem with present-day mathematics is not with ideography, or ‘ideas-graphy’, as such, but with the ideas currently being ‘graphed’, and with the missing/repressed ideas which are not yet being so ‘graphed’. 



The Problem of Nonlinearity is a conceptual problem, and a civilizational problem -- a <<mentalite'>> problem, and not merely a technical problem per se. 



Humanity, collectively, does not yet understand dialectical process, is largely blocked from understanding it, by the conditions, and by the conditioning, of capitalist, capital-value-permeated, [anti-]social life. 


However, those conditions, and that conditioning, are presently changing, as a result of the conditions created by the self-dynamics of self-accumulating, self-concentrating capital-value itself, in the growing global crisis of capital-value's present, decadent, descending phase.



The process of socio-psyche-ological evolution leading to forms of self-identity in the social individual — forms appropriately placed under the heading ‘the social[ist] ego’ — which could afford that individual an ‘internal model’ rendering dialectical process readily conceivable, are still underway, and in hot competition with processes heading toward the ‘neo-barbarian’ ego, or ‘Fascist’ ego. 


In official science, the atomistic model, belonging to the “alienated” and “alien-ized” individualist ego, still holds sway. 


Acquiring the civilizational ability to “solve” nonlinear integro-differential equations entails the formation of concepts adequate to comprehend such processes in the broad popular mind; acquisition, in other words, of the ability to think dialectically, to think like a social(ist) being. 


What is needed is not so much new symbols for the “missing functions”, but the new concepts, and new cognitive processes, which those new symbols will merely represent.
‘Dialectical’ is the nature of any process whose subject is also its object; of any process-entity which, as unified subject-[verb-]object, acts upon itself and thereby changes itself progressively, at first quantitatively, and then, at length, qualitatively, ontologically. 





Not just a human being, or a human society, collectively, but any entity whose name can properly hold the “subject” slot, in a process-descriptive English sentence, is a subject relative to the universe of discourse carved out by our forming that sentence.


And any entity whose name can properly hold both the “subject” and the “object” slots in such a sentence is the subject of a dialectical process. 





Certainly some subjects are ‘more dialectical’, more “[self-]reflexive”, than others. 


In fact, the later in cosmological evolution that one looks, the more dialectical are the systems one finds. 


Human subjectivity, latest to evolve, at least in our vicinity of the cosmos, is certainly the most dialectical subjectivity known to us. 


But [self-]reflexiveness, in graded degrees, characterizes Nature from beginning to end. 


Biospheres, as we have seen, surely qualify as such dialectical ‘subject-[verb-]objects’. 



In general, any entity x which can satisfy (“solve”) a sentence of the shape --
x (operates on) x.

-- is a dialectical subject. 



Obviously, the “solution-set” for x is not restricted to individuals of the human species as its only members.


The finitary "set of all sets" can be grasped, not as an irresolvable paradox, nor even as sequence of separate, different sets, so that no single "set of all sets" ever exists, but as a mental movement modeling, abstractly and generically, the dialectic as we have described it above --










Graphic 20: ‘Image-ination’/‘image-ization’ of the process/auto-kinesis that is the[meta-]Finitary Set of All Sets

 

[Meta-]Finitary Set of All Sets Self-[nature-]Driven, Self-[Definition-]Driven Self-Iteration   =



  




-- such that --


 




In fact, human history, on this view, including the Socialist Revolution, is but part of the Dialectic of Nature, locally the latest chapter in that vast dialogue, that great argument, which cosmological Nature is having with itself.









According to Hegel c46,  dialectical being is not just self-changing process alone. 


It is self-changing all the way to the point of self-termination and self-sublation. 


Dialectical process-beings change themselves, more and more, until, finally, this accumulated self-change amounts to a leap beyond themselves; to a changing of themselves into something else. 


The dialectical perspective, in sum, forces us to recognize the non-eternality of the present leading formation of the Nature of this Biosphere, of Earth life, namely:  ourselves. 


We must face the realization that humanity, too, will, eventually, be self-superseded in its current, ‘meristemal’, role — after bringing forth, out of the very heart of itself, something else, something beyond the human.c57

 


The dialectic does not rest.  


In all of the Cosmos, only this is at rest!





TO BE CONTINUED.


 NEXT:    

Part 7 --  The Ideology of Science.






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