Capitalist Crisis and Human Progress
by Capitalist Crisis Studies

November 21, 1982


"Committed to paper during the late 1970s through the early 1980s, this lengthy essay, "Capitalist Crisis and Human Progress", was a draft toward a self-statement of the core, foundational, methodological and theoretical principles of Capitalist Crisis Studies.

In it, we sought to unify — to intensively integrate — what we had learned from our studies of Marx's writings, and of those of others, as to the evolutionary and revolutionary 'dialectical dynamics' of the global capitalist system, with what we had learned — especially from Sinek Docchi, and his Studies in Dialectics — about the mathematics of dialectics.

This draft, only partially completed by the end of 1982, has the merit of formulating 'techno-depreciation' — the price-competition-mediated obsolescence depreciation reaction of newly-accumulating capital-value, in the form of newly-formed fixed-capital, upon the earlier vintages of accumulated fixed-capital-value — as a 'self-reflexive function' of capital: as a self-reflexive effect of capital as 'self-movement', or 'eventity': the self-refluxing action of accumulating capital upon itself in the form of a 'self-devaluation of capital-value'.

It also has the merits of (1) conceptually linking this techno-depreciation 'self-effect' of capital-as-process-of-accumulation to Marx's "Law of the Tendency of the Rate of Profit To Fall", and of (2) linking the "economic-crisis-precipitating", "capital-asset-Bubble"-forming accumulation of "fictitious capital" — of "capitalized fictitious value", beyond mere speculative excess — and the post-1913 phenomenon of "permanent inflation" to this core process of 'the self-depreciation of capital-value'.

This essay saw and explored, in concert with the findings of Sinek Docchi, the potential that the Musean hypernumbers might provide a new kind of "analytical", "closed-from" solution for non-linear partial and total integro-differential equations — solutions, at least, for those integro-differential equations whose "solution-geometries" are of the "limit-cycle", or asymptotically periodic, type.

It actually exhibits the more compact, hypernumber-valued reflexive function versions of the solutions to several linear total differential equations in its "Mathematical Preface", pages 1-viii, entitled "Hypernumbers and Linear Equations".

This essay located that potential in the possibility that the "power-orbits" of the Musean hypernumbers might form the basis for a new, previously-unrecognized class of '''self-reflexive functions''' that would exactly solve such "limit-cycle" dynamical systems, precisely reconstructing and predicting their state-space trajectories.

The ultimate goal of this draft was to clear the way, and to prepare the grounds, for the formulation of a dialectical-mathematical, psycho-historical model of the global — and self-globalizing — system of capitals. The model sought would be such as to encompass (A) the 'protoic' and ascendant phase dynamics of the capitals-system, as a predominantly '''self-organizing system''', accomplishing a quanto-qualitatively expanded social reproduction for the human species, (B) its turning point into its phase of decadence, or 'descendance', in which it becomes a 'self-dis-organizing system', increasingly delivering contracted social reproduction, and (C) its finality in proletarian revolution, or in the human-species suicide of Plutocracy-orchestrated, global, 'Meta-Nazi', "People Are Pollution" 'Exterminationism' and nuclear warfare.

Its primary contribution toward the formulation of such a model was in its "Manifolds as Operators" conception, pp. 188-205, which, at the level of detail of its consideration, was unique to this draft.

This work continues, out of public sight, for now. But this draft publicly documents the beginnings of that work, warts and all."

Capitalist Crisis Studies

Table of Contents

  1. Pages i-viii
    Title Page
    Contents Table
    Summary of the Mathematical Part
    Mathematical Preface — Hypernumbers and Linear Differential Equations

  2. Pages 1-25
    INTRODUCTION — Some Neglected Dimensions in Economic Modeling
    An Hypothesis Concerning Their Interconnection

  3. Pages 26-41
    PREPARATORY CONSIDERATIONS — Considerations on Mathematics as a Tool of Description
    The Concept of a Process Algebra
    The Noun-Verb Dichotomy
    The 'Operator' Principle: Noun-Verb Synthesis
    Processes, Rectilinear and Circular
    Nonlinearity in Light of Operator Ideogrammar

  4. Pages 42-59
    Nonlinearity in Logic
    Hypernumber Logic
    The Logic of Differential Equations
  5. Pages 60-77
    Power-Orbits and Circular Logics
    The Fundamental Theorem of Nonlinear Algebra?
    The Logic of Limit-Cycles

  6. Pages 78-89
    The Ideographic "Leverage Principle"

  7. Pages 90-101
    The Space of Processes
    The Arithmetic of States
    Application of the Process Algebra: The Semantics of H

  8. Pages 102-115
    The Fate of the "Four Basic Operations" of Ordinary Arithmetic in the Generalization to the Process-Arithmetic — The Syntax of an Operatorial Ideography

  9. Pages 116-147
    H versus Rn — Concluding Observations
    Operators 'On' and 'In' a Space
    Fields, Intrinsic and Extrinsic
    The Conceptual Meaning of Hyperfunctions
    Modeling Evolutionary Acceleration
    Hyperfunction Modeling of "Creative Processes"
    The Geometry of Hyperfunctions (and the Explicit Temporalization of State-Space)
    The Power of a Process
    The Principle of Comprehensive Connectivity and the Fundamental Theorem of Nonlinear Algebra
    Rn and H as Part and Whole
    The Space of Logic as a Subspace of H
    Summary on the Logical Application of H

  10. Pages 148-166
    How to Visualize H
    A Set-Theoretical Metaphor for Our Modeling Paradigm
    Set-Theoretical Metaphor for Evolution
    Sets as Operators — The "Heraclitean Product of Sets

  11. Pages 167-176
    Evolutionary Operators; Summary on the Set-Theoretical Metaphor

  12. Pages 177-187
    Considerations on Mathematics — Conclusion (The Reflexivity Paradigm)
    Building a Mathematical Language
    Obsolescence Depreciation as a Reflexive Effect
    A Physics Example of Self-Reflexive Process

  13. Pages 188-208
    Manifolds as Operators
    The Pervasiveness of Self-Reflexive Process

  14. Appendix

  15. Reference Notes