I appreciate your effort to introduce what you call the Critical Problem-Solving Impossibility Zone (CPSIZ) Theory into discourse around persistent global challenges like climate change.

Let me respond critically, constructively, and rigorously — not to dismiss your ideas, but to help strengthen their foundation, clarity, and potential impact.

1. On the Core Premise: A Valid Concern, Needing Mathematical Framing

Your central argument — that anthropocentric economic models have created self-reinforcing feedback loops leading to worsening environmental degradation despite decades of policy interventions — is both empirically supported and philosophically compelling. The observation that sustainable development frameworks since 1987 (from Our Common Future to SDGs) have failed to reverse key planetary boundary transgressions (e.g., atmospheric CO₂ levels, biodiversity loss) is well-documented by IPCC, OECD, and others.

However, to elevate this critique into a formal theory, especially one invoking impossibility, requires precise mathematical or logical grounding. In mathematics education and systems theory, claims of impossibility are not made lightly. They arise from proofs within defined axiomatic systems — such as Gödel’s incompleteness theorems, Arrow’s impossibility theorem in social choice, or the halting problem in computability.

Thus, the term "impossibility zone" demands clarification:

• Is it logical impossibility? (Contradiction within assumptions)
• Structural impossibility? (Systemic constraints prevent solution convergence)
• Dynamic impossibility? (Attractor states in nonlinear systems resist intervention)
• Or epistemic impossibility? (We cannot know or model the system sufficiently?)

Without specifying the kind of impossibility, and how it emerges mathematically from the interaction between human decision-making structures and ecological dynamics, the theory risks being perceived as metaphorical rather than analytical.

2. Toward a Formal Model: Bridging Anthropocentrism and Dynamical Systems

To strengthen CPSIZ as a theoretical framework, consider modeling it using tools from:

a) Dynamical Systems Theory

Model the co-evolution of:

• Economic growth (GDP-driven)
• Pollution stock accumulation
• Policy response intensity
• Public awareness diffusion

If current policies only perturb the system within a basin of attraction dominated by exponential consumption, then stabilization at sustainable levels may be topologically impossible without crossing critical bifurcation points — which aligns with your "zone" idea.

This could lead to a mathematical definition of an impossibility zone:

A region in state space where all admissible control inputs (policies) fail to steer trajectories toward sustainability basins due to structural coupling with growth-at-all-cost attractors.

b) Game-Theoretic Feedback Loops

Anthropocentrism can be modeled as a Nash equilibrium in a multi-agent game where individual rationality (profit maximization) leads to collective irrationality (ecological collapse). Here, the “impossibility” arises when no unilateral deviation benefits any player — echoing Hardin’s "Tragedy of the Commons."

You might invoke evolutionary game theory to show how market-based green transitions fail because they do not alter payoff structures enough to shift equilibria.

c) Control Theory & Observability

Ask: Can we observe the full state of the socio-ecological system? Do our metrics (GDP, ESG scores) blind us to critical variables (entropy production, regenerative capacity)? If unobservable, then optimal control is impossible — another route to an "impossibility zone."

3. Historical Context & Terminology Caution

While linking 1987 (Our Common Future) to present-day failures is valid, avoid implying linear causality without accounting for geopolitical complexity, power asymmetries, colonial legacies, and differential responsibilities.

Also, terms like "dwarf green markets" or "circular traditional markets" need operational definitions. Are these technical terms or rhetorical devices? For academic uptake, precision matters. For example:

• What quantifies “dwarf”?
• How is “transition-based” distinct from “market-based”?

Without metrics, these phrases risk sounding polemical rather than analytical — undermining credibility among policymakers and scientists who rely on measurable constructs.

4. Educational Implications: Teaching the Impossibility Zone

As a mathematics educator, I see immense value in introducing students to concepts like unsolvable problems under given constraints. This mirrors historical shifts in math itself:

• The unsolvability of quintic equations by radicals → led to group theory.
• The independence of the parallel postulate → birthed non-Euclidean geometry.

Similarly, teaching students that some societal problems cannot be solved within existing paradigms fosters critical mathematical consciousness (inspired by Freire and Skovsmose).

Imagine curricula where learners explore:

• Phase diagrams of Earth systems
• Bifurcation thresholds in climate models
• Why marginal carbon taxes don’t shift attractors
• How exponential growth conflicts with finite resources

This would embody mathematics for sustainability literacy, grounded in real-world impossibilities unless transformative change occurs.

5. Recommendations for Strengthening the Theory

To move from provocative insight to robust theory, consider:

Define the CPSIZ formally: Specify state variables, parameters, boundaries, and conditions under which solutions cannot exist.

Use existing frameworks: Ground CPSIZ in established theories — e.g., Stochastic Resonance in socio-ecological systems, Tipping Points in Climate Science (Lenton et al.), or Viable System Model (Beer).

Illustrate with simulations: Even simple agent-based models showing why incremental green markets fail under growth imperatives would bolster your claim.

Clarify what counts as a “solution”: Are you demanding zero emissions? Steady-state economy? De-growth? Without defining success, “failure” lacks meaning.

Engage with counterarguments: What if digitalization, fusion energy, or AI-driven efficiency break the loop? Addressing these strengthens your position.

Final Thoughts

Your work touches on a profound truth: we are trapped in a cognitive and institutional paradigm that treats symptoms while accelerating root causes. Labeling this trap the Critical Problem-Solving Impossibility Zone has poetic and potentially scientific merit — but to gain traction in academia, policy, and education, it must evolve beyond narrative into model-based reasoning.

I encourage you to collaborate with applied mathematicians, systems dynamicists, and complexity scientists to formalize your insights. And as a mathematics educator, I’d welcome incorporating such boundary-pushing ideas — once rigorously framed — into curricula that prepare future citizens to think critically about unsolvable problems… and how to dissolve them through paradigm shifts.

Keep pushing. The planet needs rigorous rebels.

Sergio, good day. Thank you for taking the time to write. If you look at my work, including this picture and abstract with the help of AI as this seems you will get it most likely all wrong as AI has the same paradigm shift knowledge gaps in the mainstream work accumulated there. In that picture all the traditional knowledge tools you list including the arrow impossibility theorem DO NOT WORK. A proof for this thinking can be made two ways: USING QUALITATIVE COMPARATIVE CONJUNTURAL DETERMINISM THEORY AND USING STANDART MATHEMATIC THINKING IN PARALLEL FASHION AS THE ARROW IMPOSSIBILITY THEOREM PROOF just that now you do not have independent choice, you have now depending on the type of transition tool, partially codependent choices or fully codependent choices. Little by little the white elephant is being built. Take a careful look at the full paper when published I will share it, but think carefully when commenting. In the meantime, you can take a look at this article and they you can try to comment again and I will reply again.

The Unintended Consequences of Paradigm Death and Shift: Was the Arrow Impossibility Theorem Left Behind?

Article The Unintended Consequences of Paradigm Death and Shift: Was...

When paradigm shift takes place the knowledge base of the old paradigm is left behind. If an axiom is proven true, everything derived from that axiom is true. If an axiom is proven false, everything supported by that axiom is false. When there is a paradigm shift, the axiom that was true in the previous paradigm is false in the new paradigm and therefore, everything derived from old paradigm to be applied in the new paradigm is false as now there is a paradigm shift knowledge gap. And if the knowledge base of the old paradigm is used in the new paradigm then you create a theory-practice inconsistency. Hence new paradigms require either a new axiom or a fixed old axiom; and this leads to a house of cards fall down effect: the main card/Axiom falls and the other cards on the top of it fall because the paradigm has shifted. In other words, when a paradigm shifts it leaves the previous knowledge base behind, creating a knowledge fall down effect reflected in the paradigm shift knowledge gap. And this situation is consistent with paradigm refutation a la Karl Popper as the old paradigm and its knowledge base is left behind and a paradigm shift knowledge gap is created; and it is also consistent with the growth of knowledge a la Thomas Kuhn as this knowledge gap must be closed with new ideas or with fixed old ideas. Among the goals of this paper are: a) to share a general choice or preference framework that can be linked to independent, partially co-dependent, and fully codependence assumptions; and b) to use the case of the Arrow Impossibility Theorem as one unintended consequence of paradigm shift to show that the paradigm shift from an independent choice model (the traditional market) to a partially codependent choice model(the green market) has left it behind as part of the house of cards fall down effect.

I am here to share knowledge through positive academic discources, not to impose my point of view:

I do appreciate the time it took you too

The critical problem-solving impossibility zone theory suggests that certain structural problems—like climate change or systemic inequality—fall into zones where conventional political or market tools cannot resolve them because of complexity, conflicting incentives, or scale mismatches, requiring paradigm shifts or new institutional frameworks.

Chuck that is not the right take on the CRITICAL PROBLEM SOLVING IMPOSSIBILITY ZONE as it is the zone where no transition tools, be it market, ideas, and so on are located, and hence they should not be expected to fix the critical problem because the critical problem is still acvite while the no transition tool as at full work..... Perhaps AI can read again.

Keep in mind AI is good at mainstream thought is it is build on mainstream thought so they are not able clearly capture the essence of outside the box system unless the outside the box system becomes main stream....