Listen to the companion Sparks + Embers episode for this Kindling feature article below.
From Zeroworld to Transcending the Demiurge: Foundational Axioms for Complex Thinking and the Development of Human Wisdom
RadioLab produced an episode called Zeroworld in late 2023. The episode, at its heart, explored the nature of laws: scientific, philosophical, and mathematical laws are taught as inviolable, but what happens when we discover that they are more malleable than we had been led to believe.
Zeroworld has stuck with me because of its accessibility to the metaphor of knowledge: how do we utilize what is useful without becoming subject to the tyranny of its absolutism?
An archetypal picture of this is referred to as the Hierophant or the Demiurge, the lesser creator king or god that believes he is the ultimate creator of the universe, of the all.
In the case of Zeroworld, we treat our leader Zero as a lesser creator. As the lesser creator, Zero has benefited us in many ways: it revolutionized accounting, mathematics, digital systems, and science.
Modern computers, smartphones, and all digital electronics rely on binary code, which consists of zeros and ones. Without zero, there would be no way to encode or operate digital technology, making things like internet access, digital communication, and even simple calculators impossible for everyday use
The place-value number system made possible by zero underpins all modern accounting and financial transactions. Balancing a checkbook, using ATMs, online banking, or even basic budgeting would be unworkable without zero as a placeholder and reference point, making economic life far more difficult and error-prone.
The fields of engineering and automation depend on complex mathematics like calculus and algebra, which require zero for their operations and solutions. Everyday conveniences such as safe bridges, efficient cars, modern air travel, and automated manufacturing would not be feasible without zero’s critical role in the calculations and systems that make them work.
"Goodpain is not interested in rules and answers: we trust our audience and each other to cultivate that for themselves through the conversations we are having. We trust our shared stories, shared questions, and shared wisdom are sufficient to prepare conditions for truth to emerge."
The importance of zero was taught to us all with one of the most hard-and-fast rules of foundational schooling: we cannot divide by zero.
The Zeroworld episode starts out turning that on its head: we can divide by zero. When we forget that and are forever beholden to the rule of “we cannot divide by zero” our world contracts: the rule of Zero – that gave rise to the world we currently know – becomes the Demiurge, believing there is nothing beyond its rule.
So why does the rule of Zero try to convince us that we cannot divide by zero? Well, that is where things get dicey for our world, because we learn that when a world is built upon a construct we have treated as inviolable, take it away and that world starts to fall apart.
But what is falling apart is needed in order to rebuild anew?
This is the part we are interested in at Goodpain. Through our first series, we explored the nature of Human Learning in an AI world and how we can use AI as a useful collaborator for contemplation and reflection.
We were careful not to anchor to hard-and-fast rules, because doing so, at the rate the world is changing due to AI, would increase the chances of irrelevance in near-realtime.
So how do we have conversations, develop ways of working and navigating this world, without rules? How do we prop up guidelines, principles, and policies that will draw us closer to curiosity, exploration, imagination and each other, without letting them become tyrannical demiurges that push us in the opposite direction toward narrow-mindedness, defensiveness, bias, and isolation?
There is a near word we will use instead of rule: the word is axiom and it is a basic statement we accept so we can move forward. It is a given truth, until proven otherwise. Different that a rule that tells us what we are allowed or supposed to do, we use axioms as a starting point or foundation so we can build other ideas.
Goodpain is not interested in rules and answers: we trust our audience and each other to cultivate that for themselves through the conversations we are having. We trust our shared stories, shared questions, and shared wisdom are sufficient to prepare conditions for truth to emerge.
Yet we still need language – within ourselves and between each other – to share stories, questions and wisdom. That language can come in many forms: art and science, empirical evidence and oral tradition, and objective and subjective experience are all forms of language, contribute to the emergence of language, and contribute to developing language about language itself (meta-language).
We trust that the formation of language is an inherently human experience involved in our process of individual and collective becoming. That is axiomatic for us. We will not spend time defending that axiom. And we feel it lays the groundwork for a lot of interesting questions going forward.
- How do we develop language?
- What languages are more effective than others?
- What are the traps we lay for ourselves in making the language construct axiomatic?
There are inherent risks, however, that while we hold an axiom, we become enamored with its grounding and delivery of stability. We forget new information may come along that requires us to stop treating the axioms as worthwhile. If we fail to remember that – if we treat the axioms as sacrosanct – we have established and fallen prey to the Demiurge.
So a conversation about how we approach our discussions is in order. An outline of our axioms is important.
We are embarking on another series focused on the Apprenticeship Leadership Model which will rely on and discuss research on the human condition at times. We will pull from frameworks that were used 30 years ago and are useful, however, some of their underlying science has been called into question. Nevertheless, we will use some frameworks because they currently are the best models for cultivating the conversations and discussions we are called to foster at Goodpain.
This is not without risk. But perfect is the enemy of the good (another of our axioms). And we will not be deterred from undertaking the task of seeking to navigate a way through, without embracing the myth that life is about perfect navigation.To that end, here are two key axioms we will use as be move forward through the Apprenticeship Leadership Model and subsequent series at Goodpain.
Axiom for Complex Thinking No. 1: A Lack of Empirical Support Does Not Equal False
Lack of evidence, empirical support, observational data, and/or research does not mean something is not true. The lack of evidence does, however, exclude some conclusions and use cases for which some frameworks can be applied.
In the case of Zeroworld, “We cannot divide by zero” is useful for many applications: in fact, much of our lived experience today does not conflict with and upholds the “rule” that we cannot divide by zero.
But evidence is overwhelming that we can divide by zero. As we seek to understand more and more about the world around us, we must discard this rule in order to get to greater depth and understand the nuance that is not explained in a paradigm where dividing by zero is not permitted. Quantum mechanics and singularities, quantum computing and novel number systems are all being explored in a world where dividing by zero and the infinite are leaders.
Objections to this world being explored theoretically, orbit the practical application of these concepts: we are not at a state of development where we should or would discard the “do not divide by zero” world and its advancements because there is too much practicality at stake.
But simply because we presently have a lot of our practical world tied to the “no dividing by zero” world does not make new research false. Conversely, we need to remember that new scientific advancement does not obviate what we presently know. That is the power of reminding ourselves of axioms over laws: they invite us into contextual (e.g., use case) exploration of our frameworks and paradigms, while holding them loosely enough for creativity, imagination, and discovery to expand our view and experience of the world.
Lack of evidence, for Goodpain, does not cause us to disregard prior frameworks. They may not be able to deal with all the nuance, yet we hold they may still hold some useful context for exploration.
An example of this will come up in one of our early features around the Apprenticeship Leadership Model. Joseph Chilton Pearce wrote a book in 2004, The Biology of Transcendence, that presented multiple frameworks for understanding the human capacity to rise above restriction, incapacity, or limitation (i.e., transcendence) that relies on available biological explanations of how the brain developed at the time it was published.
We have learned a lot more about the brain since. Does that mean what Pearce published at the turn of the millennium was false. In some respects yes. In others, no. The utility of some of his frameworks is accessible for discussing and exploring some aspects of our lived, shared experience and not others.
What we must remember is that experimentation and empirical methods focus much of their work on causality and where new causal explanations have emerged in our understanding, we should jettison earlier explanations that no longer explain causal behavior or outcomes.
But where there is wisdom and understanding to be explored further, and the older paradigm continue to be useful, Goodpain will seek to capitalize on that utility, reminding ourselves that we not take ourselves or our knowledge too seriously, including the immutability of frameworks like the scientific method which can disregard collective wisdom and the subjective experience because it lacks empirical data.
What does this look like in practice? When we read research papers, Axiom No. 1 changes our approach from “Is this study definitive?” to “What territory does this study illuminate, and where does it cast shadow?” We might find a 20-year-old framework for understanding team dynamics that recent neuroscience has partially contradicted. Rather than discarding the framework entirely, we ask: In which contexts does this still help us navigate team challenges? Where has it proven limited? What insights does it preserve even as its biological explanations require updating?
When designing a workshop or writing an article, this axiom shifts us from seeking the “right” theory to curating useful perspectives. We might draw from attachment theory, systems thinking, and indigenous wisdom traditions without demanding they form a perfectly consistent system. Each lens reveals different aspects of human experience. The goal becomes integration rather than elimination, holding multiple maps of the same territory.
The questions we use to help us govern our Goodpain ethic within this axiom include:
- In what real-life situations does this framework help us navigate the world?
- What strengths does this framework offer, and where does it limit our thinking?
- When new evidence challenges this framework, how willing are we to adapt it?
- Where has this framework proven false or limited, and have we adjusted accordingly?
- How do we balance respect for tested wisdom with openness to emerging understanding?
Axiom for Complex Thinking No. 2: Simplify As Much as Possible, and No Further
Oversimplification is a common criticism of early research in a domain. In our human approaches to questions, we can seek to force fit too much information and experience into a singular framework, resulting in tortured explanations or at times, the creation of loopholes or ridiculous conditions just so we can prop up the framework or worldview.
On the other end, however, is the risk that we dissect and segment the world so much, that we end up classifying all experiences into distinct particles that hold no shared meaning. This atomization of the world is one to which we are sensitive. An example we would endorse is the development of the Diagnostic and Statistical Manual of Mental Disorders (the DSM) which seeks to classify psychological pathology in a way that supports the uniform application of diagnoses and subsequent treatments. We feel the DSM has lost its effectiveness as a tool in his atomization of lived, human experience (maybe we will discuss this at some point later, but this is used as an example for atomization, and we will not defend our perspective here).
In practice, this axiom changes how we approach complexity. When writing about leadership development, we resist the urge to create seven-step programs that promise universal application. Instead, we identify the essential principles that appear across cultures and contexts, then explore how they manifest differently in various settings. We simplify toward core patterns without erasing the nuances that make those patterns come alive in specific circumstances.
This means acknowledging when simple answers don’t exist. Rather than forcing complex realities into neat categories, we learn to hold paradox: leadership requires both confidence and humility, both solitude and community, both structure and flexibility. The simplification comes not from reducing complexity but from finding the through-lines that help us navigate it.
The Goodpain focus will be to simplify as much as possible and where there is research that helps draw insight and inspiration through simplifying, we will reach for it. The questions we use to help us govern our Goodpain ethic within this simplicity axiom include:
- Does our simplified approach include diverse perspectives or exclude important voices?
- Are we clarifying for most people or oversimplifying complex realities?
- Do we test our simplified ideas against feedback, or ignore contradictory evidence?
- Does our drive for simplicity sacrifice crucial nuances that help people solve real problems?
Axiom for Comlex Thinking No. 3: Controversy is an Invitation to Explore, not a Mandate to Polarize
In our Zeroworld exploration, we discovered something interesting about the rule against dividing by zero: people become surprisingly defensive when we suggest the rule might not be absolute. Mathematicians have built entire careers on systems that assume this rule is inviolable. When presented with evidence that we can divide by zero in certain contexts, some respond as if we’re threatening their professional identity.
This reaction reveals how we often treat controversial topics – not as territories for exploration, but as battlegrounds for defending our positions.
Goodpain operates from a different premise: controversy signals that we’ve encountered something worth understanding more deeply. When people disagree passionately about something, we’re usually looking at a place where multiple truths intersect, where different frameworks illuminate different aspects of reality, or where our language hasn’t yet developed sufficient precision to hold complexity.
We embrace controversy as an invitation to get curious about why smart, thoughtful people can look at the same evidence and reach different conclusions. Rather than rushing to determine who’s “right,” we want to understand what each perspective reveals about the territory we’re exploring.
This doesn’t mean we think all viewpoints are equally valid or that truth is relative. Some perspectives have stronger evidence. Some frameworks prove more useful for navigating reality. But even flawed perspectives often contain fragments of insight that expand our understanding.
When we encounter controversial topics in the Apprenticeship Leadership Model series – like the tensions between credentialist and competency-based approaches, or the scientific critiques of certain developmental theories – we’ll model this exploratory stance. We’ll acknowledge the controversy directly, examine what makes it controversial, and seek to understand what each side illuminates about human development and leadership.
Consider what this looks like when engaging heated discussions about AI in education, or debates about traditional versus progressive parenting approaches. Rather than choosing sides, we become curious about what each perspective protects and what it fears. The traditional educator worried about AI might illuminate important concerns about deep learning and human connection that AI enthusiasts need to address. The progressive parent advocating for children’s autonomy might reveal insights about human development that traditional parents could integrate without abandoning structure.
In online discussions, this axiom transforms our participation. Instead of commenting to correct or convince, we ask questions that help everyone understand the deeper tensions at play. We become archeologists of assumption, excavating the beliefs that drive different positions rather than battling over surface-level disagreements.
The questions we use to govern our approach to controversy:
- What makes this controversial, and what does that reveal about deeper tensions?
- What insights does each perspective offer, even when we disagree?
- How can we engage controversy to deepen understanding rather than entrench positions?
- What emerges when we treat disagreement as collaborative investigation?
- How do we honor genuine concerns while still making necessary decisions?
Why These Axioms Matter: The Cost of Rigid Thinking
These axioms address a fundamental challenge we face when navigating complex questions about human development, leadership, and meaning-making. In our rush to find certainty, we often grasp frameworks that feel solid and treat them as universal laws. This creates several predictable problems.
First, we become defensive rather than curious when encountering perspectives that challenge our adopted frameworks. A parent who has built their identity around a particular educational philosophy becomes unable to learn from different approaches. An executive trained in one leadership model dismisses insights from other traditions that might serve their team.
Second, we miss the dynamic nature of human systems. What works for developing leadership in one cultural context may need significant adaptation in another. A therapeutic approach that serves one personality type might harm someone with different needs. When we treat context-dependent tools as universal truths, we create unnecessary suffering.
Third, we stop learning from the complexity that makes us human. Real leadership development, authentic community building, and meaningful contemplative practice all require us to hold multiple perspectives simultaneously. They demand the kind of thinking that can navigate paradox rather than demanding resolution.
These axioms create space for a different kind of engagement with wisdom – one that honors both the insights accumulated over centuries and the new understanding emerging from contemporary research and diverse cultural perspectives. We can draw deeply from tradition while remaining open to correction and expansion.
This matters because the challenges we face – in our families, organizations, and communities – are rarely solved by applying single frameworks with rigid consistency. They require the kind of adaptive intelligence that emerges when we hold our knowledge lightly enough to keep learning.
Beyond the Tyranny of False Laws
We return to where we began – with the discovery that what we thought was an inviolable law might be more of a useful convention. The rule that “we cannot divide by zero” serves us well in most mathematical contexts. But treating it as absolute prevents us from exploring the mathematical frontiers where dividing by zero opens new possibilities.
This captures something essential about how we’ll navigate the complex territories ahead in our Apprenticeship Leadership Model series. We’ll encounter frameworks that were developed decades ago and have since been challenged by new research. We’ll explore practices rooted in ancient wisdom that modern science both validates and complicates. We’ll wrestle with approaches to human development that work powerfully in some contexts while failing in others.
The temptation will be to treat each framework as either universally true or completely false – to create new demiurges that promise certainty but ultimately contract our world. Instead, we’ll hold our knowledge more lightly, the way a skilled craftsperson holds tools: with respect for their utility, awareness of their limitations, and readiness to set them aside when the work requires something different.
We’re not abandoning standards or embracing relativism. We’re learning to distinguish between what’s useful and what’s true, between what works in specific contexts and what works everywhere, between insights that have stood the test of time and those that need updating based on new evidence.
This is the stance we need for exploring something as complex as human development and leadership. We’ll draw wisdom from multiple sources – ancient practices, modern research, lived experience, and cultural diversity – without demanding that they all fit into a single, tidy system. We’ll use each lens to see aspects of reality that others might miss, while remaining honest about what we don’t yet understand.
The Apprenticeship Leadership Model emerges from this approach: not as another universal system that promises to solve all leadership challenges, but as a way of engaging with the ongoing question of what it means to grow into our capacity to serve something larger than ourselves. We’ll explore it thoroughly, test it against experience and evidence, and hold it lightly enough that we can continue learning from what works and what doesn’t.
In Zeroworld, the mathematicians discovered that their universe became much larger when we stopped treating “no dividing by zero” as an absolute law. Our world becomes larger, too, when we approach wisdom with this same spirit of rigorous exploration rather than defensive certainty.
We invite readers into conversations that honor both the weight of accumulated wisdom and the lightness needed to keep learning. This is how we navigate together – not as people who have arrived at final answers, but as fellow travelers committed to the ongoing work of becoming more fully human.
The Long Apprenticeship Ahead
Understanding what makes us human as conscious beings prepares us for the most important challenge: learning to be human together. Individual consciousness serves collective wisdom through our capacity for sharing of knowledge and cultural transmission.
The workshop points beyond individual craft to community wisdom. The master-apprentice relationship demonstrates how consciousness develops through relationship and serves purposes beyond individual achievement. The apprentice learns not just to shape wood but to shape their own awareness in service of the larger tradition.
We risk losing this humanity when we treat consciousness as individual rather than relational. When we optimize for efficiency over depth, answers over understanding, we erode the conditions that make conscious development possible. The conscious choice to preserve our humanity requires building communities that support both individual agency and collective wisdom.
The danger isn’t just that AI might replace human thinking but that we might stop thinking consciously ourselves. We might surrender the effortful practice of self-awareness, moral reasoning, and relational intelligence for the convenience of algorithmic processing. The preservation of human consciousness requires not just understanding what makes us unique but cultivating those capacities.
This cultivation can’t happen in isolation. Just as the craftsperson learns through relationship with masters and materials, consciousness develops through relationship with other conscious beings. We need communities that support the long apprenticeship of learning to be human together.
The recognition that consciousness is craft – something that can be developed through practice – creates both responsibility and hope. Responsibility because we must cultivate what makes us human rather than assuming it will persist. Hope because consciousness can be strengthened, shared, and transmitted to others.
Standing in the workshop of ideas, we recognize that mastery means knowing when to trust the tool and when to trust ourselves. That discernment – developed through practice, tested through difficulty, refined through community – remains human. Our humanity isn’t threatened by AI’s capabilities but by our willingness to abdicate our own.
The conscious choice to remain human requires daily practice, sustained attention, and commitment to the long apprenticeship of learning to be conscious together. This choice shapes not just our individual development but the future of human consciousness itself.
The wood continues to speak back to those who develop the sensitivity to listen. The question is whether we’ll maintain the patient attention required to hear its teaching, or whether we’ll surrender that irreplaceable capacity to systems that can process information but cannot be conscious of their own processing.
The choice remains ours, made new each day through the quality of attention we bring to the world and to each other. In that choice lies the preservation of what makes us most human: the capacity to be conscious of our own consciousness, to choose our response to reality, and to share that gift with others through the long apprenticeship of learning to be human together.
The Craftsperson’s Plans
Like Adler’s team indexing the Great Books, the craftsperson creates drawings not as decoration but as thinking tools. Each sketch shows problems invisible to imagination, exposes the relationship between components, transforms abstract vision into buildable reality.
Standing at my workbench with plans spread across the surface, I realize these drawings represent more than construction guidance. They capture thinking in visible form, creating external artifacts that make internal processing available for examination and improvement.
The plans don’t just record intention (they generate understanding). As the pencil moves across paper, solutions emerge that pure mental modeling missed. Proportions feel wrong on the page before they would fail in wood. Joint relationships clarify through visual representation.
This external thinking becomes more important when collaborating with artificial intelligence. I need ways to see my own cognitive patterns, to direct AI toward boosting rather than replacement, to maintain creative authority while benefiting from computational power.
Like Adler’s Syntopicon connecting ideas across centuries, my personal thinking tools must connect understanding across domains, show patterns invisible to linear processing, and make the invisible architecture of understanding visible enough to evaluate and improve.
The workshop teaches a fundamental principle: mastery involves not just knowing how to use tools, but knowing when each tool serves the work best. The same principle applies to thinking tools (I need multiple approaches and wisdom about when each contributes to understanding).
But something more emerges through sustained practice with these visualization tools. I begin to see thinking itself differently (not as a purely internal process that sometimes gets expressed externally, but as a collaborative process between internal consciousness and external representation that generates understanding neither could produce alone).
Making Thinking Visible Shows Something
The ability to step outside my own thinking and observe it (what philosophers call metacognition) points toward the irreplaceable nature of human awareness. When I externalize my thinking through visualization tools, I create opportunities for self-reflection that no AI system can replicate.
This metacognitive awareness enables me to evaluate my own reasoning, identify my biases, and improve my thinking processes. I can watch myself think and choose to think differently. This capacity for self-observation and self-correction represents something uniquely human that remains essential even as AI systems become more sophisticated.
The visualization tools I’ve explored (digital mapping, contemplative engagement, AI collaboration, analog capture) serve this metacognitive function by making internal processes external and therefore available for examination. Through these tools, I develop not just better thinking but better thinking about thinking.
In my next exploration, I’ll examine what this metacognitive awareness shows about the nature of consciousness itself (how the ability to observe my own thinking points toward capacities that distinguish human awareness from even the most sophisticated information processing systems). The tools for making thinking visible become windows into what makes consciousness irreplaceable in an age of artificial intelligence.
Disclosure Statement
This post was produced according to the approach outline in The Art of Transparent AI Collaboration Workflow (click to review).
