Episode Transcript

In late 2023, I was exposed a RadioLab episode to which I have returned multiple times over the last two years. 

It’s called “Zeroworld,” and it explores something we all learned in elementary school: you cannot divide by zero. Except… you can. And that simple revelation opens up a much larger question about how we hold knowledge itself.

The episode stuck with me because it perfectly captures something I’ve been wrestling with – this tension between what’s useful and what’s absolutely true. How do we use frameworks and ideas without becoming their prisoners?

Today’s discussion is a sidebar discussion about some of our beliefs and approaches here at Goodpain in anticipation of the next series we are jumping into starting next week. 

The Demiurge Metaphor

There’s an archetypal figure called the Demiurge – a lesser creator god who believes he’s the ultimate creator of everything. Zero is our mathematical Demiurge. It revolutionized accounting, made computers possible, enabled everything from ATMs to automated manufacturing. Zero literally built our modern world.

But then Zero convinced us of something else: that we cannot divide by zero. And for most practical purposes, this works fine. Your calculator won’t explode if you follow this rule. But here’s the thing – when you treat a useful convention as an absolute law, your world starts to contract. You stop exploring the territories that lie beyond that rule.

Mathematicians working in quantum mechanics and novel number systems are dividing by zero all the time now. The universe got bigger when they stopped treating “no dividing by zero” as gospel.

The Goodpain Approach

This gets to the heart of how we approach complex questions at Goodpain. We’re about to dive into a series on the Apprenticeship Leadership Model, and we’ll be drawing from frameworks that are 30 years old alongside cutting-edge research. Some of the underlying science has been challenged. Some hasn’t.

Rather than throwing out everything that isn’t perfectly current, or treating old frameworks as sacred, we want to work with what I call axioms instead of rules. An axiom is a starting point we accept so we can move forward – a given truth until proven otherwise. Different from a rule that tells us what we’re allowed to do.

The moment we treat our axioms as sacred, we’ve created our own Demiurge.

The Three Axioms

So here are three axioms that guide how we’ll navigate these complex territories together:

Axiom One: A Lack of Empirical Support Does Not Equal False

Just because something hasn’t been proven doesn’t mean it’s wrong. When we read research papers, this shifts us from asking “Is this study definitive?” to “What territory does this illuminate, and where does it cast shadow?”

We might find a framework for understanding team dynamics that recent neuroscience has partially contradicted. Rather than discarding it entirely, we ask: Where does this still help? Where has it proven limited? What insights does it preserve even as its biological explanations need updating?

When I’m designing a workshop or writing an article, this means I 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.

Axiom Two: Simplify As Much As Possible, and No Further

This one’s tricky. We can oversimplify – force complex realities into neat categories that don’t actually fit. Think about how the DSM tries to atomize every human experience into discrete diagnostic categories. That’s simplification run amok.

But we can also get lost in complexity that serves no one.

When I write about leadership development, I resist creating seven-step programs that promise universal application. Instead, I look for essential principles that appear across cultures, then explore how they manifest differently in various settings.

This means acknowledging when simple answers don’t exist. 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.

Axiom Three: Controversy is an Invitation to Explore, Not a Mandate to Polarize

Here’s what I noticed about that “dividing by zero” revelation – people get defensive when you suggest their foundational rules might not be absolute. Mathematicians have built careers on systems that assume this rule is inviolable.

But controversy usually signals we’ve hit something worth understanding more deeply. When smart, thoughtful people look at the same evidence and reach different conclusions, we’re probably looking at a place where multiple truths intersect.

Instead of rushing to determine who’s “right,” I want to understand what each perspective reveals. The traditional educator worried about AI might illuminate concerns about deep learning 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.

Why This Matters

These axioms address something we all face: the temptation to grasp frameworks that feel solid and treat them as universal laws. This creates predictable problems.

We become defensive rather than curious when encountering perspectives that challenge our adopted frameworks. A parent builds their identity around a particular educational philosophy and becomes unable to learn from different approaches. An executive trained in one leadership model dismisses insights from other traditions that might serve their team.

We miss the dynamic nature of human systems. What works for developing leadership in one cultural context may need significant adaptation in another. When we treat context-dependent tools as universal truths, we create unnecessary suffering.

Real leadership development, authentic community building, meaningful contemplative practice – they all require holding multiple perspectives simultaneously. They demand thinking that can navigate paradox rather than demanding resolution.

The Apprenticeship Model Preview

Next week we launch our next series that explores the Leadership pillar of Goodpain’s philosophy. We will be exploring the Apprenticeship Leadership Model and it is an inheritor of these axioms for complex thinking approach.

 It’s not another universal system promising to solve all leadership challenges. It’s a way of engaging with the ongoing question of what it means to grow into our capacity to serve something larger than ourselves, both the most creative expressions of ourselves as individuals, and the most imaginative possible versions of our collective expression.

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.

Closing

In Zeroworld, the mathematicians discovered their universe became much larger when they 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.

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.

We’re not people who have arrived at final answers. We’re fellow travelers committed to the ongoing work of becoming more fully human together.