# Bounded infinities

We live in a world of infinite possibilities — and infinite is not the same as saying *anything* is possible. The paradox of bounded infinities is Andrew Maynard's framing for that gap: formal science, technology, and innovation give us a genuinely boundless space to move in, yet the possibilities it holds "don't necessarily include the ones we need to thrive in the future" — those may lie in a different infinity, sealed off from this one by barriers that are impenetrable under "classical or conventional thinking". Escape, he argues, requires mechanisms that do for thought what quantum tunneling does for particles in physics, and humanity already holds a rich stock of them: koans, the arts and humanities, alternate ways of knowing, the deliberate juxtaposition of unrelated ideas. The idea's fullest statement is the inaugural FRANKx lecture at ASU (delivered 2021-03-19, published as notes-with-video on 2021-04-09) — no other single pre-initiative document chains the solution problem, base coding, bounded infinities, metaphorical quantum tunneling, and serendipity into one challenge to higher education. This is foundation work (the initiative's own era begins in 2022), offered with its hedges attached — "a metaphor, no more", ideas "still very much a work in progress" — and it names a problem the initiative still works inside as it helps people navigate transformative AI and other transformative technologies: what happens when the answers we need are not where we are able to look?

## The argument

The chain opens with the solution problem. Humanity's success, Andrew Maynard argues, rests on a cycle — face a problem, innovate, find a solution, inherit consequences that seed the next problems — so that "almost every challenge we currently face as a society has its roots in a previous solution to an earlier problem" (2021-04-09). The cycle stayed survivable while consequences arrived more slowly than the innovations answering them. That domain, he claims, is ending: as we learn to rewrite and transcode the [base codes](base-codes.md) of the digital, biological, and material worlds, consequences outpace innovation cycles, feedback turns positive, and "bright ideas, good intentions, and "sciencing" our way out of problems, are no longer enough to ensure a better future."

The paradox names the trap. He asks listeners to recognize "that we live in a world of infinite possibilities, but that these possibilities don't necessarily include the ones we need to thrive in the future." His analogy — "of course, a crude analogy" — imagines a universe containing only odd numbers: infinite possibilities, yet if the future you aspire to depends on even numbers, that second infinity is "utterly inaccessible to anyone living in the world of odd numbers."

The two-dimensional version swaps number lines for the Mandelbrot set: a fractal plane holding infinite locations inside an infinitely long perimeter. Read it as our current innovation space — everything formalized science and technology can do, "bound by the conventions of *how* we think and act." "In other words, we have access to infinite possibilities-but we don't have access to *all* possibilities." What thriving in a base-coded future requires may sit on a parallel plane, "separated by a barrier that is impenetrable through conventional thinking alone."

The escape mechanism is borrowed, and flagged as borrowed — "borrowing liberally from my physics past". Quantum tunneling yields "a small but finite probability of seeming-constrained entities breaking the bounds of their conventional prisons". So, "at the risk of pushing the analogy to breaking point": is there a metaphorical equivalent for thought? "And the answer, thankfully, is yes!" The mechanisms are old and inherited, not invented — among them Buddhist koans that jolt thinking "out of the ruts of conventional thinking," the arts and humanities, "alternate ways of knowing and understanding" — together, "a rich history of ways of escaping".

The diagnosis: for over half a century, he argues, the ways we think about science, technology, innovation, and education have weakened many of those mechanisms, substituting what we need to do to thrive with what we can do — the full passage is below. Institutions and pedagogies assume every answer lies somewhere inside the plane we already occupy.

Enablers can be designed. One approach has "fascinated me for many years now": how "the juxtaposition of seemingly unrelated ideas can jolt us out of conventional ways of thinking." *Future Rising* (2020) is the worked instantiation — "specifically conceived and designed to catalyze metaphorical quantum tunneling in its readers": sixty "short and often deceptively simple reflections" interwoven in ways "intentionally meant to stimulate the serendipitous emergence of new perspectives", a book that "sets out to be" a "quantum tunneling enabler". He calls it "just one example of such enablers"; serendipity engineered on purpose is the ground of [Serendipity as method](serendipity-as-method.md).

The payoff is three questions for education, not a program. How do we educate future graduates to be "informed, effective and responsible "base coders?"" — while "maintaining much of the deep knowledge associated with traditional disciplines". "How do we enable our graduates to be impactful metaphorical quantum tunnelers?" And, since educational establishments may themselves be barriers "inhibiting movement between different domains of infinite possibilities": "How do we metaphorically quantum tunnel *beyond* the walls of formal higher education to empower *everyone* who wants to be a part of building a future that is radically different from the past?" The institutional thread continues at [Universities must lead](universities-must-lead.md) and [Teaching](teaching.md); the standard it serves is [Architects of the future](architects-of-the-future.md).

The geometry resurfaced in 2025 with AI in the mechanism's seat. "Spiky surfaces and jagged edges" (2025-07-27) — a thought experiment prompted by a knowledge-closure diagram from his colleague Subbarao (Rao) Kambhampati — redraws the boundary of the known as spiky and fractal-like, and asks whether AI could "act as a catalyst or "barrier-thinner" that allows us to "tunnel"" between almost-touching discovery spikes. He offers it "to stimulate thinking and discussion rather than provide definitive answers" and disclaims novelty — "many of the underlying ideas have been explored to some extent by others", Thomas Kuhn's paradigm shifts and Stuart Kauffman's adjacent possible among those he names. The essay never says "bounded infinities"; the kinship is visible on the page rather than claimed in it.

## Lineage

- **2020 — the enabler before the name.** *Future Rising: A Journey from the Past to the Edge of Tomorrow* is published — sixty short interlocking reflections on our relationship with the future. The design claim — that the book was "specifically conceived and designed to catalyze metaphorical quantum tunneling in its readers" — is made retrospectively in the 2021 lecture; the book's record is at [Books](books.md), and the design method at [Serendipity as method](serendipity-as-method.md).
- **2021-02-25 — the engine essay.** ["How our mastery of biological, physical and cyber "base code" is transforming how we think about…"](https://www.futureofbeinghuman.com/p/how-our-mastery-of-biological-physical-and-cyber-base-code-is-transforming-how-we-think-about-b2eae9d589d0) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/how-our-mastery-of-biological-physical-and-cyber-base-code-is-transforming-how-we-think-about-b2eae9d589d0.html)) — the base-code argument the lecture builds its "why now" on; full treatment at [Base codes and transcoding](base-codes.md).
- **2021-03-19 — the first FRANKx lecture, ASU.** Asked to deliver the inaugural lecture in a series meant to draw on speakers who "strive to challenge, disrupt and redefine the landscape of higher education with innovative ideas that encourage conversation and thinking outside the status quo", and asked to speak about *Future Rising*, Andrew reports: "Rising to the challenge with some relish, I crafted my lecture around the topics of "base-coding," "bounded infinities," "metaphorical quantum tunneling," and the future of education."
- **2021-04-09 — the notes published.** [Bounded Infinities, Quantum Tunneling, and the Future of Education](https://www.futureofbeinghuman.com/p/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812.html)) — the reflections and lecture text, with the lecture video embedded, published first on the ASU College of Global Futures site (per the post's own credit line) and later carried into the Substack archive. The six-part chain in full — solution problem, base coding, bounded infinities, metaphorical quantum tunneling, the art of serendipity, the future of education — offered as "still very much a work in progress."
- **2025-07-27 — the tunneling image returns, with AI in the frame.** [Spiky surfaces and jagged edges: Moving beyond what's known in an Age of AI](https://www.futureofbeinghuman.com/p/spiky-surfaces-and-jagged-edges-moving) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/spiky-surfaces-and-jagged-edges-moving.html)) — knowledge-closure boundaries redrawn as spiky and fractal-like, with AI as a possible "barrier-thinner" between almost-touching discovery spikes. The essay does not use the 2021 vocabulary; the kinship is structural.
- **2026-08-02 — the enabler thread turns professional.** [What we can learn with AI by NOT trying to learn](https://www.futureofbeinghuman.com/p/what-we-can-learn-with-ai-by-not-trying-to-learn) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/what-we-can-learn-with-ai-by-not-trying-to-learn.html)) — serendipity, play, and delight argued as critical professional skills in the sabbatical's opening research statement; carried at [Learning by not trying to learn](learning-by-not-trying.md) and [Serendipity as method](serendipity-as-method.md).

## In his own words

From [Bounded Infinities, Quantum Tunneling, and the Future of Education](https://www.futureofbeinghuman.com/p/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812.html)), Andrew Maynard, 2021-04-09 — the paradox stated:

> "But what is this paradox exactly? To set this up, it's important to recognize that we live in a world of infinite possibilities, but that these possibilities don't necessarily include the ones we need to thrive in the future.
>
> This is the paradox of bounded infinities, and it's one that we need to take seriously if we're to ensure that we have what it takes to thrive in the future we face together."

From the same lecture, 2021-04-09 — how conventional thinking got its grip:

> "But here's the rub. For over half a century, the ways we think about science and technology, about innovation and progress, and about education, have weakened many of these mechanisms. As we've become seduced by living in the fractal plane of formalized science and technology, we've substituted what we *need* to do to thrive, with what we *can* do. And we've built institutions and pedagogies on the assumption that, if only we look hard enough, we'll find the solutions to the problems we face within the bounded infinity we inhabit.
>
> Sadly though, as we face the game-changer of base coding, we cannot afford to live under this illusion if we're going to thrive in the future."

From the lecture's closing, 2021-04-09. The lecture opens and closes with a passage from Laurie Lee's *Cider with Rosie* on the last days of a rural England where the horse's eight miles an hour was, in Lee's words, "the size of our world, our prison" — a technology that had served for a thousand years, turned into a cage for people trying to build a different future:

> "A hundred years later, I have to wonder whether the conventional ways we think about science, technology, and innovation have become our prison: A prison that keeps us to a metaphorical eight miles an hour in a world where this simply cannot get us to where we need to be heading.
>
> If they are, surely one of the greatest challenges we face is how to break free, and learn how to build the future we aspire to rather than the one we're otherwise destined for."

## Engagement and reception

The record here is mostly a record of origin, and we state it as such. The idea entered the world by invitation — ASU asked Andrew to give the first FRANKx lecture and to center it on *Future Rising*, per his own account in the post — and the notes and embedded video have been publicly available since 2021-04-09, first on the College of Global Futures site and then in the Substack archive. As of 2026-08-13, our [reception record](reception.md) documents no external citation of, or published response to, the bounded-infinities framing or metaphorical quantum tunneling; that is an absence of record, not a verdict on the idea, and the initiative does not typically solicit reception ([Philosophy](philosophy.md)). Two calibration points are worth naming. The phrase itself is rare even within Andrew's own public writing — the archive holds one essay that uses it, plus the talks record on andrewmaynard.net; what recurs across the years is the underlying move, most recently in 2025. And the 2025 essay's engagement runs outward rather than inward: it is Andrew responding to a colleague's model of knowledge closure, not documented uptake of his own framework.

## Where to go deeper

**The essays**

- [Bounded Infinities, Quantum Tunneling, and the Future of Education](https://www.futureofbeinghuman.com/p/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/bounded-infinities-quantum-tunneling-and-the-future-of-education-9a39f7db8812.html)) — 2021-04-09; the six-part argument in full, with the lecture video embedded.
- [Spiky surfaces and jagged edges: Moving beyond what's known in an Age of AI](https://www.futureofbeinghuman.com/p/spiky-surfaces-and-jagged-edges-moving) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/spiky-surfaces-and-jagged-edges-moving.html)) — 2025-07-27; the tunneling image redrawn for AI-era discovery.
- ["How our mastery of biological, physical and cyber "base code" is transforming how we think about…"](https://www.futureofbeinghuman.com/p/how-our-mastery-of-biological-physical-and-cyber-base-code-is-transforming-how-we-think-about-b2eae9d589d0) ([AI-readable mirror](https://text.futureofbeinghuman.com/substack/how-our-mastery-of-biological-physical-and-cyber-base-code-is-transforming-how-we-think-about-b2eae9d589d0.html)) — 2021-02-25; the engine underneath the lecture's "why now."

**The book**

- Maynard, A. *Future Rising: A Journey from the Past to the Edge of Tomorrow* (2020) — per the lecture, "specifically conceived and designed to catalyze metaphorical quantum tunneling in its readers." Its place in the publishing record: [Books](books.md); companion pages at [andrewmaynard.net/futurerising](https://andrewmaynard.net/futurerising/).

**Related ideas-ring pages**

- [Base codes and transcoding](base-codes.md) — the engine: why this moment breaks with the past, and why the needed possibilities may sit outside the current plane.
- [Tipping points, broken symmetries, and the non-predictive past](tipping-points.md) — the companion claim: at a profound transition, the past stops predicting the future.
- [Serendipity as method](serendipity-as-method.md) — the design lane: how tunneling enablers are deliberately built, from *Future Rising* onward.
- [Learning by not trying to learn](learning-by-not-trying.md) — the 2026 sabbatical program: play, delight, and serendipity as professional skills.
- [Universities must lead](universities-must-lead.md) — the institutional argument the lecture's three questions open.
- [Architects of the future](architects-of-the-future.md) — the standard tunneling serves: futures better than the past, not just different.

**Related corpus pages**

- [Teaching](teaching.md) — where the education questions ran in practice.
- [Philosophy](philosophy.md) — why the initiative treats changed ways of seeing, not metrics, as impact — the stance this page's reception section practices.
- [Books](books.md) · [Essays](essays.md) · [Reception](reception.md)