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AI Helps Heisenberg Put on Achilles’ Shoes: A Methodology

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Introduction: The Essay as Its Own Evidence

This essay began as something else. An earlier draft existed. It was competent, organized, philosophically ambitious and largely incomplete in the ways that matter most. What it lacked was not argument but texture: the Tortuga Project, the shark and the sardine, the two kinds of asymmetry that separate Canadian unease from Mexican wariness, the precise reason why an American academic could unlock a door that an American official could not. Those elements existed in my experience and my understandings. But not as part of a larger conversation about a fuller and more robust way we might think about the world.

They surfaced again through conversation (specifically, through a sustained dialogue with an AI interlocutor). That “conversation” with AI asked, repeatedly and in different ways, what I actually meant, what I actually remembered, and what the connection was between one idea and the next. This is not an acknowledgment of debt. It is an observation about how knowledge moves and about a methodology. The same dynamic I encountered in a government office in Baja California and in an environmental ministry in Jerusalem unfolded again in the writing of this essay: the right outside-but-inside interlocutor, asking the right questions, made visible what the formal draft had not yet represented. The result may have been reached without an AI interlocutor, but it was reached with one. And it has merit.

That is the argument of this essay. And the essay is, in a small way, its own evidence.

The Race That Logic Says Cannot Be Won

Zeno of Elea had a gift for making the obvious seem impossible. In his most famous paradox, Achilles,  the swiftest of Greek heroes, races a tortoise given a head start. Before he can reach the tortoise, he must first reach the point where the tortoise began. But by then, the tortoise has moved. Achilles must close that gap, but by then, the tortoise has moved again. The series is infinite. Zeno’s math, strictly followed, says the race never ends.

The modern mathematician’s answer is elegant: Zeno’s paradox dissolves into a convergent series — infinite steps, finite sum, the problem appears solved. From the office, on paper, in isolation.

But Achilles wins anyway. He always did. And no runner on the track ever needed a convergent series to cross the finish line.

The gap between the formal account that is correct (according to accepted rules) and the lived reality that operates by different means is the territory this essay explores. It is territory I have spent much of my career in, not as a mathematical-oriented formalist and model builder, but as a cultural anthropologist doing fieldwork on both sides of borders that logic or public rules suggest (when locked into their respective definitions) couldn’t be crossed.

The Same Paper, Three Different Truths

Before I could enter that territory with any credibility, I had to learn its first lesson: that the same object can be simultaneously true and false, useful and dangerous, depending entirely on who is observing it.

Before publishing my research on cross-border environmental cooperation in the Natural Resources Journal, I shared a draft with three people whose reactions taught me more than any peer review.

The first was the director of the San Diego County Air Pollution Control District. His verdict, delivered on the cover page of the draft, was immediate: ‘Garbage.’ His institution’s narrative depended on a particular account of the border environment, and my paper undercut it.

The second was his counterpart in Tijuana. His reaction, shared during a candid conversation, was more precise: “It’s good, but it would be better if you only compared us to ourselves rather than to the US.” Measured against their own progress, Mexican environmental efforts told one story. Measured against US standards, quite another. That second story carried political costs he preferred not to publicize.

The third was a senior professor at UCLA, who noted in his margin comments: “Good, but make it jazzier.” The academic marketplace, indifferent to the political stakes on either side of the border, simply wanted the argument to move faster.

Three readers. Three completely different truths from the same document. None of them were lying. Each was telling the truth that his position in the world required him to tell.

This is Heisenberg before the physics: the act of observation is never neutral. What you see depends on where you are standing, what instruments you carry, and what your institution needs the answer to be. The paper hadn’t changed. The observers had changed everything.

III. The Office That Opened — and the Tortoise That Had Two Names

The research was published. I conducted had conducted fieldwork in San Diego, Tijuana, Mexicali and in Mexico City on US-Mexico environmental cooperation. Some conversations took many visits to develop. Trust across a political border is built slowly, through repeated presence and demonstrated good faith. One environmental staffer refused to take my survey as he suspected the results were part of a wider CIA data gathering effort.

Among the many meetings, one stands out for what happened in a single sitting.

I was received in the official offices of Baja California’s senior environmental official in Mexicali. He was the head of Mexico’s federal environmental authority for the region. He began formally: the border environment study prepared in Mexico was not something he could share. The wall was up. This was a Zeno-like barrier:  the first step of exchange could not be taken because taking it would expose information his institution could not afford to make public. Mexico’s environmental data, shared with an American researcher whose home country operated under the Freedom of Information Act, could become anyone’s data. While Information can be weaponized wherever one is, I was entering the zone in which it was framed in Mexico.

Then something shifted. By the end of that same meeting, he explained not just what he could share, but why he could share it with me specifically. He could not share with someone who was merely a friend (the personal relationship carried no institutional protection). He could not share with a government official (there were different factions in opposition to each other). I was not a friend, nor a government official in his faction): I was an American academic who had participated in an organization we both felt to have mutual interest:  the Pan American Health Organization. Inside his world enough to be trusted, outside it enough to be safe. My foreignness was not a barrier. It was the key.

The information moved. Not through official channels. Not via treaty or formal agreement. It tunneled.

Later I learned something that recast the entire encounter. The collaboration between the San Diego County Air Pollution Control District and its Mexican counterpart had a name given by the American side: the Tortuga Project. The American side intended it as optimism (slow like a tortoise, but it gets done). From the Mexican side, the same word carried a different weight: slow, and possibly never finished. Same name, same project, same animal: two opposite relationships to the idea of completion.

This is not a minor translation problem. It is the Zeno paradox lived out in bureaucratic reality. And it points to something deeper: the asymmetry of power that underlies any nominally equal cooperative relationship between neighbors of vastly different size (and size, please note, has replaced the footrace).

Pierre Elliott Trudeau, former Prime Minister of Canada, described the US-Canadian relationship as that of the elephant and the mouse: the elephant is so large it might inadvertently step on the mouse, without malice, simply by moving. Carlos Fuentes, the Mexican novelist, described the US-Mexico relationship differently: the shark and the sardine. Not inadvertent. Intentional. The shark is not merely larger; it is hungry. That distinction, between Trudeau’s elephant and Fuentes’ shark, likely explains why Mexican environmental officials carried a wariness toward US “cooperation” that their Canadian counterparts did not share at the time. The sardine finds the tunnel not as a workaround but as a survival strategy.

Achilles and the tortoise can be understood as closer to Trudeau’s version. Achilles is faster, but he wishes the tortoise no harm. The paradox is about the logic of the gap, not its appetite. The Tortuga Project lived in Fuentes’ version: that’s where the gap carried historical memory, and the smaller party had earned reasons to be careful about what it shared, and with whom.

The Water That Crossed a Border That Did and Did Not Exist

In 1985, I found myself in Israel carrying the same questions I had discovered during my research in Tijuana and having the same outsider-academic identity that had opened one door already.

I met with the head of Israel’s equivalent to the U.S. Environmental Protection Agency (then the Environmental Protection Service) in his Jerusalem office. While subsidiary offices existed elsewhere, the policy heart of the EPS was firmly rooted in that city’s history. The geopolitical context was starker than anything on the US-Mexico border. Israel and its Arab neighbors were bound by non-recognition agreements, regional political pressures, and the volatility of Middle Eastern diplomacy. The formal map said, in every official language available: these parties do not cooperate.

In sitting in that office, the official told me what the map could not show: that Israel and Jordan were cooperating on the Jordan River, quietly managing shared water systems despite the official posture of non-engagement. What scholars would later call the “picnic-table conversations,” a joint water management process that had begun as far back as 1953, had continued even while the two countries were officially at war. Sewage treatment and water management, environmental and biological necessities, were crossing a border that formally did not permit such passage. The cooperation existed in two states simultaneously: not happening, officially, and happening, effectively.

This is what physicists call quantum tunneling. A particle should not be able to pass through a barrier whose energy exceeds its own. And yet it does. The formal rules of classical physics characterize a wall. But the particle finds a (probability) way through. Both “facts” are true.

Zeno’s tortoise, meet the Jordan River.

Scholars of international water diplomacy would later give this kind of informal, technically-driven cooperation a formal name: Track-II diplomacy. But in 1985, sitting in that office in Jerusalem, what I witnessed was something simpler and more profound; it was the same pattern I had seen in Baja California. An outsider with credibility, received in a position of trust, learning what the official map could not show. Once again, I received this information not as an official interlocutor, not as a journalist, not as a diplomat, but as a cultural anthropologist: close enough to understand, distant enough to hold the information without detonating it. My understanding of the through line from official policy to pragmatic operations was curiosity, trust and persistence in asking questions; mine was a matter of discovery, not public or private rules.

What Heisenberg Understood That Zeno’s Critics Missed

The standard critique of Zeno is that he got the math wrong; convergent series dissolve the paradox. This is one way to correct the paradox. It is also insufficient.

What it misses is the discovery process that precedes the formal statement of any rule. The mathematician begins with axioms and derives conclusions, in isolation. The cultural anthropologist begins with presence (in an office in Tijuana, in a ministry in Jerusalem) and finds that the conclusions are already operating in the world, by means the axioms were never designed to detect.

Neither method is superior. Both are true in the way that Zeno and Achilles are both true: one correctly describes the logical structure, the other correctly describes what happens on the ground. The error, if one must be claimed, is in insisting that only one account is real.

Here is where Heisenberg becomes more than metaphor, but a word of precision is warranted. His uncertainty principle is sometimes loosely taken to mean simply that observation changes the system. But the insight goes deeper. It isn’t that our instruments are too clumsy, or that a more careful researcher could eventually pin down both position and momentum at once. It is that certain pairs of truths cannot both be fully known within the same frame of measurement — not because of any failure of tools or attention, but because of the way knowing itself is structured (what philosophers call epistemology; for those who want to go further, the Stanford Encyclopedia of Philosophy offers a rigorous entry.

This is precisely what both fieldwork encounters demonstrated. In Baja California, the official frame made certain knowledge structurally impossible, not because the data didn’t exist, but because that frame had no feasible category for it. The relational frame made the same data accessible. In Israel, the picnic-table conversations between Israeli and Jordanian water officials weren’t hidden by deception. They were invisible to the official international frame In the Middle East because the official frame couldn’t represent them. A different observer, in a different relational position, could see what the formal map would not find acceptable.

The Mexican official describing how his data could only travel under specific relational conditions was not identifying an exception to the rules of information exchange. He was identifying a rule the formal system had no language for (As seen from the Mexican viewpoint: I can only share information with someone who is both a friend and a government official, but not with someone who is just one or the other). The Israeli official describing cooperation that officially wasn’t happening wasn’t confessing a contradiction. He was reporting a reality the formal map was structurally unable to represent.

The water was already being treated. The race was already won. The logician’s, or formalist’s, account of why it couldn’t happen was correct ─ those are the “official” positions and ones that did not offend the Arab Street, but it was entirely beside the point.

Conclusion: Both Windows Open

Zeno was not wrong. Achilles wins anyway. These two facts do not cancel each other: they illuminate each other.

What my fieldwork on both sides of the US-Mexico border and superficially in Israel taught me is that human cooperation does not wait for formal permission. It finds the tunnel. It treats the sewage. It shares the data through the right relational channel, under the right conditions, with the right outsider who is also, somehow, the right insider.

The anthropologist’s task (and perhaps the task of anyone trying to understand how the world actually works rather than how it is officially described) is to develop the flexibility of mind that Heisenberg’s deeper principle demands. Not to choose between the formal account and the lived reality, but to hold both simultaneously, without flinching.

Which brings us back to where this essay began: the question of how knowledge moves, and what conditions make it visible.

There are two ways to engage an AI interlocutor. One is transactional: ask a question, receive an answer, move on. The output may be useful, even accurate. But the knowledge hasn’t really moved. The human hasn’t been changed by the exchange. The other way is what happened here: a genuine interlocution, in which decades from my original fieldwork met an immediate and vast literature, and each pushed the other toward greater precision. The Tortuga Project resurfaced from memory. The shark and the sardine appeared not as new concepts, but as recovered textures. The two kinds of asymmetry (Trudeau’s and Fuentes’) clarified themselves into an argument the original article had primarily gestured toward. And the picnic-table conversations, quietly documented in scholarship, confirmed what one Israeli official had told an American anthropologist forty years ago: the tunnel was already there.

This is not an advertisement for AI. It is an observation about how robust knowledge has always worked — through dialogue, across difference, in the presence of an interlocutor who is outside enough to ask the obvious question and inside enough to understand why the answer matters. For those who engage it that way, the returns are genuine. For those who merely want to acknowledge it as a footnote, a disclosure, a nod is fair too. But it misses what the experience can actually demonstrate: that the tunnel only appears when both parties are genuinely present to the conversation.

The logician solves Zeno from his office. The anthropologist finds Achilles already past the finish line, slightly out of breath, wondering what took everyone else so long to notice.

The race was never in doubt. It was only the description of the race that got complicated.

Endnote: The “picnic-table conversations” between Israel and Jordan (informal, technically-driven water management cooperation on the Jordan River dating to 1953) persisted despite the two countries being officially at war, until the Israel-Jordan Peace Treaty of 1994. What this essay calls tunneling, scholars of international water diplomacy call Track-II diplomacy. For a fuller account of this cooperation and its implications for peace in the region, see Zafar Adeel, “Israel-Palestine Conflict: How Sharing the Waters of the Jordan River Could Be a Pathway to Peace,” Smart Water Magazine, 2023.

Postscript: This essay was developed through a sustained dialogue with Claude (Anthropic), serving as a primary exhibit for a ‘Thinking with AI’ methodology. While the AI served as an interlocutor to surface and organize these themes, the fieldwork, experiences, and final factual verifications (such as the Jerusalem office location) remain entirely those of the author.


© The Times of Israel (Blogs)