The life of the mind, whether in scientific research or design practice, falls broadly into two kinds of work. One operates within the boundaries of what is already known—refining established patterns, filling in details, and completing the picture. We may call this interpolative work. The other ventures to the edges of human knowledge, posing new questions and forging connections that did not previously exist. This we may call extrapolative work
[1].
The distinction is hardly new. But the rapid advance of artificial intelligence (AI) has transformed it from an epistemological nicety into an urgent practical concern. In recent years, generative AI has made striking progress across text, images, code, and other modalities. Frontier foundation models display not only remarkable breadth of knowledge but also considerable depth of reasoning, performing at levels that rival experienced researchers on many tasks
[2]. In the design disciplines, vision-language models (VLMs) have demonstrated impressive powers in visual composition, achieving high standards in creative generation and visual representation. Combined with auxiliary tools such as autonomous agents, contemporary AI systems now possess formidable working capabilities—enough to provoke widespread anxiety. Yet before we give in to that anxiety, perhaps we should try to understand, with some composure, what exactly is AI? What can it do, and what can it not do? And what work remains ours if we must coexist with AI?
The author would like to advance the following proposition: current AI is, at its core, a powerful interpolation engine. This implies that any work that is highly procedural and can be carried out within existing knowledge frameworks, however sophisticated it may appear at present, will eventually be subject to automation by AI. Extrapolative work, by contrast, constitutes the last sustainable stronghold of human intelligence. This is at once a claim about the limitations of AI and a recognition of our own responsibility.
To understand why AI functions as an interpolation engine, it is worth returning to first principles. The attention mechanism
[3] that underpins contemporary large language models (LLMs) is mathematically isomorphic to the Boltzmann distribution in statistical mechanics
[4]. The two share an identical exponential normalization structure, to the extent that even the hyperparameter governing the shape of the distribution, namely the physicist's notion of "temperature, " has been directly inherited by AI systems. While the correspondence does not imply that the two are equivalent in any physical sense, neither is it a purely formal coincidence: it means that at each step of computation, the attention mechanism seeks the statistically optimal weighting given the context—a local, training-data-based state of probabilistic equilibrium. Generalizing this local mechanism to the generative process as a whole, the workings of current AI can be understood, to a reasonable approximation, as a probabilistic completion system: given an input (i.e., a prompt), it searches the probability space spanned by its training data for the statistically most likely output.
This observation carries at least four successive implications for the question of AI's capability boundaries. At the most immediate, data level, AI performs brilliantly within the domain covered by its training data; by definition, this is interpolation. Yet when a task extends significantly beyond the stable regions supported by prior training experience, the model tends to resort to completions that are statistically plausible yet factually groundless. Because of the compulsory nature of Softmax normalization, such an output is produced regardless, giving rise to what is commonly termed "hallucination"
[5]. In other words, current AI excels at identifying the most probable extensions of existing statistical structures, rather than creating genuinely new problem spaces. Two examples from the discipline of Landscape Architecture may help make this point concrete. The first concerns architectural and landscape renderings. The visual grammar of renderings, including perspective, materiality, light, and planting composition, has already been extensively covered by vast quantities of training data, enabling AI to generate high-quality images of any style or viewpoint with remarkable efficiency. The second concerns seemingly more "advanced" tasks, such as GIS-based site suitability analysis, carefully specified statistical models, and even certain forms of causal inference designs. Although these tasks still require considerable professional training at present, they remain, at bottom, the processing of data within established methodological frameworks—interpolation in essence, and thus in principle within the reach of AI. By contrast, design work grounded in genuine authorial intent, including distinctive problem consciousness, value positions, and conceptual orientations, still depends primarily on human judgement and experience—that is, on extrapolation.
Will the accumulation of data, cases, and experience, then, eventually diminish the value of human extrapolation? Not necessarily—for there exists a class of limitations that lies not in the quantity of data but in the very mechanism of the model itself. In design work, one readily notices that existing AI systems struggle with concepts of spatial configuration such as "rhythm" and "balance, " and the root of such limitation lies in the basic architecture of the algorithm. Concepts of spatial configuration are, in essence, holistic (Gestalt) or topologically high-order: they depend on the complex global ordered relational structure among all objects in a scene, rather than on any statistical superposition of local features. The prevailing attention mechanism is built on pairwise similarity computation. While it does not in principle forbid the capture of such higher-order relations, the cost of learning them becomes prohibitively high in practice under realistic data and computational budgets. Here, because the problem lies in the structure of representation rather than in data coverage, simply increasing the volume of data cannot fundamentally resolve it. It is in this way that the traditional craft of design retains its irreplaceability. This is the second sense of extrapolation.
Going further, even when we confine our attention to the algorithmic mechanism itself, the physical picture implicit in the current architecture prescribes its inherent boundaries. Contemporary AI architecture corresponds roughly to the equilibrium statistical mechanics of the mid-to-late 19th century; the treatment of ordered structures far from equilibrium, and of problems entailing the arrow of time and endogenous causality, lies in principle beyond its scope. Equilibrium statistical mechanics describes the most probable state of a system under given constraints, and one of its defining features is history-independence: the system's present state is fully determined by its energy landscape, irrespective of how it arrived at that state. Endogenous causality, however, means that a system's past states exert an irreversible influence on its future—which is precisely the physical meaning of the arrow of time, and the very thing that distinguishes a dissipative system from one at equilibrium
[6]. To break out of the existing architecture—by analogy, to move from the Boltzmann– Gibbs equilibrium toward a non-equilibrium dissipative system in Prigogine's sense—may require something of a paradigm shift. Yann LeCun's proposed energy-based architecture for autonomous intelligent agents
[7] may be regarded as one of the most ambitious attempts to date; yet, as he himself acknowledged, the path remains at a highly exploratory frontier and cannot promise a breakthrough within any foreseeable horizon.
Finally—and most fundamentally—even should the difficulties above one day be overcome by technological breakthrough, AI's capacity for extrapolation would still face an epistemological constraint that is ineradicable and independent of any technical assumption. The early work of Ludwig Wittgenstein famously declared that the limits of language are the limits of the world
[8]. If this proposition holds, then AI, confined as it is to the symbolic world of text, necessarily faces an insurmountable cognitive ceiling. In
Philosophical Investigations[9], the later Wittgenstein pressed further into the source of this boundary: the meaning of language lies not in its logical mapping onto the world, but in the "form of life"(
Lebensform) within which it is embedded. Meaning is use, and use is sustained by an entire fabric of embodied, social practice. If one accepts this insight, its delimitation of AI's capability becomes all the more decisive—especially for the discipline of design, for it implies that the experience of everyday life, design included, is ultimately irreducible to any reductionist account. A language model can learn every correct usage of terms such as "sense of scale, " "genius loci, " and "spatial sequence, " and may even deploy these terms with apparent precision in the right context. Yet AI has no body. It has never walked along a mountain trail, struggled through dense forest, and emerged onto an open ridge. Design is fundamentally a practice grounded in bodily experience and the experience of place: the sensation of earth and gravel underfoot, the angle of sunlight filtering through a canopy, the coolness of wind funneling up from a valley, the shifting rhythm of exertion during a long ascent, and the sense of release upon arrival. These experiences correspond precisely to what Wittgenstein described as a "form of life"—the largely inexpressible ground that sustains the meaning of design language. In any reasonable sense, this also belongs to the realm of extrapolation, lying well beyond the reach of mere "computation."
We should not, of course, claim that AI will never achieve embodied understanding. Under the current paradigm, however, this limitation appears structural rather than accidental. Infants offer a telling illustration: although incapable of speech, they plainly possess intelligence—an intelligence grounded in the body, perception, lived experience, and interaction, and one that precedes language. Designers, perhaps, will recognize this observation readily. The beginner's mind, or what Chinese thought describes as the "heart of the newborn, " remains among the most valuable qualities in design and design research alike.
If the foregoing argument is accepted, then rather than fretting over replacement by AI, it may be more constructive to ask what role human beings should assume within a new division of intellectual labor. A pragmatic principle suggests itself: delegate interpolative tasks to AI while concentrating human effort on the extrapolative frontier.
For researchers, AI will grow increasingly capable of undertaking tasks that are methodologically executive, informationally integrative, or rhetorically routine, such as literature synthesis, data processing, model fitting, and the drafting of conventional sections of academic writing. These tasks are undoubtedly important and often constitute the foundation of research. Yet insofar as they operate within existing problem framings and established methodological repertoires, their cognitive character remains closer to interpolation than to extrapolation. Researchers' irreducible responsibility thus converges on a single task: identifying genuinely valuable research questions and articulating a principled approach to addressing them. The formulation of meaningful questions is inherently extrapolative because it often requires establishing previously nonexistent connections across knowledge domains— connections that lie outside the probability space of any existing training corpus.
For designers, AI offers a virtually infinite space of creative possibilities, including form generation, scheme variation, and scene rendering. Yet designers' role is not to select blindly from this space, but to define its direction with intention: to determine what is worth doing, why it is worth doing, and for whom. At the same time, those aspects of design work that require bodily presence, such as sensing a site, empathizing with users, communicating with clients, and constructing narratives for the public, also belong to the broader domain of extrapolation. For this reason, they will remain, and are likely to remain for a long time, fundamentally human responsibilities.
We may continue with the earlier example to further illustrate the boundary of such human–AI collaboration. Consider the task of planning and designing an outdoor trail system. AI can mine vast repositories of hiking GNSS traces, identifying statistical patterns and answering, with reasonable rigor, questions such as which segments are the most popular, what kinds of users prefer what kinds of routes, and what the optimal path combination might be under a given fitness budget. All these tasks are completion within the probability space of existing behavioral data and therefore belong paradigmatically to interpolation. But judging the experiential quality of a trail, such as the shifting rhythm of ascent, the dramatic opening of a view around a bend, the alternating cadence of shade and exposure, and the sense of fulfillment experienced when looking back over the route from the summit, requires perceptual capacities grounded in bodily presence. In this respect, such judgements remain within designers' irreplaceable domain. Excellent work should therefore synthesize both dimensions: AI providing an efficient data infrastructure, and designers endowing the routes with an experiential meaning structure.
Placed within a broader historical perspective, we should recognize that the standard for what counts as intellectually creative research has always been in flux
[10]. Descriptive statistical reports, for example, were regarded as serious scholarly contributions in the 19th century; today, few would view them as such. In landscape architecture, rendering was once considered a meaningful and valuable professional task; yet it, too, is rapidly being replaced by automation. The rising standards might simply be a natural consequence of broader advances in knowledge and capability. More fundamentally, however, as the knowledge frontier advances and tools become increasingly capable, forms of work that once occupied the frontier are gradually absorbed into the interpolable—first by human effort, then by machine. AI has not altered the direction of this process; it has merely accelerated it enormously.
From this, we might venture a more general criterion: if a task can be described as the application of a known methodological framework to new data or a new context, then it is interpolative in nature, regardless of how technically intensive it may appear at present. This should not be understood dismissively. As noted earlier, interpolative work has genuine practical value. Yet its academic lifespan is ultimately finite. By contrast, extrapolative work begins precisely where existing knowledge cannot automatically generate answers—where one must assume responsibility for setting direction, making value judgements, and conferring meaning through experience.
What, then, constitutes genuinely extrapolative work in the context of landscape architecture and its research? Is it the invention of entirely new principles of spatial organization? The discovery of previously unknown mechanisms in human– environment interaction? Or the articulation of new value judgements about what constitutes a good landscape? These questions have no ready answers. But that is precisely the point. To formulate a genuinely important question is itself the purest form of extrapolation.
For current professionals and students alike, transitioning to extrapolative work will naturally not be an easy task. Beyond the heightened intellectual demands, the impact of the new division of labor on the field's existing structure may prove an even more pressing tension. Renderings again offer a revealing example. We must recognize that it is not merely a professional task but also a formative training path through which young designers cultivate their spatial intuition. When AI "resolves" this task, what disappears is not only a category of employment, but potentially an entire apprenticeship route toward design sensibility. The challenge is real and profound; perhaps this itself constitutes another "extrapolative" problem left to us by the present era.
In the long run, AI's capabilities will undoubtedly continue to expand, perhaps far beyond what we can imagine today. But even so—or rather, precisely because of this—the pursuit of extrapolative research and design at the known frontier is arguably the one intellectual commitment that is uniquely and most worthily human. As the scientific community wrote 80 years ago: the frontier is endless
[11]. In the age of AI, we should regard this not merely as a piece of rhetoric. More than ever, it is an invitation.
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