Consider the talon. It is an object of menace, of capacity for violence, purely by virtue of its shape. It is exquisitely crafted by evolution to pierce through the skin of prey animals with its innate sharpness and to hold their bodies with its curvature. Remarkably, the talon is not exceptional; it’s not a uniquely exquisite thing in the grand scheme of the world’s biological heritage. Rather, everything in the chain of material reality from the protein up to the ecosystem is the result of form optimization according to the laws of Nature. The cheetah runs with explosive speed because of its musculo-skeletal perfection, the shark’s deadliness is due to the micro-vortices formed by its skin while pursuing prey in the great oceans, and even the cell’s semi-permeable membrane shapes itself as a sphere, so it can maximize productive volume while minimizing surface area. Every organism is a naturally shape-optimized survival machine.

The dominant perspective on the nature of intelligence holds it to be bound up in language. This isn’t all that surprising, given the step-change in synthetic linguistic production delivered through large language models. The Valley that created these AI models sees a deep truth to crafting intelligences that speak in the same way humans do. Although there really is something special about language and its role in the emergence of the modern human, I believe the present fixation is a red herring.

In contrast to the absolute primacy of form, language is a latter-day aberration, a monkey business that we can’t stop obsessing over because our every thought is expressed in it. But in the theater of non-human Darwinian competition, no organism argues its way out of a fight with another that has superior morphology. Confronted by a hungry tiger in the forest, you will be torn limb from limb no matter how good your rhetoric.

To get at the foundation of shape’s relation to life: anything that physically exists has a form. A form begets a certain set of functions, and evolution chooses the winners, the best expressions of function. So when Nature decrees that an organism shall go forth and multiply, the reason it survives is contained in its form. Form is the carrier of Nature’s intelligence. DNA is the plainest case: it does nothing but encode how form should arise across multiple scales within an organism. It is also the intelligence at the root of all known life.

The obvious question is why — if form is so much more primordial than language, why has language won the first round of synthetic intelligence? Theories proliferate about the origins of language and its effect on the population fitness of homo sapiens against our peers from around 50,000 years ago, but whatever the original causes and tangled web of relationships are there, the eventual reason is that language was the first thing to be transcoded into machine-readable form. Since its inception in the 1990s, Unicode has proven capable of storing every imaginable linguistic output of our crazy, babbling species, from Chinese characters to emojis. Everything ever written on the internet is, of course, part of the training data for the LLMs, but armed with digital cameras and text detection programs, the complete pre-internet textual corpus of our entire species is fair game, too.

Over millennia, we unwittingly flattened human culture into a transmissible and persistent record of binary data, so by the time the transformer architecture arrived, human intuition had already been perfectly laid out as a corpse of words for the machine beast to feast upon. In sum, the human-comprehensible structure of the world was first exposed as verbal utterances which corresponded to things we observed, then those verbal utterances were written into letters, then those letters were rapidly digitized. But language can never fully represent reality, so LLMs are fed on a second-order nature: the world as metabolized by the human.

Text saw a representational convergence on the computer with Unicode, but shape did not get the same treatment. Computerized geometry remains utterly balkanized. This is surprising given the seeming obviousness of Platonic geometric perfection in mathematics, a human truth that has been all but proved for thousands of years, but we’re relatively new to the game of simplifying the ideas of geometry to such a degree that they become comprehensible to something as stupid as a machine. So for each new intended application of shape on the computer, we invented a new representation. The idea of ‘rendering’, for instance, merely wanted to display a faux three-dimensional reality on a two-dimensional pixel grid for human viewers. This gave us things called ‘meshes’ — which are messy collections of flat surfaces stitched together. The worlds of computer aided design (CAD) and computer aided manufacturing (CAM) wanted to create solid shapes and parts that could actually be manufactured, and gave us ‘boundary representations’ (typically called B-reps), which are tidy collections of curved surfaces stitched together. Simulation software wanted to accurately represent an object’s physical behavior in the real world, and gave us ‘voxels’, which are the 3D equivalent of pixels (small cubes rather than squares). There are many other representations, too many to name here. All are dealing with the same underlying problem, and all have resulted in frustratingly dissimilar solutions.

Meshes are the most common computer-shapes one encounters. They represent a form with polygons: vertices, edges, and faces. The simplest way to create a mesh is to stitch together triangles, which are trivial in a way that computers like. Any three points define a plane, and from a plane you can very efficiently calculate something called a plane’s ‘normal vector’ — the direction that points directly away from the surface. You may even remember how to do this from high school calculus. The normal vector turns out to be the fundamental building block of photorealistic lighting, and because you can generate it so easily from a triangle, you can efficiently render faux three-dimensional scenes.

Everything from video games to the complicated sequences in movie animations rely on the same bargain downstream from meshes: if you break any surface down into small enough flat pieces, it looks smooth. It’s a clever type of discretization, very similar to the zoetrope, where images in rapid succession fool the eye into seeing continuous motion. The mesh is one of the most successful abstractions in the history of computer graphics, and its success comes from a very specific compromise. Namely, if you throw abstract perfection out of the window at the very beginning, trying only to achieve visually convincing results, you can gain a lot of efficiency.

The so-called ‘boundary representations’ that arose from the manufacturing world are less concerned with appearance and more concerned with industrial seriousness. This naturally yields a desire for precision. Whereas meshes are constrained by lots of small planar surfaces, B-reps can accommodate curved surfaces exactly, sans approximation or tricks of discretization. The most common type of B-rep surface is called the NURBS surface, a mathematical formulation powerful enough to represent a wide variety of shapes with precision. As a result, nearly all engineering necessities (e.g. spheres, cylinders, rounded edges, extrusions, etc.) are available in this framework. There’s a long list of famous CAD applications that are built on B-reps; you may recognize names like AutoCAD, Fusion, SolidWorks, NX, Rhino, or Revit.

Nearly every shape you see, in both the analog and digital worlds, was built in one or the other. On any given day, the vast majority of the buildings, cars, electronics, machines, or furniture you encounter will have been designed using B-reps; the vast majority of synthetic media you consume will have been designed using meshes. Despite B-reps being able to effectively solve many traditional engineering problems, and meshes being able to fool the eye by displaying lots of little triangles efficiently, they are both brittle. Brittleness, meaning: push one vertex of a mesh too much, or yank a single edge of a B-rep around a bit too sloppily, and the underlying abstraction falls over. What was once a plausible shape might now have faces intersecting themselves, or large gaps that make it meaningless as a manufacturable object. When the goal is a pretty picture or a part that’s the reflection of straightforward engineering intention, breakages like these are recoverable — one simply requires having a human in the loop to fix any problems that come up. But return to our initial observations about autonomous form-optimization, and the breakages become fatal.

Any optimization process that has a chance of working must anchor on some underlying representation that has the capacity to vary widely without undergoing total collapse. To be specific, the entire edifice of artificial intelligence relies on a single method of learning called ‘backpropagation,’ where a gigantic soup of numbers involved in some complex calculation (e.g. how well a large language model predicts the next word in a sentence) is tweaked around to figure out which combination of numbers gives the best result. The beauty of numbers is that they don’t break easily — in other words, that complex calculation won’t fail even if some of the numbers involved become very large or very small. In contrast, the current representations of geometry are extremely brittle. If you try to do backpropagation on the coordinates of a mesh or B-rep’s vertices, trying to minimize something like its drag in a simulated wind tunnel, the blind learning process will very quickly produce invalid shapes. A method of encoding form that routinely shatters under the fairly innocent spatial nudges that a blind learning process tries to make is plainly unsuitable for discovery of new, better shapes. Neither of the dominant ways of digitizing shape can encode intelligence-as-form. This is where something known as the ‘implicit’ representation becomes interesting.

Implicits, as they’re called, invert how a shape is defined. Rather than explicitly describing a 2D surface in terms of the 3D space, as meshes and B-reps do, you instead describe the entire 3D space in terms of your 2D surface. Specifically, you write a function that takes any point and tells you how far away that point is from your shape. If the distance is greater than zero, the point is outside the shape, if it’s less than zero, the point is inside the shape, and if it’s exactly zero, the point is on the shape’s boundary. The result is that forms defined using the implicit representation are both concisely represented as pure code and infinitely robust to variation. Those properties allow shapes that are nearly impossible with B-reps or meshes — for instance, a bolt that smoothly loses its threads and changes diameter, or a gyroid with variable density, which does extremely well at maximizing surface area for a given volume.

There is an overwhelming elegance to thinking about form this way. A simple 3D scene fits in a few lines of code, with no loss of information and no discretization tricks that would bastardize the Platonic purity of the shapes it contains. A renderer that turns a 3D scene of implicits into a 2D image on a computer screen can similarly be codified in an astonishingly compact way. Combining two primitives, like a sphere and a box which overlap, can be done with a single, purely mathematical ‘minimum’ operation. Over and over again, implicits deliver a conceptual clarity and ease that anyone who has worked with the older ways of encoding shapes on computers has only ever dreamed about.

This returns us to the talon, whose natural intelligence is inseparable from its geometry. Form is how life solves the problem of being exposed to physical law. Technological history is a meta-application of the same autopoietic natural process. The Scholastic tradition says that ‘nature natures,’ but when the human organism ‘natures,’ we say it ‘technologizes.’

The premise of technology is that the evolutionary process can be locally accelerated and directed towards specific human ends. We don’t want to wait for Nature to produce what we want. We do it by bootstrapping from our observations of nature, applying our rational faculties, and reducing the set of constraints that a fully natural system would be stuck with. The airplane, for instance, flies like a bird but doesn’t need the biological baggage of reproducing, or autonomously constructing and healing itself. This reduction of the problem size allows us to massively accelerate its development into mere decades, compared to the billions of years required to negentropically turn earthen matter into a bird.

The current fascination with language and large language models is justified but misleading. It’s justified because humans have put a massive amount of world-knowledge into speech and writing, and language is a truly powerful means of technological bootstrapping. Any machine that can understand our textual archive has acquired something very real. But the deeper and more chthonic thread of development runs wherever artificial systems participate directly in morphogenesis. This present linguistic phase of AI is a prelude, made possible by the readiness of text. Shape has lurked in the darkness, but its time is nigh.