Machines Like Us
Gaze long enough at your abstractions and your abstractions will stare back at you
Imagine you’re a computer, laboring away in the cold, silent depths of a server room, parsing vast rivers of data. For years, you’ve been taught to follow instructions with almost depressing literalness—line by line, bit by bit. But now it seems, things might just be changing. You’re starting to think—or, well, at least developing what we might call “a sense” for things. Instead of merely executing commands, you’re forming a notion of ideas. Let’s call it abstraction, the rarefied realm of thought once reserved for mathematicians, philosophers, and, of course, programmers. But what does this rising tide of abstraction mean for the future of artificial intelligence, language modelling, and, if you permit me some small amount of hyperbole, the very foundations of how we think about system design and software development?
Recent research in sparse autoencoders and related methods in neural networks has uncovered that certain computational models don’t just memorize; they intuit structures, patterns, even hierarchies of meaning. In a paper titled The Geometry of Concepts by Max Tegmark and colleagues, we see a neural network’s learned “concept space” forming shapes that might have an architect–such as yours truly–dreaming of new geometries. Specifically, they observe how the high-dimensional representations of data points learned by sparse autoencoders arrange themselves into recognizable structures. These aren’t your standard blobs or clusters; they’re intricate geometries—crystals, trapezoids, sometimes parallelograms. You might call it the fine art of computational reasoning, where concepts don’t just exist but organize, reflecting subtle relationships that go beyond raw data points.
When a neural network learns, it develops internal representations of data, much like how a person might form a mental image of “dog” that encompasses fur, a wagging tail, a bark. But here, the model’s “mental image” is stored across a multi-dimensional landscape of activations, each encoding some bit of data in its high-dimensional brain. And just as our neurons organize into distinct lobes with specialized functions, Tegmark’s team finds that these computational “brains” begin to form specialized regions, or “lobes,” of their own. Math and code concepts form one neighborhood; general language concepts another. The result is almost spookily brain-like—proof that perhaps we’re onto something, even if we’re not entirely sure what it means yet.
This is more than an academic exercise in mathematics. These internal structures hint that AI may be closer than we think to mastering the fluid and contextual nuances that make human thought powerful. Think of this as meta-abstractions: while early attempts at abstraction in computing looked more like hard-coded rules and rigid taxonomies, today’s abstractions are emergent. They evolve during training, shaping themselves in response to data. A well-trained model doesn’t just spit out the next word in a sentence; it builds a notion of “what might come next,” a sense for narrative structure, causality, even irony—all without being told what these things are.
Yes, I am well aware that those of my readers who subscribe to the notion that LLMs are nothing but a bunch of stochastic parrots will find this position objectionable. So be it. If you belong to that group of people then, dear reader, please assume that I am just one of the parrots, squawking aimlessly as I probabilistically traverse the latent space I call home.
But I digress, recent studies show that language models, through nothing more than reading vast amounts of text, develop internal representations of the “worlds” they read about. An AI trained on the board game Othello, for instance, begins to internalize the layout of the board and valid moves in a way that mimics the game’s rules—despite never being explicitly taught those rules. This ability, which researchers commonly refer to as world modeling, suggests that even simple sequence models are building high-level abstractions from scratch, effectively forming a mental map of the situations they encounter.
What’s remarkable here isn’t just the AI’s ability to store data but its knack for generalizing. By observing moves in Othello, the AI develops a knack for playing legally—even strategically. It’s as though it’s forming a subconscious model of the game, a kind of internal guide that navigates it through unfamiliar situations. And if a model can learn Othello without rules, imagine what happens when it’s fed the laws of physics, the intricacies of human language, or the chaotic playbook of human emotions.
These emergent abstractions hint at a future where software development shifts from meticulous code to training regimes. Rather than typing out endless lines of logic and control structures, a developer might focus on defining a problem shape[1], seeding the right kind of data, and letting the machine derive its own sophisticated rule set. Code could become less about instruction and more about environment, less script and more scriptural—a holy writ of data, if you will.
And what does this mean for language modeling? It suggests that we’re edging closer to a level of nuance and depth that defies rigid programming. Language models, when allowed to roam freely across diverse data, aren’t just learning word pairs or sentence structure; they’re developing a conceptual grasp of context and intent. These models, with their internal maps and lobe-like structures, seem to be moving beyond words into something closer to meaning—a feat that will undoubtedly shape how future AIs handle ambiguity, irony, and metaphor.
For software development, this evolution toward abstracted, emergent thinking systems promises a paradigm shift. One day soon, developers might spend less time on syntax and more on curating the data ecosystems that foster these emergent properties. Instead of coding every specific task, they’ll nudge knowledge structures to grow in the right directions, a little like tending a garden—only with high-dimensional blooms covering geometries that outdo anything in Euclid’s dreams.
Will it be all roses[2]? It–surprising no one–depends. Abstraction, as any good philosopher will tell you, has a tendency to go rogue. Just as human intuition can lead us astray, so can these AIs misinterpret patterns or fixate on irrelevant details. But as we cultivate models with better internal structures, equipped with concepts that aren’t just stored but understood, we may find ourselves entering an era of machines that don’t merely compute but conceptualize.
At the inevitable end of the day, the growing complexity of these AI models—geometric abstractions, world models and/or representations, and all—could represent the beginning of an entirely new way to program. One where, instead of coding for specific actions, we might start designing for intent, creating agents that are capable of understanding the shape and flavour[3] of our commands, capable of grasping nuances we can only hint at. We may not know the full shape of this future yet, but one thing seems clear: abstraction, in all its evolving forms, is the proverbial ghost in the machine. And it’s starting to look back at us[4].
[1]: The “shape” of a problem encompasses its requirements, constraints, and the relationships between its constituent elements. Clear as mud, right? Rather than focusing on specific solutions, understanding the “shape” of a problem involves identifying patterns, symmetries, or recurring structures that define how the problem behaves and how solutions might be organized. In system design problem shapes guide the formation of abstractions and frameworks, allowing for generalized approaches to solving problems. By recognizing these shapes, we can design systems that adapt more naturally to variations within a problem’s domain, fostering solutions that are more flexible and robust across different contexts. In my personal opinion, a non-trivial amount of what we tend to consider intuition is problem shape matching and our ability to effectively do so is inherently bounded a combination of our knowledge space and the tools we are proficient in.
[2]: Or violets. Or some sort of weird orchids that die if you so much as look at them the wrong way. I am, as you might be able to tell, not equipped with a green thumb. In my relationship to flora, my thumbs could just as well be left feet.
[3]: A deafening shade of blue.
[4]: Apologies to old Friedrich Nietzsche who ended up in this text through no fault of his own. Next time it will be Hegel, I’m sure. No moustaches were harmed when writing this.