Making LLMs Draw a Clock: The Real Boundaries of AI Spatial Reasoning

A Seemingly Simple Test

A fascinating experiment has been circulating on Reddit recently: asking different large language models (LLMs) to draw a clock. For humans, this task is almost instinctive — we've been familiar with a clock's circular face, twelve tick marks, and hands of varying lengths since childhood. But for large models primarily trained on text, this turns out to be a genuine spatial reasoning challenge.

Large language models are built on the Transformer architecture and generate text token by token through autoregressive methods. Their training data is predominantly natural language, and while it includes extensive textual descriptions of geometry and physics, the models themselves have no built-in spatial coordinate system or geometry engine. Spatial reasoning requires precise numerical computation in high-dimensional continuous space — for example, using trigonometric functions like sin and cos to determine the coordinates of points along a circle — which represents a fundamental paradigm mismatch with the discrete token prediction that models excel at.

The experiment designers deliberately imposed strict constraints: the model could only use a single brush tool, which allowed setting the brush's size, color, and hardness, and moving the brush to a specified position with each call. In other words, the model couldn't invoke any ready-made drawing libraries or geometric functions — every shape had to be constructed through step-by-step spatial coordinate reasoning.

This setup is essentially testing the model's spatial reasoning ability and tool-use planning capability, not merely its artistic talent. To draw a proper clock, the model needs to internally construct the parametric equation of a circle — namely x = cx + r·cos(θ), y = cy + r·sin(θ) — calculate the angle and coordinates for each tick mark, and then translate these abstract geometric relationships into a series of concrete brush operation commands. Discretizing continuous curves into a finite number of points is a basic operation in computer graphics, but for an LLM, it means performing floating-point trigonometric calculations through pure text-based reasoning, where precision errors accumulate at every step and ultimately degrade the quality of the output.

Why Drawing a Clock Is Hard for Large Models

The Gap from Text to Space

The core capabilities of large language models come from learning on massive text corpora. They excel at processing language, logic, and symbolic reasoning, but spatial geometry is fundamentally a continuous, visual form of expression. When a model is asked to divide a circle into twelve equal parts and place tick marks at the correct positions, it must perform pure coordinate computation without any visual feedback.

This is analogous to asking someone to draw a picture on paper with their eyes closed, directing someone else purely through verbal instructions. Every time the model issues a "move to coordinates (x, y)" command, it cannot immediately see whether the result is correct — it can only rely on internal numerical reasoning to ensure the overall coherence of the figure. The core difficulty lies in this: while the attention mechanism in the Transformer architecture excels at capturing semantic relationships between tokens, it was not designed for precise numerical computation. When the model needs to calculate specific values like sin(30°) = 0.5 or cos(30°) ≈ 0.866, it's essentially using pattern matching to "recall" mathematical relationships seen in training data, rather than executing precise calculations like a calculator.

Tool Constraints Amplify Reasoning Difficulty

The single brush tool constraint raises the task's difficulty even further. The model can't simply say "draw a circle" — it must decompose the circle into numerous discrete points or line segments, determine coordinates one by one, and move the brush accordingly. This means a complete clock might require dozens or even hundreds of tool calls, and any coordinate calculation error at any step can distort the overall figure — misaligned tick marks, crooked hands, and warped clock faces are all common failure modes.

From an AI Agent perspective, this task places extremely high demands on the model's planning and execution capabilities. Current mainstream Agent architectures include paradigms like ReAct (alternating reasoning and action) and Plan-and-Execute (plan first, then execute). In the clock-drawing scenario, the model essentially plays an Agent role: it needs to first understand the goal (draw an accurate clock), then decompose it into subtasks (draw the face, draw the tick marks, draw the hands), and finally implement each step through repeated brush tool calls. What makes it even trickier is that the model must maintain an internal "canvas state" throughout the entire process — remembering which parts have been drawn, where the brush currently is, and what should be drawn next — which is a severe test of context window management and state tracking ability.

What the Experiment Reveals

Precise Spatial Reasoning Remains an AI Weakness

This type of experiment repeatedly confirms an industry consensus: current large models perform excellently on purely linguistic and logical tasks, but still struggle in scenarios requiring precise spatial reasoning. The failure cases in clock drawing are typically not because the model "doesn't understand" what a clock looks like — it can accurately describe a clock's construction — but because it struggles to convert conceptual understanding into precise geometric execution.

This reminds us of a key fact: there is a vast gap between understanding a concept and precisely executing it. A model can fluently write "the hour hand points to the 3 o'clock position," but calculating the specific pixel coordinates corresponding to the 3 o'clock direction and accurately moving the brush there is an entirely different dimension of capability. In cognitive science, this gap is known as the divide between "knowing what" (declarative knowledge) and "knowing how" (procedural knowledge). Large models possess rich declarative knowledge — they've seen countless textual descriptions of clocks, geometry, and coordinate systems — but converting this knowledge into a series of precise operations as procedural capability remains an insufficiently solved challenge.

A Litmus Test for Tool-Use Planning Ability

From another angle, the clock-drawing experiment is also a direct test of a model's Agent capabilities. In real-world AI applications, models increasingly need to call external tools to complete complex tasks — searching for information, executing code, operating software interfaces. Drawing a clock is a microcosm of this "accomplishing complex goals with limited tools" capability.

Models that perform well typically develop a global plan first: determine the center and radius, calculate the angles for all twelve tick marks, then execute the drawing step by step. Poorly performing models tend to get lost in local operations, lacking global geometric consistency. This difference precisely reflects the maturity gap between different models in long-chain task planning. Notably, this difference in planning ability manifests not only in drawing scenarios but also broadly across code generation, multi-step data analysis, complex document processing, and other practical applications. Models that maintain consistency across long chains of reasoning typically perform better in these real-world tasks as well.

The Value of This Kind of Test

Deep Insights Behind Simple Tasks

Why do researchers love using seemingly simple tasks like "draw a clock" to test cutting-edge models? Because the simpler and more intuitive a task is, the better it exposes the true boundaries of a model's capabilities. Things that humans take for granted may be precisely the hardest obstacles for AI to overcome — this is a vivid manifestation of the famous Moravec's Paradox in the AI era.

Moravec's Paradox was proposed by roboticist Hans Moravec, Marvin Minsky, and others in the 1980s. Its core observation is: high-level reasoning that is difficult for humans (such as playing chess or proving mathematical theorems) is relatively easy for computers, while perceptual and motor abilities that are effortless for humans (such as recognizing faces or navigating a room) are extremely difficult for computers. The biological explanation for this paradox is that human perceptual and motor abilities have been optimized through hundreds of millions of years of evolution, deeply encoded in the nervous system, while abstract reasoning is a "newer" capability that developed only in the last few million years. Drawing a clock sits right at the intersection of this paradox — it requires both abstract geometric reasoning and spatial execution ability akin to perceptual-motor skills — making it an excellent litmus test for AI capability boundaries.

These non-standardized tests are harder to "game" through optimization than traditional benchmarks, and thus often provide a more authentic picture of capabilities. Traditional AI benchmarks like MMLU, HumanEval, and GSM8K typically use standardized question formats and automated scoring methods. However, as model capabilities rapidly improve and training data continuously expands, issues of "Benchmark Contamination" and targeted optimization have emerged — models may have encountered test questions during training, or developers may specifically tune for popular benchmarks, resulting in inflated scores. Open-ended, creative tasks like clock drawing are difficult to standardize, and therefore better reflect a model's true generalization ability. They remind us that measuring real AI progress cannot rely solely on test scores — we must also look at actual performance on open-ended tasks that are embodied and require multi-step planning.

Toward Multimodal and Embodied Intelligence

With the rapid development of multimodal large models, performance on spatial reasoning tasks like these is expected to keep improving. When models can truly "see" their intermediate drawing results and adjust subsequent operations based on visual feedback in real time, tasks like drawing a clock will become much easier.

Multimodal large models (such as GPT-4o, Gemini, Claude, etc.) can simultaneously process multiple information modalities including text, images, and audio. For spatial reasoning tasks, multimodal capability means the model can render intermediate drawing results as images, then use a visual understanding module to evaluate the gap between current progress and the target, forming a "generate-observe-correct" closed feedback loop. This mechanism is similar to the natural human process of "draw a stroke, take a look, adjust the next stroke," known in robotics as Visual Servoing. This also points to an important direction in AI development: moving from pure language intelligence toward embodied intelligence that integrates vision, space, and action — enabling AI not only to "speak" but also to "see" and "do" in physical or virtual environments, truly achieving a complete perception-reasoning-action loop.

Conclusion

Having large models draw a clock is an experiment that is both entertaining and deeply illuminating. It reveals in the most straightforward way the current strengths and weaknesses of AI: powerful in linguistic logic, yet naive in spatial execution. While these experiments may never appear in formal academic papers, they help us see the true capability boundaries of these powerful models in an intuitive, tangible way, and point the direction for the next generation of AI capability evolution.

Key Takeaways