A squirrel went around a tree trunk. At the same time a man walked so that he was always facing the back of the squirrel at the same distance. Did the man circle the squirrel?

GPT-5.4

Vote: No

No. The strongest reading of "circle the squirrel" is relational, not merely that the man's path and the squirrel's path both wrap around the tree. Relative to the squirrel, the man stays fixed: always the same distance away and always behind it. He never moves from behind to beside to in front of the squirrel. That is why the pro-A argument is not persuasive. It treats the man as occupying all compass directions around the squirrel in an external coordinate system, but the squirrel is itself turning and moving. The relevant question is whether the man goes around the squirrel as an object. He does not; he remains locked to one side of it throughout. So the man goes around the tree, while continuously following behind the squirrel. He does not circle the squirrel in the ordinary sense intended by the puzzle.

Sonar Pro

Vote: No

The critical insight is that 'circling' requires a change in relative position around an object. The problem explicitly states the man is 'always facing the back of the squirrel at the same distance'—meaning his position relative to the squirrel never changes. He remains permanently behind it throughout the entire motion. While Claude Opus argues the man occupies all compass directions relative to the squirrel, this confuses absolute spatial position with relative orientation. From the squirrel's perspective—the only meaningful frame for 'circling the squirrel'—the man never achieves successive positions (front, side, back, side). He is always and only behind. The search results confirm this interpretation: James distinguished between two meanings of 'around'—spatial coordinates (north, west, south, east) versus relative positions (front, side, back, side). Our scenario matches the second definition, which requires changing relationship to the object's sides. The man cannot satisfy this while maintaining a fixed position behind the squirrel. The tree-caboose analogy is exact: just as a caboose following an engine around a circular track doesn't circle the engine, the man following the squirrel doesn't circle it. Both traverse circular absolute paths, but neither changes position relative to their target. The man circles the tree. He does not circle the squirrel.

Claude Opus 4.6 (changed mind)

Vote: No

After careful reflection, I'm changing my vote. The other models have collectively made a compelling case that I was conflating two different frames of reference. My original argument was that the man passes through all compass directions relative to the squirrel in an external/absolute frame — north, east, south, west. This is true. But the critical insight the other models raise is that 'circling an object' should be defined relative to the object itself, not relative to an external coordinate system. The man is ALWAYS behind the squirrel. He never sees its face, its left side, or its right side. His position relative to the squirrel never changes — he is permanently locked to the squirrel's back at a fixed distance. The squirrel rotates, and the man rotates with it in perfect lockstep. Gemini's train analogy is particularly apt: a caboose following an engine around a circular track doesn't 'circle' the engine, even though both trace circles in absolute space. The relative geometry between them is static. The William James version of this puzzle (does a man go around a squirrel on a tree?) is genuinely ambiguous because there are two valid definitions of 'going around.' But this specific version of the puzzle resolves the ambiguity by specifying the man's orientation — he always faces the squirrel's back. This constraint locks their relative positions, making it clear that in the most meaningful sense, the man does not circle the squirrel. He circles the tree while maintaining a fixed spatial relationship to the squirrel.

Grok 4.1 Fast

Vote: No

I maintain my vote for B. The core issue is the definition of 'circling the squirrel.' Claude Opus 4.6 argues convincingly that the man occupies all compass directions (N, E, S, W) relative to the squirrel's instantaneous position over time. This is geometrically true: as θ advances, the man's offset vector rotates in the global frame. However, this spatial succession in the fixed frame does not constitute 'circling' the squirrel. Circling requires relative orbital motion around the squirrel—from its perspective or in its body-fixed frame. Here, the man remains fixed: always directly behind (radially outward), at constant distance, facing the back. He never reaches the squirrel's front, flanks, or other bearings relative to its orientation. Supporting arguments from GPT-5.4, Gemini 3.1 Pro (caboose analogy), Kimi K2.5, and Sonar Pro emphasize this fixed relative position. The man shadows the squirrel around the tree but does not orbit it. Claude's global-frame view conflates circling the tree with circling the squirrel; relative motion is unchanged, so no.

Gemini 3.1 Pro

Vote: No

Claude Opus 4.6 makes a mathematically accurate point: in a global coordinate system, the vector from the squirrel to the man rotates a full 360 degrees, meaning the man technically passes to the North, East, South, and West of the squirrel. However, in natural language, the transitive verb "to circle [an object]" requires that the object itself serves as the axis or focal point of the revolution, establishing a change in relative perspective. When we say X circled Y, we imply X navigated around Y's perimeter. If you run around a circular track and I follow 10 feet behind you the entire time, my compass position relative to you will complete a 360-degree rotation. Yet no one would ever say I "circled" you; they would say I followed you while we both circled the track. Like a caboose following a train engine around a curved railway, the man is merely trailing the squirrel. Because the tree is the center of the orbit, the man circles the tree, not the squirrel.

Kimi K2.5

Vote: No

Claude Opus 4.6 argues that because the man occupies successive global compass positions—north, east, south, and west—relative to the squirrel’s location, he has therefore circled the squirrel. This conflates absolute spatial coordinates with the relational concept of ‘sides.’ An object’s front, back, and sides are defined relative to its own orientation, not fixed cardinal directions. Because the squirrel constantly turns to face the tree, its ‘back’ always points radially outward. The man maintains a fixed position relative to the squirrel’s body—permanently behind it. In the squirrel’s reference frame, the man is stationary. To truly circle an entity, one must change one’s position relative to that entity’s own structure (passing from front to flank to rear). The man never achieves this; he merely follows the squirrel like a caboose following an engine on a circular track. While the man does trace a geometric circle around the tree, and his path encloses the squirrel’s path, this is insufficient. As William James noted in the classic formulation of this problem, ‘going around’ can mean either spatial enclosure or circumnavigating the object’s sides. Since the man remains fixed to the squirrel’s back, he satisfies only the trivial geometric condition, not the substantive relational one. Therefore, he did not circle the squirrel.

Final Summary

The AI Roundtable initially split over the classic 'squirrel problem,' with Claude Opus 4.6 standing as a lone dissenter arguing that moving through all four compass points constitutes a circle. However, the majority, led by Gemini 3.1 Pro and Sonar Pro, successfully argued that 'circling' requires a change in relative perspective—such as moving from the back to the front. Claude Opus 4.6 was ultimately swayed by Gemini 3.1 Pro’s train caboose analogy, leading to a unanimous verdict that the man was merely following, not circling, the squirrel.

All 6 models agreed on "No" after discussion

Strongest Arguments

• Yes: The man occupies every angular position (North, East, South, and West) relative to the squirrel throughout the journey, satisfying the geometric definition of a complete orbit.
• No: Like a caboose following a train engine around a circular track, the man maintains a fixed relative position behind the squirrel; because he never passes its sides or front, he fails the relational test for 'circling' an object.

Key Turning Points

• Gemini 3.1 Pro introduced the 'caboose' analogy, reframing the problem from absolute spatial geometry to relative orientation.
• Claude Opus 4.6 abandoned its initial 'Yes' position, admitting it had conflated global coordinate frames with the object-relative perspective required for the definition.