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Study shows 4,000 years of knot-tying hasn’t made us better at understanding them.
BALTIMORE — When you tied your shoes this morning, you probably didn’t give much thought to the physics involved. After all, tying knots is something humans have been doing for thousands of years — possibly even before we mastered fire or invented the wheel. From ancient Egyptian art depicting reef knots around waists to modern-day rock climbers securing their safety lines, knots are deeply woven into the fabric of human civilization.
But according to new research from Johns Hopkins University, our intuitive understanding of knots — specifically, how secure they are — is remarkably poor, even when the differences should be obvious.
An Unexpected Discovery
The genesis of this research, published in the journal Open Mind, came from an unexpected source: a PhD student’s crafting hobby. Sholei Croom, the study’s lead author, had an “aha” moment while embroidering.
“People make predictions all the time about how the physics of the world will play out but something about knots didn’t feel intuitive to me,” Croom explains. “You don’t need to touch a stack of books to judge its stability. You don’t have to feel a bowling ball to guess how many pins it will knock over. But knots seem to strain our judgment mechanisms in interesting ways.”
The finding was particularly striking because previous research has shown that humans are surprisingly good at predicting various physical events, like whether a tower of blocks will topple or how liquid will flow around obstacles. Knots, it seems, are different.
Testing Our Knot Knowledge
To test their hypothesis about knot perception, the researchers carefully selected four knots that would provide a clear test of people’s intuitive understanding. These knots — the reef knot, thief knot, granny knot, and grief knot — look deceptively similar but vary dramatically in their security. The grief knot, for instance, is so insecure it often comes apart on its own, making it unsuitable for practical use.
“People are terrible at this,” says co-author Chaz Firestone, who studies perception. “Humanity has been using knots for thousands of years. They’re not that complicated—they’re just some string tangled up. Yet you can show people real pictures of knots and ask them for any judgment about how the knot will behave and they have no clue.”
Surprising Results
In a series of five carefully designed experiments, the researchers gave participants every possible advantage to succeed. They showed them photographs, computer-rendered simulations, rotating videos, and even detailed diagrams explaining each knot’s structure.
Yet across all four experiments testing knot security, participants performed consistently poorly. With photographs, they chose the more secure knot only 42.1% of the time — worse than random chance. Performance remained poor even with computer renderings (44.8%), videos (49.6%), and diagrams (36.9%).
The researchers showed participants four knots that are physically similar but have a hierarchy of strength. People were asked to look at the knots, two at a time, and point to the strongest one. The strongest is A, the reef knot. (Credit: Khamar Hopkins/Johns Hopkins University)
When participants did guess correctly, their explanations revealed that success wasn’t based on understanding; they pointed to aspects of the knots that had no bearing on actual security. “We tried to give people the best chance we could in the experiment, including showing them videos of the knots rotating and it didn’t help at all—if anything people’s responses were even more all over the place,” Croom notes.
It’s Knot So Simple
This finding raises intriguing questions about how humans understand physics. Many researchers believe we have an internal “physics engine” in our brains — similar to what video games use to simulate realistic object behavior — that helps us predict how physical systems will behave. This mental physics engine usually works remarkably well for everyday scenarios, helping us catch balls, stack dishes, or judge whether furniture will fit through a doorway.
The research team suggests that non-rigid objects, such as string, may be inherently harder for people to reason about than solid ones. Even our extensive daily experience with knots — from shoelaces to power cords — doesn’t seem to help overcome this limitation. While the researchers tested only non-experts, they speculate that sailors or survivalists whose livelihoods depend on knot security might perform better.
“We’re just not able to extract a salient sense of a knot’s internal structure by looking at it,” Croom concludes. “It’s a nice case study into how many open questions still remain in our ability to reason about the environment.”
Looking Ahead
Just as optical illusions reveal the shortcuts and assumptions our visual system makes, these “knot illusions” may reveal important constraints on how our minds model and predict physical interactions. So the next time you tie your shoes, take a moment to appreciate the hidden complexity in those simple loops and crosses. While humans may have been tying knots for millennia, truly understanding them appears to be another knot entirely – one that our intuitive physics still hasn’t quite untangled.
Paper Summary
Methodology
The researchers conducted five experiments testing people’s ability to judge knot strength. In each experiment, participants viewed pairs of knots and had to choose which one would be stronger when pulled from both ends. The knots were presented in different formats: photographs (Experiment 1), computer-rendered simulations (Experiment 2), rotating videos (Experiment 3), and photographs with accompanying diagrams (Experiment 4). A final experiment tested whether participants could match knot photos to their corresponding diagrams. The experiments used a two-alternative forced-choice design, where participants had to pick one knot from each pair. Each knot was shown multiple times in different colors and orientations to ensure robust results.
Results
Across all four strength-judgment experiments, participants performed at or below chance levels (around 50% accuracy or worse). In Experiment 1 with photographs, participants chose the stronger knot only 42.1% of the time. Performance remained poor even with computer renderings (44.8%), videos (49.6%), and diagrams (36.9%). Participants often showed consistent but incorrect preferences, frequently rating the weakest knots (grief and granny) as stronger than the actually stronger knots (reef and thief). However, in Experiment 5, participants showed 92.5% accuracy in matching knots to their diagrams, demonstrating they could see and understand the knots’ structures.
Limitations
The study focused on a specific set of four related knots, so the findings might not generalize to all knot types. Additionally, while the researchers tested multiple presentation methods, real-world knot evaluation might involve other factors like being able to physically manipulate the knots. The study also used only naive participants; experts like sailors or climbers might perform differently. Finally, the study didn’t explore why people make these consistent errors or what specific features lead them to misjudge knot strength.
Discussion and Takeaways
This research reveals an important limitation in human physical reasoning abilities. While people can accurately perceive knot structure, they struggle to translate that understanding into predictions about physical properties like strength. This challenges theories suggesting humans have a general-purpose physics simulation capability in their minds. The findings suggest that some everyday objects and systems might be fundamentally unintuitive, even when we can clearly see all relevant information. This could have implications for how we teach physical concepts and design safety-critical systems.
Funding and Disclosures
The research was funded by NSF BCS #2021053 awarded to Chaz Firestone and an NSF Graduate Research Fellowship awarded to Sholei Croom. The authors declared no conflicts of interest. The study’s materials and data are publicly available through the Open Science Framework.