Algorithm for Navigating a Maze Using... Water? (film, 9 minutes)
In his latest video, Steve Mould explores an interesting simulation of water pouring through a maze created by Bergman Jo. He received many messages asking for a discussion of this clip, which inspired him to create his own real-life version of the maze. The video starts with a simpler maze and then moves on to a more complex one, with Steve showcasing the differences in how the water behaves in both designs. Interestingly, the water in the simpler maze solves the maze without making any wrong turns, which Steve compares to an algorithm that utilizes air pressure within closed spaces when encountering incorrect paths.
Steve emphasizes that his project was more challenging due to the difficulties involved in using acrylic materials to construct the maze. Instead of creating a completely water-tight version, he focused on demonstrating how geometry and surface tension influence how water flows through the maze. As viewers observe the liquid navigating the maze, Steve examines the phenomenon of resistance that occurs due to air in closed spaces.
Next, he transitions to the more complex maze, highlighting the differences in water behavior compared to Bergman Jo's simulation. With larger areas, surface tension becomes less significant, and Steve notices that the water starts to follow a different solving algorithm based on descending paths. This illustrates how the maze’s geometry affects the speed and manner in which the water can find the correct route around obstacles. He amusingly comments on how changing the color of the water once the maze is filled adds another visual effect.
While Steve approaches the topic with a hint of humor, he also addresses the challenges of recreating Bergman’s simulation. He mentions that his experiment cannot eliminate air within the maze, which significantly alters the behavior of the fluid. The video concludes with Steve introducing viewers to career exploration related to science and utilizing resources that can assist them. He encourages viewers to subscribe to his channel and check out his collaboration with the organization 80,000 Hours.
As of the time of writing this article, Steve's video has already garnered over 15,119,764 views and 303,644 likes, showcasing the popularity of this topic and the interest many people have in scientific experiments. Following Steve Mould's channel is definitely worth it for those who want to learn more about exciting theories and scientific experiments.
Toggle timeline summary
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Introduction to the water maze simulation by Bergman Joe.
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Discussion of four created mazes: two small and two large.
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Overview of the simpler maze where water solves the maze without errors.
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Characterization of water's movement as a maze-solving algorithm using air pressure.
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Comparison with Bergman Joe's simulation, which explores all paths.
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Introduction of a more complex maze that leads water back upwards.
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Explanation of why the complex maze leaks due to design flaws.
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Discussion on air resistance and surface tension affecting water movement.
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Demonstration of the simple maze showing water finding lowest points.
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Comparison of maze filling patterns between the demonstration and the simulation.
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Discussion on the challenges of recreating Bergman Joe's simulation in a vacuum.
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Description of flow reduction in water maze due to surface tension.
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Experiment with changing water color after the maze is solved.
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Conclusion on how water solves a maze differently than simulations.
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Reflection on careers advice and its relevance to making YouTube videos.
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Introduction to the sponsor, 80,000 Hours, offering career advice.
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Overview of resources available on the 80,000 Hours website.
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Call to action to access 80,000 Hours career guide.
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Closing remarks and invitation to subscribe.
Transcription
So many people sent me this simulation of water pouring through a maze by Bergman Joe, and it makes sense that you would send it to me because this is the kind of thing that I would make for real. So of course, when I saw it, I had to make it for real. I actually made four mazes in total, a simpler one and a more complex one, and I also made large versions of those two mazes. Let's look at the small mazes first, because when you see what happens with those, it'll be obvious why I made the larger versions. By the way, this simulated version does eventually fill up completely with water, and it's very satisfying, but if you want to see that ending, you'll have to go to Bergman Joe's profile link in the description. Okay, so here's the simpler maze first, and what we find, brilliantly, is that the water simply solves the maze without taking any wrong turns at all. And actually, that makes sense, because every time the water comes up against an incorrect path, well, the air inside the path has nowhere to go. So while the water is trying to push itself into the incorrect path, the air pressure inside that closed space is pushing back. If I had to characterize this as a maze-solving algorithm, the algorithm would be something like try all paths simultaneously using air pressure, which is cool. When the tank runs out, it's fun to watch the air bubbles solve the maze as well. And actually, it's quite different to Bergman Joe's simulation, where the water eventually tries every path, even after it's found the solution. What about the more complex maze? Well, for this one, I chose a maze where the solve path takes the player all the way back up to the very top again. Well, already something seems to be amiss. Like there shouldn't be any water here, or at least not yet. And there shouldn't be any water here either. Or at least there shouldn't be if this maze is following the same rules as the previous maze. So what's going on here? Well, the explanation is quite simple. I just didn't build a water-tight maze. The reason I didn't build a water-tight maze is because it's really difficult. Like, I've got three layers of laser-cut acrylic here, a black layer, that's the maze itself, and two clear layers sandwiching the black layer. And the best way to bond these layers together is with solvent that literally dissolves the acrylic on both sides so that they weld together when the solvent evaporates. That's easy enough when you're bonding the black layer to the first clear layer. The solvent simply seeps between the two bits of acrylic. But then when you put the second clear layer on top, well, how do you get the solvent in there? A fun side note, one thing you realise very quickly when you laser-cut a maze is that mazes are always made of two separate pieces. I mean, it's obvious when you think about it, but it's quite cool to see. Actually, a maze becomes very easy to solve if you colour the two parts separately. But anyway, why did I build the larger mazes? Well, look, I stated that the reason water doesn't go in here is because there is air in the way. But why doesn't the air just bubble out so the water can get in? Well, it's because of surface tension. The air is unable to bubble past the surface tension of the water. So if we make the maze bigger until surface tension isn't significant anymore, we should expect the maze to be solved in a different way. We should expect the water to use a different solving algorithm, maybe something closer to what Bergman-Jo showed in his simulation. By the way, for the larger maze, I had the genius idea of laser-cutting thin channels into the outer clear acrylic so I could squirt the solvent in once the clear sheet was in place. But anyway, here's the simple maze in action. And you can see, without the power of surface tension, the water finds the lowest possible place it can go to. Sometimes momentum plays a part, so it will fill certain paths before others as a result, but broadly, without surface tension, the water tries more paths before finding the correct one. If I had to describe it in terms of a solving algorithm, it would be something like, always take the path that takes you lower until you can't anymore, and then take the next lowest path. We'll get to the more complex maze in a second, but first, let's compare this to Bergman-Jo's simulation. So all of the maze becomes full of water, but it doesn't fill up like it does in Bergman-Jo's. Like, water can never get into this region, or this region, or any of these regions. And you can see why. Again, it's air pressure. Except it's not surface tension that's holding the water back, it's just the geometry of the thing. Like, air would have to go down before it could go up in this scenario, so it simply doesn't because air is less dense than water. So my hunch is that what's going on in Bergman-Jo's simulation is that there is no air in his simulation. It would be very difficult for me to recreate that with my setup. Like, even if I could do this in a vacuum, well, in a vacuum, the water would just boil. Maybe I could try it with a liquid that doesn't boil in a vacuum? That sounds hard. Here's the more complex maze. There is a slight leak here, but it's water leaking from the tank to the outside world. I don't think there's any significant leaks happening within the maze itself, which is a huge relief. And just like with the simpler maze, the water goes to all the lowest parts it can do before it's locked out by the geometry. They say that if you're ever stuck in a maze, just put one hand on the wall and keep walking forwards, and you'll eventually get out the maze. Though I suppose if there are two possible paths through the maze, then the maze will necessarily be made of three parts instead of the two parts of acrylic that I showed you before. And if you happen to put your hand on the middle part, then you'll just be walking around forever. But anyway, one thing I really wasn't expecting with this water maze was that the whole thing grinds to a halt when there's still water left in the tank. And I think that's because there are lots of little bits of surface tension all around the maze that need to be overcome. But together those little bits of surface tension add up to enough resistance so that the pressure of water from the tank just isn't enough to force everything through. Like there's a little bit of surface tension here, that's preventing the water coming over this lip. Another bit of surface tension here, here, here, here, here. They're all resisting the flow of water slightly, but together they present a significant amount of resistance. It's a bit like those coin games, you know, you roll your coin in, it gets pushed off the first shelf, but then nothing happens on the second shelf. Or maybe something does fall off the second shelf, but there's no way anything's happening on the third shelf. The final thing I want to show you is what happens if I change the color of the water once the maze is solved. It's fun, isn't it? You can see that the red dye solves the maze and slowly starts to creep into those stagnant areas. So there you go. Water can solve a maze. It doesn't look anything like Bergman-Joe's simulation. Not that Bergman-Joe's simulation is wrong. It's just simulating something that I couldn't recreate here in my studio. When I was given careers advice at school, I can tell you for sure that making science videos on YouTube was not one of the suggestions that they made, mainly because YouTube didn't exist back then. But also I feel like they probably weren't asking the right questions. So how do you find good careers advice? Well, for people that are interested in finding a fulfilling career that makes a difference in the world, then I strongly recommend checking out the sponsor of this video, 80,000 Hours. And I'll say at the top that what they offer is absolutely free. They're a non-profit organization that focuses on helping people find careers that solve the world's biggest problems. And there are two things that I really like about it. The first is that it's evidence-based. Their insights come from 10 years of research alongside academics at Oxford University. The second thing I like is just the sheer breadth of different tools available on their website. You could start by looking at their problem profiles, for example. Those are the things in the world that need fixing. Or you could start with their decision-making tools that help you to find a career based on what you are like. Or you can dive straight into looking at specific careers. There's even a podcast if you enjoy learning that way. And then there's the job board, which they have curated based on what their research says are high-impact careers. The best way to get started is to go to 80,000hours.org forward slash Steve to be sent a free copy of their in-depth career guide in which you can learn about what makes a high-impact career, get new ideas for impactful paths, make a new plan based on what you've learned, and put it into action. The link is also in the description. So check out 80,000 Hours today. I hope you enjoyed this video. If you did, don't forget to hit subscribe. And the Algorithm thinks she'll enjoy this video next.