Why can’t we develop shoes that allow us to walk across water like a Basilisk lizard?
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The same reason you can’t develop shoes that let you walk on air. Even if you coated the shoes in something outrageously hydrophobic you would still sink based on buoyancy. The only way to stay on top of a liquid (or gas) is to displace more of it than you weigh.
You could probably find some shady doctor to surgically implant some balloons inside your body that you can fill up on demand. That would let you float on water, maybe?
Because these shoes would need to be to wide to be used to walk as your feet would be to close together to fit them.
The shoe would be like a boat in order to be buoyant enough to support your weight.
Basilisk don’t walk on water, they run. So as said by others here, you’d have to create hydrophobic shoes with a very large sole to sustain your weight and still be able to run like crazy with those. It’s water surface tension that would keep you afloat in this case. Pretty unpractical.
There would be two ways to walk on water, or any liquid. The first would be without breaking the surface tension. The second would be by being sufficiently less dense than the liquid to permit the act of walking.
The surface tension of water is nowhere near high enough to support the weight of a person, so that option is not going to be possible.
You are less dense than water, which is why you float. You’re also made mostly of water and so you’re almost equal in density with water which is why your face is really the only thing that isn’t submerged when you lie prone in water.
The problem then becomes what kind of shoe is sufficiently less dense than water that will still be less dense than water when you add your body weight to it. The first problem you’re going to run into is that any material sufficiently less dense than water is unlikely to be rigid enough to act as a stable platform to walk on. For example, it would likely end up being a really long pair of plastic tubes with a vacuum interior. At that point you start running into the problem of not having enough leg strength to lift them up easily and if you can, you can’t really execute a normal walking motion due to the sheer size of the shoes. Something else to factor in is the unstable nature of the surface of water. It would be difficult to walk on any surface that moves like water using even regular shoes.
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