The Final Twist of the Donut

In my last post eleven days ago, I made the proclamation that I had finally bent water. In the post I presented teaser figure of the rough equations that allowed me to show how an entangled pair of arrays of water molecules can twist into a shape that bends in space and time. While the above sentence might not mean much to you, dear reader, it actually is more or less the solution to the curvature of spacetime. Or the first mathematically accurate step in the theory of everything.

So, this past week and a half I’ve been going through the mathematics and made sure that the equations are correct. And now I can confidently say that they are indeed correct. The only thing left is to apply the equations to my experimental results as a qualitative solution and they should be publishable in a top journal (I’m still aiming for Nature).

One curious thing I’ve realized with the theory is that I can freely skip all of the bits where I’m not fully confident and center the paper on just this twisting of a water donut. And then tie this accurate mathematical theory to the tangible electron microscopy of lignin. And also show that by applying the understanding of the properties of water, one can make high performance adhesives and coatings. And once I’ve done this, someone else can take the basic theory and build upon it. I don’t have to have all the answers. I just need to present something that makes mathematical sense.

Next, you’ll be asking, what are these famous equations. I’ll show them now.

Here are the inside half-helices:

and here are the outside half-helices:

I already showed plots of these equations in the last post, so I won’t be showing them again. However, now that the equations are correct, I can show how they can be stacked on top of each other into toroidal segments:

Here you only see the location of molecules at the exact point where the molecule cross thex-z plane at y = 0. The yellow circles depicting molecules of one array of molecules and the blue circles depicting its entangled neighboring array. And of course, here I assume a spherical molecule.

Plotting a full circle, you get this:

In an earlier version of this post I still had a tiny error in the figure, but this was easily corrected.

Anyhow, if you wish to try to generate your own plots, here is an Excel file with the equations:

Water bending 2025_09_25-phi.xlsx

Download XLSX • 145KB

It’s not very difficult to handle, if you know Excel well enough. However, you do have to know both Excel and a bit of mathematics to get the hang of it. I'll write proper explanations on how to interpret the Excel file as soon as I can.

Things are beginning to look clearer and clearer. It shouldn’t take too long for me to have the manuscript in generally publishable shape. Now, it seems that the limiting factor are actually some experiments on the adhesives that would add heft to the claims but in principle I should be able to publish a preprint even before this. The last time I attempted to send a preprint to ChemRxiv the attempt backfired, as I didn’t have much experimental work in the paper. This time I actually try to balance the theory with the experiments, which should allow me to publish  the preprint before peer-review.