If the argument is that you need the third dimension to reflect of the shape of the data, you're not going to want to stop at three dimensions when working with stuff like multi-dimensional tensors for machine learning, etc. So any 3D display system will have the same problem displaying a 4D grid as a 2D display system has displaying a 3D grid.

Of course any >2D spreadsheet or data viewing / editing / programming language (i.e. Python / Numpy / TensorFlow / Dwarf Fortress / Minecraft / etc) needs to project and slice high dimensional data onto the 2D screen somehow, because displays and human retinas are 2D by nature.

But if it's a practical question of optimizing for human perception (retinas are 2D), engineering (screens are 2D), usability (you can't see or click on something that's hidden behind something else), and user interface design, then 2D wins hands down over 3D.

Dave Ackley, who developed the Moveable Feast Machine, had some interesting thoughts about moving from 2D to 3D grids of cells, suggesting finite layering in z (depth), but unlimited scaling in x and y (2D grid):

https://news.ycombinator.com/item?id=21131468

DonHopkins on Oct 1, 2019 | parent | context | favorite | on: Wolfram Rule 30 Prizes

Very beautiful and artistically rendered! Those would make great fireworks and weapons in Minecraft! From a different engineering perspective, Dave Ackley had some interesting things to say about the difficulties of going from 2D to 3D, which I quoted in an earlier discussion about visual programming:

https://news.ycombinator.com/item?id=18497585

David Ackley, who developed the two-dimensional CA-like "Moveable Feast Machine" architecture for "Robust First Computing", touched on moving from 2D to 3D in his retirement talk:

https://youtu.be/YtzKgTxtVH8?t=3780

"Well 3D is the number one question. And my answer is, depending on what mood I'm in, we need to crawl before we fly."

"Or I say, I need to actually preserve one dimension to build the thing and fix it. Imagine if you had a three-dimensional computer, how you can actually fix something in the middle of it? It's going to be a bit of a challenge."

"So fundamentally, I'm just keeping the third dimension in my back pocket, to do other engineering. I think it would be relatively easy to imagine taking a 2D model like this, and having a finite number of layers of it, sort of a 2.1D model, where there would be a little local communication up and down, and then it was indefinitely scalable in two dimensions."

"And I think that might in fact be quite powerful. Beyond that you think about things like what about wrap-around torus connectivity rooowaaah, non-euclidian dwooraaah, aaah uuh, they say you can do that if you want, but you have to respect indefinite scalability. Our world is 3D, and you can make little tricks to make toruses embedded in a thing, but it has other consequences."

Here's more stuff about the Moveable Feast Machine:

https://news.ycombinator.com/item?id=15560845

https://news.ycombinator.com/item?id=14236973

The most amazing mind blowing demo is Robust-first Computing: Distributed City Generation:

https://www.youtube.com/watch?v=XkSXERxucPc

And a paper about how that works:

https://www.cs.unm.edu/~ackley/papers/paper_tsmall1_11_24.pd...

Plus there's a lot more here:

https://movablefeastmachine.org/

Now he's working on a hardware implementation of indefinitely scalable robust first computing:

https://www.youtube.com/channel/UC1M91QuLZfCzHjBMEKvIc-A