I think the idea is that the geometry of straight lines in 4D should be similar enough to picture using the same mental abilities.

How we see is frozen by not only physics, but also biology. We can't actually see in 3D, only in the 2D of our retinae (and the embedded 2D of light-exposed surfaces). That's true for both 3D and 4D objects. I suppose fish, with their electroreceptive abilities, might be the only animals that can sorta "see" in true, volumetric 3D.

> It is sometimes associated with our inability to think of new colors, but I think this is a completely different problem.

As an aside, thinking of a new color is relatively easy. You can sorta actually see new colors just by making a really good pigment[0], or shooting cone cells with lasers[1].

But there's also the possibility of having a new photoreceptor. In which case, you don't just gain 1 new color. You gain 3 new secondary colors, plus an entire new type of 4 "tertiary colors", each of which is as visually distinct as cyan, magenta, and yellow are. And the colorspace itself becomes a 4-dimensional volume, with every existing color able to blend into smooth graduations of the new cone cell signal.

[0] https://www.youtube.com/watch?v=_NzVmtbPOrM [1] https://en.wikipedia.org/wiki/Olo_(color)

Are you sure we can't visualize 4D objects? Or rather, what exactly does that mean?

Can we visualize 3D objects? Or do we reason about 3D objects, but only visualize a 2D projection of 2D boundary surfaces embedded in 3D space? I'm definitely not thinking about the inside of my desk lamp, or even its back side, even though those are as much a part of the 3D object as the front surface.

Can you visualize a 1D projection of a 2D object? Probably, but is it a little tricky? How about a 1D projection of a 3D object? And when that 3D object moves? How about a 2D projection of a 3D object, but seen from the inside out with a Hammer retroazimuthal projection, instead of viewed from a distance with the embodied camera eye and wonderfully simple rectilinear(ish) projections that we're so familiar with?

Arguably, I think we can visualize 4D objects. They just look the same as 3D objects, because the visualization is itself a 2D projection. If they move, they look like wobbly 3D objects, as we pick up a different "slice" or "surface".

Now, we don't know very many 4D shapes, because we don't encounter them in our lives. But I think that's fully explained by familiarity, without invoking the idea of an arbitrary limitation. We've all seen lines, sheets, boxes, balls, pyramids— Try describing to a random stranger what a Strandbeest or a Klein bottle looks like.`

Magical thinking is rarely constructive as an argument, but as a fig leaf, it might keep opposition talking for long enough to force through a fait accompli.

> I take your meaning with the wax and such, but I think my solution would just be to go bigger and store less data. And I mean bigger like, 20 characters per print bed, or something. But then, at that scale, maybe a QR code would hold up well enough in plastic, too?

Only way to know is to try it! I think you might be surprised. QR codes (with high redundancy settings) are very resistant to corruption.

The idea with the wax is to transfer the data into a more durable final product... Lost wax casting, you print wax, cover the wax in plaster, melt the wax, pour a metal (or epoxy) into the plaster mold.