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.
biology plays the role, certainly, but nature was trying to capture a model for 3D physical interactions first of all, physics first. And final choice of two 2D sensors is explicitly optimal and minimally effective for 3D - so it can not be similarly descriptive for 4D, just not fair to expect results on same level imho.
For meaningful 4D perception on similar level our body need three volumetric sensors, separated, to define volume with 4D direction
> 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.
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.
Titanium gets hype, but is it actually the best option considering chemical and fatigue properties? I find it implausible that tensile strength-to-weight would be the weakest part even for good old fashioned stainless steel.
The advantage is much more durability. Hardier materials, and the print can lose an entire paper sheet's worth of mass/thickness, and still be readable.
Those properties sound beneficial in non-obvious corner cases.
In particular those when a sheet of paper’s thickness does not impact the required data density.
While storing data on a wear surface is desirable and necessary to system design.
And when conventional use of a engraved number as index to extended data is insufficient.
> But... is anyone doing that with a 3D printer? Or a CNC machine, for that matter?
Do you count plaques on public landmarks?
> I think some of the other answered showed that people are, it's just pretty niche. Not something a hobbyist can (currently) do, but definitely the same idea at a production scale.
Definitely is doable, having done it myself. You can probably hit your century target using the more specialized FDM/SLA/DLP hobby feedstock, if you can guarantee climate-controlled storage. Millenia if you shell out high double to low triple digits for a print service with fancy industrial machines, or if you combine a home printer with ceramics or metal jewellery skills.
I've experimented with this using one of the commercial print-on-demand services. Not filament, a binder-jet sintering marine stainless steel type of process, IIRC. Slightly modified Noto Sans Extracondensed font with... Let me check the files... 0.1mm line width, 0.45mm lower-case "m" width, dense letter and line spacing, gets 3KB ASCII per square inch. ...Engrave, don't emboss, or the letters will come off with impact and corrosion!
Filling the engraved letters with black wax makes it optically legible under a good handheld magnifying glass. Then rub with vaseline/mineral oil/wax/ACF-50, mount on a brass holder (check relative galvanic corrosion order!), store pressed against aluminium or zinc sheet sacrificial anodes Just In Case(TM), inside polyamide or ABS case. Should last basically forever.
I designed it for manual reading, so the holder doubles as the "reader". Basically just a spindle going through a hole in the disk, holding a margin in the edge and center of the disk. The text is a spiral, so you can spin the disk to help keep the viewed region aligned under a higher-power microscope.
For home printing, probably the way to go is Formlabs wax resin (or equivalent), then either learn brass casting yourself or hire a jeweller to do it. Though you won't get as good resolution/density as the metal process I tried. And really, laser engraving'll probably be cheaper and better. Consider if good-quality paper and ink, maybe laminated, inside a Pelican case'll be more practical.
I wouldn't personally trust any of the common plastic printing materials to hold up for important data under oxygen, UV, fatigue, heat cycles. Are you sure the resin's not overcured or undercured, the filament fused correctly and won't delaminate, it won't reach the glass transition temperature during summer? And bacteria is already evolving to eat plastics. Maybe SLS/MJF polyamide's okay, but in that case, I'm not sure I'd trust the sintered structure for small details (and they don't have great resolution anyway).
> The assumption was that using common 3D printer measurement tools (like for bed-leveling) would provide a way to read back whatever data was encoded onto the surface.
> And then, obviously, if that proof of concept exists, I'd wonder about some kind of advanced version that used specialized equipment for the reading (and possibly the writing/printing).
At these small amounts of data, specialized read hardware just adds risk IMO. Plain text can be read manually or with OCR. QR codes can automate reading with a standard flatbed scanner or smartphone camera.
Consider ideas for encoding: Plain text, B64, hex, Reed-Solomon codes... 1-bit depth structure turns most of 3D printing's storage density into redundancy, but anything truly 3D adds read risk. If you insist on automating reading, QR codes will get you error correction, encode/decode software, and COTS hardware for "free". Personally I think human readability is a big advantage too. Maybe OCR text, and put error codes in a QR beside the text for byte-perfect computer input?
Compare: Memory of Mankind uses ceramic tablets in a desert cave. Arch Mission Foundation project uses holographic glass. Long Now Rosetta Disk engraves with electron beam on nickel, IIRC was/is also commercially available for personallized jewellery. M-Disc and Bluray (HTL?) have modern digital storage density, good stability, work with commodity hardware. ...See design considerations of prior art for digital storage in 2D, naïve 3D version is to just use these as a heightmap:
Also, don't sleep on the centuries of work done by archivists and historians! The top comment is right; acid-free archival paper has very good overall cost, density, stability.
You make great points! I appreciate the detail of the comment, and I don't particularly disagree with any of it. I think someone else mentioned gravestones that are etched and filled with black, so your suggestion of just doing that with sensible scales and fonts seems like a slam dunk, to me.
Bummer that it doesn't really seem feasible for a hobbyist, though. 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?
Overall, I think I've mostly learned that "archiving format" is a broad term that really needs to be collapsed by describing how the archive will be stored (and what extremes/complications to expect). In any case, thanks for the links and again for the detailed discussion!
> 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.
Framed another way: The market rejects the product at the price it would cost to provide, so companies have turned to addictive designs, skeevy tracking, and information asymmetry/user ignorance to recoup their investment.
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.
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