Could three-dimensional beings engineer a multi-dimensional structure?

Question

Consider the bigger-on-the-inside concept of sci-fi staples like the TARDIS from Doctor Who. A generally accepted explanation for how a space’s interior could be larger than its exterior shape and “container”, without having a wormhole door or other sort of separate interior merely connected to the exterior structure, is that the whole structure itself is like a tesseract—it’s composed of more spatial dimensions than just our three, and we only perceive one particular part projecting into our 3D world.

If I want a society to have developed the technology to create structures, buildings, etc using this “bigger on the inside” concept, could it be done by beings that are still just three-dimensional creatures from a three-dimensional world like us, given that they have advanced enough mathematics and computer or physics tech to do it? (Perhaps artificial/computer intelligence is the secret to this; lines of programming and digital mathematics don’t necessarily have to have their understanding of reality contained to a 3D world—the question then is just if 3D beings could make something that can think beyond their own spatial dimensions.)

If my alien race isn’t a bunch of multidimensional beings beyond what we can envision, they’re just evolved creatures with a 3D structure (or at least, a 3D perception of the world) akin to our own, could they still—through trial and error with advanced studies of physics, computer science, math, and engineering—eventually figure out how to build something bigger on the inside using that manipulation of space beyond just three dimensions? Or is it just too inconceivable to a race of 3D beings for them to be likely to ever build it on their own?

Answer 1

That depends on how physics works in your story world. Is there some physical effect accessible to us 3D creatures that can give us access to higher-dimensional spaces? Then yes. Otherwise, no. Right now, even within the structure of, for example, brane theory, which explicitly hypothesizes the additional macroscopic dimensions, there is no known physical operation we could perform within our own brane that would give us access to them.

But assuming the basic physics problems are solved, making higher dimensions accessible to engineering, we could definitely design structures to take advantage of them. We have already done so in video games and simulations.

Answer 2

You can surely create a setting where bigger from inside might work. The various string theories dictate that there are many hyper-dimensions beyond the familiar (3+1) space-time. But let us restrict our focus to just M-theory which is the superior of all. It tells that there are total 11 dimensions meaning 7 extra than usual (3+1) space-time. In other words, there are 10 space dimensions and just 1 time dimension.

To quote Wikipedia

there exist scenarios in which there could actually be more than four dimensions of spacetime which have nonetheless managed to escape detection.

It is also implied that these dimensions are highly curled up among themselves at such a small scale that we wouldn't observe them in usual 3-D space. This means that there could be a kind of extra volume if those curled up dimensions are considered.

But note that this hyper-volume (volume of hyper-dimensional space) might not be utilised in the same way 3-D volume is. The hyper-dimensional volume might pack up some yet unknown sort of energy that can be used if you build the appropriate technology. Once you figure out how that hyper-volume energy can be converted into useful work by the concerned technology, a 3 dimensional organism would have learnt to utilize and manipulate the higher dimensional volume and it's content to it's will.

Answer 3

If your story creates such a capability like Dr. Who did, then the answer is yes.

Relying on physics however, the answer is unanswerable. What the question seems to ask is if we have 4 dimensions a,b,c, and d; can I borrow space from dimension "d" to expand stuff in dimensions "a, b, and c."? Well, do the math with the three we have. You have a dining room table with a 2-dimensional surface. Assume it can fit 20 pieces of paper on it. Can you borrow the space 2 inches above it to make more space in those two dimensions? Only by physically relocating that space down to the table surface. But that removes the extra space from its own higher dimension, right? You didn't "create" any more space on the table surface, and the same 20 pieces of paper can fit on it. But now 20 more can fit to the left of it. But wait, what used to be to the left of the table? Oh, that is a wall that we have to remove.

So if physics is involved, the the laws of conservation are involved.

You can't get free space from anywhere without removing it from somewhere else. You're asking for physics to give you a free lunch, and there is no free lunch within the almighty equality sign that governs our natural world.

If you are OK with occupying another dimension, then you have to explain that you are somehow folding space-time. For example, you can put 40 pieces of paper on your dining room table if you folded them all in half. Now, half of each paper is beyond the table surface, one page thickness above it, but still connected to the half below it through the molecular bonds of the paper cellulose.

But, as you can imagine, folding paper makes it difficult to read or use practically in our world. To be utilized, it has to be unfolded. This is the obstacle your world has to overcome. How do you "fold" a 3D human into extra dimension without breaking it? How can blood still move through its veins, and air through its lungs, and accomplish all such things which rely on the proximity of one thing to another? This is the part your story has to fill in. The invention allows seamless transportation of mass between the dimensional spaces at the sub-atomic level, preserving all energies and forces which define objects. Just as a folded paper "appears" to be half the original size when observed from the table surface, folded objects in extra-dimensional space will appear to only be a fraction of their true volume in 3D space.

Because a paper can enter multiple 2D spaces by being folded, a 3D object can enter extra dimensional space by being likewise folded. Your story is left to explain why the results are not horrifying.