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?