Since the cube itself would be an object in the universe it would also have to be represented, showing it representing.....you end with an infinite regression.

There may be an answer here, but I'll get caught out if I try to fake an understanding of it.

@Allan Well, all objects except the cube itself. Thats why the brain can never have a full image of itself.

@Allan if our universe is a simulation, easily done. Cube just contains a reference to the "whole universe" data descriptor :)

@Deschele Schilder what if another civilization also wants a cube like that? Do we need a list of "excluded objects"?

@Alexander They are allowed to have one too. Everyone is allowed. Maybe they are even mass produced.

What good is such a cube? The state of the universe evolves over time so that this cube is out of date one instant after it's created.

"Object" and "represent" and pretty slippery words here. What constitutes one object? A particle? An atom? A molecule? ... take that line of questioning all the way up to a planet? And then what does represent mean? An electron could "represent" an entire star, if I say it does. It might not encode much information, but there lies the question - what information needs to be contained?

@GrumptyYoung It updates every hour. To inform everyone in all galaxies who have almost direct acces. Like this they know whats going on on the other side of the universe. You can update it maybe in real time.

@UndeadFish See it like how your brain can virtually represent all objects in the universe. And thats only small as compared to this cube. An electron does not represent a planet.

Some casual reading suggests that the answer seems to be no. Estimates of the about of bits of information that can fit into a finite volume exist; see physics.stackexchange.com/questions/2281/… and en.wikipedia.org/wiki/Bekenstein_bound . However, the amount of bits needed to represent even small volumes of the universe is "effectively infinite": physics.stackexchange.com/questions/8895/…

@Deschele Schilder "To inform everyone in all galaxies" - so, with a "science-based" tag, we have a little problem of FTL travel here.

@Alexander I wrote in the question that wormholes are used. Its an accepted vacuum solution of Einstein's equations.

@Deschele Schilder so we will need a dense network of wormholes (spaced less than 1 light hour apart), and, likely, a wormhole must be part of cube's design.

@Alexander Indeed. The wormholes are connected from the cube to other cubes scattered over the universe. A kind of neuron netwerk with wormhole dendrites.

How small is an object, is a planet and object, an atom, a quark?

@JonSG All sizes. All that you can imagine. A whole planets insides and outsides can be in it. Subquarks an subleptons. Atoms. Electron clouds. All fish. It can all be there and if asked for generated. Just as, if I ask you, you can envision whole planets, their whole surfaces (just think about them in your mind; your mind can think of virtually all structures in the universe; if you would life forever your memory would encompass the whole universe)

I recall that because black holes seems to effectively "deletes data" and that's impossible because of entropy, all of the data of a black hole is encoded onto its surface. Effectively, that means that a black hole is the most informationally dense "medium" in the universe and that your cube will have to have at minimum the surface area of a black hole with the mass of the universe. A biiiig black hole.

@HenryShao Yes, thats the holographic principle. I dont wanna use that. The max. information would lay on the surface around the cube. The max of info is the number of planck sutfaces in that surface. This is not what I mean though. Maybe temporily this info has that max but the content can change accirding to what is needed. The structure inside selfadjusts.

Your question is tagged "science-based" so you aren't permitted say "I dont wanna use that (science)" . That's the best estimate of maximum possible information density that science has and it still isn't enough.

@GrumpyYoung Thats why I asked. The brain can represent more stuff thsn the stuff its made up of. I mean that kind of structure. Now you might say thats impossible but is it?

No, the brain can't represent more stuff than the stuff it's made of. You'd be hard-pressed even to mentally iterate a fractal. We're very good at conceiving of things, but not of many things. It would be difficult for most people to envision a billion dimes, and they certainly couldn't individually envision the dates on each dime.

@jdunlop Of course it can. If I had eternal life I could phantasize all atoms in the universe.

Yes, but not all at the same time. The apollo moon lander

Only had 32 kilo bytes but landed on the moon. It did that by erasing old data. So it couldn’t remember the beginning of the flight at the end. Same for the cube. Just because you can process the universe doesn’t mean you can remember it all at the same time.