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Virtual space and beings living in it are a staple of science fiction. Usually, these are either artificial, i.e. artilects, or were once human, i.e. uploaded minds. Fictional examples of such beings living in virtual environments are among many others in the extended Revelation Space Universe by Alistair Reynolds, The Corporation Wars by Ken McLeod, or the Bobiverse by Denis E. Tayler. Usually, these "Virtuals" and their environments remain fairly similar to the baseline universe.

I was wondering, however, if there is any fundamental reason why one would have to simulate the virtual environment so realistically, i.e. with 3 spatial and one temporal dimension. Could one modify or create a mind so that it can cope with for example 4 spatial dimensions and let it live in such an environment?

I think that this might be very interesting, as it would allow the exploration of more dimensional space by beings that can actually intuitively exist in it and not just comprehend it. This might be quite useful for data visualization. I'm not sure how exactly this could be used, but I believe that visualizing the complex parts functions or depicting the past states of a three-dimensional system over time might be an option if I understand it correctly. What one might do with even more dimensions is anyone's guess.

So is there any fundamental reason why such a being couldn't be created? And are my ideas about what it could do right, wrong or did I miss more interesting applications?

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    $\begingroup$ I don't see why not. As a programmer, I deal with multi-dimensional data quite often. Sure, that's nota virtual environment, but am capable of producing code that interprets and manipulates datasets in more than 3 dimensions. That's not even an AI or anything resembling intelligence. An actual entity can easily work in terms of any number of dimensions. $\endgroup$
    – VLAZ
    Jan 21, 2021 at 18:11
  • $\begingroup$ Spatial dimensions can be of any number. Temporal dimensions though are constrained by the universe in which the simulator itself runs, at least if you care about the runtime within that universe. $\endgroup$
    – John O
    Jan 21, 2021 at 20:03

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It is surely possible, we have programs which can handle more than 4 dimension in the same time, however you might need to limit somehow the details of the simulation. Why?

According to this wikipedia page on the anthropic principle

enter image description here

a spacetime with more than 3 spatial dimensions is unstable.

I think therefore that you can simulate it as long as you skip the implementation of some of the basic laws which would exploit that instability (which are they it's beyond me). Basically, to simulate a 5 dimensional spacetime you have to not let it be a complete spacetime.

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Computational complexity.

Using naïve spatial-grid simulation, with increasing number of dimensions the number of "cells" grows exponentially (this is a real problem in simulating physical systems with a multidimensional Hilbert space sample).

Consider a very primitive "Full HD window" of 4000 pixel long side - in two dimensions, you have to simulate 16 million pixels. In three dimensions, 64 (short scale) billion. In four dimensions, 256 (short scale) trillion, etc.

In fact, you might get along with decreasing the number of dimensions by one - we are mostly two dimensional creatures, our senses are more or less one dimensional, with the exception of vision, which is basically a two dimensional image projected on our retina (times two). This is kind of similar to the holographic principle.

Also, the compulsory reading is mathematically rather sound and well researched Greg Egan's Diaspora - much of the action takes place in (a) 5+1 dimensional universe(s), including simulation of 5+1 universe within our 3+1, and 3+1 within 5+1, and the Wang's Carpets chapter goes even much further.

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There you go.

Miegakure

Unfortunately...

The game is currently in development and the goal is to release it in downloadable form for Windows/Mac/Linux. It will be available on Steam and Playstation 4. There is no announced date yet.

And has been so for years.

But, to reply your question, yes you can clearly imagine AI characters interacting in this world. With themselves and possibly occasional visitors from 3D space.

With the inevitable XKCD enter image description here

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