We can’t physically see or understand how complex numbers exist or work in our world in a nice way, but we know they do exist. Because we’ve made massive advancements in science and technology off the assumption that they exist and work, and our understanding of many things in the world including stuff as basic as the solutions to quadratic equations would fall apart. By the same token, there are many problems for which vectors and problem spaces of nth degree are used, where n>3, and there’s that whole adage where time is considered a 4th dimension. In that way, we often solve many problems, even rudimentary linear algebra ones, using sets in R⁴, R⁵, etc, and there are many, many invisible forces at work in our world such as gravity. We know how easily our brain can trick us, we still are easily fooled by optical illusions even when we know they’re there and what they are/how they work, despite our visual cortex being the one of the most powerful and most used part of our brain. So the idea of forces and things which we don’t have the capacity to perceive existing in the world is not anything new or foreign. There are frequencies we can’t hear, colors we can’t see, etc which other animals can and do. So why is the concept of n dimensions in the world so widely rejected? There must be a simple reason, I have heard that it has to do with the volume of a gas in a container being proportionate to its dimensionality or something
In: 2497
There are three things that get confounded: physical _reality_, our _perceptions_, and our _models_ of it.
What we perceive is clearly 3D. Our world behaves in such a way that our brains have evolved to interpret position and velocity as 3D. There are left-right, front-back and up-down, and maybe time. Not more, not less, according to every human. So we can be pretty sure that our perception says we live in three spatial dimensions, not more, not less.
Our models of physics also work quite fine with 3+1 dimensions. We modelled the world based on our perception and found that it can describe a lot of things very well. So we stuck with it, as no other dimensional count so far has done equally good or better. There are a few propositions of there actually being more (or even less) dimensions in string theory and holographic universe, but those are mere suggestions without any verified example where they work better than the 3D theories; they even usually explain how all sane amounts of mass and energy result in exactly 3D behaviour.
The true reality, if that is even a thing, however might be quite different. We could be 2D holograms considering themselves 3D, or shadows of 23-dimensional objects. Quantum physics (just a model again!) already involves infinitely-dimensional things, so that is also an option. Maybe the concept of dimension doesn’t even apply to the actual universe!
However, if the universe at least satisfies some structures we consider “sane”, we could claim that the part we actually interact within, what is called a _submanifold_, might truly be 3 space and 1 time dimension. So there is more, but it is forever impossible to perceive or interact in any way, and the part left to us is truly the size we think. We could never actually verify that, but that doesn’t change that it _might_ be that way.
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