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
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> How come we know there’s only 3 dimensions
A better way to phrase that statement is to say we’ve found no evidence of any dimensions exceeding the three we’re familiar with. Scientists are certainly open to the possibility of more. There are even some theories that predict they might exist. We’ve just haven’t found any experimental evidence they exist. The best phrase is therefore, to date, we have no evidence any spatial dimensions above three exist.
What we know physics is consistent with a universe that only has three dimensions. If any forces were disappearing into higher dimensions, that would reflect in the equations that model how those phenomena propagate. Take light for instance. When we compare the amount of light an object outputs versus what we predict, we find none of it is disappearing into a higher dimension. All of it’s there, and the equation that models the way it spreads perfectly correlates to three dimensions.
There are some theories that predict extra dimensions, but they lack experimental evidence. Right now they only exist on paper. Most of them predict dimensions higher than four! One thing to keep in mind is that higher dimensions aren’t necessarily large and infinite. Some theories predict extra spatial dimensions to be crumpled up into impossibly small spaces. So even if extra spatial dimensions exist, you might be unable to enter a bank vault by shimmying down the fourth dimensional axis.
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