I think the maths describe alternate dimensions of reality in the same way that gravitational theories describe the reality of gravity we experience here & now. The perception would be a direct experiencing, and the maths would be the description of it.
"This dimensions physics and laws would be different from ours so that no bleed into each others reality could corrupt the other, so it's more than dimensions, its alternative realities".
I think of our dimension as being nested within higher dimensions, rather than separate. Like Russian dolls. We can glimpse higher dimensions when our frequency is high enough. Say the ego is a certain freqeuncy. As the ego is transcended, we begin to perceive more of what was there all along. But it's all still part of the one universe.
There's hundreds of different radio waves floating around each of us right now. We can't perceive them until we're tuned in to a certain frequency - but they're still there. Sometimes there's 'bleed through' when your dial is sitting between 2 stations. I think that's a good analogy becauise encounters with interdimensional beings are often accompanied by 'high strangeness'. Things such as missing time, for example. Time is created by the egoic frequency, so it makes sense to me that it would go missing until the ego frequency comes back on line.
Actual physical craft - so called 'nuts and bolts' - are unlikely to be from other dimensions because of the factors you mention. They are more likely to be advanced US tech. However, interdimensional orbs may have the ability to appear physical even if they're not. Our visual system makes lots of guesses and will fill in the blanks when something doesn't fit expectations.
