Beyond the 3rd dimension

Because the word dimension was conceived from a brain that evolved it's ability to function directly from the three dimensions that influenced it, there can only be the three tangible dimensions and all other dimensions are beyond "dimension"—that is, beyond threshold, beyond confinement, beyond our perceivable ability to distinguish between. Therefore there are the three familiar dimensions and then the 4th dimension which, for all intents and purposes, is the "other" category. In this "all of the above" category, we can lump in all that may very well be but who knows¹.
I have ambiguous inclinations that mathematicians may be able to conceptualize these other dimensions better than we because they are fluent in a language much more universal than the one we use to describe, say, the color of the sky("It's sky blue, brohem" vs. "It's 0, 127, 255, brohem"). However, as to my roommates aspirations of traveling to far off dimensions, my conclusion remains: You can't get there from here.
I do maintain, though, that these extracurricular dimensions are present and explorable albeit intangibly so. We're soaking in it, but we just can't see, smell, taste, touch, hear, or read its palms. I think that many of the accounts of psychonautical expeditions, such as those of elenakulikova, are examples of heightened perceptions expedited by drugs. Mushrooms, for instance, insight a very visually enhanced experience for many. Alternatively, marijuana enhances, for some, the minds ability to perceive cognitively. I imagine these drugs to be symbolic of the way x-ray technicians use radioactive dyes to illuminate blood flow in a human body. Imagine perceiving a landscape setting, lucidly, through our three dimensions. There's a tree at the end of a field of tall grass waving in the wind. Add the "cognitive dye" of a Psilocybin mushroom and suddenly you become aware of what is not visual in nature but can suddenly be represented visually. Now this landscape is populated by people, but not necessarily people*. The tree feels warm, but not warm*. There is a horsefly that flies in throaty ellipses around a horses tail that wafts, each strand a little melancholy, a little salty—but...not...exactly*. The experiences described are often prefaced as being generally indescribable.
To sum up: extracurricular dimensions are fun yet not real*. Drugs, alternatively, are just fun and real. Do them and meet exciting and super intelligent shades of blue.
¹ emphasis added to stress the idea of knowledge as the brains systematic accumulation and categorization of that which is perceived*.
* emphasis added to stress the idea that perception is limited to what the brain can experience via electrical stimulation of neural receptors on various parts of the body.