I complain about the word "dimension" because it has a meaning (darned if I can say what it is -- but that "mens" sure sounds like "measure" to me, which sure sounds like it has "extent"). I would say there are "measures" and "extents" that we know about today that were incomprehensible to those of 500 years ago. The same will be true 500 years from now. Many scientists today consider time itself to be a "dimension". I couldn't begin to tell you "where" time is. :)
I think by your measureless dimension you are headed in the same direction as we are with our non-existent being. But, of course, we're right an you're not, nyah.
OK, OK, I give, I give. A good lawyer knows when he's beat. :)
Of the four dimensions (Up-down, left-right, ahead-behind, before-after)Certainly by Newton's time were considered mathematically. Time is perpendicular to the other three, as are each of them to the others. This can't be visualized but it can sure be worked with mathematically. One of the two books I used to teach myself Celestial Navigation (just in time for computers and satellites to make all that work unnecessary) had a section on air and space navigation. All four-dimensional stuff. (and all definitely an Excedrin headache, believe me. I kind of skimmed those parts.)
Amy good introduction to Relativity (caution, do NOT try to read after the first Bourbon) will help with the presentation of time as a spatial dimension.
Haddon's excellent novel The Curious Incident of the Dog in the Night-Time,
which I cannot recommend strongly enough, not only shows how to tesselate St. George's crosses (knowledge without which my life was incomplete) but also presents a very easy way to understand time as truly spatial.
But once you've eaten of that tree, then the math for "many dimensions" becomes easy enough to understand, though incredibly tedious to do.
I couldn't begin to tell you "where" time is. :)
That-a-way.