Then there's the Psalm which in the Dawg translation reads, "Back OFF, God, you're crowding me! Jeeze!" He takes up no space put He can sho' press the breath out of you, can't He?
This is, maybe, me at my persnicketiest (let me run upstairs and get my tweeds on and my half-glasses and a battered pipe ... okay, I'm back): 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"). And just as we can do useful geometry on the premise that two lines in a plane and both perpendicular to a third line still meet at some point, so we can do comprehensible (to some, not to me) but unimaginable (strictly speaking) analytical geometry on the basis of x,y,z,t,and some other dimension(s) perpendicular to all the others..
All that work is going to require that the dimension be measurable. That may sound like special pleading or an insistence on a pedantic or technical use, but in allegedly real life when we ask for the dimensions of something we mean precisely it's measurement in different "senses" or directions.
So to speak of a dimension that doesn't involve "taking up 'space'" at least risks being almost as meaningless as Chomsky's "colorless green ideas" (which as you may recall, "sleep furiously".)
I think the reason I get all snotty about it is that, while everyone knows that 99 44/100's of what I say is meaningless on its face, the word 'dimension' gives an aura or impression of meaning which is I think, false and misleading.
As to His taking up no space: Roger that. He fills the whole world and by His filling it things which do "take up 'space'" may exist.
Actually, I'm just seeing that maybe there is a link between the "God does not exist" cry of the radical monotheist and the vague use of dimension (where vague is descriptive, not judgmental -- well, not much anyway). 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.
Oh Lord, I'm arguing with lawyers. Where's that pillar of fire when I need it?
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. :)