The reality of dimensions

[Simeon]

It's usually said that the geometry exists for multi-dimensional systems which are not known to qualify any known actual construct or created universe.
However, inn't the concept of 'empty space' itself an abstraction? Space devoid of energy and matter and position can only be visualised via geometry. So is geometry a space-derivative, or is space a geometry-derivative?
If space is no more than a mnemonic for the convenient intellectual assimilation of separate objects - just as time may be a mnemonic for imposing sequential order on events (so that they can be become causes and effects) - then it perhaps has no intrinsic geometry or dimensions, but is an abstract medium upon which any number of dimensions may be imposed.
The notion that (say) 3 dimensions of space are 'real', and any more 'imaginary' is akin to that of numbers not being 'real' if they cannot be applied to the denumeration of anything. As if mathematicians were to discover a numeral, far short of infinity, beyond which - for some unfathomable/unaccountable reason - addition suddenly became impossible. A kind of hole in numbers.
This leads to supposition that it is absurd to postulate a finite number of dimensions exists; though there may be geometries of n-dimensions which have never been 'activated'. That such constructs are imposed upon, and not inherent in, what we call 'space'.
In a universe of infinite spatial dimensions, only the ultimate one has any valid solidity. And there is no ultimate. So all that remains is a network of shadows!
Simeon

[alkaline]

well, if you want to get philisophical, you can say that everything we know is an abstraction, and the knowledge in our head only has correlations with instances of real objects. Thus, matter is abstract, and so is empty space. If you don't want to take it that far, and just say that matter is concrete, i see no reason why you wouldn't consider empty space "concrete" also.

Geometry is an abstraction of the world as we perceive it. Thus it is an attempt to model the real world, and thus it is a derivative of space. But, being the creative and intelligent beings we are, we can create hypothetical geometries that may or may not actually correlate with real spacial systems that do exist.

Even if we use the word space to denote a concept that doesn't have intrinsic dimension doesn't mean that the actual universe also doesn't have intrinsic dimension. Naming things doesn't change reality. In general, the word space refers to three dimensions - i don't know if anyone has created a general word for "space" of n-dimensions.

I don't think there's anything that mandates the existence of an infinite number of dimensions. Numbers are abstract; spatial dimensions are the real world. The real world sometimes has arbitrary limits and doesn't work "perfectly". Just because I jump three times in a row doesn't mean i'm necessarily going to jump a fourth time.

I don't understand your logic behind the claim that if you have infinite spatial dimensions, the "ultimate" one is the only one with valid solidity.