The Evolutionistic Faith

In basic multivariable calculus you can manipulate mathematical conSTructs in an arbitrarily large (but, IIRC, not infinite) number of dimensions. Any correspondence between such manipulations and the real world has to be established on a cas-by-case basis. The ability to manipulate constructs in an arbitrarily large number of dimensions proves nothing other than the ability to manipulate constructs in an arbitrarily large number of dimensions.

No, we're saying that because it's mathematics it doesn't necessarily have any relationship to the real world. All mathematics is manipulating symbols by a set of rules. That's all there is. There is no more. (However, there is art and elegance in figuring out how to manipulate the symbols to achieve some desired end configuration of symbols).Sometimes those manipulations produce something that we can correlate with something in the real world. Other times they do not; the manipulations are abstract and have nothing to do with reality.The fact of being able to manipulate mathematical symbols as if they were objects in any number of dimensions does not prove the actual existence of any such dimensions. If you wish to claim the existence of dimensions beyond those we sense, you need actual real-world evidence that is best explained by the existence of such dimensions.There are some pretty strong indications that the existing evidence may best be explained by eleven-dimensional M-theory or something pretty close to it. The indications aren't strong enough yet for anyone to claim that the existence of eleven dimensions is established. The extra dimensions, if they do exist, are wrapped up in a way that's so weird it's probably impossible for humans to visulaize them accurately.