If we live in a 3D world, we say the dimensions are length, width, and height.
We can add Time in there for another dimension.
There is (a lot of) talk that we actually live in a 10+ dimensional world. I've heard tell that the other dimensions are theorized to be crazy shapes that fold in on themselves. ( Calabi-Yau shapes )
Does anyone understand this concept?
And can anyone tell me why, if length and time are dimensions why are ... say... rotation (orientation) or even temperature not considered dimensions?
They can all be measured and quantified.
Rotation is the direction of the dimension to be measured. Temperature is also a variable.
We LIVE in lenght width and depth, 3 D , then with space time we get into time being a dimension relative to our own space but then again time and space are one entity alone. With that our space alters and the dimensions we realize are many.
The most fundamental problem with the higher dimension theories is that they fail to yield spacetime from within their theories. The term 'emergent spacetime' will link into quantum gravity theory, yet they still do not have it. It turns out that by generalizing sign pure arithmetic carries correspondence with spacetime, including unidirectional zero dimensional time [bandtech.com] . The fact is that the three dimensions of ordinary space are observable and so provable within our local extent. That said these 'dimensions' are inherently tied to the real line as fundamental, which polysign makes a break with. The simplex coordinate system as a family of geometries use the ray as fundamental, and in hindsight it is clear that the ray is more fundamental than the line; the line being composed of two rays. Rather than needing six directions to address 3D space(up, down, left, right, forward, backward) P4 needs only four directions(minus, plus, star, sharp).
Physics has offended mathematics and logic in the last century, but humans go on mimicing, with academia enforcing that mimicry. For instance tensor mathematics requires consistency such that the rotations the OP mentions can be carried out universally and still preserve the substance that those arbitrary rotations act upon. Einstein did this on spacetime, claiming it to work out, but where are the discussions of unidirectional time being converted into a bidirectional real line of spatial extent? This is about the simplest rotation possible and it does not work. In hindsight Einstein quickly backs away from the tensor generality to the lightcone projection, which dissolves that 4D state. The simplest vector into this denial of mine is to question whether time is even bidirectional. This then leads into doubt on the isotriopy of spacetime. Portions of relativity may be correct, but that does not mean that there is a next step, for we are engaged in a progression that is not yet done.
Isotropy of space is a fundamental claim within cosmology, yet it is always carefully stated to be on average. This stipulation is ridiculous as we see that anything will turn out isotropic on average. Instead we should consider that spacetime is structured. As elements of spacetime we may not have access to its fundaments. This leaves us guessing and constructing from thin air with correspondence our principal measure. This is where we are at. The problem is open to future superior solutions. The system as I see it deserves to be dissected and parts of it disposed of so that the next generation does not face the vast accumulation that ours has. It used to be in Newtons time a complete library of human knowledge could be contained in a modest building on paper.
How much of modern physics is science fiction? I do not believe that the quantum computer will work out as they predict. If not will there be consequences on the theory of quantum physics? Let's not forget that these are humans; descended from apes; doing this work. We cannot bow nor defer to the greats though they be great apes who are truly impressive. The system must ultimately be left open to future and revolutionary ideas. We have been taught to eat particle/wave duality, yet some youngster who reads this may one day find an answer so far aside from modern theory that carries consistency that he should express it here, and like Shakespeare's monkeys we may eventually land on a convergence that plainly ousts the divergence that is modern physics. PhD's need niches and journals to publish in and so the quantity of PhD's and their system of funding could be directly blamed for the situation we face. Doctor's of Philosophy? Most of them in the physics community tossed philosophy aside roughly a century ago.
Through polysign there may be a semiclassical approach that does yield, for though polysign is general dimensional it still carries support for spacetime, and that said with unidirectional time. The assumption of the real number as fundamental is disproven, and this casts the progeny back in time some four hundred years; to a simper time when the mysteries abounded; and still do.
You Would Have Too Go Into The Realm Of Quantum Theory Too Answer That.Ie Imaginary Numbers, The Box Is Both Full And Empty,Till It's Opened.Physics Is Based On Maths, So You Have Proven Absolutes.Quantum Theory,You Can Make All Short Of Shit Up,And Dare Someone Too Disprove It!
I don't have the answers for this and I have heard all the theories. All I know is that it seems direction is only valid while on a sphere like our earth. The universe (which may have always existed) is traveling and expanding. We are ourselves time traveling but it seems like we can only go forward. We appear to only be able to guess at how big the universe really is.