How do physicists approach dimensions higher than 3rd?

[ElDiplodocus]

I know modern physics theories make use of really high number of spatial dimensions, I wonder how relevant these high dimensions are for physics. I am only a guy from High school interested in physics, but I would like if possible a formal answer

 

[Simon Bridge]

Welcome to PF.
We do it with maths... carefully describing the relationships between the dimensions.
At this stage the thing you need to understand is that each dimension is just a separate thing that can be measured. Its a different axis on a graph... making it a space axis is just a matter of picking the units we record it in... i.e. time becomes space if we multiply by the speed of light.
Something like a 10-speed bike needs a lot of dimensions to describe it... there are 3 dimensions for its position, then there is the angle of the handlebars, that's another dimension... the angle the wheels have rotated through (2 more) and so on.
So there is nothing very mysterious about having more than 3 dimensions.

A dimension is higher than another one or not depending on how we order them... some people count time as the 1st dimension and others as the 4th for example. It doesn't matter.

 

[phinds]

While Simon is completely correct, I think what he is describing is coordinates within the 3 spatial dimensions in which we exist and I interpret your question as being about actual physical dimensions. String Theory posits 9 spatial dimensions (or other numbers depending on which specific theory) but there is currently zero evidence that any such thing exists as anything other than mathematical niceties with no correspondence to reality.

 

[Simon Bridge]

I'm being entirely general about "dimensions".
i.e. a thermodynamic state vector would have three entirely non-spacial dimensions and special properties.
The position 4-vector has 4 space dimensions, but does not follow euclidean rules. Iirc thevstring theory dimensions are also space dimensions... but some have lots of curvature.
We'd usually refer to components rather dimensions.

 

[sophiecentaur]

If we look at Dimensions as variables, then we have no real problem. If we want to relate multi-dimensions to the spatial ones we can see and touch, then we are going to be disappointed; the 'distances' between objects in several dimensions are not going to make direct sense if these extra dimensions are not 'like' our XYZ representation. Maths neatly takes care of the problem but you must trust what it does and accept the resulting answers (a bit of a leap of faith, like with a lot of maths answers).
We accept that a 3D picture can be represented on 2D paper so it should not be too big a step to appreciate how 4D could be represented on a 3D model - which in turn, could be photographed and put on a 2D surface.
http://fathom-the-universe.tumblr.com/post/61285845800/this-is-a-calabi-yau-manifold-it-is-a shows one approach to representing multi-dimensions. Very pretty but it is a different matter to relate it to personal experience of 3D.
PS You have started your PF career with a really hard one!