I will be referring to the additional dimension as "4th" (in quotes), because who is there to say which one comes first? - Btw, a hint on titles that are questions, the answer is often "no".
I have a tribe that is completely isolated from the outside world and there is a shaman that can see in 4 dimensions.
This has the implication that there is some form of radiation that works outside of the traditional 3 dimensions. Something that this shaman is able to perceive.
All radiation we know follow the inverse-square law:
Inverse-square law - we find examples of it in gravitation and elecromagnetism.
The fact that we measure that the intensity decreases following the inverse of the square of the distance and not to the inverse of the cube of the distance, suggest that the front of the propagation has two dimension (it is a sphere, in ideal conditions).
If we were measure a radiation that decreases by the inverse of the cube of the distance, we would hypothesize that the radiation is somehow escaping the traditional three dimensions.
Note: with the intensity of this radiation falling much faster than the ones we know... if this is what the shaman sees, everything will be very dark. I will assume the perception will be adapted to that.
Now, if this shaman sees in 4 dimensions, it must be by perceiving some radiation that has that property. Evidently this would something that nobody else perceives or knows how to measure, making it an exclusive trait of the shaman.
This 4th dimension would be purely spatial, he is not able to travel in time. He can only see in 4 dimensions.
I will take this as you saying that the shaman does not control his position on the "4th" dimension. In addition, therefore there is no "4th" dimension travel.
Below is the part where I go technical on you... because, you know, technically correct is the best kind of correct.
The shaman does time travel, like everybody else, tight to the frame of reference of the environment on which the shaman lives... which I would expect marches forward in time...
Also know that we can make space dimension work like time dimensions. As you know, in our everyday lives, we all move inexorably in a single direction in time (to the future, and you cannot go back). Inside a black hole, space moves inexorably in a single direction (to the singularity, and you cannot go back). And you die.
All of that without considering tightly curved dimensions as those proposed in string theory.
I understand that you intend your "4th" dimension to be a flat spatial one. Yet, it is good to consider some alternatives.
What would the extent of this power be? I assume he can see inside people (using the 4th dimension), but is this correct?
There is a problem with looking inside of people. Drawing parallelism with looking inside of the people of flatland, is that you need a vantage point.
You can see - for example - a drawing on the floor which is two dimensional♪, yet that is only possible because you are above the floor. If you were trying to look at the drawing on the floor from the same height of the floor (imagine you are in a hole such that the eyes are just at floor level) then you will not be able to see the drawing.
♪: If we go by fractal dimensions then the number of dimensions depend on the level of detail we take into account. For my purposes, the floor is flat, because I do not care about corrugations for this example. Ok? Ok.
Because of that, being able to see in more dimension does not always translate into looking inside of things of lower dimensions.
Even working around the above, you have another problem... whatever radiation the shaman perceives is one that does not interact with other things. That is, if this radiation only passes through everything, then everything is transparent to it.
One simple tweak would be to say that this fourth dimensional radiation actually interacts with the world in other ways, and there you have your chi / ki / chakra / aura / cosmos / mana / ether that fuels magic. Not everybody needs to be able to perceive it, but everybody would interact with it, intentionally or not.
If you allow this fourth dimensional radiation to have
weak low energy interactions with matter, then perceiving it allows to see everything as translucent, semi-transparent, like x-rays.
Why did you just give the shaman a broader perception of the electromagnetic spectrum? Too cliché? Ok.
There one more problem left. The problem of perspective!
We perceive projections of our 3D environment. Flat 2D images (that we compose to get depth perception). However, when you perceive a 4D environment, how do you distinguish the two additional dimensions? I mean, the image has two dimensions, we figure out an additional one for our 3D environment, but the shaman has to work out another one besides that.
Our two eyes resolve depth by providing two points of view (and a lot of brainwork: identify common features, triangulate, etc...). In a 3D environment a third eye may add some accuracy or expand the field of view... but if you can get a third eye slightly displaced into the "4th" dimension, then you have a solution for the vantage point and the resolution of the "4th" dimension.
The interesting part of a third eye displaced on the "4th" dimension is that it will not be visible to others (unless they also have fourth dimensional perception) and being displaced, it can be in the same 3D position as another body part.
Perhaps it does not look like an eye; it could be more like third ear. In fact, I do not expect regular eyes to function for fourth dimensional perception, but I digress.
The shaman needs to have some connecting tissue that extends on the "4th" dimension. That is, some way the extra eye(s) stay connected to his body and brain. This implies extra dimensional neurons. In fact, given that we need to brain capacity to process fourth dimensional perception, we could be talking of extra dimensional brain extension.
And are there other things he would be able to do that I'm not thinking about?
Not much, actually. This fourth dimensional radiation is less effective than electromagnetism. First, because it follows the inverse-cube law, and second because matter interaction with it is not very energetic.
Yet, for people sensitive to it, some things could be possible: 1) the shaman will be able to recognize others with this power, and 2) they may, to some extent, mess with each other. I guess this leads easily to telepathy, although I imagine it more like a sign language in four dimensions. Yet, if you and your opponent have body parts in extra dimensions, you may hit each other in extra dimensions.
While we are in the concept of four-dimensional battles, they are not one person sitting over here and the other over there, and some extra dimensional fireball flying from one to the other… they are more like boxing, with limbs, which nobody else can see.
Then why not weapons, or armor? If these battles are common, there might be battle gear for them. How to build such gear? I do not know. However the shaman got his powers, that is how.
As for your radiation source, I would propose to use the stars, just have it be an extra form of radiation. One that new to science. Which means that our calculation of the energy of stars is wrong. In addition, there you have a solution for dark matter (whatever is in the star that it turns into fourth dimensional radiation).
I want to expand on nijineko's idea of flipping. If we assume that atoms have fourth dimensional symmetry♪, then the rotation conserves chemical bonds, but not their
handiness chirality. The flipped versions of chemicals are likely to be able to interact with the same or similar chemical receptors but with different effect. It could be as simple as changing taste or smell, or you could convert L-methamphetamine into D-methamphetamine and become a drug lord.
♪: Because otherwise, their rotation on the "4th" dimension means boom. Edit: Not necessarily. Depending on the 4D shape of atoms we can think about what would it mean for an atom to be rotated... yet, I'm assuming all the fundamental forces we know are constraint to 3D, and thus won't hold the atom, thus boom. Take your artistic license on this.
Flipping a living being is a different case. The problem is not the flip, as they stay internally consistent, but that their chemistry needs to work with the environment. Thankfully, oxygen, CO2 and water are symmetric. Glucose is chiral, yet as far as I know we have no problem consuming the two versions of glucose. However, proteins!
The RNA is able to select proteins with the correct chirality. Yet, what used to be the correct chirality for the organism, once flipped, it no longer is. The flipped organism will have to find sources of the flipped versions of the essential proteins to eat.
Sadly I am unware of studies that discriminate concentration of proteins by chirality in food (separating molecules by chirality is hard as it is). Because of that, I cannot tell you what they will need to eat - yet, I do not expect them to be rare, just let them follow their taste and gut.
What really worries me are microbes. Flipping a virus will create a new strand for which the population may not have defenses; the epidemic could be devastating for a small population.