As an artist
If you’re an artist, why does any of this matter to you at all? Your tool pipeline should be handling all of this for you; you shouldn’t be working with tangent space at all. If you’re being told to deal with tangent space vs. object space, then your tools are terrible and you should get new ones.
I would argue that non-visualisable abstract space is problematic because the visual imagination cannot go there and posit how things might be if the light were a different shade, if it struck the surface at a different angle or with more specularity.
Except that two people have explained that tangent space is not a “non-visualisable abstract space.” Your own unfamiliarity with this space does not make it “non-visualisable.” Or to put it simply, there is nothing abstract about tangent space.
Also, lights don’t have “specularity”. Surfaces determine how much light they reflect, not lights.
And I can see no reason why such a map should not be applicable to different models because the offsets are always offset from the top of the model’s normals.
Which is not surprising, since by your own admission, you don’t understand the mathematics behind tangent space.
“Up” in object-space has a specific direction. And it is always the same direction for each point on the model. If you have an object-space offset that moves a normal “up”, then it is moving the normal upwards in object-space.
Let’s take a sphere with some kind of object-space bump map applied to it. Now, the left-most point has a normal, and the value from the object-space map biases that normal “up”. This up direction is in object-space.
Now, let’s rotate this texture around. Not the sphere itself; the object-space transform doesn’t change. Just the texture coordinates. We will leave the value of the texture coordinate at the point of interest alone, but we’re rotating the normal map by 180 degrees.
Because this point’s texture coordinate didn’t change, the normal it gets will still be pointed “upward”. But we rotated the texture coordinates around.
Remember: a normal map is just a simulation of a bump map (a height field). If we rotate a height-field around 180 degrees, those bumps that were pointed up before are now pointed down.
This didn’t happen with the normals; the normals no longer follow the bumps properly. Object space normals do not take into account the direction of the texture coordinate mapping. Therefore, object space normals are dependent on the texture coordinate mapping; if you change the texture coordinate mapping, you must modify the normals you get based on that.
The technique used to modify the normals based on the texture coordinate orientation relative to object-space is called… tangent space normal mapping. You store the offsets in tangent space. And you provide every point on the surface with a transformation matrix from object space to tangent space.
Time, as a fourth dimension is very visualisable… I can visualise how long it will take to get from a to b if I know a and b well, I can visualise how I could hit a tennis ball that came off a server’s racket.
Fair enough. So how do you visualized curved fourth-dimensional space-time (aka: gravity)? Or time dilation? You can make 2D or 3D approximations, but those are exactly that: approximations.