Let's move the camera to [0, 0, 4] in world coordinates. This means four units from the origin on the positive z-axis. Remember, at this point, we do not know about a matrix that moves the camera. We only know how to move the world (with the Model-View matrix). If we applied:

mat4.translate(modelViewMatrix, modelViewMatrix, [0, 0, 4]);

In such a case, the world would be translated 4 units on the positive z-axis, and since the camera position has not been changed, it would be located at [0, 0, -4], which is exactly the opposite of what we want.

Now, say that we applied the translation in the opposite direction:

mat4.translate(modelViewMatrix, modelViewMatrix, [0, 0, -4]);

In such a case, the world would be moved 4 units on the negative z-axis and then the camera would be located at [0, 0, 4] in the new world-coordinate system.

In the following section, we will explore translations in both world space and camera space.