I was referring as new as some orthogonal dimension in the same space. If we're referring to your definition, any slight changes in the parameters results in something new. I was arguing more about if the model knows about axes x and y, then it's output is constrained to a plane unless you add z. But more often than not it's output will be a cylinder (extruded from a circle in the x,y plane) instead of a sphere.
The same thing goes for image generation. Every picture is new, but it's a combination of the pictures it founds. It does not learn about things like perspectives, values, forms, anatomy,... the way an artist does which are the proper dimensions of drawing.
> that humans somehow exceed the Turing computable
Already done by Gödel's incompleteness theorems[0] and the halting problem[1]. Meaning that we can do some stuff that no algorithm can do.
[0]: https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_...