It is also very highly constrained by how _we_ observe the universe. Beings with different sensory/cognitive capacities could develop very different models.
> equivalences between apparently dissimilar modes of presentation
If there was some mathematical equivalence between their models and ours, which is already a leap to assume, there is still a question about whether the specific measure used would be translated to something equivalent to our object length measure in their model, which gets much stronger than just some equivalence assumption. And it’s even stronger to assume that this equivalence could just be inferred without any other information apart from the disk.