Been There, Done That, Got The T-Shirt...

[Shepherd]

DeputyJones wrote:

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Theory books would likely also be a bust since, by the time Doug leaves, he'll
have a better understanding of their spellcasting paradigm than they do.

...Where did that idea come from?

The fact that, according to the released chapters, the Potterverse wizards haven't come up with a Unified Theory of Magic and don't know how to translate spells between magical systems. In order to teach Dumbledore about dimensional magic, Doug is learning Arithmancy so he can translate knowledge he possesses as a theoretical expert in multiple types of magic into a system of magical notation which Dumbledore can understand. Thus, Doug will potentially end up with a deeper understanding of magic than any native Potterverse caster.
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"Anyone can be a winner if their definition of victory is flexible enough." - The DM of the Rings XXXV