The isomorphism *isn't*, in some sense, enough. For instance, the rationals can be philosophically different than the integers. Sure we can identify them via diagonal argument, but when we want a field we don't reach for the integers. I claim that something similar is happening here and that the point of the article is missed when we jump to the isomorphism. Gisin would have just talked about the rationals if he meant the rationals, instead, he invokes Chaitin and computability on purpose. The truncation simplification obfuscates the deeper point. He is making an ontological claim about the universe and one that theoreticians of quantum theory may appreciate but applied mathematicians will not. The subjectivity of an observer is forced on us by classical logic. Here he constructs a physics over a completely different topos and what follows is not needing to make the observer interpretation. This point is significant enough to think about as being *more* than just truncation, it establishes what can be meant by randomness and the possibility that determinacy may be an illusion, even in macroscopic physics.
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