3. The mind existed twice, during the “forward pass”, and during the reversion, since they’re isomorphic computations.
They’re not isomorphic. “Dual” would be a better word, or you could just say that one is a mirror image/inversion of the other.
In which case, the question is: Does a sequence of computations that compose up to a morally-relevant-mind-moment also compose up to a morally-relevant-mind-moment if you compose their inverses?
MR(◯ni=1fi)=⊤?⟹MR(◯1i=nf−1i)=⊤
I don’t have an informed view here, but it is the case that reality doesn’t always treat dual pairs equally. E.g., I recall davidad saying somewhere that he preferred using colimits instead of limits for modeling things (even though limits would also work) because they’re computationally more tractable[1] or something (in the context of world modelling for the Safeguarded AI program).
Which is to say, it’s not immediately obvious that a chain of reversible operations that composes up to a mind-process will also compose up to a mind-process if you invert it.
It would actually be a kind of fun situation if computation that is the inversion of a reversible computation that would normally instantiate a stream of experience, would “undo” those experiences (in the morally relevant sense or whatever other relevant sense).
Which makes sense on first glance because colimits generalize disjoint sums (which add cardinalities: |A⊔B|=|A|+|B|), whereas limits generalize cartesian products (which multiply cardinalities: |A×B|=|A|⋅|B|).
They’re not isomorphic. “Dual” would be a better word, or you could just say that one is a mirror image/inversion of the other.
In which case, the question is: Does a sequence of computations that compose up to a morally-relevant-mind-moment also compose up to a morally-relevant-mind-moment if you compose their inverses?
MR(◯ni=1fi)=⊤?⟹MR(◯1i=nf−1i)=⊤
I don’t have an informed view here, but it is the case that reality doesn’t always treat dual pairs equally. E.g., I recall davidad saying somewhere that he preferred using colimits instead of limits for modeling things (even though limits would also work) because they’re computationally more tractable[1] or something (in the context of world modelling for the Safeguarded AI program).
Which is to say, it’s not immediately obvious that a chain of reversible operations that composes up to a mind-process will also compose up to a mind-process if you invert it.
It would actually be a kind of fun situation if computation that is the inversion of a reversible computation that would normally instantiate a stream of experience, would “undo” those experiences (in the morally relevant sense or whatever other relevant sense).
Which makes sense on first glance because colimits generalize disjoint sums (which add cardinalities: |A⊔B|=|A|+|B|), whereas limits generalize cartesian products (which multiply cardinalities: |A×B|=|A|⋅|B|).