Hacker News Reader

Comment by GoblinSlayer | Hacker News Reader

Instantaneous as in FTL?

An implementation map assigns computational states to physical states. It is instantaneous if its verdict for t is a function of physical state x_tau alone.

You hypothesize that a merger can fail when it's supposed to succeed? But the merger is a part of computation, so if it's required by computation, then it shouldn't fail, otherwise computation is not implemented.

Indistinguishability of merging states: π(x)=π(x’’)=q

Continuation during merge: δ(q,i)=δ(π(x),i)=δ(π(x’’),i)

I hypothesise in an informed manner. Paying for the Λ is what engineers in foundries do for us. This argument specifically is addressed in section 7: The natural objection — a substrate that realises A already has reliable transitions — is a dilemma. If “realises” is structural, such substrates exist and the theorem stands. If “realises” requires persistence, then by Lemma 4 it requires excluding the substrates with Λ < 1 — asserting Λ ≥1, a substrate fact about the relaxation timescale, not part of A and not a function of x_t — and neutrality is lost. The repair is the concession.

If the substrate is unreliable and breaks, then computation isn't implemented after breakage, the computation is still implemented before breakage.

Do I understand it right that you claim that computer programs are nonportable if you assume Λ≥1? But computers have Λ<1, at least it's difficult to imagine something else.

Relaxation time is not a defect (breakage) but an attribute of substrates. A claim that implementation is dependent on reliable substrates, is essentially the trilemma and its conclusion that introduces covariant substrate independence. Implementation requires >= 1. I would not confuse this with computer program portability. Not the subject matter, even if it is a good source of first intuition. I would recommend the sources I reference as very good readings on the subject if you’re interested. Definitely more tested and accepted than mine. Anderson and Piccinini also has a very good introduction and probably the most advanced treatment.

Breakage is broken merger, which doesn't merge, i.e. results in distinguishable states. Correctly implemented merger must produce indistinguishable states. If the substrate tries to implement merger, but fails, then the substrate is broken and doesn't implement computation.

>Implementation requires >= 1.

No, you require computation to work on a broken substrate, and that's an inadequate requirement. It's agreeable that your requirement isn't met and computation can't work on a broken substrate, but this doesn't imply that computation can't work on a working substrate.

We agree in intuition more than it seems you think we do. This paper is mapping the intuition to the philosophical discourse of substrate independence. Track its course from Putnam and Searle to Chalmers Shagrir and Anderson Piccinini, and you will see where it fits as a small contribution. The part we will keep on disagreeing though is calling whatever is inconvenient broken …

Oh, you intended to disprove the supernatural assumption Λ≥1? Is it Chalmers who postulates it?

Reply on news.ycombinator.com