3 ms·
My thinking, tangential to the temporal section, is an Implementation Trilemma, a CAP style theorem. An implementation map can be: 1. instantaneous and faithfu
by cgio 2mo ago
My thinking, tangential to the temporal section, is an Implementation Trilemma, a CAP style theorem. An implementation map can be:
1. instantaneous and faithful, at the cost of depending upon substrate-specific persistence parameters;
2. faithful and substrate-neutral, at the cost of requiring historical information;
3. instantaneous and substrate-neutral, at the cost of losing faithfulness.
No implementation map can satisfy all three simultaneously.
https://philarchive.org/rec/GIOTIT https://philarchive.org/rec/GIOTIT
- elendilm 2mo agoTo anyone who has ever built, designed or debugged physical hardware, the paper's "groundbreaking conclusion" is a mundane reality of physics that a state isn't practically a state unless it lasts long enough to be read.
- cgio 2mo agoExactly the intent of it! Does not claim inventing any physics, just relating it to implementation in philosophy. The graded theory is a bit more advanced on the physics front but not ready yet.
- elendilm 2mo agoCurious about your paper (assuming you are the author). Clarify if I misunderstood. Doesn't introducing separate time slices automatically forces you into a continuum of time and therefore the "Instantaneous" requirement "I" become meaningless. One can't evaluate physical state transitions without continuous time or atleast some form of mathematical ordering. But if you strip away continuous time and keep only the abstract "ordering", you are again back in the world of pure mathematics where states never decay and memory never fades.
- cgio 2mo agoI wouldn’t call an instant as meaningless in a continuum. It is indeed, though, non primitive and idealised as traditionally in physics (the physical state at time t, given as the limit of arbitrarily fine time resolution). If I understand your question correctly, the interesting issue is not whether instants exist as an idealisation, but how independent observations can be synchronised well enough to assess a physical implementation of an abstract mapping. That is a genuinely difficult problem, and one that appears even if time is discrete. It is one of my current work subjects. Anyone who has worked on distributed systems will recognise that ordering events is one thing, establishing a common notion of “now” is another. Once again, no “grand conclusions“ from me!
- GoblinSlayer 2mo agoInstantaneous as in FTL?
- cgio 2mo agoAn 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.
- GoblinSlayer 2mo agoYou 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)
- cgio 2mo agoI 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.
- GoblinSlayer 2mo agoIf 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.
- 2mo ago