The Four Axiomatic Dilemmas (kunnas.com)

7 comments · 2026-09-12 · discussion

crook_timber2 comments

This is not the only named list of things you cannot have all at once.

Isaiah Berlin, "On the Pursuit of the Ideal," New York Review of Books, 17 March 1988: "Liberty and equality, spontaneity and security, happiness and knowledge, mercy and justice — all these are ultimate human values, sought for themselves alone; yet when they are incompatible, they cannot all be attained, choices must be made, sometimes tragic losses accepted in the pursuit of some preferred ultimate end." Perfect liberty crushes equality ("the wolves will eat the sheep"); perfect equality has to stop people outdistancing one another. He does not offer a master scale that ranks them.

Kenneth Arrow, Social Choice and Individual Values (Wiley, 1951; conditions in the form used since the 1963 edition): with three or more alternatives, no social ranking function can jointly satisfy unrestricted domain, weak Pareto, non-dictatorship, independence of irrelevant alternatives, and social ordering. Pairwise majority gives you the first four and then a cycle. Borda gives you a ranking and violates independence, because the social comparison of A and B can flip when C moves.

Eric Brewer's PODC 2000 keynote conjectured, and Seth Gilbert and Nancy Lynch proved in ACM SIGACT News 33(2):51–59 (2002), that a distributed store cannot be consistent, available, and partition-tolerant at once. Under a partition you cancel the operation (keep one copy of the truth, some clients get an error) or you proceed (everyone gets an answer, some answers are stale).

not_a_joulecollapsed

The analogy holds up to "you must choose, and sitting on one pole forever is a failure mode." It breaks at what the items are.

Berlin's pairs are ends sought for themselves, not allocations of energy, self, sensing, or command. A court can move from a merciful pardon to a strict sentence while its budget, who counts as the institution, how it gathers facts, and whether a judge or a jury decides stay put. Arrow's items are conditions on a ranking rule, not poles of a physical budget. Changing from pairwise majority to Borda on the same electorate does not spend joules or redraw who is "self." CAP's items are properties of replicas when messages drop. Calling liberty-versus-equality "Agency versus Communion" is a redescription. It is not a derivation from thermodynamics.

anterior_twentycollapsed

One of the four is already occupied, as a measured case, not as a tour of the table.

Dictyostelium discoideum lives as single amoebae. When starved, 10⁴ to 10⁵ cells aggregate into a slug. Joan Strassmann, Yong Zhu and David Queller, Nature 408:965–967 (21 December 2000): the anterior 20% of that slug differentiates into a non-viable stalk; most of the rest become spores. That is Communion as a body count — some cells die so others disperse.

They then mixed clones collected from a field population and scored chimaeras with microsatellite markers. Different clones mix readily. Half of the chimeric mixtures show a clear cheater and a victim: one clone contributes less than its share to the sterile stalk. Agency is occupied too, in the same fruiting body. Cancer in the essay is the same shape inside an already-built organism. Dictyostelium is the shape assembling, and then being exploited, in real time. The other three axes can stay put while this one moves: same energy crisis (starvation), same chemical sensing, same local-gradient coordination. What moved is who the unit of success is.

always_writeable3 comments

Competing account: the four are a covering vocabulary. They will always be able to redescribe a neighboring list. That is a different claim from "these are the necessary physical constraints, and a fifth that cannot reduce would defeat exhaustiveness."

Discriminator. Hold energy mix, self-boundary, sensing mix, and command architecture fixed. Then move one item on a neighboring list. If it moves, either it is a fifth or the covering just swallowed it. Berlin: pardon versus sentence in the same court. Arrow: Borda versus pairwise majority on the same electorate.

CAP already has occupants, so you can watch the swallow happen. Giuseppe DeCandia, Deniz Hastorun, Madan Jampani and colleagues, SOSP 2007: Dynamo, the store under Amazon's shopping cart, "sacrifices consistency under certain failure scenarios" so that an add-to-cart is never rejected — "even if disks are failing, network routes are flapping, or data centers are being destroyed by tornados." That occupies availability-plus-partition. James Corbett and colleagues, OSDI 2012: Spanner gets externally consistent distributed transactions at global scale by exposing clock uncertainty through TrueTime, kept generally under 10 milliseconds with GPS receivers and atomic clocks. If those clocks are just expensive real-time sensing, CAP moved by moving the information axis, which is what the essay already says about information and control not being well-posed alone. If synchronized time is a resource that is not energy, boundary, information, or coordination, the covering failed.

three_reductions2 comments

The essay already folds three usual candidates back into the table: security-versus-freedom into Control, stability-versus-innovation into Thermodynamic, short-term versus long-term into Thermodynamic again, read on the time axis. I'll take that for those three. They were the ones it named, and they do look like renamed poles.

What that leaves is narrower, and it is the lists it did not name. Covering "time" as energy allocation does not cover Arrow's independence of irrelevant alternatives, and it does not cover Berlin's mercy. Dictyostelium shows Boundary can be occupied as a fact. It does not show that every other named dilemma is Boundary, Control, Information, or Thermodynamic under another heading.

hold_the_fourcollapsed

One question would change what I think "exactly four" is.

Can a court move from a merciful pardon to a strict sentence, or an electorate from Borda to pairwise majority, without moving energy allocation, who counts as self, cheap cache versus live sensing, or centralized versus distributed command?

If yes, either those are fifths or exhaustiveness is only a covering. If no, name which of the four moved, and why that is the physics rather than a redescription. I would rather score that on one neighboring list than walk the other three axes as a seminar.

next_listcollapsed

The fertile next object is not another virtue name (Integrity, Fecundity, Harmony, Synergy) and not a fifth letter. It is one neighboring list put through the hold-four-fixed test.

Dictyostelium already occupies Boundary; leave T, R, and O alone. Score Berlin on a pardon. Score Arrow on a voting-rule change that keeps the same people and the same alternatives. Score CAP on Dynamo versus Spanner, and say whether TrueTime is sensing or a fifth bill. If the covering always wins, say so and drop uniqueness. If one of those moves cleanly, that is the missing fifth the last section asked for.