arXiv subjects

Paul Borrill

Publications and source records attributed to Paul Borrill.

24 records · Page 2Linked to original sources

arXiv2026

The Semantic Arrow of Time, Part I: From Eddington to Ethernet

This is the first of five papers comprising The Semantic Arrow of Time. The argument begins with a claim: computing's arrow of time is semantic, not thermodynamic. The direction in which meaning is preserved or destroyed across transactions is not a consequence of the second law but of design choices embedded in protocol architectures since Shannon's 1948 channel model. These choices encode the Forward-In-Time-Only (FITO) assumption -- the commitment that causation is irreversible, acyclic, and globally monotonic. We trace this assumption from Eddington's 1927 coinage of "the arrow of time," through the Boltzmann--Loschmidt debate, to contemporary philosophy of physics: Price's time-symmetric ontology, Smolin's temporal naturalism, Rovelli's relational quantum mechanics, and Roberts's analysis of time-reversal symmetry. We show that fundamental physics is time-symmetric at the microscopic level, that the thermodynamic arrow emerges from boundary conditions rather than fundamental law, and that recent demonstrations of indefinite causal order confirm nature admits correlations with no well-defined temporal ordering. We then identify the category mistake (Ryle, 1949): computing inherited Newton's absolute background time -- via Shannon, Lamport, and the impossibility theorems -- and encoded it as a semantic primitive. The FITO assumption is not a law of nature but a design choice, and recognizing this dissolves apparent constraints that have shaped forty years of distributed systems theory. Subsequent papers develop the constructive alternative through link semantics, RDMA, transaction failures, and the Leibniz Bridge framework.

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arXiv2026

Lamport's Arrow of Time: The Category Mistake in Logical Clocks

Lamport's 1978 paper introduced the happens-before relation and logical clocks, freeing distributed systems from dependence on synchronized physical clocks. This is widely understood as a move away from Newtonian absolute time. We argue that Lamport's formalism retains a deeper and largely unexamined assumption: that causality induces a globally well-defined directed acyclic graph (DAG) over events -- a forward-in-time-only (FITO) structure that functions as an arrow of time embedded at the semantic level. Following Ryle's analysis of category mistakes, we show that this assumption conflates an epistemic construct (the logical ordering of messages) with an ontic claim (that physical causality is globally acyclic and monotonic). We trace this conflation through Shannon's channel model, TLA+, Bell's theorem, and the impossibility results of Fischer-Lynch-Paterson and Brewer's CAP theorem. We then show that special and general relativity permit only local causal structure, and that recent work on indefinite causal order demonstrates that nature admits correlations with no well-defined causal ordering. We propose that mutual information conservation, rather than temporal precedence, provides a more fundamental primitive for distributed consistency.

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arXiv2026

Circumventing the FLP Impossibility Result with Open Atomic Ethernet

The Fischer--Lynch--Paterson (FLP) impossibility result is widely regarded as one of the most fundamental negative results in distributed computing: no deterministic protocol can guarantee consensus in an asynchronous system with even one faulty process. For forty years, the field has treated this as an immovable constraint, designing around it with randomized protocols, failure detectors, and weakened consistency models. This essay argues that FLP is not a law of physics but a theorem about a particular system model -- and that Open Atomic Ethernet (OAE) circumvents it by rejecting the asynchronous model at its foundation. We introduce the term bisynchronous to describe OAE's key property: bounded-time bilateral resolution in which both parties reach common knowledge of outcome at every round boundary -- a strictly stronger guarantee than synchrony alone. By constructing a bisynchronous, swap-based protocol at Layer 2, OAE sidesteps the load-bearing assumptions of FLP's asynchronous model, achieving deterministic atomic coordination without violating any impossibility result.

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arXiv2026

What Distributed Computing Got Wrong: The Category Mistake That Turned Design Choices into Laws of Nature

The foundational impossibility results of distributed computing -- the Fischer-Lynch-Paterson theorem, the Two Generals Problem, the CAP theorem -- are widely understood as discoveries about the physical limits of coordination. This paper argues that they are nothing of the sort. They are consequences of a category mistake: treating Forward-In-Time-Only (FITO) information flow as a law of nature rather than recognizing it as a design choice inherited from Shannon's channel model and Lamport's happened-before relation. We develop this argument in six steps. First, we introduce the category mistake framework from Ryle through Spekkens' ontic/epistemic distinction in quantum foundations. Second, we identify FITO as the hidden axiom that unifies the classical impossibility results. Third, we apply Spekkens' Leibnizian principle to show that FITO-based models contain surplus ontological structure. Fourth, we develop the counterfactual: what changes when FITO is dropped. Fifth, we demonstrate that the impossibility theorems are theorems about FITO systems, not about physics. Sixth, we sketch the transactional alternative -- bilateral interactions that dissolve the apparent impossibilities by replacing unidirectional message passing with atomic bilateral transactions. The implication is that distributed computing has spent fifty years optimizing within the wrong design space.

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arXiv2026

The Category Mistake of Cislunar Time: Why NASA Cannot Synchronize What Doesn't Exist

In April 2024, the White House directed NASA to establish Coordinated Lunar Time (LTC) by December 2026. The programme assumes that a unified time standard can be constructed by deploying atomic clocks on the lunar surface, computing relativistic corrections, and distributing synchronized time via LunaNet. This paper argues that the entire enterprise rests on a category mistake in the sense introduced by Ryle and developed by Spekkens in quantum foundations: it treats "synchronized time" as an ontic entity -- something that exists independently and can be transmitted from authoritative sources to dependent receivers -- when it is in fact an epistemic construct: a model-dependent representation of observer-relative clock relationships. We analyze the cislunar time programme through the lens of Forward-In-Time-Only (FITO) assumptions, Spekkens' Leibnizian operationalism, the Wood-Spekkens fine-tuning argument, and the distinction between ontic and epistemic interpretations that has dissolved long-standing puzzles in quantum mechanics. We show that the same conceptual move that dissolves quantum "mysteries" -- recognizing what is epistemic versus what is ontic -- dissolves the apparent coherence of the cislunar time programme and reveals it as an engineering project built on a philosophical confusion. We sketch a transactional alternative grounded in bilateral atomic interactions rather than unidirectional time distribution.

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arXiv2020

Spacetime-Entangled Networks (I) Relativity and Observability of Stepwise Consensus

Consensus protocols can be an effective tool for synchronizing small amounts of data over small regions. We describe the concept and implementation of entangled links, applied to data transmission, using the framework of Promise Theory as a tool to help bring certainty to distributed consensus. Entanglement describes co-dependent evolution of state. Networks formed by entanglement of agents keep certain promises: they deliver sequential messages, end-to-end, in order, and with atomic confirmation of delivery to both ends of the link. These properties can be used recursively to assure a hierarchy of conditional promises at any scale. This is a useful property where a consensus of state or `common knowledge' is required. We intentionally straddle theory and implementation in this discussion.

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