Paul Borrill

Paul Borrill

We define \emph{engineered simultaneity}: the construction of a system that requires temporal comparison of events at spacelike-separated locations, implements this comparison via an implicit simultaneity convention, and represents the result as an objective measurement rather than a conventional choice. We show that the National Best Bid and Offer (NBBO) -- the regulatory cornerstone of U.S. equity markets -- is an instance of engineered simultaneity. The NBBO requires determining ``current'' prices across exchanges whose spatial separation places their price events outside each other's light cones. Special relativity proves that the temporal ordering of such events is frame-dependent: there exist inertial reference frames in which the NBBO differs from the value reported by the Securities Information Processor. The impossibility is not approximate; it is exact and unavoidable within the causal structure of Minkowski spacetime. General relativity compounds the impossibility: gravitational time dilation introduces frame-rate discrepancies between exchanges at different altitudes, and recent work on indefinite causal order in quantum information theory undermines the premise of a fixed causal structure altogether. We formalize the special-relativistic argument using the causal precedence relation, connect it to Lamport's theorem on distributed ordering, and note that approximately \$5~billion per year in latency arbitrage profits are extracted from the gap between the NBBO's implicit simultaneity convention and physical reality.

Paul Borrill

Civilization maintains an elaborate infrastructure devoted to the maintenance of synchronized time. Governments mandate daylight saving time. Standards bodies insert leap seconds into Coordinated Universal Time. Engineers debate leap milliseconds and leap nanoseconds. The Global Positioning System applies relativistic corrections at the nanosecond level. All of these adjustments attempt to preserve an assumption: that a single global time exists and that clocks can be made to agree upon it. This paper argues that this assumption constitutes a category mistake in the sense of Ryle (1949). We show that special and general relativity prohibit absolute simultaneity, that the one-way speed of light is conventionally defined rather than measured, and that recent experiments on indefinite causal order demonstrate nature admits correlations with no well-defined temporal sequence. We trace the consequences of this category mistake through distributed computing, where it manifests as the Forward-In-Time-Only (FITO) assumption that underlies Lamport's logical clocks (1978), the impossibility results of Fischer-Lynch-Paterson (1985), and the CAP theorem (2000). From this perspective, daylight saving time and leap seconds are not corrections to time but corrections to conventions -- they sharpen the guillotine of synchronization in preparation for executing something that does not exist.

Paul Borrill

In July 1976, Metcalfe and Boggs published their foundational paper on Ethernet in Communications of the ACM. Their efficiency model -- E = (P/C)/(P/C + W*T) -- measures the fraction of Ether time carrying good forward packets under contention. For fifty years this model has defined how the networking community thinks about Ethernet performance. We argue that the model, while correct for its intended purpose, measures only the forward channel and is silent on the question that matters for modern distributed systems: bilateral transaction efficiency -- the fraction of link time that produces committed agreements between sender and receiver. We show that Metcalfe and Boggs themselves understood this distinction intuitively. Their EFTP "end-dally" protocol (Section 7.2.2 of the original paper) is a three-phase bilateral handshake that attempts to achieve mutual knowledge of transfer completion -- precisely the property that their efficiency model cannot capture. We connect this observation to the Open Atomic Ethernet's bilateral transaction primitive, to the back-to-back Shannon channel formulation with Perfect Information Feedback, and to the Two-State Vector Formalism (TSVF) from physics, which provides the theoretical framework for understanding why both boundary conditions -- sender and receiver -- must be specified for a transaction to have definite value. The correction to Table 1 of Metcalfe and Boggs is not a different set of numbers. It is a different question.

Paul Borrill

The datacenter industry is converging on SmartNIC-based resource management. Wave (Humphries et al., ASPLOS '25) demonstrates the practical feasibility of offloading kernel thread scheduling, memory management, and RPC stacks to the ARM cores of Intel's Mount Evans Infrastructure Processing Unit (IPU). The engineering is careful and the results are honest: without Wave's PCIe latency mitigations, offloaded workloads degrade by 350%. We argue that this 350% degradation is not an engineering problem to be optimized away but a diagnostic symptom of a deeper architectural issue: Wave's communication model is Forward-In-Time-Only (FITO). Every interaction between host and SmartNIC is a unidirectional message -- event forward, decision back -- creating a temporal vulnerability window in which decisions can become stale before they are enforced. Wave's entire optimization stack (write-combining page table entries, prestaging, prefetching, atomic transaction abort) exists to hide or tolerate this window. We apply the FITO diagnostic to Wave's architecture systematically, identify the category mistake it inherits from Lamport's happened-before and Shannon's channel model, and show how Open Atomic Ethernet's bilateral swap primitive -- implemented on the same Intel IPU hardware -- dissolves the latency, atomicity, and timeout problems without engineering around them. The SmartNIC is the right location for resource management; what is missing is the right communication primitive at that location.

Paul Borrill

The Markov approximation is arguably the most ubiquitous tool in physics, underpinning quantum master equations, stochastic processes, and -- via Shannon's channel model and Lamport's logical clocks -- the foundational assumptions of distributed computing. It is widely assumed that Markovianity inherently implies temporal asymmetry: that the Markov property is a forward-in-time-only (FITO) construct. We show that this assumption is a category mistake in the sense of Ryle (1949). Guff, Shastry, and Rocco (2025) have recently demonstrated that the Markov approximation applied to the Caldeira-Leggett model -- a paradigmatic open quantum system -- maintains time-reversal symmetry in the derived equations of motion. The resulting time-symmetric formulations of quantum Brownian motion, Lindblad master equations, and Pauli master equations describe thermalisation that can occur in two opposing temporal directions. Asymmetry arises not from the dynamics but from boundary conditions. We trace how Markovianity's assumed directionality propagated from physics through Shannon's information theory to Lamport's happens-before relation and the impossibility theorems of distributed computing (FLP, CAP, Two Generals). Each step encodes FITO as convention, then treats it as physical law -- the same category mistake repeated across domains. The Surrey result establishes that this conflation is not merely philosophically suspect but mathematically unnecessary: the most fundamental approximation used to derive irreversibility is itself time-symmetric.

Paul Borrill

This supplement documents the intellectual trajectory that led to the Category Mistake framework and the Forward-In-Time-Only (FITO) analysis presented in our recent arXiv papers. The ideas crystallized over fifteen years of research, conversation, and engineering practice -- beginning with a 2014 Stanford EE380 lecture on the physics of time in computing, sharpened through a 2016 email exchange with Leslie Lamport following a Papers We Love presentation of his seminal 1978 paper, and matured through the development of Open Atomic Ethernet (OAE). This document traces the concept development from its origins in the physics of entanglement and background-free time, through the recognition that Lamport's "happened-before" relation embeds a category mistake, to the practical engineering consequences documented in "Why iCloud Fails" and "What Distributed Computing Got Wrong." It is intended as archival supplementary material for future arXiv submission.

Paul Borrill

For fifty years, networking has fragmented whenever new workloads exposed hidden assumptions about time, ordering, failure, and trust. This paper argues that the current interconnect landscape -- NVLink, UALink, Ultra Ethernet, AELink/Aethernet, TTPoE, and classical RDMA -- suffers from a semantic crisis: vendor-specific divergence disguised as optimization. We trace this crisis to the Forward-In-Time-Only (FITO) category mistake embedded in every major fabric stack, and show how each pathology -- aspirational RDMA completion, fire-and-forget GPU semantics, opaque proprietary stacks, incompatible multi-cloud ordering, universal fencing -- arises from the same failure to define explicit, testable link semantics from APIs to bits on the wire. We conjecture that RDMA achieves reliability through universal fencing that collapses concurrency into serialized checkpoints, and that precise minimal semantics can maintain correctness without global barriers, as superscalar architectures separated execution from retirement. We describe how Open Atomic Ethernet (OAE) under the Open Compute Project addresses the crisis through bilateral transaction primitives with explicit ordering, completion, and failure visibility. Drawing on Helland's analysis of scalable OLTP isolation (the "BIG DEAL"), we show the crisis pervades the entire stack. We assess whether convergence on a single open standard is still possible or whether fragmentation is now structural.