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Experiments, Computability, and the Existence of Physical Functions
Pith reviewed 2026-05-09 20:54 UTC · model grok-4.3
The pith
Reproducible experiments compute definite maps from inputs to outputs once protocols are fixed.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Assuming an explicit physical Church-Turing bridge principle, a reproducible experiment therefore computes a map from admissible inputs to outputs, and the corresponding function exists in the sense appropriate to those outputs. Furthermore, computable analysis allows us to explain why this conclusion is compatible with finite-precision measurement since in this case what matters is a systematic approximation to a requested accuracy, not the production of exact real numbers in a single step. Neither protocol dependence nor stochasticity undermines the existence claim. Rather, they specify which map is realized by a given protocol and what additional assumptions are required for stronger cla
What carries the argument
The explicit physical Church-Turing bridge principle that links fixed laboratory protocols to algorithmic computations of input-output maps.
If this is right
- Once a protocol is fixed, the experiment realizes one definite function from inputs to outputs.
- Finite-precision data are handled as systematic approximations rather than exact values.
- Stochasticity and protocol dependence identify the realized map without removing the function's existence.
- Results from different protocols count as measurements of the same quantity only under extra assumptions.
- The three questions of existence, computability, and cross-protocol equivalence are kept distinct.
Where Pith is reading between the lines
- The same separation of existence from protocol dependence could clarify disputes over whether a given physical constant is a well-defined function.
- Chaotic or quantum systems might still yield computable maps under fixed protocols even when exact trajectories are unpredictable.
- One could test the framework by checking whether a sequence of increasingly precise measurements of the same quantity converges in the sense of computable analysis.
Load-bearing premise
There exists an explicit physical Church-Turing bridge principle that turns fixed laboratory procedures into computations of input-output maps.
What would settle it
A reproducible experimental protocol whose input-output behavior cannot be approximated algorithmically to arbitrary accuracy would falsify the claim.
read the original abstract
Experimental science usually relies on laboratory procedures that, after finitely many steps, terminate with numerical reports on physical quantities. This paper argues that such procedures can be understood as algorithmic once the protocol, background conditions, and reporting rules are fixed. Assuming an explicit physical Church--Turing bridge principle, a reproducible experiment therefore computes a map from admissible inputs to outputs, and the corresponding function exists in the sense appropriate to those outputs. Furthermore, computable analysis allows us to explain why this conclusion is compatible with finite-precision measurement since in this case what matters is a systematic approximation to a requested accuracy, not the production of exact real numbers in a single step. Neither protocol dependence nor stochasticity undermines the existence claim. Rather, they specify which map is realized by a given protocol and what additional assumptions are required for stronger claims about a single protocol-independent quantity. The paper therefore separates three questions that are often conflated: whether the function exists, whether it is computable, and when results obtained under different protocols may be treated as measurements of the same quantity.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims that, once a laboratory protocol, background conditions, and reporting rules are fixed, experimental procedures can be understood as algorithmic. Assuming an explicit physical Church-Turing bridge principle, a reproducible experiment therefore computes a map from admissible inputs to outputs, so the corresponding function exists in the appropriate sense. Computable analysis is invoked to reconcile this with finite-precision measurement (systematic approximation to requested accuracy rather than exact reals). Protocol dependence and stochasticity are argued not to undermine existence but to specify the realized map and the extra assumptions needed for protocol-independent quantities. The paper separates three questions: existence of the function, its computability, and when distinct protocols measure the same quantity.
Significance. If the bridge principle is granted, the manuscript supplies a useful conceptual clarification in the philosophy of physics and computable analysis. It cleanly disentangles existence from computability and from protocol-independence, and correctly notes that finite-precision reporting is compatible with computable approximation. The argument is conditional and does not claim to derive the bridge principle itself; this modesty is a strength. No machine-checked proofs or new empirical predictions are offered, but the separation of the three questions is a clear contribution to ongoing discussions of physical computability.
major comments (1)
- [Abstract and introductory sections] The central existence claim is explicitly conditional on the physical Church-Turing bridge principle (stated in the abstract and presumably elaborated in the opening sections). The manuscript does not supply an independent argument for this principle or examine its empirical status; without it the inference from 'reproducible protocol' to 'computes a map' does not go through. A brief discussion of candidate formulations (e.g., references to Pour-El & Richards or other computable-analysis literature) and of possible counter-examples would make the load-bearing assumption explicit.
minor comments (2)
- Notation for the 'admissible inputs' and 'reporting rules' could be introduced more formally (perhaps a short definitional paragraph) to aid readers unfamiliar with computable analysis.
- The treatment of stochasticity is mentioned but not developed; a short paragraph clarifying whether the map is to a probability distribution or to a deterministic output under fixed randomness would improve clarity.
Simulated Author's Rebuttal
We thank the referee for the careful reading and constructive suggestion. We agree that the central claim is conditional on the physical Church-Turing bridge principle and will add a brief discussion of formulations and counter-examples to make this assumption more explicit.
read point-by-point responses
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Referee: [Abstract and introductory sections] The central existence claim is explicitly conditional on the physical Church-Turing bridge principle (stated in the abstract and presumably elaborated in the opening sections). The manuscript does not supply an independent argument for this principle or examine its empirical status; without it the inference from 'reproducible protocol' to 'computes a map' does not go through. A brief discussion of candidate formulations (e.g., references to Pour-El & Richards or other computable-analysis literature) and of possible counter-examples would make the load-bearing assumption explicit.
Authors: We agree that the existence claim is conditional on the physical Church-Turing bridge principle, which is stated explicitly in the abstract and introduction rather than derived. The paper's contribution lies in exploring the consequences of this assumption for the existence of physical functions and in separating existence, computability, and protocol-independence; it does not attempt to justify the principle itself or assess its empirical status, as that would exceed the manuscript's scope. We will add a concise paragraph in the introduction referencing key formulations in the computable-analysis literature, including Pour-El and Richards, and briefly noting possible counter-examples such as those discussed in connection with hypercomputation. This revision will clarify the assumption without altering the conditional nature of the main argument. revision: yes
Circularity Check
No significant circularity; central claim is conditional on an external assumption
full rationale
The paper's derivation explicitly assumes an external physical Church-Turing bridge principle linking fixed laboratory protocols to computable maps, then concludes that reproducible experiments realize functions whose existence follows in the appropriate sense. It further invokes computable analysis to address finite-precision reporting and separates the questions of existence, computability, and protocol-independence. No equations, definitions, or self-citations within the provided text reduce the conclusion to its inputs by construction, nor does the argument derive the bridge principle itself or rename known results. The structure is self-contained against the stated assumption.
Axiom & Free-Parameter Ledger
axioms (1)
- domain assumption physical Church-Turing bridge principle
Reference graph
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