When Biological Tests Are Underdetermined

Karl Popper's central demand remains useful: a scientific claim should expose itself to possible failure. Real experiments complicate that demand because a prediction depends on the hypothesis, auxiliary assumptions, instruments, preprocessing, and a decision rule.

Biology makes those dependencies hard to ignore. A null result may mean the hypothesis is wrong, the effect is absent at the measured scale, the instrument discarded the relevant distinction, or the model linked its variables to the assay incorrectly. Those possibilities create underdetermination. They do not make biology exempt from testing.

The cylinder problem, corrected

Shine light on a cylinder from one direction and its shadow can be circular. From another direction it can be rectangular. The shadows disagree only if “shape” is left undefined.

Once the projection geometry is known, the two observations are compatible and jointly informative. With enough controlled views, one can reconstruct the cylinder. Tomography works for exactly this reason.

The lesson is not that every observer is right. It is that every observation comes through a map. A useful analysis states:

• the source variables under consideration;
• the observation map and its resolution;
• the noise and intervention model;
• the property the test is meant to preserve;
• which source states remain observationally equivalent.

Different maps can support different conclusions. Some maps can also be shown inadequate for the target claim.

Three sources of underdetermination

The paper The Limits of Falsifiability organizes the problem into three levels. The careful versions are narrower than “falsifiability breaks down.”

1. Physical measurement limits

Signals compete with thermal noise, instrument noise, drift, finite sampling, and measurement backaction. A weak effect at one component may still be detectable after spatial or temporal integration. The relevant limit is set by the full detection problem, not by comparing a signal energy with $k_BT\ln 2$.

Landauer's bound is not a universal measurement threshold. It constrains the heat required by a logically irreversible operation such as resetting a physical memory under stated conditions. Detection, amplification, reversible correlation, durable registration, and reset are different operations.

A physical limit matters only after the detector, error probability, integration time, and thermodynamic cycle are specified.

2. Observation and compression

A binary decision carries at most one bit, but a binary test is rarely intended to reconstruct an organism's full microstate. It may estimate one task-relevant parameter or discriminate two models. Comparing that one-bit output with the combinatorial size of every neural microstate does not show that the test discarded 99.7% of the relevant information.

The right question is sufficiency: does the observation preserve the distinction on which the rival predictions differ?

High dimension can make generic reconstruction expensive. Sparsity, symmetry, low-dimensional task structure, causal interventions, and informative priors can reduce the burden. Any impossibility claim needs a source class and an error criterion.

3. Framework and auxiliary assumptions

Experiments depend on choices about variables, endpoints, exclusion rules, preprocessing, and statistical models. Those choices are not outside science. They can be exposed through sensitivity analysis, preregistration, calibration, negative controls, alternative operationalizations, and replication under different interventions.

A framework cannot validate itself by fit alone when a rival framework makes the same predictions. The response is to find an experiment on which the frameworks disagree, or to admit that the available data do not identify between them.

A successful description need not identify the physical mechanism that produced the data. Fit and realization are different questions.

Why controlled physics often looks cleaner

Some physical systems allow unusually precise isolation, symmetry, repeatability, and invariant measurement. Those conditions support sharp predictions. Physics also contains turbulence, strongly coupled many-body systems, climate dynamics, and inverse problems where identifiability and model dependence are severe.

Biology combines multiscale dynamics, historical contingency, adaptation, heterogeneity, and intervention-sensitive measurement. That makes decisive tests difficult, not impossible. It also means that a result from a narrow assay should not be promoted to an ontological statement about the organism.

Bayesian inference does not remove the observation map

Bayesian methods make assumptions explicit through a likelihood and prior. They can represent uncertainty rather than forcing an immediate yes/no decision. They still depend on the variables, model class, observation process, and computational approximation.

High-dimensional posteriors can be difficult to compute, but “Bayesian” is not synonymous with intractable. Structure, conjugacy, factorization, sequential methods, variational approximations, and modern samplers make many problems feasible. Approximation error should be diagnosed rather than treated as proof that inference cannot begin.

The same rule applies across statistical traditions: a posterior or $p$-value only answers the question encoded by the model and data-generating assumptions.

How to make a biological claim lose

A strong biological claim should name a failure condition. A practical checklist is:

1. Define the causal or predictive quantity, not only a broad construct label.
2. State the observation and intervention maps.
3. Identify source states or models that the current assay cannot distinguish.
4. Specify an error tolerance and the range over which the claim applies.
5. Compare rival mechanisms on an intervention where their responses differ.
6. Test robustness to preprocessing, scale, and plausible auxiliary assumptions.
7. Treat unresolved equivalence as underdetermination, not confirmation.

More data from the same lossy channel may not resolve a dispute. A new intervention, timescale, modality, or physical realization might.

Falsifiability is therefore not a binary property bestowed by low dimension. It is a relationship among a claim, a model class, and an experimental repertoire. The aim is to enlarge that repertoire until the alternatives make different predictions, then let the result rule something out.

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This essay is a critical reconstruction of ideas discussed in The Limits of Falsifiability in High-Dimensional Systems, published in BioSystems (2025). It narrows the public claim from “biology cannot be falsified” to protocol-relative underdetermination and explicit test design.