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A cross-sectional age association need not equal within-person growth. The following alternatives each suggest a concrete extension of the study.

These explanations are hypotheses to be checked, not established facts about the participants. Neither a small p-value nor an approximately linear scatter plot excludes them.

Place discrete hazards $q_j$ at the ordered distinct event times $t_j$. If $d_j$ events occur among $r_j$ individuals at risk immediately before $t_j$, the nonparametric empirical likelihood isEquivalently, an observed event at $x$ contributes the probability mass at $x$, while a right-censored observation contributes the survivor probability beyond its censoring time. Maximization gives ${\hat{q}}_j=d_j/r_j$ and the Kaplan–Meier estimator

Left truncation means an individual is observed only conditional on surviving beyond an entry time $L$. Ignoring it overrepresents long survivors and creates survivorship bias. A subject with event or censoring time $X>L$ contributes its usual likelihood divided by $S(L)$; in risk-set form, that individual enters each $r_j$ only for event times satisfying $L<t_j\le X$.

Practising scientists can learn how evidence, instruments and disciplinary assumptions acquire authority, provided history is treated as a critical investigation rather than a collection of motivational stories. The useful question is not whether the past supplies a universal recipe for discovery, but which specific habits of reasoning become visible when earlier problems are reconstructed with the evidence their participants actually possessed.

First, history can discipline judgements about evidence. Early critics of Newton's law of universal gravitation faced a genuine distinction between a successful force law and an unexplained physical cause. Reconstructing that distinction discourages equating disagreement with stupidity. Conversely, the quantitative successes of Newtonian mechanics show that scepticism must answer the best available evidence, rather than invoking general uncertainty indefinitely. The transferable lesson is to separate measured regularities, modelling assumptions and causal interpretation.

Second, experiments have histories of reliability. Cathode ray measurements required vacuum control, calibrated fields and competing accounts of what a discharge tube produced. Rutherford scattering required sensitive counting, geometrical control and a statistical interpretation of rare events. These examples make instrument performance and data selection part of the argument rather than invisible background. For current practice this supports explicit calibration, reporting uncertainty, checking alternative explanations and distinguishing a missing event from a detector's failure to register it.

Third, productive models can rest on concepts later replaced. Sadi Carnot's reasoning retained an enduring reversible-engine comparison while using caloric theory. This encourages scientists to identify which conclusions depend on which premises, instead of accepting or rejecting a model as an indivisible whole. It does not mean false assumptions are harmless: their usefulness has to be established for particular questions and tested limits. Likewise an elegant idealization is not automatically a workable machine.

Fourth, the organization of work matters. Shared apparatus, trained technicians, correspondence and laboratory traditions affected which observations became possible and credible. Historical reconstruction can recover contributions obscured by a single-discoverer narrative and reveal why a method that worked in one laboratory failed elsewhere. Scientists can use that awareness to improve documentation, replication and credit without treating social context as a substitute for empirical evaluation.

There are limits. Historical episodes are not controlled experiments on “the scientific method”; selecting only successful cases produces survivorship bias, and later knowledge can make a discovery appear inevitable. Neither a slogan about revolutions nor an analogy with a famous controversy settles a present scientific dispute. Practical lessons need to be modest and specific: track assumptions, preserve evidence, inspect instruments, compare rival explanations fairly and remain alert to unrecorded work. On those terms the history of science offers intellectual tools for better scientific judgement, while leaving present claims answerable to present evidence.

Survivorship bias occurs when analysis conditions on remaining observable or event-free long enough to enter a sample, thereby excluding earlier failures and overrepresenting longer survivors.