Red Trees

A forest contains only blue trees. Someone plants red trees among them, then removes the records of the planting. Ten years later, the red trees look established. A visitor reasonably assumes that both kinds have always grown there.

Future researchers work hard. They measure the trees and compare their distribution. Their measurements can be accurate and their reasoning competent. Yet their explanations of the forest’s history begin from evidence that someone altered before they arrived.

The damage extends beyond the original deception. A planted tree becomes evidence for a history that never happened. That history supplies premises for further questions. Research accumulates around the insertion until distinguishing the inherited error from the later discoveries becomes expensive.

Knowledge can develop this way. But the forest needs one amendment: most errors arrive without a planter. Some grow from faulty instruments. Others come from true observations assembled into an unrepresentative picture. A useful prediction can support a mistaken explanation. A correction can remove one error while discrediting work that did not depend on it.

The question is which conclusions depend on the planted trees, and how that dependence can be discovered. Counting trees will not answer it.

The parable grants its narrator a complete view of the original forest. A researcher inside it has no such privilege. Even after discovering the planting, reconstructing the earlier state requires surviving records or some independent way to date the trees. Exposing a deception can therefore replace a confident answer with an unresolved question. That is an improvement in knowledge, although it leaves less of a story to tell.

Can one falsehood contaminate everything?

Consider a historian who accepts a forged letter. The letter places a meeting in a particular city. That meeting becomes evidence for an alliance, which then explains a later decision. Exposing the letter damages this chain. It need not damage a tax register independently establishing the city’s population.

The distinction is dependence. A false premise can undermine conclusions that require it. Mere association with the same subject is weaker. Two claims can concern the same ruler without sharing evidence. Conversely, papers written in different countries can depend on the same defective measurement.

Quine’s web of belief gives this problem a philosophical form. An observation usually tests several beliefs together, including assumptions about the instrument and the conditions of observation. When prediction fails, the result does not specify which belief to discard. The network creates room for different revisions. It does not establish that every local error infects every other belief. Stanford Encyclopedia of Philosophy, “Underdetermination of Scientific Theory.”

Suppose a thermometer reports an impossible temperature. The room may have changed, the thermometer may be defective, or an assumption about the measurement may be wrong. Confidence in the surrounding evidence determines where suspicion falls. This is often sensible. Throwing out a well-tested physical theory whenever a cheap sensor fails would make learning impossible.

Jon Dorling illustrated this asymmetry in a Bayesian example: a failed prediction could barely reduce confidence in the central theory because uncertainty elsewhere absorbed the failure. Michael Strevens later challenged the standard Bayesian treatment and proposed a different solution. Dorling, 1979; Strevens, 2001.

This leaves a practical vulnerability. A belief can survive many failed predictions if each failure has a plausible local explanation. Persistence becomes dangerous when nobody tests the assumption shared by those explanations. The evidence needed is a test that changes which parts of the system are being taken for granted.

How does one result become a hundred witnesses?

Ten people who independently watched an event provide different evidence from ten people repeating the same account. A bibliography can conceal that difference.

Steven Greenberg reconstructed a network of 242 papers and 675 citation links around a claim about beta-amyloid and muscle damage in inclusion body myositis. Supporting publications attracted attention while weakening evidence was neglected. Later texts converted hypotheses into statements of fact. Some papers amplified the belief without adding data that tested it. The citation network created authority beyond what the underlying observations justified. Greenberg, 2009.

A reader entering near the end encounters an established proposition with a substantial bibliography. Following one reference leads to a review, which leads to another paper that also assumes the proposition. The references are real. The apparent number of independent reasons is inflated.

Mikhail Simkin and Vwani Roychowdhury approached citation copying through an unusually useful trace: repeated misprints. Independently typed references should not repeatedly acquire the same rare error. Their model estimated that only about 20% of citers had read the original. That number is an inference from assumptions about copying, not a direct observation of reading. A person can copy a reference after reading its paper. Simkin and Roychowdhury, 2003.

A more circular route is citogenesis. An unsupported statement appears on Wikipedia. A writer repeats it in a publication. That publication then becomes a citation supporting the original statement. Randall Munroe named the mechanism in an xkcd comic. Its defining feature is the return journey: the apparent corroboration descends from the claim it supposedly confirms. “Citogenesis.”

Laurent Bossavit traced comparable transformations in software folklore. Gwern’s “Leprechaun Hunting & Citogenesis” collects academic examples and research on unchecked references. Both make source tracing central to the problem. The additional question is what happens after the original source has been found. It may be accurately quoted and still rest on a faulty instrument, a selected sample, or an untested explanation. Bossavit, The Leprechauns of Software Engineering; Gwern, “Leprechaun Hunting & Citogenesis.”

A provenance trail establishes where a claim came from. Evaluating the claim also requires examining how its evidence was produced.

What baited the astronomers?

The obvious explanation for geocentrism is that people trusted appearances. The sky moves overhead while the ground feels stationary. There is something correct in that account, but it leaves out the strongest part of the historical problem: alternative models had to explain the same observations and satisfy the available physics.

Ptolemaic astronomy supplied a mathematical account of planetary positions. Copernicus changed the arrangement, but retained the demand for uniform circular motion and much circular machinery. The transition involved competing calculations and physical explanations. The familiar claim that geocentrism lasted 2,200 years combines ancient philosophy, changing mathematical models, and later institutional restrictions into one duration. It should not imply an unchanged model or uninterrupted agreement. Stanford Encyclopedia of Philosophy, “Nicolaus Copernicus.”

Epicycles also deserve a less contemptuous reputation. Combining circular motions can represent complicated periodic movement. There is a mathematical connection to Fourier representations, which decompose motion into periodic components. That connection explains how circles can fit observed paths without their geometry identifying the physical cause. Giovanni Gallavotti, “Quasi periodic motions from Hipparchus to Kolmogorov.”

There was also a serious third option. In Tycho Brahe’s system, the planets circled the Sun while the Sun circled a stationary Earth. Telescopic evidence that defeated the traditional Ptolemaic arrangement, including the phases of Venus, could remain compatible with a Tychonic arrangement. Showing that Venus circled the Sun did not by itself demonstrate that Earth did too. Cambridge’s General History of Astronomy, volume 2A.

Stellar parallax raised a harder problem. If Earth travels around the Sun, nearby stars should shift in apparent position against more distant ones over the year. Astronomers could not detect that shift. Copernican astronomy could accommodate its absence by placing the stars enormously far away. But distance interacted with another observation.

Early telescopes showed stars as small disks. Astronomers measured those disks as though they were the visible bodies of stars. Put an object with an appreciable apparent diameter at a vast distance and its inferred physical size becomes enormous. Christopher Graney’s analysis of Riccioli’s 1651 measurements shows why the combination supplied evidence against Copernicus: the implied stars dwarfed the Sun and even Earth’s orbit. Graney, “Riccioli Measures the Stars,” 2010.

The disks were optical artifacts caused by diffraction. The telescope was producing an image whose diameter was not the star’s physical diameter. This was not obvious from careful measurement of the image. Repeating the observation could reproduce the misleading appearance. The later account of stellar images required a better understanding of optics. Graney and Grayson, “On the telescopic disks of stars.”

Graney’s broader historical work shows that scientific objections to Copernicus remained substantial well into the seventeenth century. That finding explains resistance; it does not turn every objection into a good one or justify coercion. Particular observations, interpreted through mistaken but reasonable assumptions, made Tycho difficult to dismiss. Setting Aside All Authority, 2015.

The hypothesis that astronomers confused relative appearance with absolute reality identifies part of the problem. It cannot be the whole explanation. Galileo explicitly reasoned about shared motion using a ship: objects aboard can behave normally while the vessel moves. Astronomers were capable of asking whether apparent celestial motion came from the observer. Stanford Encyclopedia of Philosophy, “Galileo Galilei.”

Changing viewpoint also does not supply a view from nowhere. An Earth-centered coordinate system remains usable. The physical claim that Earth is stationary requires evidence beyond the convenience of those coordinates. The historical difficulty was deciding which motions and physical assumptions explained the observations, with instruments that introduced errors their users could not yet recognize.

Can the story of an error become another error?

A familiar account says that the Church killed people for discovering that Earth circles the Sun. It often places Galileo and Giordano Bruno in the same category. The distinction between their cases is necessary to understand what happened.

Galileo was condemned in 1633 and lived under house arrest. He was not executed. His punishment was coercive, and the existence of scientific objections does not excuse it.His own arguments were also fallible: his proposed proof from the tides was wrong. Getting the main astronomical question right did not make every argument he offered correct. Stanford Encyclopedia of Philosophy, “Galileo Galilei.”

Bruno was burned in 1600 following heresy proceedings. His cosmology belonged to a wider philosophical and theological system. Treating the execution as punishment for one astronomical proposition misdescribes that system and the proceedings. Claiming astronomy had nothing to do with the case would go too far in the other direction.The final list of eight condemned propositions is lost, which limits precise reconstructions of the sentence. Stanford Encyclopedia of Philosophy, “Giordano Bruno.”

Another familiar story says medieval Europeans generally believed Earth was flat until Columbus proved otherwise. Jeffrey Burton Russell traced the modern spread of this misconception through nineteenth-century writers, including Washington Irving. The belief supplies a satisfying account of intelligence defeating inherited stupidity. Its appeal helps obscure the historical evidence against it. Russell, Inventing the Flat Earth, 1991.

The larger idea of a permanent war between science and religion also compresses different institutions and disputes into one plot. The scholarly essays collected by Ronald Numbers examine specific myths that sustain that account. Individual conflicts remain real; a universal storyline is a further historical claim requiring its own evidence. Galileo Goes to Jail and Other Myths about Science and Religion, 2009.

A story about how people once became deceived can therefore reproduce the process it condemns. It selects memorable examples, discards awkward distinctions, and gives the reader an explanation that travels well. Correcting it requires giving up some of the satisfaction of being on the enlightened side.

Can accurate evidence produce a false picture?

Imagine a shelf containing every experiment conducted on a treatment. Half its reports are favorable. Now imagine a second shelf stocked mainly with the favorable reports. A careful reader can accurately summarize the second shelf and reach a distorted conclusion.

Erick Turner and colleagues compared published antidepressant trials with FDA records. Their sample covered 74 studies of 12 drugs. The published literature appeared 94% positive, while the FDA assessment classified 51% as positive. Missing studies and favorable presentation changed the apparent evidence. The comparison did not show that all the drugs were ineffective. It showed that the literature available to readers overstated how consistently the trials supported them. Turner et al., 2008.

This resembles the forest with some trees removed. Nothing requires each surviving report to be fabricated. A distortion in which results survive can change the meaning of the collection. Looking harder at the surviving trees will not recover the absent ones.

Selection can also be strategic. James Weatherall, Cailin O’Connor, and Justin Bruner modeled a propagandist who selectively shares findings with policymakers. The audience can update consistently on the evidence it receives and still develop mistaken beliefs. The propagandist need not falsify every experiment; favorable outcomes occur in imperfect research and can be disproportionately circulated. The model demonstrates a mechanism under specified assumptions, not its prevalence in all scientific disputes. “How to Beat Science and Influence People,” 2020.

Holman and Bruner modeled another route: a participant whose bias persists while other members learn from evidence. In their setup, such an agent could prevent convergence to the truth. This qualifies the hope that adding connections and exchanging more information must improve a community’s beliefs. What enters the network, and how participants respond, matters. “The Problem of Intransigently Biased Agents,” 2015.

The defense requires evidence about selection. Trial registrations and administrative records can reveal studies absent from journals. Funding disclosures identify relationships that deserve examination. Neither substitutes for checking the results, but both expose parts of the process that a published bibliography can hide.

What does deliberate planting look like?

Some red trees were planted deliberately, and their histories can be established without treating suspicion as evidence.

The Donation of Constantine purported to record an ancient imperial grant supporting papal authority. Lorenzo Valla’s 1440 attack examined whether its language and historical details belonged to the period it claimed. A document that had supplied authority became an object of investigation. Its status as an old, repeatedly invoked text could not settle its authenticity. Valla, Discourse on the Forgery of the Alleged Donation of Constantine; Matzukis, “The Donation of Constantine: History and Forgery.”

Exposure changes the document’s evidential role. It ceases to establish an ancient grant. It remains evidence that somebody later wanted such a grant to exist. The same artifact can be false evidence for one proposition and useful evidence for another.

Piltdown Man supplied a physical insertion. Announced in 1912, the supposed early human combined human cranial material with an orangutan jaw and altered teeth. The forgery was exposed in 1953. Genetic and morphological work published in 2016 found consistent materials and methods across specimens, supporting a single-forger explanation. A manufactured specimen had entered the collection against which ideas about human origins were assessed. De Groote et al., 2016.

The sugar industry case shows a less tangible intervention. Cristin Kearns, Laura Schmidt, and Stanton Glantz examined internal documents concerning a review published in 1967. The Sugar Research Foundation funded the work, shaped its objective, supplied material, and received drafts. The review downplayed evidence implicating sugar while emphasizing fat and cholesterol. The funding relationship was not disclosed. Kearns et al., 2016.

The documents establish interference in how evidence was presented. They do not establish that every conclusion about dietary fat was false. Expanding a specific documentary finding into a claim that an entire subject was invented would recreate the distortion under examination.

Tobacco companies developed a strategy of promoting uncertainty about smoking’s harms. Oreskes and Conway describe how scientific standing and selective communication were used to sustain doubt. The desired public condition could be indecision, sufficient to postpone action, rather than settled belief in a detailed alternative account. Merchants of Doubt, 2010.

Proctor and Schiebinger call attention to this production of ignorance through agnotology. Knowledge can be obstructed by changing which questions receive attention and which uncertainties remain prominent. A successful campaign may leave its audience saying that the evidence is still too confused to use. Agnotology, 2008.

What happens when a system punishes honesty?

During the Hundred Flowers period, Mao encouraged criticism. Intellectuals initially hesitated, then spoke more openly in 1957. Surviving statements include objections to doctrinaire control and the Party’s treatment of public life. These were specific criticisms made under an apparent invitation. Columbia University, “Intellectual Opinions from the Hundred Flowers Period.”

The Anti-Rightist campaign turned criticism into a source of danger. Julia Andrews documents its effects on artists, including a sculpture instructor sent to a labor camp after refusing to testify against the artist Jiang Feng. The consequences reached people who would not cooperate in condemning others as well as those who had spoken themselves. “Traditional Painting in New China: Guohua and the Anti-Rightist Campaign.”

Calling the initial invitation a trap asserts something about Mao’s intention from the outset. The sequence alone cannot establish that. The systemic consequence requires no such verdict: an invitation followed by punishment teaches observers that apparent permission offers little protection.

The same problem appears in any organization. A manager asks whether a project is failing. Everyone knows that the previous person who answered yes was punished. Agreement now becomes compatible with both success and concealed failure. It carries less information. A leader who takes the silence as reassurance can become less informed while gaining more control.

Lysenkoism shows what happens when political authority controls the capacity to investigate. State support for Lysenko accompanied the suppression of genetics research and teaching in the Soviet Union. The damage concerned laboratories and trained researchers as well as propositions in textbooks. Valery Soyfer, 2001.

The counterfactual loss is harder to inventory than the forbidden statements. A suppressed researcher cannot perform the next experiment, teach the next cohort, or preserve a technique through ordinary use. The lost branch contains discoveries that were never made. That is one defensible meaning of a submerged network of knowledge, even when its eventual contents cannot be named.

Why does a red tree keep looking native after correction?

Repetition changes how information is processed. In experiments by Lisa Fazio and colleagues, repeating false statements increased their judged truth even when participants possessed relevant knowledge. Familiarity could influence judgment despite an available correct answer. Fazio et al., 2015.

A correction also has to change the explanation built around the claim. Research reviewed by Stephan Lewandowsky and colleagues shows that people can remember a correction yet continue using the original misinformation in later reasoning. Providing a plausible replacement account can reduce the gap left by retraction. Lewandowsky et al., 2012.

Suppose an accident was first explained as a mechanical failure. A notice later says that the alleged failure did not occur. Remembering that notice leaves the accident unexplained. An account of what did happen gives subsequent reasoning something else to use. Where the cause remains unknown, the replacement must preserve that uncertainty rather than invent an explanation to make the story complete.

The popular advice that correcting a myth usually makes it stronger is itself too broad. In two experiments examining standalone corrections, backfire did not appear either immediately or after a week. Persistence and backfire are different outcomes: a correction can help without removing every influence of the original claim. “Examining the replicability of backfire effects after standalone corrections,” 2023.

Publications have an analogous problem. Jodi Schneider and colleagues followed a fabricated clinical trial that was retracted in 2008. Among 112 direct post-retraction citations whose context they could assess, 107 did not mention the retraction. They also examined second-generation citations, where the original result could travel through another paper. The finding concerns one traced case. Schneider et al., 2020.

A notice attached to the original article cannot by itself update every review or saved copy. Correction has to reach the claims that used the result. Otherwise the original tree can be removed while its descendants remain in the accepted account.

Can a failed replication add knowledge?

The expectation that every disagreement exposes a false finding leaves out a third possibility: the findings describe different conditions that their investigators did not recognize.

Two laboratories studying human breast cells encountered this problem. Each obtained consistent results, yet they could not reproduce the other’s cell-sorting profiles using apparently equivalent materials and methods. Their investigation identified differences in tissue processing. Hines and colleagues described the experience in “Sorting Out the FACS: A Devil in the Details.” A routine preparation step could change what the later measurement appeared to reveal. Hines et al., 2014.

An ordinary recipe shows how this happens. Told to mix until smooth, two cooks can follow that instruction sincerely and work for different lengths of time. A written procedure compresses actions. Some details are omitted because they seem irrelevant; others are so habitual that the person writing the procedure never thinks to specify them. Agreement about the words can conceal disagreement about the operation.

The repair differs from deleting a fabricated observation. A researcher must discover which condition varied and whether it explains the difference. The revised claim can then become narrower: this result occurs with this preparation. The failed replication has identified part of the phenomenon’s boundary.

This also changes what counts as independence. Two laboratories using the same protocol may share an unnoticed weakness. Two laboratories that disagree because their methods differ may jointly expose it. Agreement is evidence whose value depends on how it was obtained; disagreement can be evidence about a missing variable.

The forest’s colors are consequently an imperfect representation of knowledge. Some trees need a more precise label. A claim can be sound within one range and fail outside it, or be accurately observed but incorrectly generalized. Treating every revision as an exposure of falsehood makes learning look more destructive than it is and encourages suspicion where a better specification would suffice.

Can uprooting a red tree damage blue ones?

Correction can spread further than warranted. A nearby result may lose standing even when it never relied on the discredited finding.

Pierre Azoulay and colleagues studied more than 1,100 retractions. Related papers published before the retraction subsequently received roughly 5–10% fewer citations than controls. The penalty was greater around fraud or misconduct, and research activity also declined. The pattern is consistent with stigma, although some decline may reflect reasonable reassessment of a field’s foundations. The study cannot classify every avoided paper as a lost discovery. Azoulay et al., 2015.

This is a second network effect. Error spreads through dependence, while suspicion can spread through proximity. Treating these relations as equivalent risks discarding sound work. The relevant question after a retraction is which conclusions actually used the invalid evidence.

The 2024 retraction of Sylvain Lesne and colleagues’ 2006 Nature paper illustrates the need to specify that scope. The paper concerned a particular amyloid-beta assembly, Aβ*56, and memory impairment. The retraction withdrew that paper; it did not retract every amyloid finding. Nature retraction notice; original article, marked retracted.

One expansive account says the paper sent Alzheimer’s research down the wrong path for almost two decades. That claim needs a counterfactual: what would researchers have done without it? Citation totals cannot answer. The broader amyloid cascade hypothesis was already explicitly presented by John Hardy and Gerald Higgins in 1992, fourteen years earlier. Establishing that chronology does not settle the hypothesis’s merits. It rules out treating the 2006 paper as the origin of the entire program. Hardy and Higgins, 1992.

The correct unit of repair is the dependent claim. Sometimes that means abandoning a result. Sometimes it means testing a method again. Where the evidence was independent, the retraction supplies a reason for inspection rather than an automatic verdict.

What might look correct today and fail tomorrow?

A useful place to look is where an observable target substitutes for the outcome that matters.

After a heart attack, ventricular rhythm disturbances were associated with danger. Drugs could suppress those disturbances. It was tempting to infer that successful suppression would improve survival. The Cardiac Arrhythmia Suppression Trial tested the intervention. In its 1989 preliminary report, arrhythmic deaths or nonfatal cardiac arrests occurred in 33 of 730 patients receiving encainide or flecainide, compared with 9 of 725 receiving placebo. Improving the intermediate measure had not guaranteed safety. CAST Investigators, 1989.

The causal gap is general. A gauge can indicate a dangerous process without being a safe control for it. Altering the gauge’s value through one mechanism may have different consequences from altering the underlying process through another. Prediction and intervention ask different questions.

Medical reversals show that accepted practice can survive until a better comparison is made. Vinay Prasad and colleagues examined a decade of original articles in the New England Journal of Medicine. Of 363 articles testing established practices, 146 reversed them and 138 reaffirmed them. The often-repeated 40.2% reversal figure belongs to that selected set of tests. It is not an estimate that 40.2% of all medicine is wrong. Prasad et al., 2013.

Historical theory change poses a related problem. Larry Laudan used successful theories later discarded to challenge the inference that predictive achievement guarantees a true account of underlying reality. The challenge leaves room to retain reliable observations and useful calculations. A theory can need replacement without every measurement made under it becoming false. Laudan, 1981.

Samuel Arbesman’s “half-life of facts” offers a reminder that accepted knowledge changes. A half-life for all belief, however, would hide differences between a stable measurement, a changing population statistic, and an unsettled causal explanation. Their reasons for revision differ. The Half-Life of Facts, 2012.

Future errors cannot be identified merely by choosing today’s most unfashionable belief. Better targets for scrutiny are recognizable structures: a surrogate used without outcome validation, apparent corroboration built on shared inputs, or an evidence base that loses its unfavorable results. These identify where a mistake could persist. They do not predetermine what a better investigation will find.

How can a claim be checked without distrusting everything?

Start with a claim narrow enough to inspect. “This field is corrupt” has no clear evidential boundary. “These three reviews rely on the same experiment” can be checked. So can the date of a document, the outcome measured by a trial, or whether a later paper acknowledged a retraction.

Trace the claim to the observation that supports it. Record what each source contributes. A paper may offer a new measurement, summarize existing results, or merely repeat a premise. Sources that do the last two jobs should not be counted as additional experiments.

Then vary the route of verification. Repeating the same analysis with the same data checks one kind of failure. New data or a different instrument can challenge assumptions the first check preserves. The National Academies distinguishes computational reproducibility from replication and cautions that nonreplication can have several causes. Reproducibility and Replicability in Science, 2019.

For example, three teams can independently analyze a dataset while inheriting an incorrect label attached to every observation. Agreement among their calculations would show that the result survives those analyses. It would leave the labeling error untouched. Another dataset, or an audit of how labels were assigned, addresses a different question. Counting teams cannot replace identifying the possible common cause of their agreement.

Apply this discipline to claims of conspiracy too. The sugar documents support particular acts of sponsorship and influence. A motive alone would not. Nor does the discovery of one coordinated deception supply evidence for a separate allegation.

A popular shortcut says large conspiracies inevitably collapse because someone must talk. David Robert Grimes modeled leakage using participant numbers and estimates from exposed cases.The paper later required a correction to its treatment of changing populations. Scholarly criticism also questions whether the historical disclosures used for calibration match the insider-leak mechanism being modeled. The model cannot supply a universal deadline after which a secret is impossible. Grimes, 2016; “Betting on Conspiracy,” 2024.

The opposite shortcut is equally unhelpful: treating every missing record as proof of concealment and every objection as evidence of complicity. An allegation needs possible findings that would count against it. Otherwise inquiry can accumulate indefinitely without changing the answer.

Chesterton’s fence supplies a useful restraint. In The Thing, his reformer is asked to understand a fence’s purpose before removing it. Applied to knowledge, the point is to establish what a belief explains and which evidence supports it before deciding what should replace it. Familiarity is insufficient reason to preserve it; unfamiliarity is insufficient reason to destroy it.

The cost of checking everything is prohibitive. Attention should go first to premises that determine important decisions or support many later claims. When one fails, the repair can follow its actual dependants. A correction should specify which conclusions need to be revisited. Future readers also need to know which evidence survived.

Appendix

Method

Sources were checked in September 2026 against the papers, publisher pages, university copies or reference works linked in the text; numbers are quoted from them. Some questions stayed open: whether the Hundred Flowers invitation was a trap from the start, how much the retracted 2006 amyloid paper actually cost Alzheimer’s research, and whether any general error rate or deadline for conspiracies exists. None of those is claimed here.

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