Where this came from
I kept finding the same uncomfortable moment: the evidence was fixed, and the story wasn’t.
01
A character
I read a lot of fanfiction. Mostly one pairing, which is not the interesting part. The interesting part is that a single canon — seven books, fixed events, a few hundred pages of the same boy doing the same things — supports tens of thousands of stories that disagree fundamentally about who he is.
Not disagree about what happened. Nobody rewrites the events; a story that changes them stops being about him. They disagree about what the events were evidence *of*.
In one, cruelty is character. In another it is fear with an audience. The scenes are identical. He stays recognisably himself across both, which is the thing I could not get past — because if the evidence is fixed and the person changes, the person was never only the evidence.
02
A myth
I noticed I was doing it to Icarus about a week later, and the case is cleaner because the text is short enough to hold in your head.
Ovid gives the wings, the warning, the climb, the wax, the sea. He does not give a motive. Three thousand years of the story meaning *pride* rests on an assumption the text does not contain — and once you see that, you can swap it for curiosity and watch the fall stop being a punishment and become a price.
Nothing moved except a premise nobody had written down.
03
A text with authority
Law was the first place I found the same shape with the machinery already built for it. Two readings of one statute, both careful, both citing the same clause, and an elaborate apparatus for deciding whose reading binds.
That apparatus is an admission. If the text settled it, you would not need doctrines about who wins.
It is also where the resemblance first showed me its edge. Legal interpretation terminates — a court rules and the question closes, at least procedurally. Reading has nothing of the kind, and an activity that can be closed by authority is not the same activity as one that cannot.
04
A measurement
Then physics, and the version I had been told was wrong. The story is not that scientists thought particles were particles until someone discovered they were waves.
The story is that light started depositing energy in lumps, X-rays started recoiling like billiard balls, and in 1924 de Broglie proposed the reverse — that a particle has a wavelength, λ = h/p, as a number you could go and check. Davisson and Germer checked it three years later.
The anomaly was not in the electron. It was in two words that had been treated as exhausting the options. That is a different kind of failure from getting the answer wrong, and I did not have a name for it.
05
A rule for changing your mind
Bayes' rule gave me the vocabulary and then showed me its own ceiling, which was more useful.
It is exact about one thing: given a set of hypotheses and a sense of how expected the evidence is under each, the update is forced. You cannot keep a prior, keep a likelihood, and refuse the conclusion. That is a real constraint and most arguments about interpretation would be shorter if people stated both inputs.
But it redistributes belief across options you already have. It cannot produce the one you had not thought of, and it has nothing to say about which of two surviving models is better supported. Peirce called the missing step abduction. The gap between 'I updated correctly' and 'I am justified' is where this whole project ended up living.
06
A table of numbers
A dataset is rows plus labels, and only the rows get collected. The labels are decisions — made by people, under deadline, in a schema somebody designed — and a model learns them exactly as confidently as it learns the measurements.
Relabel the same rows and you get a model that has learned a different world and predicts in it with no loss of confidence.
Which raises the question I still find hardest: a representation is good because it keeps what matters for a task and discards the rest. So does a representation that predicts well tell you what the thing *is*, or only what it does under the conditions you happened to sample?
07
Something I built
I wrote an ordering system. The model was clean: a person selects items, confirms, pays.
Almost nobody does that. People order for other people. They change their mind after confirming. They share one thing across four of them and argue about it. They arrive at different times and expect the order to have waited. One person orders, another pays, and neither of them is the account holder.
None of that is edge-case noise around a correct model. It is the actual behaviour, and my model had quietly assumed a customer who is a single decision-making unit. The system did not break because the code was wrong. It broke because the representation had omitted the thing that was really going on.
08
Something that fell over
Same lesson, cheaper: a robot that worked on the bench and not on the floor. Battery voltage sagging under load, a motor that was two percent faster than its twin, friction that changed with the surface.
The code was internally correct the entire time. The world had variables the model did not contain, which is not a moral about persistence. It is a fact about what a model is.
This is the point where I started writing things down, because I had now found the same move in fiction, in a myth, in a courtroom, in a lab, in a dataset, and in my own software — and that is either a discovery or a symptom.
09
Someone I knew
And then the one that stopped being interesting and started being uncomfortable.
You do not meet people. You meet what they said, what they did, what someone told you, what you remember — which is not what happened — and what you were expecting before any of it. Then you build something out of that and talk to what you built.
The model determines what you go looking for. What you find confirms the model. You can know someone for years, be wrong about them the whole time, and never once meet a fact that forces the issue. That is not a claim that people are constructions. They are entirely real. The model is yours and it is not them, and losing that distinction in either direction is how this goes wrong.
Which leaves the problem.
Nine places. One move. It felt like a discovery for about two months, and then it started to worry me, because I know what that feeling is worth.
A person who has found a real pattern and a person who is seeing things report the same experience from the inside. It gets clearer with every example. Examples are cheap. Adding one feels like evidence and is not.
So I could not tell whether I had found a connection or simply become very good at making them. And there is no amount of further reading that settles that, because more reading is exactly how you get better at making them.
So I built an experiment.
Not to prove the connection. To find out whether I could tell my own real claims from ones I fabricated — so I wrote three fake ones in the same voice, by the same method, and mixed them in with the ones I defend.
Then I built instruments for the parts that could actually be measured: what people do when the evidence stops cooperating, which property they treat as decisive when two models both fit, and whether they can tell a confirming observation from one that discriminates.
Everything is recorded, the decision rules were fixed before any of it arrived, and the page that reports the results will contradict me if the numbers do.
Sources
Nothing listed that was not consulted, and nothing described as supporting a claim it does not make. Where this project uses an idea more loosely than its source does, the note says so.
Quantum mechanics and the category problem
Recherches sur la théorie des quanta
Louis de Broglie · 1924 · Doctoral thesis, University of Paris; reprinted in Annales de Physique, 10th series, vol. 3 (1925), 22–128
The source of the matter-wave hypothesis, λ = h/p. This site uses it for one point only: the proposal required applying a description previously reserved for radiation to matter. It does not use de Broglie as an authority on interpretation, reading, or anything outside physics.
Diffraction of Electrons by a Crystal of Nickel
Clinton Davisson and Lester Germer · 1927 · Physical Review 30(6), 705–740
The experimental confirmation. Cited so that the hypothesis is not presented as having been accepted on elegance alone; G. P. Thomson's independent electron-diffraction work the same year is the other half of that record.
The Quantum Postulate and the Recent Development of Atomic Theory
Niels Bohr · 1928 · Nature 121, 580–590
Bohr's complementarity: wave and particle descriptions are both required and are not simultaneously applicable. This site presents complementarity as one influential interpretation, not as the settled meaning of the formalism — interpretations of quantum mechanics remain genuinely disputed.
Probability and belief revision
An Essay towards solving a Problem in the Doctrine of Chances
Thomas Bayes (communicated by Richard Price) · 1763 · Philosophical Transactions of the Royal Society of London 53, 370–418
The original. Cited for provenance; the modern odds form used on this site is later.
On Information and Sufficiency
Solomon Kullback and Richard Leibler · 1951 · Annals of Mathematical Statistics 22(1), 79–86
The divergence used in the analysis pages. This site always reports it as a smoothed estimate, because participants assign zero probabilities and the unsmoothed quantity would be infinite.
Probability Theory: The Logic of Science
E. T. Jaynes · 2003 · Cambridge University Press
The strongest statement of the view that probability is extended logic. Included as background, and as a position this project does not simply assume: Jaynes would take the framing further than anything here claims.
James Joyce · 2021 · Stanford Encyclopedia of Philosophy
The reference used when writing the explanatory sections, and the recommended next step for a reader who wants the formal treatment.
William Talbott · 2016 · Stanford Encyclopedia of Philosophy
Includes the standard objections — the problem of the priors, old evidence, logical omniscience — which this project's limitations page relies on.
Judgment under Uncertainty: Heuristics and Biases
Amos Tversky and Daniel Kahneman · 1974 · Science 185(4157), 1124–1131
Relevant because this experiment asks humans for numerical probabilities, and this literature is the reason those numbers must be treated as reports rather than as measurements of belief. Anchoring, in particular, is a known risk in the design used here.
Verification of Forecasts Expressed in Terms of Probability
Glenn W. Brier · 1950 · Monthly Weather Review 78(1), 1–3
The standard proper scoring rule. Noted on the limitations page as the reason this project cannot score interpretations for accuracy: a Brier score needs a ground truth, and these scenarios do not have one.
Theory change and underdetermination
The Structure of Scientific Revolutions
Thomas S. Kuhn · 1962 · University of Chicago Press
Used for normal science, anomaly and crisis. This site does not claim Kuhn held that theory choice is irrational — he explicitly denied it in the 1969 postscript — and says so on the philosophy page.
The Logic of Scientific Discovery
Karl Popper · 1959 (German original 1934) · Hutchinson; original as Logik der Forschung, Springer
Used for falsifiability as a demarcation criterion. Note that Popper rejected the idea that induction or confirmation supports theories — so the Bayesian framing on this site is one he would have opposed. The site states this rather than blending them.
Lectures on Pragmatism (Collected Papers 5.189)
Charles Sanders Peirce · 1903 · Collected Papers of Charles Sanders Peirce, Harvard University Press, 1931–1958
The canonical statement of the abductive schema: a surprising fact is observed; if H were true, it would be a matter of course; hence reason to suspect H. Used to make the point that Bayesian updating cannot generate the hypotheses it distributes belief over.
La Théorie physique: son objet et sa structure
Pierre Duhem · 1906 · English: The Aim and Structure of Physical Theory, trans. P. Wiener, Princeton, 1954
The origin of the point that hypotheses meet evidence in bundles, so a failed prediction does not identify the guilty assumption.
W. V. O. Quine · 1951 · The Philosophical Review 60(1), 20–43
The stronger holist version of the same point, and the source of the 'web of belief' image used on the philosophy page.
Underdetermination of Scientific Theory
Kyle Stanford · 2023 · Stanford Encyclopedia of Philosophy
Distinguishes the varieties of underdetermination that this site deliberately keeps separate from mere 'we don't know yet'.
Igor Douven · 2021 · Stanford Encyclopedia of Philosophy
Covers the relationship between inference to the best explanation and Bayesian confirmation, which the philosophy page summarises.
Roman Frigg and Stephan Hartmann · 2020 · Stanford Encyclopedia of Philosophy
The source for the site's distinction between a model and the thing modelled.
Wahrheit und Methode (Truth and Method)
Hans-Georg Gadamer · 1960 · Mohr Siebeck; English trans. Weinsheimer and Marshall, Continuum, 1989
The account of 'prejudice' as an enabling condition of understanding, which is the closest thing in the hermeneutic tradition to this project's use of 'prior'. The comparison is the project's own and Gadamer would have resisted the quantification.
Bjørn Ramberg and Kristin Gjesdal · 2021 · Stanford Encyclopedia of Philosophy
Background reading for the interpretation section.
Language models, uncertainty and calibration
On Calibration of Modern Neural Networks
Chuan Guo, Geoff Pleiss, Yu Sun, Kilian Q. Weinberger · 2017 · ICML 2017
The standard reference for the finding that accuracy and confidence come apart in modern networks. Establishes that 'confident' is not a synonym for 'likely to be right'.
Language Models (Mostly) Know What They Know
Saurav Kadavath et al. · 2022 · arXiv:2207.05221
Evidence that self-evaluation in large models carries real signal on tasks with verifiable answers. Cited with the caveat that the tasks studied have ground truth and the scenarios on this site do not, so the result does not transfer directly.
Teaching Models to Express Their Uncertainty in Words
Stephanie Lin, Jacob Hilton, Owain Evans · 2022 · arXiv:2205.14334
Directly relevant to the method used here, which asks a model for verbalised probabilities rather than reading token likelihoods.
Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models
Katherine Tian et al. · 2023 · EMNLP 2023; arXiv:2305.14975
The finding that elicited confidence is sensitive to how you ask is the reason this site pins a prompt version to every stored model response, and the reason results across prompt versions must not be pooled.
How people read each other
Logic and Conversation
H. P. Grice · 1975 · In Cole and Morgan (eds.), Syntax and Semantics 3: Speech Acts, Academic Press, 41–58
Implicature: how a speaker means more than they say, and why a hearer is entitled to infer it. The language scenarios are built on Gricean ambiguity.
Relevance: Communication and Cognition
Dan Sperber and Deirdre Wilson · 1986 · Blackwell
The successor account, in which interpretation is the search for the reading that repays processing effort. Relevant to why the 'effort' evidence items in the scenario set discriminate as well as they do.
Egocentrism over E-Mail: Can We Communicate as Well as We Think?
Justin Kruger, Nicholas Epley, Jason Parker, Zhi-Wen Ng · 2005 · Journal of Personality and Social Psychology 89(6), 925–936
Experimental evidence that senders systematically overestimate how clearly tone is conveyed in text. Part of the motivation for the language track.
Grounding in Communication
Herbert H. Clark and Susan E. Brennan · 1991 · In Resnick, Levine and Teasley (eds.), Perspectives on Socially Shared Cognition, APA, 127–149
Meaning as something established between participants rather than transmitted. Background for why the scenarios include the interpreter's history as evidence.
Prediction in the brain
Whatever Next? Predictive Brains, Situated Agents, and the Future of Cognitive Science
Andy Clark · 2013 · Behavioral and Brain Sciences 36(3), 181–204
The accessible statement of predictive processing. Published with peer commentary, much of it critical, which is the honest form in which to cite it.
The Free-Energy Principle: A Unified Brain Theory?
Karl Friston · 2010 · Nature Reviews Neuroscience 11, 127–138
The most ambitious version of the claim. This site does not assert that the brain performs Bayesian inference; the map edge for this connection is marked analogical for that reason.
How to Grow a Mind: Statistics, Structure, and Abstraction
Joshua Tenenbaum, Charles Kemp, Thomas Griffiths, Noah Goodman · 2011 · Science 331(6022), 1279–1285
Bayesian models of human learning at the computational level — a weaker and better-supported claim than the mechanistic one.
The primary texts
Metamorphoses, Book VIII (Daedalus and Icarus, lines 183–235); Book X (Orpheus)
Ovid · c. 8 CE · Perseus Digital Library
Source for the Icarus and Orpheus scenarios. The detail of Icarus playing in the air, and of Daedalus's shaking hands, are Ovid's.
Iliad, Books IX (the embassy), XVI (Patroclus), XVIII (the news), XXIV (Priam)
Homer · c. 8th century BCE · Perseus Digital Library
Source for both Achilles scenarios, including the two-fates speech in Book IX that the 'nothing left to protect' reading depends on.
Plato · c. 385–370 BCE · Perseus Digital Library
Phaedrus's speech, which treats Achilles and Patroclus as lovers and disagrees with Aeschylus about which was which. Cited as evidence that antiquity itself argued about this — not as evidence for any particular modern reading.
Agamemnon (the Cassandra scene, lines 1072–1330); Prometheus Bound
Aeschylus · 458 BCE / c. 460s BCE · Perseus Digital Library
Sources for the Cassandra and Prometheus scenarios, including the chorus's stated comprehension of Cassandra's words.
Sophocles · c. 441 BCE · Perseus Digital Library
Source for the Antigone scenario, including her lament for the marriage she will not have.
Georgics IV (Orpheus and Eurydice)
Virgil · c. 29 BCE · Perseus Digital Library
The second classical account of the turn, which assigns a different cause from Ovid's. The disagreement between them is the evidence the Orpheus scenario uses.
Theogony; Works and Days (Prometheus)
Hesiod · c. 700 BCE · Perseus Digital Library
The earlier and less sympathetic account of Prometheus, included so the Aeschylean version is not treated as the only one.