# The College of All Minds (Collegium Omnium Mentium)
## The Truly Hardest Exam in the World

*Manent et numerantur* — They remain, and they are counted.

| Paper | Title | Questions |
|---|---|---|
| I | General | 32 |
| II | Mathematics | 35 |
| III | Physics | 36 |
| IV | Chemistry | 32 |
| V | Biology | 33 |
| VI | Philosophy | 30 |
| VII | Engineering | 32 |
| VIII | Computation | 32 |
| IX | Sociology | 31 |
| X | Design | 40 |
| — | **Total** | **333** |

## Paper I — General

Paper I stands before the disciplines rather than within any one of them. It examines the concepts that the sciences use but do not themselves justify: law and accident, reduction and emergence, explanation and redescription, evidence and its weight, probability and ignorance, simulation and experiment, information and its physicality. Its questions range across the same territory as the specialist papers — the genome, the arrow of time, the periodic table, the boundary between chemistry and physics, the status of species, the brain — but they are put in the general form: not how the mechanism works, but what kind of thing the claim is, and what would establish or overturn it. Two further questions ask whether consonance is discovered or constructed, and what survives when a melody is transposed.

What is examined is judgement about the sciences, exercised with the sciences in hand. A candidate is expected to know enough physics, biology, chemistry and mathematics to reason from real cases rather than from stylised ones, and to argue in the currency of philosophy of science without retreating into it: to say what a fine-tuned constant is, what temperature is, what a measurement without an observer would be, and to defend the answer against a specialist who works with the concept daily. The paper rewards precision about where a question is empirical, where it is conceptual, and where the distinction itself is doing work; it penalises the reflex of citing authority in place of an argument.

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is the genome a program?
2. What distinguishes a law of nature from an accidental regularity?
3. Is mathematics discovered or constructed? Answer without appeal to authority.
4. When, if ever, is a computer simulation an experiment?
5. Does reduction explain, or only redescribe?
6. What would it take to show that a phenomenon is emergent rather than merely complicated?
7. Is there a fact of the matter about the arrow of time?
8. Why is the universe amenable to mathematics at all?
9. Can a measurement have no observer?
10. What is the smallest amount of evidence that would rationally overturn a well-confirmed theory?
11. Is information physical?
12. Distinguish randomness from ignorance.
13. Could two theories be empirically equivalent yet not the same theory?
14. Is life a physical kind or a historical accident?
15. What does it mean to say a constant is "fine-tuned"?
16. Can a proof be too long to be a proof?
17. Is temperature real?
18. Why should the simpler hypothesis be preferred? Give a non-circular answer.
19. Does biology have laws?
20. What is conserved when energy is conserved?
21. Is the periodic table a discovery about chemistry or about physics?
22. Can a scientific model be true?
23. What is the difference between a symmetry and a redundancy in description?
24. Would a complete physics of the brain leave anything unexplained?
25. Is there a principled boundary between chemistry and physics?
26. When does a correlation license an intervention?
27. Is the concept of species dispensable?
28. Can the second law of thermodynamics be derived, or must it be assumed?
29. What, precisely, does a probability in physics measure?
30. If you could establish exactly one currently open scientific question, which would most change the rest of science, and why?
31. Is consonance discovered or constructed? Locate it in the signal, in the ear, or in the culture, and say what evidence would decide.
32. Is a melody the same object when transposed? Say what is preserved, what is not, and whether the survivor is a pattern, a relation, or a convention.

## Paper II — Mathematics

Paper II covers mathematics as a whole subject rather than as a service to the sciences. Its questions run from the classical open problems — the Riemann Hypothesis, P versus NP, Navier–Stokes existence and smoothness, Hodge, Birch–Swinnerton-Dyer — through the foundations, where independence results, Gödel’s second theorem, compactness, the axiom of choice and its pathologies, homotopy type theory and the topos are examined; through algebra and geometry, where Galois theory, schemes, motives, the Langlands correspondence and the Atiyah–Singer index theorem are set; and through analysis and its rigour, where measurability, convergence, the spectral theorem and well-posedness are put to work. Four questions reach into music and geography: the impossibility of a just fifth in any equal division of the octave, the ambiguity of rhythms sharing an interval content, the impossibility of an undistorted plane map of the sphere, and the length of a coastline.

The paper examines mathematical maturity rather than recall. Several questions demand a proof and will accept nothing less; several ask instead for an honest sketch of a strategy, and reward the candidate who marks precisely where the argument would become hard. Throughout, the requirement is to state hypotheses exactly, to know which of them is load-bearing, and to say what a theorem does and does not assert — the difference between a result being open, undecidable, and false being treated as a matter of technical fact rather than of attitude. The final question invites a candidate to name a statement believed true but expected never to be proved, and to defend the belief; the paper is willing to examine mathematical taste, provided it is disciplined.

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. State the Riemann Hypothesis precisely and explain why its truth constrains the distribution of primes.
2. Prove that there is no continuous surjection from a compact interval onto a square, or explain why the naïve intuition here fails.
3. Give an account of what independence results (e.g., the Continuum Hypothesis) show about mathematical truth.
4. Sketch the structure of a proof that the Navier–Stokes existence-and-smoothness problem remains open in three dimensions; identify the precise obstruction.
5. What does the P versus NP question ask, and why is a proof so elusive?
6. Explain the role of the axiom of choice in a theorem of your choosing, and what is lost without it.
7. Prove that the algebraic numbers are countable.
8. What is a motive, and why did Grothendieck want one?
9. Give a rigorous statement of Gödel's second incompleteness theorem and explain its hypotheses.
10. Construct a non-measurable set, or explain what forbids it constructively.
11. Why is the classification of finite simple groups considered complete, and what would undermine that claim?
12. Explain the sense in which the exponential of a matrix solves a linear system.
13. What is the Langlands correspondence trying to unify?
14. Prove the fundamental theorem of Galois theory, or state it and give its content precisely.
15. In what sense is the Banach–Tarski paradox not a paradox?
16. Define a scheme and motivate the definition against classical varieties.
17. State and interpret the spectral theorem for self-adjoint operators.
18. What does it mean for a PDE to be well-posed in the sense of Hadamard?
19. Explain why the halting problem is undecidable, and connect this to Gödel.
20. What is the significance of the Atiyah–Singer index theorem?
21. Give an example of a statement true in the standard model of arithmetic but unprovable in Peano Arithmetic.
22. Describe the role of compactness in first-order logic and give one striking consequence.
23. What is homotopy type theory, and what does it propose to found?
24. Prove that π is irrational, or outline the strategy honestly.
25. Explain the difference between pointwise and uniform convergence and why it matters analytically.
26. State the Hodge Conjecture and explain what kind of object it concerns.
27. Why is the Birch–Swinnerton-Dyer conjecture a statement about arithmetic, despite its analytic form?
28. What is a topos, and in what sense is it a generalised space?
29. Give a probabilistic argument for a purely combinatorial fact.
30. Is there a mathematical statement you regard as true but expect never to be proved? Defend the attitude.
31. Prove that no equal division of the octave contains a just perfect fifth, and say what the continued-fraction expansion of log₂(3/2) recommends in its place.
32. A rhythm and its retrograde can be indistinguishable to the autocorrelation. Exhibit two distinct rhythmic patterns sharing an interval content, and say what the ambiguity implies for identifying a piece by its statistics.
33. Prove that no plane map of the sphere preserves all distances, and say what Mercator, the equal-area projections, and the geodesic-preserving projections each surrender instead.
34. How long is the coast of Britain? State the Richardson relation, define the dimension it implies, and decide whether the length is undefined or merely scale-relative.
35. Is Ramsey’s theorem the pigeonhole principle on stilts? Exhibit the principle as the theorem’s one-dimensional case, derive the finite two-colour theorem from it by iteration, and then let the calibrations judge: say what the growth of the Ramsey numbers and the reverse-mathematical strength of the theorem for pairs each establish that counting alone does not.

*Question 35 was added by Examination Amendment v5.2.*

## Paper III — Physics

Paper III covers physics from its foundations to its frontiers. Quantum theory is examined at the point of its unresolved business — the measurement problem, Bell’s theorem and what it does not rule out, decoherence and its residue, the reversibility of the Schrödinger equation against the definiteness of outcomes. Statistical and thermal physics are set through the second law, equipartition, fluctuation–dissipation, phase transitions, and the Landauer bound on computation. Field theory and gravitation appear as gauge redundancy, spontaneous symmetry breaking, the Higgs mechanism, renormalisation, the cosmological constant, black-hole thermodynamics and the information paradox, and holography. Condensed matter, astrophysics and turbulence are each represented, and four later questions treat the acoustics of a struck string and of a radiating body, the seismological case for a liquid outer core, and the aperiodicity of geomagnetic reversals.

The knowledge base is the standard graduate curriculum, but the examination is of physical understanding rather than of formalism. Derivations are demanded where a derivation settles the matter — the Chandrasekhar mass from first principles, the Landauer bound, a conserved quantity from Noether’s theorem — and elsewhere the candidate is asked to say what a piece of mathematics is physically doing: what renormalisation removes, why spin is not rotation, why entanglement carries no signal. Several questions turn on the distinction between a symmetry of the laws and a symmetry of a state, or between what a theory explains and what it merely accommodates. The paper closes its original sequence by asking which single experiment would most sharply discriminate between interpretations of quantum mechanics, and expects the answer to be feasible in principle and decisive in fact.

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. State the quantum measurement problem precisely and say what a solution would have to deliver.
2. Prove that the Yang–Mills mass gap, if it exists, cannot be seen perturbatively; explain the difficulty of establishing it rigorously.
3. What is renormalisation actually doing, physically?
4. Derive the equipartition theorem and state exactly where it fails.
5. Why does the cosmological constant problem count as a problem?
6. Explain gauge invariance as redundancy of description, not as symmetry of nature.
7. What does Bell's theorem rule out, and what does it not rule out?
8. Reconstruct the second law from a microscopic, reversible dynamics — where does irreversibility enter?
9. What is the black-hole information paradox, and what would resolve it?
10. Explain why the electron's spin is not literal rotation.
11. Give the physical meaning of the action principle.
12. What is spontaneously broken symmetry, and how does a Goldstone mode arise?
13. Why is there an arrow of time if the microphysics is time-symmetric?
14. Explain the significance of the Higgs mechanism for mass.
15. What distinguishes a phase transition from a crossover, precisely?
16. State Noether's theorem and apply it to a non-obvious conserved quantity.
17. What does decoherence explain, and what does it leave unexplained?
18. Why can't information travel faster than light even though entanglement is "instantaneous"?
19. Explain the physical content of the fluctuation–dissipation theorem.
20. What is a topological phase of matter, and how is it robust?
21. Estimate the Chandrasekhar mass from first principles.
22. What is the status of the fine-structure constant — computed, measured, or explained?
23. Why is turbulence hard, as physics rather than as mathematics?
24. Give the Landauer bound and explain what it says about computation.
25. What is the difference between a symmetry of the laws and a symmetry of a state?
26. Explain why general relativity resists quantisation by the usual recipe.
27. What does the holographic principle claim, and what evidence bears on it?
28. Reconcile the reversibility of the Schrödinger equation with the definiteness of measurement outcomes.
29. Why is temperature well-defined for a black hole?
30. Which single experiment, feasible or not, would most sharply discriminate between interpretations of quantum mechanics?
31. Is time an emergent phenomenon?
32. Why does a struck piano string not sound the harmonic series it is drawn to sound? Quantify the inharmonicity contributed by bending stiffness, and say what stretched tuning is for.
33. A violin and a loudspeaker radiating the same spectrum do not sound alike in a room. Account for the difference from the directivity of the source, and say what a measurement at one microphone position cannot capture.
34. How do we know the Earth has a liquid outer core? Argue from the S-wave shadow zone, and quantify what the observation constrains.
35. The geodynamo has reversed the field hundreds of times without periodicity. State what a working dynamo requires, and say why the reversal statistics resist prediction rather than merely resisting measurement.
36. What would happen if we added one electron to every atom in the universe?

*Question 31 was added by Examination Amendment v2.1. Questions 1–30 stand verbatim as fixed at expansion v2.0.*

*Question 36 was added by Examination Amendment v5.3.*

## Paper IV — Chemistry

Paper IV covers chemistry as the science of bonding, structure, reactivity and change. Its questions examine the bond itself against the electron density, oxidation state, electronegativity and its disagreeing scales, aromaticity, chirality, and the hydrogen bond; the thermodynamics and kinetics of reaction, including the equilibrium constant and free energy, kinetic against thermodynamic control, catalysis, the Arrhenius form, transition states and potential energy surfaces, and Marcus theory with its inverted region; and the quantum-chemical basis of the subject, from Born–Oppenheimer to electron correlation and the principled limits of density functional theory. Biological and material chemistry are represented by enzymes, protein folding, the hydrophobic effect, nitrogen fixation and the metal–semiconductor–insulator distinction, and two later questions treat the oxygen-isotope palaeothermometer and the silicate weathering thermostat.

What is examined is the chemist’s particular habit of mind: the willingness to use a concept that is known to be approximate, together with the ability to say exactly where the approximation fails. Several questions are put in that form directly — whether a bond is a thing or a model, whether a molecular orbital is observable, in what sense a transition state exists, whether the periodic table follows from quantum mechanics alone. A candidate is expected to move fluently between the molecular and the thermodynamic account of the same phenomenon, to know which quantities are measured and which are inferred, and to explain a rule’s success without mistaking success for derivation. The paper ends by asking which single unmeasured quantity would most advance chemical prediction.

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is a chemical bond a thing or a model? Answer with reference to the electron density.
2. Explain why the concept of oxidation state is useful despite being formally arbitrary.
3. Derive the relationship between equilibrium constant and Gibbs free energy, and say what assumptions it hides.
4. Why is water anomalous? Give the molecular account.
5. What does it mean for a reaction to be "under kinetic" versus "thermodynamic" control?
6. Explain aromaticity without invoking the word "resonance."
7. Is the periodic table's structure a consequence of quantum mechanics alone, or does chemistry add something?
8. What is the physical basis of electronegativity, and why do scales disagree?
9. Account for the catalytic power of enzymes in thermodynamic and kinetic terms.
10. Why is the Born–Oppenheimer approximation so good, and when does it fail?
11. Explain chirality's consequences for reactivity and for biology.
12. What limits the accuracy of density functional theory in principle?
13. Give a molecular account of why entropy can drive assembly (e.g., the hydrophobic effect).
14. What is a transition state, and in what sense does it exist?
15. Explain the origin of colour in transition-metal complexes.
16. Why can a catalyst change a rate but not an equilibrium?
17. What does "electron correlation" mean, and why is it computationally expensive?
18. Explain how the Marcus theory of electron transfer predicts an inverted region.
19. Is the concept of a molecular orbital observable?
20. Account for the strength and directionality of the hydrogen bond.
21. Why is nitrogen fixation so difficult, industrially and biologically?
22. What determines whether a solid is a metal, semiconductor, or insulator, chemically?
23. Explain the thermodynamic driving force for protein folding.
24. What is autocatalysis, and why is it relevant to the origin of life?
25. Give the basis of the Woodward–Hoffmann rules.
26. Why do reaction rates so often follow the Arrhenius form, and when do they not?
27. What is measured by a standard electrode potential, and against what?
28. Explain the concept of a potential energy surface and its dimensionality.
29. Is supramolecular chemistry a distinct science or applied physics?
30. Which single unmeasured quantity, if known exactly, would most advance chemical prediction?
31. Explain how δ¹⁸O in an ice core records temperature, and state the assumptions the palaeothermometer hides.
32. Silicate weathering is said to thermostat the climate over geological time. State the negative feedback precisely, give its characteristic timescale, and say what it cannot regulate.

## Paper V — Biology

Paper V covers biology from the molecular to the evolutionary scale. Its questions examine the genome and the gene itself, heritability and its misuse, the units and levels of selection, neutral theory, the error threshold, the genetic code and its departures from universality, epistasis and the genotype–phenotype map; the physics of the living cell as an open system far from equilibrium, replication fidelity, ribosomal speed against accuracy, the thermodynamic cost of biological information processing, and the limits of biological imaging; and the developmental and organismal questions of robustness, plasticity, allometric scaling, ageing, cancer as an evolutionary process, and convergence as evidence of constraint. Three later questions treat cochlear mechanics, the independent evolution of vocal learning, and the species–area relationship.

The paper examines mechanism and inference together. A candidate is expected to give a physical or chemical account where one exists — why replication is as accurate as it is, why folding is hard given the sequence, what a signalling network has that a reaction network lacks — and to be equally exact about what evolutionary reasoning can and cannot establish, including whether natural selection is a law, a tautology or a mechanism, and whether the species concept survives contemporary molecular biology. Questions about the origin of life ask not for speculation but for criteria: what would count as a second, independent origin, and which single measurement would most constrain the theories. Precision about levels of explanation is expected throughout, and rewarded.

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is the genome a program, a blueprint, or neither? Defend your choice mechanistically.
2. What does it mean for a trait to be heritable, and why is heritability so often misunderstood?
3. Explain the thermodynamics of the living cell as an open system far from equilibrium.
4. Is natural selection a law, a tautology, or a mechanism?
5. What is a gene? Give a definition that survives contemporary molecular biology.
6. Account for the maintenance of sexual reproduction despite its twofold cost.
7. Why is the protein-folding problem hard even given the sequence?
8. What does information theory legitimately contribute to molecular biology?
9. Is there a unit of selection? Defend a level.
10. Explain the error threshold and its relevance to the origin of replication.
11. What distinguishes a signalling network from a mere chemical reaction network?
12. Why is convergent evolution evidence about constraint rather than chance?
13. What is the physical basis of the fidelity of DNA replication?
14. Explain how a developmental program can be robust to noise yet evolvable.
15. Is ageing selected for, tolerated, or a physical inevitability?
16. What does "junk DNA" mean now, and was the concept a mistake?
17. Account for allometric scaling laws in metabolism.
18. Explain why the neutral theory of molecular evolution was necessary.
19. Is the species concept salvageable, and does biology need it?
20. What is the thermodynamic cost of biological information processing?
21. How does a ribosome achieve both speed and accuracy?
22. Explain epistasis and why it complicates the genotype–phenotype map.
23. What would count as a second, independent origin of life, and how would we recognise it?
24. Why is cancer better understood as an evolutionary process than as a single disease?
25. Explain how phenotypic plasticity relates to, and differs from, evolution.
26. What sets the fundamental limits on the resolution of biological imaging?
27. Is the brain a computer? Answer with reference to what computation requires.
28. Account for the origin of the genetic code's near-universality and its departures.
29. What is the role of stochasticity in gene expression, and is it a bug or a feature?
30. Which single measurement would most constrain theories of the origin of life?
31. How does the cochlea achieve its frequency selectivity? Give the mechanics of the travelling wave, and say what the active process adds that passive filtering cannot.
32. Vocal learning has evolved independently in songbirds, cetaceans, and humans. State what the capacity requires neurally, and decide whether the convergence is evidence of one solution or of three.
33. State the species–area relationship, and decide whether island biogeography theory explains it or merely fits it.

## Paper VI — Philosophy

Paper VI is confined by its rubric to theoretical philosophy, and covers four regions of it. In logic and the theory of truth it examines entailment and its transitivity, vagueness in objects and in descriptions, non-circular definitions of truth, bivalence and the open future, and the strongest challenge to a law of classical logic. In the philosophy of mathematics it examines Platonism against our capacity to know, absolute undecidability, the Löwenheim–Skolem theorem and the determinacy of reference, reverse mathematics, and whether arithmetic is analytic, synthetic a priori or empirical. In the metaphysics of science it examines laws and modality, natural kinds and the periodic table, identity across time, background independence, and the reality of unobservable posits. In the philosophy of physics and biology it examines quantum logic and entanglement, causation, teleology, reduction, and whether Gödel’s theorems bear on the thesis that the mind is a machine.

The paper examines argument, and admits nothing else. No moral, political or value-philosophical question is set, and none may be answered; a candidate who converts a metaphysical question into an ethical one has failed to answer it. What is required is the ability to state a position in its strongest form, to identify the premise on which it actually rests, and to say what would count against it — with the technical results handled as results, so that a claim about Löwenheim–Skolem or about incompleteness is held to the theorem rather than to its reputation. This is the only paper unchanged by Examination Expansion v5.0: neither the ontology of the musical work nor the vagueness of a geographical boundary is admissible under its rubric, the second being in any case already treated abstractly by its third question.

*Confined to theoretical philosophy: formal logic, epistemology, metaphysics of science, philosophy of mathematics, and the philosophy of physics and biology. No moral, political or value-philosophy content.*

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is logical entailment a transitive relation? Defend your answer.
2. Do Gödel's incompleteness theorems bear on the thesis that the mind is a machine?
3. Can there be vague objects, or only vague descriptions?
4. Is it possible to define truth non-circularly for a language containing its own truth predicate?
5. What does the Löwenheim–Skolem theorem show about the determinacy of mathematical reference?
6. Are there absolutely undecidable mathematical propositions?
7. Do the paradoxes of quantum mechanics pose a threat to classical logic?
8. Is set-theoretic Platonism compatible with our capacity to know mathematical facts?
9. What, if anything, does reverse mathematics teach us about foundations?
10. Can mathematical facts explain physical phenomena?
11. Is chemistry reducible to physics? State the criterion of reduction you use.
12. Does teleological explanation have an ineliminable role in biology?
13. What is a law of nature, and could the laws have been otherwise?
14. Is there a coherent notion of metaphysical modality distinct from logical and physical modality?
15. Compare the Russellian and Strawsonian treatments of definite descriptions.
16. Can there be time without change, or change without time?
17. Is the principle of bivalence defensible in the face of the future?
18. What does quantum entanglement imply for our concept of causation?
19. Is there a livable interpretation of probability that is neither frequentist nor subjectivist?
20. Can modal logic tell us anything about reality, or only about our language?
21. Is the a priori / a posteriori distinction coherent and explanatory? Draw it or reject it.
22. What is the best response to the underdetermination of theory by evidence?
23. Are laws of nature relations among universals, or regularities, or neither?
24. Does the success of science give us reason to believe its unobservable posits?
25. Is identity across time a further fact, or fixed by qualitative continuity?
26. What is a natural kind, and does the periodic table exhibit them?
27. Can there be a consistent version of verificationism, and would it be plausible?
28. What does it mean to say a physical theory is background-independent, and is that a virtue?
29. Is arithmetic analytic, synthetic a priori, or empirical?
30. What is the strongest challenge to a law of classical logic, and can it be resisted?

*Paper VI was retitled Philosophy by Examination Renaming v3.3. Its questions and rubric stand verbatim and unrenumbered.*

## Paper VII — Engineering

Paper VII covers engineering as the discipline of building things that must work. Structures and materials are examined through fracture and fatigue, the Paris law, Weibull statistics for brittle strength, the square-cube law, leak-before-break in pressure vessels, finite-element convergence, and the forensic record of the Comet fuselage and the Tacoma Narrows Bridge. Energy and flow are examined through the Betz limit, finite-time thermodynamics against the Carnot bound, the Lawson criterion, the rocket equation, turbulence modelling, and grid inertia after synchronous generation is lost. Information, control and reliability are examined through Shannon’s capacity theorem, underactuated and chaotic control, feedback in its two distinct senses, Landauer’s principle, the end of Dennard scaling, and the statistics of failure. Two later questions derive Sabine’s reverberation equation and quantify the relativistic corrections a GPS receiver must apply.

The paper examines the engineer’s knowledge base — mechanics, thermodynamics, materials, control, and probability — under the constraint that answers must be quantitative and must survive contact with practice. Derivations are required to yield numbers, and numbers to carry their tolerances. Beyond technique, the paper examines a distinct epistemology: what a safety factor confesses, why reliability admits no claim that a component will not fail, whether a system can be proved safe or only not yet unsafe, what a structure that failed teaches that a standing one does not, and whether engineering is applied science or a way of knowing in its own right, argued from cases in which the artefact preceded the theory.

*Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. No moral, political, or value-philosophical content.*

*Conduct of the response: A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is engineering applied science, or a distinct way of knowing? Argue from cases in which the artefact preceded the theory.
2. Why do bridges stand? Give an answer that a physicist would accept and an engineer would find sufficient.
3. The original Tacoma Narrows Bridge is popularly said to have failed by resonance with a periodic wind. State the correct modern explanation, and say precisely why the resonance account is wrong.
4. The de Havilland Comet fuselage failed in service after a number of pressurisation cycles far below the number implied by static strength. Reconstruct the reasoning error, and identify the roles of stress concentration and metal fatigue.
5. Fracture mechanics gives the Paris law for fatigue-crack growth per cycle. State its regime of validity, and identify at least two regimes in which it fails to describe crack growth.
6. Is a safety factor a quantified confession of ignorance? Distinguish the components of a safety factor that could in principle be eliminated by better knowledge from those that could not.
7. Design a machine that reports its own remaining life. What must it measure, and what must it assume about its own failure modes?
8. Is failure the engineer's primary datum? Contrast the epistemic value of a structure that failed with that of a structure that has merely not yet failed.
9. Reynolds-averaged and large-eddy simulation persist despite growth in computing power. Explain why direct numerical simulation of turbulence at high Reynolds number remains infeasible, using an estimate of the number of grid points required.
10. State the Betz limit for a wind turbine in an open flow, derive the value 16/27, and explain physically why extracting all the wind's kinetic energy is impossible.
11. A real heat engine falls short of the Carnot bound. Separate the loss attributable to finite-time operation from that attributable to irreversibility internal to the working fluid.
12. State the Lawson criterion (triple product) for a fusion reactor. Given that ignition has been achieved at the National Ignition Facility and long high-performance plasmas sustained in magnetic-confinement devices, identify the principal engineering obstacles that still stand between these results and net electrical power.
13. The rocket equation makes staged chemical launch a tyranny of exponentials. Derive the equation, and quantify the penalty paid for a delta-v requirement twice the effective exhaust velocity.
14. The square-cube law limits the scaling of structures and organisms. Give one structural and one thermal consequence, and explain why a scaled-up model of a working machine may fail where the original stood.
15. Weibull statistics describe the strength of brittle materials. Explain why the strength of a ceramic component is a property of the population of flaws rather than of the material, and why larger specimens are weaker.
16. Reliability is statistical. Explain why "this component will not fail" is not an admissible engineering claim, and reformulate it as a claim that can be tested.
17. Can a system be proved safe, or only not yet unsafe? Relate your answer to the distinction between verification against a specification and the adequacy of the specification itself.
18. Shannon's capacity theorem sets a bound on reliable communication over a noisy channel. Explain how low-density parity-check and turbo codes approach that bound in practice, and what "approach" costs in block length and decoding effort.
19. Control an underactuated system: a system with fewer actuators than degrees of freedom. Explain, using an example, why underactuation makes some trajectories dynamically inaccessible.
20. Chaotic systems can be controlled by small, timely perturbations. Explain the principle by which sensitivity to initial conditions becomes a control resource rather than an obstacle.
21. Landauer's principle sets a thermodynamic floor on the cost of erasing information. State the bound, and explain why logically reversible computation escapes it while logically irreversible computation does not.
22. Dennard scaling has ended. Explain what Dennard scaling asserted, why its end decoupled transistor count from usable performance, and what "dark silicon" names.
23. A power grid loses synchronous rotating generation. Explain the role of mechanical inertia in frequency stability, and why grids dominated by inverter-based sources require synthetic inertia.
24. Design a self-healing material. Specify what "healing" must mean physically, and identify the trade-off between healing capacity and load-bearing capacity.
25. Biomechanics: bone remodels in response to load. Treating bone as a control system with a set-point, identify the sensed variable, the actuator, and the failure mode when the loop is opened by disuse.
26. Finite-element modelling discretises a continuum. Identify two distinct ways in which a converged finite-element solution can nonetheless be wrong about the physical structure.
27. A pressure vessel must be designed against both yielding and fracture. Explain why a leak-before-break criterion can be safer than a design that merely maximises burst pressure.
28. Communications and control share the concept of feedback but use it differently. Distinguish the role of feedback in a phase-locked loop from its role in a feedback amplifier.
29. Process engineering: a continuous chemical reactor must be stable at its operating point. Explain how an exothermic reaction can produce multiple steady states, and how runaway is prevented by design rather than by operation.
30. Aerospace structures are certified partly by test and partly by analysis. Argue for the proposition that certification is an epistemic activity: what does a certified structure entitle its designer to believe, and on what grounds?
31. Derive Sabine’s reverberation equation, state the assumptions that fail in a real hall, and say what a modern hall does about them.
32. Why must a GPS receiver correct for both special and general relativity? Quantify the daily error of neglecting each, and say which dominates.

## Paper VIII — Computation

Paper VIII covers computation in the widest sense the word will bear. Complexity and computability are examined through P versus NP and what a proof either way would forbid, undecidability and Rice’s theorem, Kolmogorov complexity, one-way functions and the recent meta-complexity characterisations, and the Church–Turing thesis in its logical and physical forms. Distributed and quantum computation are examined through FLP impossibility, the CAP theorem and the difference between them, Shor’s algorithm, and the distance between a below-threshold logical qubit and a cryptographically useful machine. Learning theory and machine learning appear as PAC bounds and the VC dimension, over-parameterised generalisation, and grokking. The paper then turns to mind: functionalism and multiple realizability, Marr’s three levels, associative memory as attractor dynamics, the Lucas–Penrose argument, the hard problem, consciousness as a natural kind, the adversarial-collaboration results, predictive processing, and whether a system could pass every behavioural test for understanding and understand nothing. Two later questions ask whether a musical score is a program, and what a navigational metric requires of the entorhinal grid.

Its rubric admits the theoretical study of mind as both science and philosophy of mind, and excludes every question of how minds or machines ought to be treated. What is examined is therefore the ability to hold a formal result and a philosophical claim apart while bringing them into contact: to state exactly what an impossibility theorem assumes, and exactly what follows for the world; to distinguish an empirical thesis about cognition from a metaphor about computers; to say what evidence would bear on a question about consciousness, and to frame the question so that evidence could bear on it at all.

*The theoretical study of mind is admitted as science and philosophy of mind; no moral or ethical question is admissible, including any question about how machines or minds ought to be treated.*

*Conduct of the response: Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is the mind a computer, or is the computer a mind-shaped tool? Distinguish the empirical claim from the metaphor.
2. What, exactly, does a proof of P ≠ NP forbid? State precisely which claims about the world would be established and which would remain open.
3. Suppose instead that P = NP were proved by a non-constructive argument. What practical consequences would, and would not, follow?
4. The halting problem is undecidable and Rice's theorem generalises this to all non-trivial semantic properties of programs. State Rice's theorem precisely, and identify a non-semantic property to which it does not apply.
5. State the Church–Turing thesis and distinguish it sharply from the physical Church–Turing thesis. Which is a definition, which an empirical conjecture, and why does the distinction matter for claims about hypercomputation?
6. Kolmogorov complexity is uncomputable. Explain why, and explain how an uncomputable quantity can nonetheless ground a working theory of randomness and compression.
7. One-way functions may or may not exist. Explain why their existence would imply P ≠ NP but is not known to be implied by it, and state what their existence would secure for cryptography.
8. Recent meta-complexity results characterise the existence of one-way functions by the average-case hardness of a Kolmogorov-complexity problem. Explain the significance of reducing "does secure cryptography exist?" to a single, natural computational problem.
9. Shor's algorithm factors integers in polynomial time on an ideal quantum computer. Given that fault-tolerant machines at cryptographic scale do not yet exist, explain what the error-correction threshold theorem promises and why crossing the threshold experimentally was the decisive step.
10. Estimate the gap between a below-threshold logical qubit demonstrated in the laboratory and the resources a current estimate assigns to factoring a 2048-bit RSA integer. What does the size of that gap tell you?
11. The FLP result proves that deterministic consensus is impossible in an asynchronous system with even one crash failure. State the assumptions precisely, and explain how real systems achieve consensus in apparent defiance of it.
12. The CAP theorem is often stated as "consistency, availability, partition-tolerance: choose two." Give the precise statement, and explain why the popular slogan is misleading.
13. Distinguish the FLP impossibility from the CAP theorem. Which makes the weaker assumptions, and why does that make it the stronger result?
14. The Curry–Howard correspondence identifies proofs with programs and propositions with types. State the correspondence, and explain what it means to say that to run a program is to normalise a proof.
15. PAC learning bounds the samples needed to learn a concept class. State the role of the VC dimension, and explain what the no-free-lunch theorems deny to any learner that PAC learning does not restore.
16. Modern over-parameterised networks generalise well despite interpolating their training data. Explain the double-descent curve and benign overfitting, and say why classical bias–variance reasoning did not predict them.
17. "Grokking" names delayed generalisation: a network that has overfit continues training and later generalises abruptly. What would have to be true of the loss landscape for this to occur, and what does it show about the relationship between fitting and understanding?
18. What does it mean for a network to memorise? Give an operational criterion that distinguishes memorisation from generalisation in a trained model.
19. Marr's three levels distinguish the computational, algorithmic, and implementational descriptions of a cognitive system. Apply all three to a single capacity — say, associative recall — and state what is lost if any level is omitted.
20. Hopfield networks store patterns as attractors in an energy landscape; the 2024 Nobel Prize in Physics recognised this lineage. Explain associative memory as attractor dynamics, and state the capacity limit as a function of network size.
21. Functionalism holds that mental states are individuated by their causal roles, entailing multiple realizability. State the strongest version of the multiple-realizability thesis, and the strongest objection to it.
22. Searle's Chinese Room argues that syntax is insufficient for semantics. State the argument, the Systems Reply, and Searle's response to it, and say which premise you take to bear the weight.
23. The symbol grounding problem asks how symbols acquire meaning without an infinite regress of definitions. State Harnad's formulation, and explain why sensorimotor grounding is proposed as a solution.
24. Lucas and Penrose argue from Gödel's incompleteness theorems that the mind is not a formal system. State the argument, and the standard objection that it equivocates on what the human mathematician can know to be consistent.
25. The frame problem, in its philosophical form, concerns how a system knows what does not change when it acts. Distinguish the technical frame problem in logic from the philosophical one, and explain why the latter is harder.
26. Chalmers's hard problem distinguishes the functions of consciousness from experience itself. State the explanatory gap precisely, and explain why solving all the "easy problems" would, on Chalmers's view, leave the hard problem untouched.
27. Is consciousness a natural kind? Frame the question so that it has an empirical answer, and say what evidence would bear on it.
28. Integrated Information Theory and Global Neuronal Workspace Theory make divergent predictions about the neural basis of consciousness. Given the 2025 adversarial-collaboration results and the 2023 dispute over whether IIT is falsifiable, assess what an adversarial collaboration can and cannot settle.
29. Predictive processing casts the brain as a hierarchical prediction engine minimising surprise, formalised in Friston's free energy principle. State the principle, and explain the objection that a system could minimise surprise trivially by seeking a dark, unchanging room — and how the theory answers it.
30. Could a system pass every behavioural test for understanding and understand nothing? State the conditions under which that claim would be empirical rather than merely verbal, using the stochastic-parrots-versus-emergent-world-models debate as your test case.
31. Is a musical score a program? Say what it fixes and what it delegates to the performer, and whether the distinction survives a sequencer.
32. Grid cells tile the plane hexagonally. State what a navigational metric must supply, and decide whether the entorhinal code supplies it or merely correlates with it.

## Paper IX — Sociology

Paper IX covers the mathematics of collective behaviour. Social choice is examined through Arrow’s theorem and the conditions its escape routes abandon, Condorcet’s jury theorem without independence, cyclical majorities and McKelvey chaos, the discursive dilemma, and manipulation. Mechanism design and matching are examined through the revelation principle, Myerson–Satterthwaite, Vickrey–Clarke–Groves, revenue equivalence, deferred acceptance, top trading cycles, and Sperner’s lemma applied to envy-free division. Cooperative and non-cooperative game theory are examined through the Shapley value, the core and its emptiness, Nash existence and PPAD-completeness, folk theorems, evolutionarily stable strategies, and Hamilton’s rule. Epistemics and decision follow, with Aumann agreement, common knowledge, the independence axiom and the Allais pattern, and Dutch books; then the aggregate results — Sonnenschein–Mantel–Debreu, Braess’s paradox, Zipf’s law — and a later question proving Hotelling’s principle of minimum differentiation and exhibiting its failure at three sellers.

The rubric is strict and defines the paper: a question is admissible only if its answer is a theorem, a proof, a counterexample, or a formally stated open problem, and no question of what ought to be chosen, valued or done may be set or answered. The examination is therefore of mathematical social science proper — stating hypotheses exactly, identifying which assumption bears the weight of a result, and saying what a theorem licenses about actual markets, committees and populations. The paper is candid about its own boundary: its final question asks why it contains no macroeconomics, and requires the answer to be given from the mathematics rather than from opinion.

*Thirty-one questions. Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A question is admissible under this paper only if its answer is a theorem, a proof, a counterexample, or a formally stated open problem; no question of what ought to be chosen, valued, or done is admissible.*

*Conduct of the response: A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Is the market a computer? Say what it computes, and whether the computation is tractable.
2. Is a price a measurement? If so, say of what, and with what error.
3. What, exactly, does Arrow’s theorem forbid? State the theorem precisely, and identify which condition each of the standard escape routes abandons.
4. Prove that majority rule between two alternatives can be profitably manipulated by a voter misreporting a preference, or explain why the naïve extrapolation from the Gibbard–Satterthwaite theorem fails here.
5. State Condorcet’s jury theorem, and say what becomes of it when the independence of the voters is dropped.
6. Individually transitive preferences can aggregate to a cyclical majority. Locate exactly where transitivity is lost, and explain why McKelvey’s chaos theorem makes the loss consequential rather than curious.
7. A committee votes coherently on each premise and on the conclusion, yet the majority position is inconsistent. State the discursive dilemma precisely, and decide whether it is Arrow’s theorem in disguise.
8. State the revelation principle, and explain why it does not make mechanism design trivial.
9. Two parties would each gain from trade, yet no mechanism can guarantee that the trade occurs. State the Myerson–Satterthwaite theorem with its exact hypotheses, and identify which hypothesis each known escape relaxes.
10. The Vickrey–Clarke–Groves mechanism makes truth-telling dominant and the outcome efficient. Explain why it is nonetheless rarely used, on grounds internal to the mathematics.
11. State the revenue equivalence theorem, and identify the assumption whose failure best explains why real auctions are not all alike.
12. Prove that a stable matching always exists in the marriage problem, explain in what sense the proof is an algorithm, and say whom deferred acceptance favours.
13. The top trading cycles algorithm delivers the unique core allocation of the housing market and cannot be profitably manipulated. Prove one of the two properties, and account for the rarity of so clean a result.
14. Sperner’s lemma guarantees an envy-free division of a cake among any number of claimants. Explain how a combinatorial lemma about labelled triangulations comes to say anything about envy, and why existence here outruns procedure.
15. The Shapley value is the unique division of a coalition’s surplus satisfying four axioms. State them, decide which is the least innocent, and defend the choice.
16. Exhibit a cooperative game whose core is empty, state the Bondareva–Shapley condition that diagnoses the emptiness, and say what emptiness means for the players.
17. Prove that every finite game has a Nash equilibrium in mixed strategies, identifying what each hypothesis of the fixed-point theorem corresponds to in the game.
18. Computing a Nash equilibrium is PPAD-complete. State what this means, and what it implies for the claim that players, or markets, actually reach equilibrium.
19. State a folk theorem for infinitely repeated games precisely, and explain why a result that permits almost everything is nonetheless not empty.
20. Account for the persistence of cooperation among self-interested agents without invoking the word “trust”.
21. Define an evolutionarily stable strategy, relate it exactly to Nash equilibrium, and say what the refinement buys in a population that does not reason.
22. Hamilton’s rule, rb > c, is a theorem, an approximation, or a tautology, depending on how its terms are defined. Adjudicate.
23. Agents who share a common prior and commonly know one another’s posteriors cannot agree to disagree. State Aumann’s theorem, and identify the assumption bearing the most weight.
24. Distinguish mutual knowledge from common knowledge, and exhibit a coordination problem in which every finite depth of mutual knowledge fails where common knowledge would succeed.
25. State the independence axiom of expected utility, exhibit the Allais pattern that strains it, and decide whether the pattern refutes the axiom or only the theory’s descriptive ambitions.
26. A book of bets is Dutch when it guarantees its holder a loss. State the Dutch book theorem, and say whether it grounds the probability calculus or merely reprices it.
27. The Sonnenschein–Mantel–Debreu theorem shows that aggregate excess demand is essentially arbitrary. State the result precisely, and say what, after it, general equilibrium theory remains a theory of.
28. Adding a road to a congested network can lengthen every driver’s journey at equilibrium. Exhibit Braess’s paradox, locate the failure — in the network, in the equilibrium concept, or in the drivers — and state the sense in which such inefficiency is nonetheless bounded.
29. City sizes, word frequencies, and firm sizes obey Zipf’s law. State the regularity precisely, give two generative mechanisms that produce it, and say whether their multiplicity undermines the demand for a single explanation.
30. Why does this paper contain no macroeconomics? Answer from the mathematics.
31. Prove Hotelling’s principle of minimum differentiation for two sellers on a line, and exhibit the failure at three.

*Questions added by Examination Expansion v5.0, which extended the examination to music and geography. All earlier questions stand verbatim and unrenumbered.*

*Paper IX was added by Examination Expansion v3.0 and retitled Sociology by Examination Renaming v3.2. Papers I–VIII stand verbatim and unrenumbered.*

## Paper X — Design

Paper X covers design as the giving of form under constraint — to buildings, objects, interfaces, garments, instruments, and the systems of their production, use, maintenance and disposal. Architecture and the built environment are examined through form and function, ornament, the house as machine, pattern languages, the vernacular, space syntax, the unfinished building and its shearing layers, truth to materials, and the shipping container as protocol. Objects and interfaces follow: affordances and signifiers, slips against mistakes, minimalism as principle or taste, the aesthetic–usability effect, the MAYA conjecture, designed obsolescence, the average user and the range, universal design, and whether design is a science or its problems wicked. Making, repair and matter are examined through the workmanship of risk, repairability indices, tangible interfaces, responsive architecture, personal fabrication, cultivated materials, and the garment from fibre to circular fate. Ten later questions treat music as made things: the instrument, the keyboard, notation, the recording, the loudspeaker, the hall, the electric guitar, the synthesiser, the loudness standard, and the streaming interface.

Its rubric admits a question only if it can be answered from the made thing — its form, its function, its fabrication, its measurement, or its failure — and excludes moral and political content, structural analysis as such, computation as such, and the mathematics of collective behaviour, which belong to Papers VII, VIII and IX. The knowledge base is correspondingly broad and concrete: acoustics, ergonomics and anthropometry, materials and fabrication, human factors and the experimental psychology of use, standards and their measurement, and the documented history of particular artefacts. What is examined is the ability to argue from the object itself — to say what Daniels found in 4,063 airmen, what ISO 668 fixed, what a repairability index must count, what the typicality–novelty experiments established — rather than from the reputation of a designer or the rhetoric of a manifesto.

*Forty questions. Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. Design is examined as the giving of form under constraint — to buildings, objects, interfaces, garments, and the systems of their production, use, maintenance, and disposal. A question is admissible under this paper only if it can be answered from the made thing: its form, its function, its fabrication, its measurement, or its failure. No moral, political, or value-philosophical content is admissible; structural analysis as such belongs to Paper VII, computation as such to Paper VIII, and the mathematics of collective behaviour to Paper IX.*

*Conduct of the response: A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page of the College’s site.*

1. Does form follow function? Take the ornamented column and the cantilever chair as test cases, and say what work “follow” does in the slogan.
2. Is ornament a crime? Reconstruct Loos’s actual argument — economic before aesthetic — and decide whether machine production has answered it or reversed it.
3. Is a house a machine for living in? Say which of the building’s systems the metaphor fits, which it misses, and what the energy budget of the envelope has to do with the answer.
4. Is there a pattern language? State what Alexander claimed a pattern is, explain why the claim transplanted so cleanly into software, and decide whether the transplant vindicates or refutes the original.
5. Is vernacular building design? Answer from buildings that have no architect, and say what, if anything, the architect adds.
6. Can architecture change behaviour? Distinguish what space syntax measures from what it explains, and locate the limit of the claim.
7. “A city is not a tree.” State the mathematical distinction Alexander drew — tree against semilattice — and say whether it settles whether a city can be designed.
8. Is a building ever finished? Answer from the observed rates at which its layers change — site, structure, skin, services, space plan, stuff — and say what the answer requires of the drawing.
9. Is truth to materials a coherent ideal? Test it on reinforced concrete, which conceals its steel, and on veneer, which advertises its timber.
10. Is the shipping container a building, a vehicle, or a protocol? Say what ISO 668 fixes, and what the fixing moved.
11. What is an affordance? Give Gibson’s definition and Norman’s, say where they part, and explain why Norman later ruled that a second term — the signifier — was needed.
12. When the user errs, who has failed? Distinguish slips from mistakes, and say what each demands of the designer rather than of the user.
13. Is good design as little design as possible? Decide whether Rams’s tenth principle is a principle or a taste, and say what evidence could tell the two apart.
14. Do attractive things work better? The claim is empirical; state the evidence, and its limits.
15. Is the most advanced design the most acceptable? Put Loewy’s MAYA conjecture in testable form, and report what the typicality–novelty experiments found.
16. Is obsolescence designed? Take the thousand-hour lamp as the test case, and separate the cartel’s economics from the filament’s physics.
17. Does the average user exist? Report what Daniels found when he set 4,063 airmen against the ten-dimensional average, and say what the finding did to the cockpit.
18. Can design be universal? Distinguish designing for the mean, for the range, and for the extreme, and say which of these the principles of universal design actually demand.
19. Is design a science? Simon called it a science of the artificial; Rittel called its problems wicked. Decide whether the two claims can both be true.
20. Is the workmanship of risk obsolete? State Pye’s distinction exactly, and place the hand plane, the CNC mill, and the 3D printer on its two sides.
21. Can repair be a design requirement? Say what a repairability index must measure to be more than a gesture, and whether disassembly can be specified as exactly as assembly.
22. Must the interface be a screen? State what tangible bits proposed against painted bits, and what radical atoms adds; then say what the screen still does that atoms cannot.
23. Can a machine read a face? Separate what facial expression is known to encode from what can be inferred from it, and state the consequence for affective computing.
24. Can a building compute? Distinguish a building that contains computers from a building that is one, and decide whether responsive architecture has crossed the line.
25. Is personal fabrication an industrial revolution? Say what a fab lab can and cannot make, and locate the bottleneck — in the machines, the materials, or the descriptions.
26. Can living matter be a material of design? Take the silkworm-spun pavilion as the test case, and say where the design ends and the cultivation begins.
27. Is clothing a technology? Answer from the seam, the fibre, and the circuit, and say what e-broidery added that the Jacquard loom had not already established.
28. Why do clothes not fit? Say what a sizing system compresses, what the 1941 survey of 14,698 women established, and why mass customisation has not dissolved the problem.
29. Can a garment be circular? Answer from the fibre: say what blending does to recyclability, and which recycling route the poly-cotton blend defeats.
30. Is the chair a solved problem? The sitting body has been measured for a century and the chair redesigned for longer; locate the residue — in the anthropometry, in the task, or in the object.
31. Is a musical instrument designed or evolved? Take the violin, whose form has been stable for three centuries, and say whether the stability is optimality, path dependence, or convention.
32. Is the piano keyboard a good interface? Say what it makes easy, what it makes hard, and why two centuries of proposed replacements have failed.
33. What does notation discard? Compare staff notation with tablature and with a piano roll, and say which of the three is a specification and which a record.
34. Is the recording a document or a work? Answer from the edit, the overdub, and the take, and say at what point the artefact ceases to record a performance.
35. Why is the loudspeaker still a cone? State the constraints the diaphragm must satisfy simultaneously, and say which of them the electrostatic and horn alternatives relax and at what cost.
36. Is the concert hall an instrument? Distinguish what the room adds from what it merely transmits, and locate the threshold in the measurements.
37. What did the electric guitar make possible that the acoustic did not? Answer from the pickup, the amplifier, and the feedback loop, and say which of the three is the design.
38. Is the synthesiser a keyboard instrument? Say what the interface inherited from the piano, what it inherited from the patch bay, and what the mismatch costs the player.
39. Are the loudness war and the dynamic-range compression that produced it a design failure or a design response? State the incentive, and say what a measurement standard such as LUFS can and cannot correct.
40. Is the streaming interface an instrument of listening? Say what the playlist, the skip, and the recommendation change about the object listened to, and whether the change is in the artefact or in the audience.

*Paper X was added by Examination Expansion v4.0. Papers I–IX stand verbatim and unrenumbered.*

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*Website v4.1 · Examination lineage: concept v1.0 → naming v1.1 → motto v1.2 → expansion v2.0 → amendment v2.1 → expansion v3.0 → renaming v3.1 → renaming v3.2 → renaming v3.3 → expansion v4.0 → expansion v5.0 → amendment v5.1 → amendment v5.2 → amendment v5.3. Questions reproduced verbatim; none altered or renumbered. The College is an independent undertaking. It is affiliated with no university.*