--- title: "Section 5: Inferences, Hypotheses, Explanations" description: "The last six sessions of Winfree's schedule (25-30): from pooled data to theory, reading Chamberlin, Platt, Judson and Feynman while the class holds rival hypotheses, settles wagers and discovers the laws of a toy universe." type: Lesson tags: [course, student-facing, section-5, inference, hypotheses, explanation] status: stable generated: by: "claude/opus-5" at: "2026-09-16T00:00:00Z" sources: - id: winfree-handout resource: "https://web.archive.org/web/20070214070741/http://eebweb.arizona.edu/faculty/winfree/Handout_479.htm" title: "The Art of Scientific Discovery (EEB 479): course handout, Web Archive capture of 2007-02-14" author: "Arthur T. Winfree" - id: aosd-syllabus resource: "https://github.com/tyson-swetnam/aosd/blob/main/docs/assets/aosd_syllabus.pdf" title: "The Art of Scientific Discovery: original course syllabus (PDF)" author: "Arthur T. Winfree" --- # Section 5: Inferences, Hypotheses, Explanations Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License. *Six sessions of building theories and trying to kill them* ## Overview Section 4 collected regularities. Section 5 asks why they hold. The syllabus titles it "Inferences, Hypotheses, Explanations", and its readings run in a line: Chamberlin on multiple working hypotheses, Platt on strong inference, Judson on strong predictions, Feynman on the character of physical law, and Judson again on theory. The syllabus describes the course's exercises as practice "of cultivating multiple alternative solutions, of eliminating rejectable candidate solutions", and asks you to "generate several alternative guesses, and test them for workability". The problems here have that shape: several explanations fit, and the work is finding the observation that separates them. Three of the activities are group labs that begin with experiments and end with a theory: Stacked Cantilevers, LoShu and the toy universe. They depend on the class, since for some problems no one person can collect enough data, "but if we pool data, reality will come into focus". ## The sessions The syllabus gives little more than a name for each problem, so every problem page in this section is the editors' reconstruction of the exercise. For The Miracle of FujiYama and Antigen Invasions even the subject is a guess. ### Session 25: Multiple working hypotheses **Readings due:** Chamberlin, *The Method of Multiple Working Hypotheses*. "Further collaborations on Stacked Cantilevers". The [Stacked Cantilevers Lab](https://tyson-swetnam.github.io/aosd/problems/stacked-cantilevers-lab/index.md) began in session 24, the last session of [Section 4](https://tyson-swetnam.github.io/aosd/section4/index.md), and closes in session 26. The class pools measurements of how far a pile of blocks can lean out over a table edge. ### Session 26: Theory and wagers **Readings due:** listed in the schedule as TBA. "Theory of stacking cantilevers, resolution of wagers", closing the lab. Then [Summing a Series](https://tyson-swetnam.github.io/aosd/problems/summing-a-series/index.md): the block theory produces 1 + 1/2 + 1/3 + ... + 1/n, and the question is whether it has a limit. Then [Stalactites](https://tyson-swetnam.github.io/aosd/problems/stalactites/index.md): why dripping water leaves stone hanging from a cave ceiling, why it has that shape, and how old it is. ### Session 27: Strong inference **Readings due:** Platt, *Strong Inference*. "Start LoShu lab experiments in class". The [LoShu Lab](https://tyson-swetnam.github.io/aosd/problems/loshu-lab/index.md) runs two experiments, a pick-three-to-make-15 card game and 3 x 3 magic squares, and asks for one theory that explains both. The Thanksgiving break falls between this session and the next. ### Session 28: Strong predictions **Readings due:** Judson, Chapter 7: *Strong Predictions*. Deal with [The Miracle of FujiYama](https://tyson-swetnam.github.io/aosd/problems/miracle-of-fujiyama/index.md), reconstructed as a row of eight coupled reactors that stores three patterns: where must the row settle? Then "Finish complete theory of LoShu." Then "Start discovering laws of a toy universe in class": the [Laws of a Toy Universe](https://tyson-swetnam.github.io/aosd/problems/laws-of-toy-universe/index.md) lab, which continues into session 29. ### Session 29: The character of physical law **Readings due:** Feynman, *The Character of Physical Law*. Deal with [Antigen Invasions](https://tyson-swetnam.github.io/aosd/problems/antigen-invasions/index.md), reconstructed as a record of repeated invasions by foreign substances, and [Martian DNA](https://tyson-swetnam.github.io/aosd/problems/martian-dna/index.md), a picture captioned as Martian hereditary material. "Finish collaborative discovery of The Laws." The syllabus adds: "All GamesWorth books collected for inspection". ### Session 30: Theory **Readings due:** Judson, Chapter 9: *Theory*. Deal with [Bacterial Hybrids](https://tyson-swetnam.github.io/aosd/problems/bacterial-hybrids/index.md): two strains that cannot grow alone give colonies when mixed. It is the last problem in the schedule. The final exam follows in exam week. ## Key ideas **Multiple working hypotheses.** Chamberlin, a geologist, traces how a favoured explanation hardens into a ruling theory that bends every new fact to fit. His remedy is to keep several hypotheses alive together, so that fondness for one cannot decide the question. Stalactites and Antigen Invasions both reward writing the whole list before choosing. **Strong inference.** Platt turns Chamberlin's attitude into a routine: devise alternative hypotheses; devise a crucial experiment whose possible outcomes each exclude one or more of them; run it cleanly; then recycle with whatever survives. A card game or a toy universe is a cheap place to practise the cycle, because a test takes minutes. **Strong predictions and silent zones.** A useful theory names the outcome before the run, so one run can embarrass it. The FujiYama reconstruction adds the complement: find the cases where your theory predicts nothing, since those are where it cannot be tested. **No finite data forces one law.** A class can agree on The Laws and still be wrong about a case its runs never visited, and a series can look settled for a thousand terms. This is session 04's "distinguishing things we know vs only imagine", now applied to theories. **Where the claim came from.** Martian DNA asks which conclusions came from the picture and which from its caption, the section's version of session 04's "facts before explanations of facts". ## GamesWorth focus for this section - Before the cantilever theory is worked out, write your wager and the reasoning behind it in the notebook, dated. After session 26, do a morning-after on why it won or lost. - For Stalactites, Antigen Invasions and Bacterial Hybrids, list every explanation you can before judging any, then write the one observation that would separate your top two. - In the LoShu and toy-universe labs, record each hunch as a testable rule, the test you ran, and whether the rule died. - For Summing a Series, note the point where your numbers stopped being evidence and you needed an argument. - For Martian DNA, split a page in two: what the picture shows, and what you took from the caption. The syllabus explains that the name GamesWorth alludes to "how much thought it takes to play one game of serious chess". Winfree's own puzzles in that spirit are introduced in his [*Adventures in Discovery*](https://web.archive.org/web/20030114041921/http://eebweb.arizona.edu/faculty/winfree/SAS/asdIntro.html){target=_blank} 🔓 column. ## Readings for this section - **T. C. Chamberlin**, *The Method of Multiple Working Hypotheses* (1890; reprinted in *Science*, 1965) (session 25). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#chamberlin); [PDF](https://www.whoi.edu/cms/files/chamberlin65sci_72744.pdf){target=_blank} 🔓 - **John R. Platt**, *Strong Inference*, *Science* (1964) (session 27). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#platt-strong-inference); [PDF](https://www.whoi.edu/cms/files/platt64sci_72743.pdf){target=_blank} 🔓 - **Horace Freeland Judson**, *The Search for Solutions*, Chapter 7: *Strong Predictions* (session 28). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#judson); [Internet Archive](https://archive.org/details/searchforsolutio00juds){target=_blank} 🔓 *(borrow)* - **Richard P. Feynman**, *The Character of Physical Law* (1964 Messenger Lectures; MIT Press, 1965) (session 29). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#feynman-character-of-physical-law); [lectures at the Internet Archive](https://archive.org/details/the-messenger-lectures){target=_blank} 🔓 - **Horace Freeland Judson**, *The Search for Solutions*, Chapter 9: *Theory* (session 30). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#judson); [Internet Archive](https://archive.org/details/searchforsolutio00juds){target=_blank} 🔓 *(borrow)* ## Problems in this section | Session | Problem | Kind | What it trains | | :-- | :-- | :-- | :-- | | 24-26 | [Stacked Cantilevers Lab](https://tyson-swetnam.github.io/aosd/problems/stacked-cantilevers-lab/index.md) | lab | Pooling measurements, placing wagers, then building the theory that settles them | | 26 | [Summing a Series](https://tyson-swetnam.github.io/aosd/problems/summing-a-series/index.md) | puzzle | Not trusting the first thousand terms; deciding by argument | | 26 | [Stalactites](https://tyson-swetnam.github.io/aosd/problems/stalactites/index.md) | puzzle | Multiple working hypotheses; finding the hidden assumption in an age estimate | | 27-28 | [LoShu Lab](https://tyson-swetnam.github.io/aosd/problems/loshu-lab/index.md) | lab | Experiments first, then one theory that explains two different games | | 28 | [The Miracle of FujiYama](https://tyson-swetnam.github.io/aosd/problems/miracle-of-fujiyama/index.md) | puzzle | Making a strong prediction and finding where it goes silent (editors' reconstruction) | | 28-29 | [Laws of a Toy Universe](https://tyson-swetnam.github.io/aosd/problems/laws-of-toy-universe/index.md) | lab | Inferring hidden laws and designing the experiment that could refute them | | 29 | [Antigen Invasions](https://tyson-swetnam.github.io/aosd/problems/antigen-invasions/index.md) | puzzle | Stating rules from a record, inventing rival mechanisms, finding the deciding observation (editors' reconstruction) | | 29 | [Martian DNA](https://tyson-swetnam.github.io/aosd/problems/martian-dna/index.md) | puzzle | Separating what the picture shows from what the caption suggests | | 30 | [Bacterial Hybrids](https://tyson-swetnam.github.io/aosd/problems/bacterial-hybrids/index.md) | puzzle | Listing every explanation, reading linkage from counts, killing the rival | See the [problem index](https://tyson-swetnam.github.io/aosd/problems/index.md) for every problem in the course. --- *At the final exam you choose problems and "exhibit as many distinct approaches as you can, and as many cross-checking distinct solutions as you can."*