Section 3: Observations and Questions¶

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Six sessions of looking hard, pooling what you see, and asking questions an observation can answer

Overview¶

The syllabus names this section "Observations and Questions". Among the course's aims it lists practice in "recognizing ignorance" and "posing questions". Section 3 opens by discussing the class's outdoor observations at a pedestrian crosswalk. It then runs a chemical pattern-formation lab across three sessions.

Much of this work cannot be done alone. In Winfree's words: "Class meetings will also prove essential for some problems in which no one individual can collect enough data, but if we pool data, reality will come into focus."

The paper problems in between test the same habits. What have you never seen, and why did you never notice? When do your eyes deceive you? When does a careful drawing or a stack of filters overrule a confident guess? Session 04's "facts before explanations of facts" now meets real data.

The syllabus gives most problems only a title. Each problem page says how sure the editors are of what Winfree meant.

The sessions¶

Session 13: Crosswalk and bridges¶

Readings due: none listed.

Discuss Ant Walk and Seven Bridges of Königsberg. Seven Bridges asks whether a walk can cross every bridge exactly once. Ant Walk cannot be identified from its title; its page is the editors' reconstruction of a similar walk along wires.

Discuss observations outdoors on the Pedestrian Crosswalk Mystery. This lab straddles the sections: it began in session 12, the last session of Section 2. Its original text is lost, so its page is also a reconstruction. Start the Chemical Pattern-Formation Lab, which runs through session 15.

Session 14: What isn't there¶

Readings due: Judson, Chapter 4: Chance; Anderson on research strategy.

The lab continues with "More chemical observations". Discuss What Isn't There (Surprisingly Hard); the parenthesis is the syllabus's own.

Session 15: Evidence and the senses¶

Readings due: Judson, Chapter 8: Evidence.

The session takes up Mother Nature as Magician; Hallucinations. The chemical lab ends with "Last chemical observations". Discuss Rainbow Moon, Winfree's own puzzle about the Moon inside a rainbow's colour band.

Session 16: Hairy People, Green Stars, Escher¶

Readings due: Ehrlich, Chapter 2: "More Guns Means Less Crime".

Discuss Hairy People, Green Stars and Escher Print Gallery.

Session 17: Zygotes and honeycombs¶

Readings due: Ehrlich, Chapter 3: "AIDS Is Not Caused by HIV".

Discuss Zygotes and Martian HoneyCombs. Neither can be identified from its title, so both pages are the editors' reconstructions.

Session 18: Cevians and filters¶

Readings due: Ehrlich, Chapter 4: "Sun Exposure Is Beneficial".

Discuss Cevians and Superposed Filters.

Key ideas¶

Observation is not interpretation¶

A notebook entry should separate what you saw from what you concluded. "Four people stepped out before the car had stopped" is an observation. "People here trust drivers" is an inference. The crosswalk and the chemical dish both reward writing the first kind of sentence before the second. That is session 04's "distinguishing things we know vs only imagine", applied to data you collected yourself.

Absences are data¶

Some absences are obvious and some are not. Winfree made this point in a later column, SAS08 🔓: some things that never happen are easy to notice, and others are hard. What Isn't There, Green Stars and Rainbow Moon each start from something nobody sees. The work is to turn "never seen" into a prediction that could fail.

Honest senses, false conclusions¶

In an illusion, the eye reports faithfully and the inference goes wrong. In a hallucination, the percept has no outside cause at all. Escher's loops add a third trap: every local piece passes inspection, and the error shows only when you follow the whole.

Questions that observations can answer¶

These are the editors' categories, not Winfree's. They are useful prompts for these problems:

Descriptive: What exactly happens, in what order, and how often? (crosswalk, chemical dish)
Absence: What never happens here, and would I have noticed if it did? (What Isn't There, Green Stars)
Counting and constraint: What property decides whether a route or an answer can exist at all? (Seven Bridges, Ant Walk, Hairy People)
Test: What would I see if my first guess were wrong? (Cevians, Superposed Filters, Rainbow Moon)

Pooled observation¶

One observer at a crossing sees one corner for one stretch of time. A class sees many. Pooling only works if each record is legible to others: time, place, what was counted, and what was guessed.

GamesWorth focus for this section¶

Before explaining the crosswalk or the chemical dish, write a plain log of what happened, with times.
Over a week, list things that never happen, then mark which ones you would actually have noticed.
For Rainbow Moon, Cevians and Superposed Filters, write your prediction down before you check it. Record how far off it was.
For Hairy People and Seven Bridges, note the moment you stopped trying cases and started counting.
For the problems whose original statements are lost (Ant Walk, Pedestrian Crosswalk Mystery, Zygotes, Martian HoneyCombs), list every assumption your version of the problem depends on.

Readings for this section¶

Horace Freeland Judson, The Search for Solutions, Chapter 4: Chance (session 14). Reading list entry; Internet Archive 🔓 (borrow)
Anderson on research strategy (session 14). The syllabus names no title; the editors identify it as Philip W. Anderson, More Is Different, Science 177, 393-396 (1972). Reading list entry; PDF 🔓
Horace Freeland Judson, The Search for Solutions, Chapter 8: Evidence (session 15). Reading list entry; Internet Archive 🔓 (borrow)
Robert Ehrlich, Nine Crazy Ideas in Science: A Few Might Even Be True, Chapter 2: "More Guns Means Less Crime" (session 16). Reading list entry; publisher 🔒
Robert Ehrlich, Nine Crazy Ideas in Science, Chapter 3: "AIDS Is Not Caused by HIV" (session 17). Reading list entry; publisher 🔒
Robert Ehrlich, Nine Crazy Ideas in Science, Chapter 4: "Sun Exposure Is Beneficial" (session 18). Reading list entry; publisher 🔒

Problems in this section¶

Session	Problem	Kind	What it trains
12-13	Pedestrian Crosswalk Mystery	lab	Logging a real street scene before explaining it; pooling the class's records (editors' reconstruction)
13	Ant Walk	puzzle	Counting wires at each corner instead of tracing routes (editors' reconstruction)
13	Seven Bridges of Königsberg	puzzle	Keeping only the connections and asking what decides whether a walk exists
13-15	Chemical Pattern-Formation Lab	lab	Recording chemical waves over three sessions before explaining them
14	What Isn't There (Surprisingly Hard)	discussion	Noticing absences and turning them into testable expectations
15	Mother Nature as Magician; Hallucinations	discussion	Separating honest perception from false inference
15	Rainbow Moon	puzzle	Reading a failed prediction as evidence about your assumptions
16	Hairy People	puzzle	Proving what nobody could observe, and checking the upper bound it rests on
16	Green Stars	puzzle	Asking whether a missing colour lies in the stars or in the eye
16	Escher Print Gallery	puzzle	Checking the whole loop, not just each local step
17	Zygotes	puzzle	Counting the unseen from the seen, and naming the assumptions (editors' reconstruction)
17	Martian HoneyCombs	thought experiment	Sorting "facts" into mathematics, physics, biology and the unmeasured (editors' reconstruction)
18	Cevians	puzzle	Trusting a careful measurement over a confident first guess
18	Superposed Filters	puzzle	Writing the prediction down, then looking

See the problem index for every problem in the course.

Good questions are worth more than quick answers, and careful observation is where every one of them starts.

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