--- title: "Section 2: Creative Blocks" description: "Sessions 7 to 12 of Winfree's course: Adams's perceptual, emotional, cultural and intellectual blocks and his blockbusters, practised on trap puzzles, a cross-checking exercise and the start of an outdoor lab, with the readings each session assigns." type: Lesson tags: [course, student-facing, section-2, creative-blocks, conceptual-blockbusting] 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 2: Creative Blocks Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License. *Six sessions on the blocks that stop ideas before they start* ## Overview Section 2, which the [syllabus](https://tyson-swetnam.github.io/aosd/syllabus/index.md) calls simply "Creative Blocks", asks why good ideas fail to arrive at all. Its backbone is James Adams's *Conceptual Blockbusting*, one of the course's two required books. Sessions 7 to 10 take his chapters on perceptual, emotional, cultural and intellectual blocks in turn; session 11 takes his chapter on blockbusters. Some people suppose problem-solving cannot be taught: you are born with the ability or you are not. Winfree disagreed: "I think we are all born with it and mostly lose it during and because of schooling and the general intimidation that comes with any competitive society." A block is one form that loss takes. Several puzzles here are traps whose obstacle is a rule you added yourself. Getting stuck is part of the design: the course aims for a feeling of "disorientation and hopeless lost-ness", Winfree wrote, so that you "learn not to despair in paralysis but instead focus on method, generate several alternative guesses, and test them for workability." The section ends with an exercise in cross-checking and the start of an outdoor lab that leads into Section 3. ## The sessions ### Session 07: Perceptual blocks **Readings due:** Adams Chapter 2: Perceptual blocks. Discuss [Weird Organism](https://tyson-swetnam.github.io/aosd/problems/weird-organism/index.md), reconstructed as a familiar organism described so plainly that a stereotype hides it. Discuss [Rearranged Triangle](https://tyson-swetnam.github.io/aosd/problems/rearranged-triangle/index.md): the same four pieces fill a triangle, then leave one square over. Start the [Dominoes (group lab)](https://tyson-swetnam.github.io/aosd/problems/dominoes-lab/index.md), reconstructed as the cut-chessboard puzzle done with plain blocks. ### Session 08: Emotional blocks **Readings due:** [The Barometer Story](https://tyson-swetnam.github.io/aosd/problems/barometer-story/index.md) (Calandra) and Adams Chapter 3: Emotional blocks. Discuss [Telltale Number](https://tyson-swetnam.github.io/aosd/problems/telltale-number/index.md), a ten-digit number that describes itself. Then "About assumptions and [Tying Knots](https://tyson-swetnam.github.io/aosd/problems/tying-knots/index.md)". The puzzle as reconstructed: tie a knot in a rope while holding one end in each hand, without letting go. ### Session 09: Cultural blocks **Readings due:** Adams Chapter 4: Cultural blocks; Platt, *Diversity*. Discuss [Mercury's Mysterious Hidden Hemisphere](https://tyson-swetnam.github.io/aosd/problems/mercurys-hidden-hemisphere/index.md): a "fact" repeated in textbooks for 75 years until radar tested it in 1965. ### Session 10: Intellectual blocks **Readings due:** Adams Chapter 5: Intellectual blocks. [Taboo Questions](https://tyson-swetnam.github.io/aosd/problems/taboo-questions/index.md): the questions a scientist is not supposed to ask. [Paths Through Mazes](https://tyson-swetnam.github.io/aosd/problems/paths-through-mazes/index.md): count the ways to read ABRACADABRA down a diamond of letters, then check the count another way. ### Session 11: Blockbusters **Readings due:** Adams Chapter 7: Blockbusters. [Walking Through Walls](https://tyson-swetnam.github.io/aosd/problems/walking-through-walls/index.md), the only problem listed that day: a drill in restating the problem before solving it. ### Session 12: Cross-checks and unfashionable pursuits **Readings due:** Dyson, *Unfashionable Pursuits*; a one-page biography of Mario Capecchi; Narlikar on venture funding. [Sums of Integers](https://tyson-swetnam.github.io/aosd/problems/sums-of-integers/index.md): "like a jig-saw puzzle of cross-checks". Find the formula for 1 + 2 + ... + *n* by as many independent routes as you can. Then the [Pedestrian Crosswalk Mystery](https://tyson-swetnam.github.io/aosd/problems/pedestrian-crosswalk-mystery/index.md) (lab), reconstructed as a group log of a real street crossing. It begins here and continues in session 13, the first of [Section 3](https://tyson-swetnam.github.io/aosd/section3/index.md), where the class discusses its "observations outdoors"; it is listed with that section's problems. ## Key ideas ### Adams's four kinds of block - **Perceptual blocks** stop you seeing the problem, or the information that would solve it: seeing what you expect (stereotyping), drawing the problem's boundaries too tightly, never changing viewpoint. Rearranged Triangle and Weird Organism are built to be misperceived. - **Emotional blocks** include fear of looking foolish, dislike of ambiguity, and judging ideas before you have finished producing them. The syllabus asks for the opposite in class: "braving social opprobrium by blurting out nutty ideas, and risking devastating counter-attack by publicly objecting to nonsense blurted by others." - **Cultural blocks** come from the society around you: taboos, the belief that play wastes time, the belief that tradition beats change. A claim every textbook repeats, like Mercury's frozen hemisphere, is hard to question. - **Intellectual blocks** are about your tools: thinking in words when the problem needs a sketch or a count, reusing the same few strategies, working with missing or wrong information. Paths Through Mazes rewards whoever stops listing paths one by one. ### Hidden rules and restated problems Several of these puzzles cannot be solved until you notice a rule you invented. Tying Knots seems impossible because of how you pick up the rope. Telltale Number collapses once you notice a fact the puzzle never states. In The Barometer Story, an instructor wanted to give zero to a correct answer that was not the one he had in mind. Each time, list the rules you are obeying and check which were actually given. Walking Through Walls, set for the blockbusters session and built on Adams's door example, attacks the same trap from the other side: ask for "a better door" and you get a better slab on hinges; ask for a better way through a wall and the answers multiply. ### Cross-checks and unusual routes One derivation is only a claim; several independent routes that agree, "like a jig-saw puzzle of cross-checks", are evidence. The final exam asks for exactly this: "exhibit as many distinct approaches as you can, and as many cross-checking distinct solutions as you can." The session 12 readings push from another direction: Dyson on unfashionable pursuits and Narlikar on venture funding both concern the value of a route few others are taking. ## GamesWorth focus for this section - Before you try Tying Knots, Telltale Number or Rearranged Triangle, write down every rule you think you must obey. Afterwards, mark which rules were really stated. - When stuck, name the block: perceptual, emotional, cultural or intellectual. Tally which one catches you most often. - Solve Paths Through Mazes and Sums of Integers at least two independent ways, and record where the routes agree or expose a mistake. - For Walking Through Walls, write three ever-broader restatements of the problem, and list every idea for each before judging any of them. - In a morning-after entry on a left-hand page, ask which block slowed you down on a Section 1 problem you struggled with. - At the crosswalk, write down what happens before you try to explain it. Winfree's later *Adventures in Discovery* columns ([introduction, archived](https://web.archive.org/web/20030114041921/http://eebweb.arizona.edu/faculty/winfree/SAS/asdIntro.html){target=_blank} 🔓) collect puzzles he worked through as his own daily GamesWorths. See also the [GamesWorth page](https://tyson-swetnam.github.io/aosd/gamesworth/index.md). ## Readings for this section - **James L. Adams**, *Conceptual Blockbusting: A Guide to Better Ideas*, Chapter 2: Perceptual blocks (session 7), Chapter 3: Emotional blocks (session 8), Chapter 4: Cultural blocks (session 9), Chapter 5: Intellectual blocks (session 10) and Chapter 7: Blockbusters (session 11). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#adams); [publisher](https://www.hachettebookgroup.com/titles/james-l-adams/conceptual-blockbusting/9781541674059/?lens=basic-books){target=_blank} 🔒; 1980 second edition at the [Internet Archive](https://archive.org/details/conceptualblockb0000adam){target=_blank} 🔓 *(borrow)*. Chapter numbers may differ slightly between editions. - **Alexander Calandra**, *The Barometer Story* ("Angels on the Head of a Pin"), *Saturday Review*, 21 December 1968 (session 8). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#barometer-story); [text](https://www.stephenhicks.org/2022/07/10/angels-on-the-head-of-a-pin-by-alexander-calandra/){target=_blank} 🔓 - **John R. Platt**, *Diversity*, *Science* 154, 1132-1139 (1966) (session 9). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#platt-diversity); [Science](https://doi.org/10.1126/science.154.3753.1132){target=_blank} 🔒 - **Freeman Dyson**, *Unfashionable Pursuits*, *The Mathematical Intelligencer* 5(3), 47-54 (1983) (session 12). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#dyson); [journal](https://doi.org/10.1007/BF03026573){target=_blank} 🔒 - **Capecchi one-page biography** (session 12). The syllabus does not say which one. [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#capecchi); Capecchi's later [Nobel Prize autobiography](https://www.nobelprize.org/prizes/medicine/2007/capecchi/biographical/){target=_blank} 🔓 (2007) is a free account of his life. - **Jayant V. Narlikar**, *Venture funding for new ideas*, *Nature* 404, 707 (2000) (session 12). [Reading list entry](https://tyson-swetnam.github.io/aosd/readings/index.md#narlikar); [Nature](https://doi.org/10.1038/35008158){target=_blank} 🔒 ## Problems in this section | Session | Problem | Kind | What it trains | | :-- | :-- | :-- | :-- | | 07 | [Weird Organism](https://tyson-swetnam.github.io/aosd/problems/weird-organism/index.md) | puzzle | Seeing past a stereotype (editors' reconstruction) | | 07 | [Rearranged Triangle](https://tyson-swetnam.github.io/aosd/problems/rearranged-triangle/index.md) | puzzle | Distrusting what the eye reports | | 07 | [Dominoes (group lab)](https://tyson-swetnam.github.io/aosd/problems/dominoes-lab/index.md) | lab | Pooling failed attempts until the reason for failure shows (editors' reconstruction) | | 08 | [The Barometer Story](https://tyson-swetnam.github.io/aosd/problems/barometer-story/index.md) | case study | Noticing the unstated expectation behind a question | | 08 | [Telltale Number](https://tyson-swetnam.github.io/aosd/problems/telltale-number/index.md) | puzzle | Finding the fact a puzzle never states | | 08 | [Tying Knots](https://tyson-swetnam.github.io/aosd/problems/tying-knots/index.md) | puzzle | Separating the rules given from the rules assumed | | 09 | [Mercury's Mysterious Hidden Hemisphere](https://tyson-swetnam.github.io/aosd/problems/mercurys-hidden-hemisphere/index.md) | case study | Questioning what every textbook repeats | | 10 | [Taboo Questions](https://tyson-swetnam.github.io/aosd/problems/taboo-questions/index.md) | discussion | Asking the question you were not supposed to ask | | 10 | [Paths Through Mazes](https://tyson-swetnam.github.io/aosd/problems/paths-through-mazes/index.md) | puzzle | Changing strategy, and checking a count a second way | | 11 | [Walking Through Walls](https://tyson-swetnam.github.io/aosd/problems/walking-through-walls/index.md) | thought experiment | Restating the problem before solving it | | 12 | [Sums of Integers](https://tyson-swetnam.github.io/aosd/problems/sums-of-integers/index.md) | puzzle | Independent derivations that check one another | See the [problem index](https://tyson-swetnam.github.io/aosd/problems/index.md) for every problem in the course. --- *The goal is not to eliminate all blocks (impossible), but to recognize them when they occur and have strategies for working around them.*