--- title: "The Mirror Mystery" description: "Why does a mirror seem to swap left and right but not up and down? A household observation that everyone believes, and a lesson in checking the facts before explaining them." type: Activity tags: [course, student-facing, problem, section-4, mirrors, symmetry, handedness, empirical-generalization] status: stable problem: section: 4 session: 23 identification: probable kind: puzzle generated: by: "claude/opus-5" at: "2026-09-16T00:00:00Z" sources: - id: plato-timaeus-lamb resource: "http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0180%3Atext%3DTim.%3Asection%3D46b" title: "Timaeus 46a-c (on mirrors: why right appears as left)" author: "Plato, translated by W. R. M. Lamb" - id: lucretius-leonard resource: "https://www.gutenberg.org/ebooks/785" title: "On the Nature of Things (De Rerum Natura), Book IV" author: "Lucretius, translated by William Ellery Leonard" - id: kant-prolegomena-carus resource: "https://www.gutenberg.org/ebooks/52821" title: "Prolegomena to Any Future Metaphysics, Section 13" author: "Immanuel Kant, translated by Paul Carus" - id: gardner-1964 resource: "https://archive.org/details/ambidextrousuniv0000gard_i3y0" title: "The Ambidextrous Universe" author: "Martin Gardner" - id: block-1974 resource: "https://doi.org/10.2307/2024963" title: "Why do Mirrors Reverse Right/Left but not Up/Down?" author: "Ned Block" - id: denyer-1994 resource: "https://doi.org/10.1017/S0031819100046842" title: "Why do Mirrors Reverse Left/Right and not Up/Down?" author: "Nicholas Denyer" - id: gregory-1997 resource: "https://archive.org/details/mirrorsinmind0000greg" title: "Mirrors in Mind" author: "Richard L. Gregory" - id: corballis-2000 resource: "https://doi.org/10.3758/BF03210736" title: "Much ado about mirrors" author: "Michael C. Corballis" - id: feynman-fun-to-imagine resource: "https://archive.org/details/FunToImagine" title: "Richard Feynman: Fun to Imagine (BBC, 1983)" author: "Richard P. Feynman / BBC" - id: commons-mirror-writing resource: "https://commons.wikimedia.org/wiki/File:Mirror_writing2.jpg" title: "Ottoman calligraphic panel in mirror writing (Wikimedia Commons)" author: "Mahmoud Ibrahim" - id: winfree-handout-2002 resource: "https://web.archive.org/web/20020420212713/http://eebweb.arizona.edu/Faculty/Winfree/handout_479.htm" title: "The Art of Scientific Discovery (ECOL 479/579): course handout, archived 20 April 2002" author: "Arthur T. Winfree" - id: winfree-associativity resource: "https://web.archive.org/web/20030114050407/http://eebweb.arizona.edu/faculty/winfree/Associativity.htm" title: "How to use this in ASD (floating-point associativity and a broken mirror symmetry)" 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" --- # The Mirror Mystery Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License. *[Section 4](https://tyson-swetnam.github.io/aosd/section4/index.md), session 23. In the same session the class plays [Eleusis](https://tyson-swetnam.github.io/aosd/problems/eleusis/index.md).* !!! abstract "The problem" Reconstructed from the syllabus: the syllabus gives only the name, and this is the editors' statement of the classic puzzle it most probably means. None of the wording is Winfree's. Stand in front of a mirror and raise your right hand. The person in the glass seems to raise a left hand. Writing held up to the glass comes back backwards. Yet your head is still at the top and your feet at the bottom. **Why does a mirror reverse left and right but not up and down?** Before explaining, make sure you have the fact right. Check against a real mirror: - Which way does your reflection's nose point? - Point straight at the mirror. Which way does the reflected arm point? - Write a word on tracing paper. Hold it up with the writing facing you, not turned round, and read the word in the mirror through the paper. Where did the reversal go? - Lie on your side in front of a long mirror. What is swapped now? Record what you believed at the start, which observations survived, and what you believe now. ## Why it is in the course Section 4 is "Patterns, Empirical Generalizations", and its problems test generalizations people hold with confidence. "Mirrors reverse left and right" is a pure specimen: everyone believes it, and almost nobody has varied the observation. The same class period plays Eleusis, a card game that penalizes a guessed rule which only fits the cards you happen to have seen. It also echoes Section 1: "facts before explanations of facts" and "distinguishing things we know vs only imagine". Most people explain the reversal before checking that it happens. It needs no equipment, and the syllabus says the puzzles exist "to slow you down for a few minutes so you can examine the working of your own mind". Here you can watch yourself defend a wrong statement of the facts. ## Where it comes from The question is ancient. Plato's *Timaeus* (46b) says "Left appears as right, because contact takes place between opposite portions of the visual stream and opposite portions of the object, contrary to the regular mode of collision". Lucretius, in Book IV of *On the Nature of Things*, pictures the image flung back like a plaster mask thrown against a post before it dries, so that "now the right eye is the left, / The left the right". Kant made the neighbouring point famous in his *Prolegomena* (1783): a hand and its mirror image match in every part, yet "the glove of one hand cannot be used for the other". Martin Gardner opened *The Ambidextrous Universe* (1964) with the mirror question. Later it became a question about the mind: Ned Block (1974) argued that the answer lies in how we assign left and right to a body, and replies and surveys followed from Nicholas Denyer (1994), Richard Gregory (*Mirrors in Mind*, 1997) and Michael Corballis (2000). Feynman took it up in his 1983 BBC series *Fun to Imagine*. The difficulty was never the optics. ![An 18th-century Ottoman calligraphic panel in which a phrase is written twice, once as the mirror image of the other](https://tyson-swetnam.github.io/aosd/assets/images/problems/mirror-mystery-levha.jpg){ width="560" } *Mahmoud Ibrahim, Ottoman calligraphic panel in mirror writing (c. 1720-1730), Library of Congress, via Wikimedia Commons. Public domain.* ??? tip "Hints" - Say exactly what is reversed and what is not, without the words "left" and "right". - Change your own orientation: lie down, or put the mirror on the floor. Does the mirror care how you stand? - Point your arm across the mirror, then up, then straight at the glass. Which of the three reflected arms points the opposite way? - How do you decide which hand of the figure in the glass is *its* right hand? What do you do, in your head, to decide? ??? success "Resolution" A plane mirror reverses one direction only: the one perpendicular to its surface. With *x* across the mirror, *y* up it and *z* out of it, the point (*x*, *y*, *z*) appears at (*x*, *y*, โˆ’*z*). Left-right and up-down are both untouched; reversing front and back is enough to turn a right hand into a left one. The left-right swap is supplied by you. To name the reflection's left and right, you imagine yourself turned through 180 degrees about a vertical axis to stand where it stands, and that rotation exchanges left and right. Imagine turning head over heels instead and the same reflection reads as upside down, with left and right intact. ![Plan view from above. Left: a person facing a mirror and the image behind it, with the right hand and its image on the same side. Right: the same scene plus the person imagined turned round to face the way the image faces, which puts the right hand on the other side](https://tyson-swetnam.github.io/aosd/assets/images/problems/mirror-mystery.svg){ width="560" } *Seen from above; the red dot is your right hand. Left: the mirror reverses only the direction through the glass. Right: turning round in your head to face the way the image faces is what moves your right hand to the other side. Drawn for this site (CC BY 4.0).* Writing works the same way. Leave the tracing paper facing you and the word seen through the paper in the mirror reads normally. Turn the sheet round to face the glass and the reflection reads backwards, exactly as the sheet itself looks from behind. The reversal came from turning the page, not from the mirror. We make the imagined turn about a vertical axis because that is how we turn to face anyone, and gravity keeps the vertical fixed. Lie down beside the mirror and the mystery lies down with you. The lesson: a question can be unanswerable because it contains a false statement of the facts. Restate the facts rather than hunting harder for a cause. ## Sources - **Plato**, *Timaeus* 46aโ€“c, translated by W. R. M. Lamb (1925) โ€” [Perseus](http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0180%3Atext%3DTim.%3Asection%3D46b){target=_blank} ๐Ÿ”“ - **Lucretius**, *On the Nature of Things*, Book IV, translated by William Ellery Leonard (1916) โ€” [Project Gutenberg](https://www.gutenberg.org/ebooks/785){target=_blank} ๐Ÿ”“ - **Immanuel Kant**, *Prolegomena to Any Future Metaphysics*, Section 13, translated by Paul Carus (1902) โ€” [Project Gutenberg](https://www.gutenberg.org/ebooks/52821){target=_blank} ๐Ÿ”“ - **Martin Gardner**, *The Ambidextrous Universe* (1964) โ€” [Internet Archive](https://archive.org/details/ambidextrousuniv0000gard_i3y0){target=_blank} ๐Ÿ”“ *(borrow)* - **Ned Block**, "Why do Mirrors Reverse Right/Left but not Up/Down?", *Journal of Philosophy* 71(9), 259โ€“277 (1974) โ€” [doi:10.2307/2024963](https://doi.org/10.2307/2024963){target=_blank} ๐Ÿ”’ - **Nicholas Denyer**, "Why do Mirrors Reverse Left/Right and not Up/Down?", *Philosophy* 69(268), 205โ€“210 (1994) โ€” [doi:10.1017/S0031819100046842](https://doi.org/10.1017/S0031819100046842){target=_blank} ๐Ÿ”’ - **Richard L. Gregory**, *Mirrors in Mind* (1997) โ€” [Internet Archive](https://archive.org/details/mirrorsinmind0000greg){target=_blank} ๐Ÿ”“ *(borrow)* - **Michael C. Corballis**, "Much ado about mirrors", *Psychonomic Bulletin & Review* 7(1), 163โ€“169 (2000) โ€” [doi:10.3758/BF03210736](https://doi.org/10.3758/BF03210736){target=_blank} ๐Ÿ”’ - **Richard P. Feynman / BBC**, *Fun to Imagine* (1983) โ€” [Internet Archive](https://archive.org/details/FunToImagine){target=_blank} ๐Ÿ”“ - **Mahmoud Ibrahim**, calligraphic panel in mirror writing (c. 1720โ€“1730) โ€” [Wikimedia Commons](https://commons.wikimedia.org/wiki/File:Mirror_writing2.jpg){target=_blank} ๐Ÿ”“ - **Arthur T. Winfree**, *The Art of Scientific Discovery* (ECOL 479/579): course handout, archived 20 April 2002 โ€” [Wayback Machine](https://web.archive.org/web/20020420212713/http://eebweb.arizona.edu/Faculty/Winfree/handout_479.htm){target=_blank} ๐Ÿ”“ - **Arthur T. Winfree**, "How to use this in ASD" (floating-point arithmetic and a broken mirror symmetry; a candidate, not a source for this problem, see the note below) โ€” [Wayback Machine](https://web.archive.org/web/20030114050407/http://eebweb.arizona.edu/faculty/winfree/Associativity.htm){target=_blank} ๐Ÿ”“ - **Arthur T. Winfree**, *The Art of Scientific Discovery*: original course syllabus โ€” [PDF](https://github.com/tyson-swetnam/aosd/blob/main/docs/assets/aosd_syllabus.pdf){target=_blank} ๐Ÿ”“ !!! note "How sure are we that this is Winfree's problem?" Probable, not certain. The syllabus, like Winfree's archived handout, says only "Deal with the Mirror Mystery", and no other surviving Winfree page uses the name. The classic puzzle fits the name, needs no apparatus, and suits a section about generalizations. Other readings: - **Winfree's own broken symmetry.** His archived page "How to use this in ASD" describes a mirror-symmetric simulation that loses its symmetry because adding numbers in a different order gives a different sum. It never uses the name, needs a computer, and seems to belong with the error-checking sessions (6 or 12). - **The half-height mirror**: how much mirror you need to see all of yourself; usually a physics exercise. - **Mirror-image molecules in living things**: needs subject knowledge the syllabus avoids; untested. --- *Back to [Section 4](https://tyson-swetnam.github.io/aosd/section4/index.md) ยท [All problems](https://tyson-swetnam.github.io/aosd/problems/index.md) ยท [The schedule](https://tyson-swetnam.github.io/aosd/syllabus/index.md#section-4-patterns-empirical-generalizations)*