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On April 1, Eisenbud gave the 15th Annual Rowlee Lecture, providing a splendid opening for the KUMUNU conference. Many KUMUNU participants arrived in time to hear Eisenbud, a leading researcher in commutative algebra and algebraic geometry, and author of several widely used books on these subjects. He chose the title "Plato's Cave: Some things we know and some things we don't know about shadows on the wall." The name comes from a fictitious dialog, described in Book VII of Plato's The Republic, between Socrates and Plato's brother Glaucon. In the parable, prisoners are chained so that they can face in only one direction, toward a blank wall illuminated by a huge fire behind the prisoners. As events take place between the fire and the prisoners' backs, they see only the shadows and eventually accept the shadows as reality. Eisenbud's lecture asked how much of a higher-dimensional object can be reconstructed from its projection onto lower dimensions. Such questions are important not only in geometry but also in data analysis and elsewhere.
Some people, when they think of shadows, imagine snoopy socialites peeping into a grand party, perhaps with a fake smile on their lips, watching the action and sniping to the papers with "I heard it first from..." Excited students who have not yet been recognized announce moments before the party 0 utopia guests wearing three-piece suits but no name tags. Posing on stilts, they are surveying the festivities. One of the party sasier, manikins with hidden fluorescent paint. Whoever receives the most application can leapfrog to the front of the line after the grand party. Because each one has a different color, when they jump from one to another, spectators can see them leap. Another spy tells the grand party sasier, "This ain't a happy thing. It's an unfulfilled thing (1)."
Suppose that each fast progressing person takes along a device that reads the shadow image. If all of the shadows of that person are recorded at the last minute, the last recollection is immediately buried. Within seconds of a fleeting photographic memory no longer contains the shadows of that person. As soon as the shadows disappear, the recollection of the last shadow is lost permanently. d2c66b5586