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In Proceedings, 20th IEEE Symposium on Foundations of Computer Science, Chicago, November 1982 u 21 C O D nlaing, M Sharir and C Yap Retraction: A new approach to motion planning In 15th ACM Symposium on the Theory of Computing, Boston, MA, 1983 22 T Lozano-P rez Automatic planning of manupulator transfer movements IEEE e Transactions on Systems, Man, and Cybernetics SMC-11(10):681 698, 1981 23 J O Rourke Convex hulls, Voronoi diagrams, and terrain navigation In Proceedings of the Pecora IX Remote Sensing Symposium, Sioux Falls, SD, 1984 24 D Pieper The kinematics of manipulators under computer control PhD thesis, Mechanical Engineering Department, Stanford University, 1972 25 S Udupa Collision detection and avoidance in computer controlled manipulators In Proceedings of 5th Joint International Conference on Arti cial Intelligence, Cambridge, MA, 1977 26 B Faverjon Obstacle avoidance using an octree in the con guration space of a manipulator.

In Proceedings of the IEEE International Conference on Robotics and Automation, Atlanta, GA, March 1984 27 T Lozano-P rez and M Wesley An algorithm for planning collision-free paths e among polyhedral obstacles Communications of the ACM 22:560 570, 1979 28 H Moravec The Stanford cart and the CMU rover Proceedings of the IEEE 71(7):872 874, July 1983 29 R Brooks Solving the nd-path problem by good representation of free space IEEE Transactions on Systems, Man, and Cybernetics, 13(3):190 197, 1983 30 T Binford Visual perception by computer In Proc IEEE International Conference Systems, Science, and Cybernetics, Miami, FL, 1971 31 R Paul Modeling trajectory calculation and servoying of a computer controlled arm PhD thesis, Stanford University, 1972 32 J Canny A new algebraic method for robot motion planning and real geometry In Proceedings of the 28th IEEE Symposium on Foundations of Computer Science, Los Angeles, CA, 1987 33 L.

In the 17th century, the mathematician Leibniz postulated that a mathematical theory must be simpler than the system it describes, otherwise it has no use as a theory. This is a very profound statement and one that has a direct corollary to modern engineering. If a new form of abstract design is not simpler to comprehend or easier to design with than a previous form, then it is of little or no use to us in the real world. Some high-level design techniques that have been developed

We laughed By now I knew that I was overstaying my welcome I had asked more questions than I can remember and write about here, and he had happily answered all of them He spent his time so willingly with me that day that it seemed like he was paying me back for something that I had done for him, which obviously was impossible I know you gotta go, I told him Yes I do We ve got some economic news coming out at two Fomsee interest rate decision Fomsee He spelled it out: F-O-M-C Federal Open Market Committee Alan Greenspan and Company of the Federal Reserve make a decision on whether to raise interest rates This decision even no decision can move the dollar 100 points in sixty seconds That might not have sounded thrilling to any of the people sitting around me.

Meijdam and A de Zeeuw On expectations, information, and dynamic game equilibria In Dynamic Games and Applications in Economics, T Basar, ed, Springer-Verlag, New York, 1986..

34 E Moore The ring squad synchronization problem In Sequential Machines: Selected Papers, E Moore, ed, Reading, Addison-Wesley, MA, 1964 35 M Blum and D Kozen On the power of the compass (or, why mazes are easier to search than graphs) In Proceedings of the 19th Annual Symposium on Foundation of Computer Science (FOCS), Ann Arbor, MI, 1978 36 H Abelson and A diSessa Turtle Geometry, MIT Press, Cambridge, MA, 1981 37 J Traub, G Wasilkowski, and H Wozniakowski Information, Uncertainty, Complexity, Addison-Wesley, Reading, MA, 1983 38 L Euler Commentationes Arithmeticae Collectae, St Petersburg Academy, St Petersburg, 1766 39 C Berge Graphs and Hypergraphs, North-Holland, Amsterdam, 1973 40 Hermann Kern Labyrinthe Erscheinungsformen und Deutungen 5000 Jahre Gegenwart eines Urbilds, Prestel-Verlag, Munich, 1982 41 Hermann Kern Through the Labyrinth: Designs and Meanings over 5,000 Years, Prestel Publishing, Munich, 2000 42 O Ore.

over the past 10 15 years certainly fall under the category of lateral abstraction, or new design techniques that are no more abstract than existing technologies. These technologies are slow to catch on; that is, if there is any bene t at all. This chapter discusses techniques that do provide the true bene ts of abstraction and that can increase the effectiveness of a designer.

But now I considered trading my future, and I was determined that as soon as I got back to the office I was going to log on at my desk, and spend as much of my employer s time as possible trying to find out what the FOMC said about interest rates and how it moved the US Dollar I thanked him for meeting with me He nodded and said that a few years before, someone had done the same for him, and he owed it back So that s why I had the feeling that he owed me something Well, it wasn t me, but it was someone else Maybe it had been Anderson We shook hands, and he started to leave But before he left, he reached into his coat pocket and reached for the drink coaster, but then hesitated He was thinking deeply.