Geometry without points

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• Dana Scott
• Thursday 12 May 2016, 11:00-12:00
• Mechanical Engineering, G33.

If you have a question about this talk, please contact Achim Jung.

Ever since the compilers of Euclid’s Elements gave the “definitions” that “a point is that which has no part” and “a line is breadthless length”, philosophers and mathematicians have worried that the the basic concepts of geometry are too abstract and too idealized. In the 20th century writers such as Husserl, Lesniewski, Whitehead, Tarski, Blumenthal, and von Neumann have proposed “pointless” approaches. A problem more recent authors have emphasized it that there are difficulties in having a rich theory of a part-whole relationship without atoms and providing both size and geometric dimension as part of the theory. A possible solution is proposed using the Boolean algebra of measurable sets modulo null sets along with relations derived from the group of rigid motions in Euclidean n-space.

This talk is part of the Computer Science Distinguished Seminar series.

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• Computer Science Distinguished Seminar
• Mechanical Engineering, G33

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