Hamming, "n-Dimensional Space" (April 14, 1995)
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Intro: When I became a professor, after 30 years of active research at Bell Telephone Laboratories, mainly in the math research department, I recalled that professors are supposed to think and digest past experiences. So I put my feet up on the desk and began to consider my past. In the early years I had been mainly in computing so naturally I was involved in many large projects that required computing. Thinking about how things worked out on several of the large engineering systems I was partially involved in, I began, now that I had some distance from them, to see that they had some common elements. Slowly I began to realize that the design problems all took place in a space of n-dimensions, where n is the number of independent parameters. Yes, we build three dimensional objects, but their design is in a high dimensional space, one dimension for each design parameter. The Art of Doing Science and Engineering: Learning to Learn" was the capstone course by Dr. Richard W. Hamming (1915-1998) for graduate students at the Naval Postgraduate School (NPS) in Monterey California. This course is intended to instill a "style of thinking" that will enhance one's ability to function as a problem solver of complex technical issues. With respect, students sometimes called the course "Hamming on Hamming" because he relates many research collaborations, discoveries, inventions and achievements of his own. This collection of stories and carefully distilled insights relates how those discoveries came about. Most importantly, these presentations provide objective analysis about the thought processes and reasoning that took place as Dr. Hamming, his associates and other major thinkers, in computer science and electronics, progressed through the grand challenges of science and engineering in the twentieth century.
Comments
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Very interesting to me , altho I'm not sure what the point was of the ( very impressive , intense ) working out of the Γ function .
Hamming makes a number of important observations about nature of higher dimensional spaces . One is that almost all vectors in high n space are nearly orthogonal , ie : their correlation , ie : the cosine of the angle between them , , is near 0 .
I think stereosphere is correct in his "explanation" of the sphere in the center of surrounding spheres sticking out of the cube at 10 or more dimensions . I created an APL algorithm for minimal paths around n-cubes back in 1979 and drew 2-D projections of cubes up to 9 dimensions . See the projections of the 6-cube at http://cosy.com/cosylogo.htm . You'll see the relative "flattening-out" of the cube versus any 1 dimension which stereosphere also works out . -
is it possible to solve problems using N dimensional analysis for lower dimensions.
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Design synthesis is extremely useful for creating the N dimensional space assumptions.
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so perceivably is possible up to 11 dimensions and higher ones are just impossible. though they exist it will never cross reality or imagination..
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way too complex, probably skipping this ep. as if it didn't exist
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At 28:20 Hamming presents a paradox in 10d space. I believe I have an explanation of the problem. I learned a lot from thinking about it. The video is "Hamming's 10D paradox" on the Stereosphere channel. It is only 50 seconds long. I welcome any comments. This is a wonderful series of lectures. He knew Konrad Zuse, and worked on the differential analyzer!
50m 19sLenght
24Rating