Blog Category: mathematics

Quantum Computing for Technology Managers

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Wiley’s Handbook of Technology Management, which includes my entry on Quantum Computing, just appeared. I received my tome in the mail today. It is definitely the biggest, weightiest, and most expensive publication I’ve contributed to yet! I was only willing to write the entry if I could also post it on the ArXiv. Wiley agreed, so you can find my entry on the ArXiv as “An Overview of Quantum Computing for Technology Managers.”

I hope the entry conveys the excitement of the field while eliminating some of the hype.  It is focused on what is known about what quantum computers can and cannot do. It does not try to explain how they do what they do. (For that, my tutorial with Wolfgang Polak remains a good starting place.) While the entry discusses well known aspects of quantum computation, such as Shor’s algorithm, quantum key distribution, and quantum teleportation,  it also discusses many lesser known results including more recent algorithmic results and established limitations on quantum computation. I had the pleasure of writing about some of my favorite topics in quantum computing, including purely classical results inspired by the quantum information processing point of view, the elegant cluster state model of quantum computation, and Aaronson’s suggestion that limits on computational power be considered a fundamental guiding principle for physical theories, much like the laws of thermodynamics.

Comments and questions welcome!

Mathematical and Musical Adventures

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The next talk in the Bay Area Mathematical Adventures series is this Friday. Robert Bryant, the current director of MSRI, will speak on “Rolling and Tumbling—The idea of Holonomy.” It sounds like a fun talk; he’ll illustrate his talk with “everyday and some not-so-everyday toys.”

I’ve posted the slides from my Bay Area Mathematical Adventures talk last month on From Photographs to Models: The Mathematics of Image-Based Modeling. I blogged about that experience here. I had hoped to post a link to the video at the same time, but it isn’t ready yet. I never feel that a talk is fully captured from just the slides, especially one that was designed to be interactive. I will post a link to the video once it is up.

I’d be tempted to go to Bryant’s talk except that I’m singing that night. Two FXPAL folks, Bill van Melle and I, sing in the 40 voice Bay Choral Guild. We have concerts Fri, Sat, and Sun at various Bay Area locations. Come if you are in the area and would enjoy a concert of festive Baroque choral works performed by our excellent group together with an outstanding group of soloists and musicians!

My dream virtual (almost) reality exhibit

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A couple of weeks ago I attended the SIAM/ACM Joint Conference on Geometric and Physical Modeling and heard a lovely talk by Richard Riesenfeld. Riesenfeld and his wife Elaine Cohen were this year’s Bézier award winners for their work in computer aided geometric design (CAGD). He spoke about his correspondence with Bézier and showed us many of the letters they sent back and forth in the early days of CAD/CAM, with their many hand drawn diagrams and the typed text with the math symbols added in by hand. I spent the time marveling at how they managed to have an effective collaboration over such an impoverished communication channel. But even with all of the wonderful 3D rendering capabilities we have today, it is still hard to communicate about 3D objects and spaces over a distance. Having a visual rendering is not sufficient. Spatial reasoning requires more. Riesenfeld mentioned Bézier’s view that “touch is more discriminative than eyes.”

This theme reminded me that I’ve been meaning to describe and send to the math factory folks  a suggestion for an exhibit in the math museum. Instead, I’ll first write about it here.

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More mathematical adventures

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In early August I thumbed through a copy of The New Yorker idly wondering which article I’d like to read when the name “Glen Whitney” popped out. A close friend of mine from graduate school is named Glen Whitney. Could it be the same person? Sure enough, with the article called Math-hattan, it had to be! The article talks about his efforts to create a math museum and describes the math tours he is currently giving of Manhattan.

The museum itself is still in the planning stages, but the exhibit Math Midway gathered a lot of press during its tour this summer. I love the picture of Glen riding the square wheeled tricycle that’s part of the exhibit. (Before looking at the pictures, how did they succeed in making the ride smooth?) Like the  Bay Area Mathematical Adventures series, this exhibit is great outreach. I hope eventually it will come west.

In graduate school, I found Glen’s enthusiasm for many things, particularly for mathematics, inspiring and infectious. It is great to see him so successfully pursuing this dream.

Search and/or geometry challenge!

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Some friends of mine believe that “search” has been solved. They explain that they can almost always find what they are looking for, and quickly, using keyword search. My life is much more frustrating! There are all sorts of things I look for and can’t find. An additional source of frustration is that I don’t know when to give up, when to conclude that what I’m looking for isn’t there.

Recently I had this experience with a question I thought would make a good blog challenge:

Does there exist a polyhedron such that all of its faces are nonconvex?

If you can think up a proof or example, please post your answer in the comments section, but with “Spoiler alert:” at its start. If you find an answer through a web search, give us the URL and tell us your search strategy. A URL pointing to discussion of this exact question would also be acceptable, even if the discussion doesn’t provide an answer.

I’d like to give a prize, and thought about various prizes (a Tcho chocolate bar? treating the winner to coffee? …) but decided in true blog spirit to ask for suggestions for an appropriate prize.

P.S. I thought about defining  terms such as “polyhedron” and “nonconvex” here.  But since this is a search and/or geometry challenge, any readers who do not know the meaning of these 3D geometry terms can still participate. I would be particularly delighted if someone who did not understand the question initially was able to find a solution.

Update: An answer has been found. Congratulations, Francine. However I realize I mixed up two searches, and this one isn’t as hard as I thought I remembered.

Can’t find that symbol?

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Via Dave Bacon’s blog, I came across Detexify, a cool tool that enables you to find the LaTeX command for a symbol by drawing the symbol.  LaTeX is the standard typesetting system for researchers in the mathematical sciences.  One indication of its popularity is that Scott Aaronson lists “The authors don’t use TeX” as the first of his “Ten Signs a Claimed Mathematical Breakthrough is Wrong.” Unfair I know, but so it is.

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Advice for researchers

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The Princeton Companion to Mathematics, which came out just a few month ago, contains a wonderful short section entitled “Advice to a Young Mathematician” with advice from five eminent mathematicians. I was in the need of inspiration this weekend, and found some in these personal statements. Below the fold you will find a few excerpts applicable to any researcher of any age.

Readers: Please help me and other readers of this blog by posting in the comments section pointers to your favorite sources of research advice.

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