Blog Category: Puzzles and Challenges

Research advice and a search challenge

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I was intending to write a post on the varied reasons mathematicians give for taking long walks as an aid to research. I couldn’t find my favorite quote, so instead I’m posting a search challenge.

I thought I remembered reading, in the book Littlewood’s Miscellany, something along the lines of the following advice:

Researchers spend the vast majority of their time feeling frustrated. To improve the ratio of time feeling fulfilled to time feeling frustrated, whenever you find a new result or succeed in completing a proof, take the time to enjoy it, preferably by taking a long walk.  Definitely don’t dive into the next problem, or go back and check the proof. There is plenty of time for that later.

However, it doesn’t seem to be in that book. Littlewood certainly approved of walking, and the tone of much of his advice is consistent with this quote, but this particular piece of advice doesn’t appear to be there.  I couldn’t find it in a web search either.

I would love to know the true source for this piece of wisdom.

Tcho chocolate bar to anyone who can track down the source!

Which 2009 research results excited you the most?

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Which research result excited you the most in the past year? We’re not asking for the one you thought most important, or the one that would be most exciting to everyone, but which one got you, personally, most excited.

I’ll start things off with a result that delighted me so much I went around smiling all day, only feeling sad that more people couldn’t appreciate it! The result, that appeared in two papers almost simultaneously, is that some quantum states are too entangled to be able to compute one way. The result enchants me because it is surprising, fundamental, and related to topics close to my heart. Prior to these papers, the conventional wisdom held that more entanglement could only help quantum computation. It came as a complete surprise that it could hurt!  Dave Bacon writes beautifully and succinctly about these startling results in his viewpoint, published in Physics, about the two papers published together in Physics Review Letters 102 last May. Here I give an briefer account in order to explain why these result delighted me so much.

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Never mind about the Turkers, what do YOU think?

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Let’s do an experiment. Here’s a TREC topic that specifies an information need

Food/Drug Laws

Description: What are the laws dealing with the quality and processing of food, beverages, or drugs?

Narrative: A relevant document will contain specific information on the laws dealing with such matters as quality control in processing, the use of additives and preservatives, the avoidance of impurities and poisonous substances, spoilage prevention, nutritional enrichment, and/or the grading of meat and vegetables. Relevant information includes, but is not limited to, federal regulations targeting three major areas of label abuse: deceptive definitions, misleading health claims, and untrue serving sizes and proposed standard definitions for such terms as high fiber and low fat.

Below are links to four documents that have been identified by some systems as being relevant to the above topic. Are they?

(I apologize in advance for the primitive nature of this form and its many usability defects.)

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.