He used the extreme value theorem. The theorem asserts that a continuous function on a compact set (for our purposes closed and bounded set) has a maximum (and a minimum). In this case the the closed and bounded set is the sphere of all possible orientations for solar panels. The theorem is mentioned in most introductory calculus courses, but the proof is definitely not 'trivial'.

http://en.wikipedia.org/wiki/Extreme_value_theorem

That's not actually sufficient to show unique extrema; there an be a set of points on which a function achieves the same, maximal, value.

i.e. cos(x) over x <- [0,4π] -- multiple maxima at {0,2π,4π}.

But we don't really need unique extrema here. Oversight on my part -- there can be (although I believe there aren't) multiple optimal panel orientations. Then the optimal array is an array with each panel having any one of the optimal orientations.

Well, the Calc 1 version isn't good enough because there are several variables here. You have to consider a continuous function defined on the sphere -- to capture all possible orientations of the panel. In fact, it could be a closed subset of the sphere -- to take care of all possible shadows, obstructions, etc. This is nice, you don't see a lot of direct applications of pure existence theorems...

Of course, they just making an offer, and, like any gift, they are under no obligation to make good on it.

If they refused to honor the offer in the event that they lose, they would not likely be worried about their reputation.

It's only what, $8000? A drop in the ocean for Lodsys, and $1000 isn't going to do anything for these developers.

This is the second time that Jeff Atwood's heavy handed approach has cost Math.SE a generous helpful member who is also a well respected professional mathematician. The first incident occurred in November.

In both cases, if he had expressed his concerns to the moderators, and let them address his concerns, I am confident the issues would have been resolved amicably. As it stands, there are a lot of angry people, including the moderators at Math.SE.

Based on a quick glance at my bookshelf:

“Brian Greene: You seem intelligent. Write about more shit than just String Theory. You're boring, and a total fan boy. It's just getting old now.”

“Stephen Hawking: You seem intelligent ...

“Stephen Gould: You seem intelligent ...

etc. etc.

There seems to be a consensus that SEO is distorting Google search. I think I can refine that a bit. It appears that Google is using a "don't feed the trolls" strategy in response to link spam. Here's my evidence:

"The Modbookish" is an inconsequential six member Ning social network, but doing a Google search on "Modbookish" is interesting. There are the annoying 'Google thinks you are stupid' hits like the site in which there is a sentence ending with "mod" followed by a sentence beginning with "Bookish". The remaining results are sites that link to the Modbookish. However, the Modbookish itself is NOT in the results. As Google ads are on the site, there is no doubt that the Google bot visited it shortly after it went online. Nonetheless, Google has refused to put the site into its web index for a couple months now. Clearly, (and not without cause), it is assuming that the pages that link to the site are link spam. It is probably waiting for some semi-authoritative link to appear before it indexes it.

So, why is this bad? It undermines Google search purpose: to provide the most relevant results. When Google got started, I recall that when Sergey or Larry were asked why Google search was better they often offered the Harvard example. If one enters the search term "Harvard" with no other terms into a web search box, there is really only one reasonable search result: the Harvard University website. However, in the search engines of the time, the university often ended up on page five or six. On Google, it was search result number one. By the same token, if you enter "Modbookish" (no spaces) there is only one reasonable result, and Google doesn't offer it. In contrast, both Duck-Duck-Go and Yahoo list it in the first spot.

Why is this really bad? Many (Most?) websites do not do their own site indexing; they let Google do it for them. Clearly if Google refuses to index a certain important but only occasionally referenced page, that is a problem.

Quicksilver's object-action approach and the huge pile of plug-ins make it a pain to set up, but they also make it both powerful and flexible. So, where the article suggests that it provides a way of getting rid of the mouse, others can use Quicksilver without a keyboard. See: http://modbookish.ning.com/profiles/blogs/pen-gestures-on-th....