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Timothy Gowers
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Timothy Gowers

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This is a very interesting article by John Bohannon, from Science, to whom Alexandra Elbakyan gave access to a huge dataset about use of SciHub. One of the most interesting messages is that a lot of people who use SciHub are people who have legal access to the papers through their universities. So why are they using SciHub? Because it has a much better and more convenient platform than those provided by the big publishers. (I, by the way, have never seen SciHub's platform -- I think I've got more to lose than gain by breaking the law in this way, but my situation is not at all typical.) Elbakyan herself, now in her late 20s, is the subject of a lawsuit by Elsevier, who are suing her for billions of dollars. (Whether Elsevier has actually lost that amount in revenue is apparently not the point, legally speaking.) She now lives in hiding, rather than face extradition and the likelihood of a lengthy jail sentence. 
An exclusive look at data from the controversial web site Sci-Hub reveals that the whole world, both poor and rich, is reading pirated research papers.
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Btw, what's scihub.org? Is this elsevier trying to lure in potential users of sci-hub? 
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I've just been to a spectacularly good lecture given by +Ravi Vakil. It was aimed at undergraduates, and therefore comprehensible (but more than that, it was completely absorbing and very entertaining). It included the following amazing gem of a proof. I'll give the problem and then leave some space, since I strongly recommend thinking about it for yourself. We didn't get the chance to do this, so I'm left feeling very curious about how it might be possible to come up with the argument.

The problem, he told us, originated in Russia. A train company stipulates that suitcases (which for the purposes of the problem are cuboids) must have height plus width plus depth equal to at most one metre. Is it possible to cheat the system by enclosing an illegal suitcase in a legal one? Equivalently, if d is the sum of the sidelengths, can a cuboid with larger d fit inside one with smaller d?

Now for the space.





















First hint (which makes the problem massively easier). Define the r-neighbourhood of a suitcase to be the set of all points within distance r from that suitcase.



















Second hint. OK, if you need it spelt out: consider the volume of the r-neighbourhood.
 
























Third hint. I didn't actually say this, but the volume in question is easy to compute, and once you've computed it, the answer to the question drops out.























OK, here's the answer (in sketch form). The r-neighbourhood can be chopped up naturally into pieces. One piece is the original cuboid. Six pieces are cuboids with one side of length r and a face in common with the original cuboid. Twelve pieces are quarters of cylinders of radius r that go round edges. And eight pieces are octants of a sphere of radius r.

When r is large, each kind of contribution contributes far more to the volume than the one before. But the spherical contributions are the same for the two suitcases, so the dominant term in the difference comes from the cylindrical contributions, which add up to pi r^2 times the sum of the height, width and depth. If one shape sits inside another, then so does its r-neighbourhood. Putting this together solves the problem.

So my question is, what should induce us to think of considering r-neighbourhoods? (I would be satisfied with an answer that said, "That's just a very nice way of expressing the proof, but here is an essentially equivalent argument that doesn't explicitly mention r-neighbourhoods," as long as the argument was clearly something one could have been expected to come up with.)
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I paused at your first blank space and came up with a less elegant solution. Suppose we can fit a bigger one inside a small one. Let's assume the inside one is tilted in the most generic orientation. Then I can linearly jointly stretch the two suitcases in any coordinate direction. The effect is that the inside one would get more total length stretch than the outside one, because all three sides are affected whereas the outside one only gets one side affected. This allows me to make the outside suitcase of any shape, hence an infinite descent argument gives a contradiction. Now that I think about it, it's not so different from your (or Ravi's) proof, since I can skip the last infinite descent part and just stretch once by a large amount. 
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This could be interesting ...
 
I am thinking of starting an effort to mount an arxiv-based overlay journal in logic, in the style of Discrete Analysis (https://gowers.wordpress.com/2015/09/10/discrete-analysis-an-arxiv-overlay-journal/).

My idea would be a completely open-access journal focussing on topics in mathematical and philosophical logic, on the overlay journal concept.

Please let me know below if there is interest in supporting such a venture. Would you submit your research articles to such a journal? Would you serve as referee? As editor? To what extend would the community support such a venture?

Please vote-up or share this post if this is a venture that you would support. If there is strong support for such an effort, I will take it more seriously to make it happen.
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I've just heard the terrible news that David MacKay has died of cancer aged 48. Although it was public news that he was ill, I had not heard about it: the link below is to his blog, which contains a number of incredible, moving, and humorous posts about the progress of his illness.

He was a hero of mine for more than one reason. For one thing, he was an expert on Bayesian reasoning, neural networks and other topics that I find fascinating, and wrote an excellent textbook on the subject. Better still, he made the book freely available online. (I myself bought a physical copy.) Here's the link:  http://www.inference.phy.cam.ac.uk/itila/book.html .

But the main reason I admired him was that he campaigned for better action on climate change. He wrote a wonderful book on the subject in which he urged people to discuss it quantitatively and not just qualitatively. For example, it sticks in my mind that if you leave a phone charger on overnight, that will lead to carbon emissions roughly equivalent to those caused by two seconds of a car idling. (There are two ways of taking that. I have taken to switching my car engine off when I am at traffic lights -- and of course using my car as little as possible.) He became a government adviser, and although his advice was probably treated in the way politicians usually treat scientific advice, I can't imagine anyone better than him doing that job. He also practised what he preached, doing far more than most people to reduce his own personal carbon footprint. His climate book Sustainable Energy Without The Hot Air is also freely available online: http://www.withouthotair.com/  
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RIP DR
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A recent holiday snap, taken at Etretat in Normandy, that +John Baez might like ...
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The best I can say for the weather there is that the forecast was worse than the reality.
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What is it like to do maths?

About 99% of the time it's like this. 
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/sub
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Timothy Gowers

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It's not often that one comes across a fractal structure in which five levels can be seen, so I rather enjoyed this very thick rope that was part of a structure in a children's playground: it is a twist made of smaller twists that are made of smaller twists that are made of smaller twists that are made of smaller twists. The bottom level is not easy to see in the photo, but just about possible if you blow it up.
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+Terence Tao I'll be damned!!  You're right!!  The noodle making looks like making rope.  Big rope made of little ropes.  Good thinking!!
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On May 25th, Exxon Mobil and Chevron will have their AGMs. There are moves amongst shareholders to get them to take stop denying the need to take action on climate change and start to take the problem seriously. If you are an academic, the link below is to two letters you could sign. One is an open letter to the investment officer of your institution, urging him/her to vote in favour of shareholder resolutions. This you can sign if you are at one of Brown, Chicago, Columbia, Cornell, Dartmouth, Duke, Durham (UK), Emory, Harvard, Imperial, King Abdullah University of Science and Technology, LSE, Michigan, MIT, Northwestern, Oxford, Penn, Princeton, Stanford, UCL, University of California, Notre Dame, University of Texas, Texas A&M, Washington University St Louis, or Yale, all of which have investments in these companies (if I understand correctly). There is also an "other" option, but I'm not sure what happens if you go for that, or whether the list above is exhaustive. The second letter is a general letter from the academic community to shareholders of these two companies.
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It would be really good to have more data about how people feel about mathematics journals. If you haven't already done this short survey and are involved in some way in mathematical publication, do consider doing it.
 
The international survey of opinion on mathematical journal reform has 432 responses so far. Please join in if you are in the target group: reader, author, reviewer or editor for a mathematical sciences journal in the last 3 years.


https://docs.google.com/forms/d/1r4LBUJk1VF9e4Dl4aXgS4fW-O8HR9yz1cqmXdzz0CjM/edit
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maths....
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And this is where I was when I took the first photo. The trees in the top left-hand corner give some idea of the extraordinary size of this rock formation. When one walks above it, one has no sensation at all of being on a bridge.
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I feel so sori
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The new linguistics journal Glossa has now published its first few articles. This journal, you may recall, is the "flipped" version of Lingua, a linguistics journal published by Elsevier. Lingua still exists, but its editorial board resigned en masse and moved to Glossa. So is Glossa the new Lingua or is it a new journal? That depends whether you think that identity resides with the title and publisher or whether editorial continuity is more important. I know what I think. I hope some mathematics journals will be emboldened to follow the example set by the linguists.

Johan Rooryck, the managing editor of Glossa, writes this at the beginning of an editorial entitled Introducing Glossa.

The editors of Glossa are proud to present the first four publications of our journal. The publication of these articles marks a milestone. Indeed, we have been able to flip our journal from subscription to Open Access in about four months. In this way, we provide proof of concept that it is possible to quickly and seamlessly move an entire editorial team, its editorial board, its authors and its readers to a new publishing platform. This transition could not have been achieved without the unwavering support and enthusiasm of authors, readers, and reviewers via social media, the press, and personal e-mails. Many authors whose paper was under consideration at Lingua withdrew their submission there to entrust it to Glossa. No less than 10 Special Issue editors and their authors did the same. In addition to these Special Issues, Glossa currently has over 110 papers under consideration for publication.
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One wouldn't normally mention the split infinitive but when it occurs in an editorial in a linguistics journal... Well, anyway, this is the most exciting thing since http://discreteanalysisjournal.com/ launched. Stefan Müller refusing to hire somebody for siding with Elsevier seems a bit belligerent though.
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I asked the Guardian if they'd be interested in a riposte to Simon Jenkins (http://www.theguardian.com/commentisfree/2016/mar/10/fixation-maths-doesnt-add-up-targets). They agreed, but the way things work I was operating under a few constraints that meant I couldn't say everything I wanted to say: it had to be at most 800 words, and it had to be a free-standing article rather than a point-by-point rebuttal. Also, the title and lede were not written by me. So some of the points I was trying to make got a bit oversimplified. (For example, it might look as though I think there's no point in people learning to solve quadratic equations. Nothing could be further from the truth, but I do think that for many people it is made pointless by the way it is taught.) 
Critics including Simon Jenkins think higher maths serves no useful purpose. This is the result of an unimaginative curriculum
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Yes I spotted those too but had assumed that there wasn't much I could do about it. Perhaps that was a bit lazy of me: I should at least ask.
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