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Timothy Gowers
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Timothy Gowers

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The article below is about arXiv overlay journals and mentions Discrete Analysis, which, by the way, is now scheduled to be launched on March 1st. It has been accepting submissions since September -- the launch will be of the journal website, with some papers already accepted and others well on the way through the peer-review process. If you happen to have a suitable paper, we'll be delighted to receive it. When the launch happens, I'll post again to discuss a few things about the website that make it a little different from, and in my view better than, journal websites you may be used to.
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One of the joys of following cricket is the seemingly endless scope for new records to be set. There is a well known limerick (of the old-fashioned kind where the first and last lines end in the same word) that makes fun of this:

There was once a young man of Dover,
Who bowled thirty wides in one over,
Which had never been done
By a clergyman's son
On a Sunday in August in Dover.

A major disappointment a few years ago came in a match between England and India. India were all set to make the highest ever score in an innings in which no batsman made a century (that is, reached 100 runs -- if you're not a cricket fan, there are eleven batsmen per team, each of whom gets two innings, so potentially 44 innings in total, and in a typical match one might expect between 0 and 2 of those to be centuries). Then Anil Kumble, whose speciality was bowling rather than batting, spoilt everything by making his first ever century, which led to India winning the match. The one small compensation was that Kumble set another record instead -- it was his 118th innings in test cricket, and no batsmen had ever gone that long before scoring a maiden century.

It was against that background that I was immensely cheered by a record set yesterday. England are currently in the middle of a (five-day) match against South Africa, and in South Africa's first innings they set two records of a similar kind to the one that India failed to set in the match mentioned above. It was the lowest ever score (313) by a team in which every batsman has reached double figures (which itself is fairly unusual). It was also the first time ever that every batsman has reached double figures without any of them reaching 50. 

I don't know for sure, but I would guess that the ratio of the top score to the lowest score, which were 46 and 12, respectively, is the lowest ever. I'll be very surprised if it is lowered again during my lifetime.
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And yet another great record! South Africa scored 475 in their first innings, which is the lowest ever score in an innings in which three batsmen have scored centuries.
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Interesting: another Elsevier journal is considering following the example of Lingua, which made some demands that were very reasonable from an academic perspective and utterly unreasonable from the perspective of a major publisher that wants to protect its (huge) profits. When Elsevier refused, they switched to a new publishing platform and changed their name to Glossa. (Or, from Elsevier's perspective, the editors resigned and founded a new journal. I notice that for now the editors are all described on Lingua's website as "interim" editors. I wonder who they are and what that means.)  

The journal that might end up following suit, though at the moment it is right at the beginning of whatever it is doing, is called Cognition. The link below is to a statement they have put out.
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Amazingly, someone has put last night's University Challenge match on Youtube already. So you don't have to be in Britain (which at the moment I'm not) to watch it, though you may have to be British to want to watch it.
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Well done Tim and all!
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Possibly the most nervous I've ever been

If you're British, you'll know about University Challenge, a long-running quiz show that pits teams from various universities and Oxbridge colleges against each other. Two or three months ago I was asked whether I would be ready to represent Trinity College Cambridge in a Christmas Special series, where the teams are made up of alumni rather than current students. I thought long and hard about it and eventually decided that my fear of regretting not doing it outweighed my fear of turning myself into a national laughing stock. I then had to endure several weeks of gradually increasing nerves that culminated in the filming of the show about three weeks ago. I don't think I've known anything quite like it: the best comparison I can give for the feeling of walking through the huge building to the studio is the feeling I had when being wheeled to an operating theatre for a heart operation. I spent much of the day before, and also the train journey to Manchester, desperately brushing up on various categories, trying to make sure that when I did know something it wouldn't take me 30 seconds to retrieve it from some dark corner of my brain.

The photo below was taken just before we started. The other three on the team were Zoe Heron, Faisal Islam and Bee Wilson. We were up against Oriel College Oxford. If you want to know how we did (or just have a good laugh at my expense) and are British, then you can watch it at 8pm next Monday or (I presume) on iPlayer after that. More than that I am not allowed to say ...
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Great show!  It was a nail-biting finish but glad the team came through.  Well done!
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I'm glad to say that I don't know anyone directly caught up in the attacks in Paris (not a trivial statement given that my wife is from Paris and has many close relatives living there). The nearest I get is a chain of length five where each link in the chain is either "is the partner of" or "is a sibling of" which ends up with someone (whom I know) who had tickets for the concert at the Bataclan Theatre but ended up unexpectedly having to work yesterday evening. 

The article linked to below is, as it says, long. But it is also an interesting insight into what motivates ISIS. It supports the argument that it is not Islam that's the big problem: rather, it is the fact that ISIS believes in a millenarian version of Islam -- that they are helping to fulfil prophecies and usher in a glorious new era. So although there are important differences, there are also similarities with, for example, Christians who welcome turbulence in the Middle East because it may be a sign that the second coming is getting near.

From the article: 

The jihadis instead saw themselves at the vanguard of a war that many among them believed had been preordained in the formative days of Islam.

One of the earliest sayings of the Prophet Muhammad – a hadith – mentions Dabiq as the location of a fateful showdown between Christians and Muslims which will be a precursor to the apocalypse. According to another prophecy, this confrontation will come after a period of truce between Muslims and Christians, during which Muslims – and only puritanical Sunnis fit the definition – would fight an undefined enemy, which in northern Syria today is deemed to be “Persians”.

“The Hour will not be established until the Romans [Christians] land at Dabiq,” the hadith says. “Then an army from Medina of the best people on the earth at that time will leave for them … So they will fight them. Then one third of [the fighters] will flee; Allah will never forgive them. One third will be killed; they will be the best martyrs with Allah. And one third will conquer them; they will never be afflicted with sorrow. Then they will conquer Constantinople.”

Now, close to 1,500 years later, have come waves of fighters who paid strict heed to these prophecies – and see the rise of Islamic State as a crucial turning point in a centuries-long battle of civilisations. For their purposes, the “Persians” today are not simply Iran, but also the Alawite regime that controls Syria and the Shia militias from around the region who have come to its defence.
The long read: Jihadi fighters in Iraq and Syria reveal the apocalyptic motivations of the militant movement that has hijacked the Syrian uprising – and transformed the Middle East
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I guess they have nothing better to do. Duh...
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Timothy Gowers

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Frankl's union-closed conjecture is the following easy sounding statement. Let A_1,...,A_n be n subsets of a set X and suppose that for each i and j the union of A_i and A_j is one of the subsets (so the collection of sets is closed under taking unions). Then there is an element x of X that belongs to at least n/2 of the sets.

Seems simple? Then why not help me prove it? But I should mention, by way of a mild warning, that it is not even known whether there must be an element of X that belongs to at least n/1,000,000 of the sets (or indeed cn for any fixed constant c>0). But in a way that makes it easier to make progress -- even a statement that falls quite some way short of the conjecture would be an advance. 
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There is also the recent integer programming formulation from Pulaj, Raymond and Theis, http://arxiv.org/abs/1512.00083 .

I feel there is a foot in the door now for further computational studies.
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Here's a typical example of the problems that arise when one's knowledge about an area is based on words, so to speak, rather than the actual mathematics of which those words are a pale reflection.

Today it is in the news that gravitational waves might have been detected. How am I supposed to reconcile the idea of a gravitational wave with the idea that I've read many times that gravity is "just" the geometry of spacetime? 

Is it that a perturbation in the geometry of spacetime should spread out like a wave? If so, then perhaps I (very vaguely) understand it after all. But I still know that I don't really understand it. For that I would need to digest some equations.
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before you can understand gravitational waves you'll need to understand time and how space and time are related.   In particular how a unit of length can be 1 unit long in one context & the same length can be .5 units in another.   And the same for time.

see: http://www.designerscience.com/ObjectiveRelativity/time-what-it-is-how-it-works-2/ 

Once you have that under your belt, then think about a table one light year in diameter.  Then consider this... if you push one edge, it will take one light year for the other edge to move.  (ignoring the mass of the table of course :)   The causal part of "the push" has to propagate as a wave of "push" that propagates at the speed of light.

The same goes for moving a gravitating object.   
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The mathematics of vineyards in winter

I'm in a part of southern France where there are lots of vineyards, which, because it is winter, means that there are many views like this one, of two-dimensional integer lattices seen from the side. I enjoy looking at these and finding various different directions in which the posts line up nicely. 

An obvious question about this is what the distance will be between the rows in a given direction. Suppose, for example, that the posts are placed at all integer points (m,n). What will be the distance between lines that go in the direction (1,2)?

One way of working this out is to do a rather boring calculation. But a much easier way, familiar to people who work in the geometry of numbers, is to consider how many posts there must be in a large area A. We can count this in two ways. One way is to say that as long as the area is a reasonably nice shape, then the number of posts will be approximately A (because there is one post per unit square). The other way is to say that in each line in direction (1,2) you get posts appearing at distance the square root of 5 (by Pythagoras's theorem). So the density of points in each line is 5^{-1/2}. Since the density of integer points in the plane is 1, the spacing between the lines must be 5^{-1/2}. More generally, if m and n are coprime, this argument shows that the distance between the lines in direction (m,n) must be (m^2+n^2)^{-1/2}. To give a simple example, the lines in direction (1,1) are at distance 2^{-1/2} -- something that can also be seen easily by direct calculation. In the picture below we see some lines of maximal width (which would be 1 if the posts really were at integer points) and a selection of rows that are closer together but with the posts at a greater distance from each other to compensate.
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Braggs for the win! (Sorry: they are Adelaide University's claim to fame, Nobel-winning research and all)
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My carbon footprint

Two or three months ago I posted to say that I had invested in a bike that can carry children, and that the result of that investment was that I would be able to use my car much less. That has indeed been the case, so I have cut down my carbon footprint. I have also switched my gas and electricity provider to a company that uses renewable energy -- for the electricity at least. It took me a short while to work out how switching could do any good, given that I'm still getting the electricity from the national grid, but of course the answer is that my paying this new company means that they have to supply a certain amount of electricity to the national grid (which they do using a combination of wind, solar and tidal power) that would otherwise have had to be supplied by a company that burns carbon.

But all this has to be set against the fact that I accepted an invitation to speak at the joint AMS-MAA meeting in Seattle in January, and the amount of carbon I'll be responsible for emitting will dwarf the amounts that I have not emitted as a result of the measures described above. This bugs me, so I've done something else to try to salve my conscience, which is to give a donation to a charity called Cool Earth.

Cool Earth's mission is to save rainforest from destruction. This has many good effects -- helping to preserve the lifestyles of indigenous people, maintaining biodiversity, etc. -- but the one that concerns me most is that it stops a carbon sink being destroyed, which has a double benefit since burning the forest itself emits a lot of carbon. Moreover, Cool Earth tries to use your money as efficiently as possible, creating "shields" of protected forest that make other bits of forest inaccessible and therefore also unlikely to be destroyed.

I've no idea how reliable the following estimates are, but they say that the £120 I have given them is equivalent to saving two acres of rainforest, and elsewhere they say that saving an acre of rainforest is stopping emissions that are equivalent to driving a car 32 times round the world, or 800,000 miles. (I went for two acres rather than one because of this uncertainty.)

I realize that this kind of action is controversial. Some people object to the idea that one can merrily emit carbon and then pay for a few trees to make up for it: better, they say, not to emit the carbon in the first place. But it's not obviously better. In fact, I'd say it is decidedly better to emit carbon and save trees if the total amount of carbon that will be emitted is significantly less. (Yes, I could have not gone to Seattle and still paid for two acres of rainforest, but I'm not claiming to have optimized my behaviour -- for that I'd need to do things like moving to a smaller house and using the difference in price to save hundreds of acres of rainforest.) Another issue is that this solution doesn't scale up, since if everybody did it then there wouldn't be enough rainforest that could be saved, or at least not as efficiently as it currently can. To which I reply that for the time being few enough people are doing it that this problem has not yet arisen. I may make it harder for people in the future to reduce their carbon footprints, but I'll still have done some good during the years before the difficulty becomes noticeable. 

Yet another objection is that even if I'm doing the best I can carbon-wise for the money, it might still be better to spend the money on another charity, such as one of the charities recommended by GiveWell (which tries to work out how you can do most good per pound spent). To counter this objection I will try not to make the money spent on Cool Earth subtract from what I would have spent on GiveWell. Of course, that's not an entirely rational argument, since if I could do more good per pound with GiveWell, then surely I ought to do that. But climate change seems such a big threat that I want to do my bit to mitigate it. And part of the reason I'm writing this post is to publicize the activities of Cool Earth: maybe by doing so I can have a bigger effect. 

Here's a recommendation to anyone who is organizing a conference: add to your budget enough money to save a few acres of rainforest to make up for all those plane journeys that your conference is causing to happen. I'm wondering whether in future I should accept invitations to travel only if my hosts are prepared to make my trip carbon neutral in this way.
The charity that works alongside indigenous villages putting local people back in control with the resources they need to keep their rainforest intact.
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Actually that's something I could have mentioned in my post: I've reduced my meat intake since about a year ago. Not to zero, and mostly for health reasons, but I hope that that way I'm making a further small contribution.
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I'm sharing this because it's important. I've heard very interesting anecdotal evidence about the effect of subtly (or not so subtly) gendered language. It's not just the writers of references who should take note: if you're on a hiring committee and read one of these trigger words like "diligent", you may well think, "Aha, that's the referee's way of damning with faint praise -- we don't want this candidate." But the fact that a word like that occurs more often in references for women should make us all very cautious about drawing that kind of inference.
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Then one needs to think very hard about the possible consequences of choosing to mention that fact.
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