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[The following statement is signed by several mathematicians at Stanford and MIT in support of one of their recently admitted graduate students, and I am happy to post it here on my blog. -T]
We were saddened and horrified to learn that Ilya Dumanski, a brilliant young mathematician who has been admitted to our graduate programs at Stanford and MIT, has been imprisoned in Russia, along with several other mathematicians, for participation in a peaceful demonstration. Our thoughts are with them. We urge their rapid release, and failing that, that they be kept in humane conditions. A petition in their support has been started at
https://www.ipetitions.com/petition/a-call-for-immediate-release-of-arrested-students/
Signed,
Roman Bezrukavnikov (MIT)
Alexei Borodin (MIT)
Daniel Bump (Stanford)
Sourav Chatterjee (Stanford)
Otis Chodosh (Stanford)
Ralph Cohen (Stanford)
Henry Cohn (MIT)
Brian Conrad (Stanford)
Joern Dunkel (MIT)
Pavel Etingof (MIT)
Jacob Fox (Stanford)
Michel Goemans (MIT)
Eleny Ionel (Stanford)
Steven Kerckhoff (Stanford)
Jonathan Luk (Stanford)
Eugenia Malinnikova (Stanford)
Davesh Maulik (MIT)
Rafe Mazzeo (Stanford)
Haynes Miller (MIT)
Ankur Moitra (MIT)
Elchanan Mossel (MIT)
Tomasz Mrowka (MIT)
Bjorn Poonen (MIT)
Alex Postnikov (MIT)
Lenya Ryzhik (Stanford)
Paul Seidel (MIT)
Mike Sipser (MIT)
Kannan Soundararajan (Stanford)
Gigliola Staffilani (MIT)
Nike Sun (MIT)
Richard Taylor (Stanford)
Ravi Vakil (Stanford)
Andras Vasy (Stanford)
Jan Vondrak (Stanford)
Brian White (Stanford)
Zhiwei Yun (MIT)
In logic, there is a subtle but important distinction between the concept of mutual knowledge – information that everyone (or almost everyone) knows – and common knowledge, which is not only knowledge that (almost) everyone knows, but something that (almost) everyone knows that everyone else knows (and that everyone knows that everyone else knows that everyone else knows, and so forth). A classic example arises from Hans Christian Andersens’ fable of the Emperor’s New Clothes: the fact that the emperor in fact has no clothes is mutual knowledge, but not common knowledge, because everyone (save, eventually, for a small child) is refusing to acknowledge the emperor’s nakedness, thus perpetuating the charade that the emperor is actually wearing some incredibly expensive and special clothing that is only visible to a select few. My own personal favourite example of the distinction comes from the blue-eyed islander puzzle, discussed previously here, here and here on the blog. (By the way, I would ask that any commentary about that puzzle be directed to those blog posts, rather than to the current one.)
I believe that there is now a real-life instance of this situation in the US presidential election, regarding the following
Proposition 1. The presumptive nominee of the Republican Party, Donald Trump, is not even remotely qualified to carry out the duties of the presidency of the United States of America.
Proposition 1 is a statement which I think is approaching the level of mutual knowledge amongst the US population (and probably a large proportion of people following US politics overseas): even many of Trump’s nominal supporters secretly suspect that this proposition is true, even if they are hesitant to say it out loud. And there have been many prominent people, from both major parties, that have made the case for Proposition 1: for instance Mitt Romney, the Republican presidential nominee in 2012, did so back in March, and just a few days ago Hillary Clinton, the likely Democratic presidential nominee this year, did so in this speech:
I highly recommend watching the entirety of the (35 mins or so) speech, followed by the entirety of Trump’s rebuttal.
However, even if Proposition 1 is approaching the status of “mutual knowledge”, it does not yet seem to be close to the status of “common knowledge”: one may secretly believe that Trump cannot be considered as a serious candidate for the US presidency, but must continue to entertain this possibility, because they feel that others around them, or in politics or the media, appear to be doing so. To reconcile these views can require taking on some implausible hypotheses that are not otherwise supported by any evidence, such as the hypothesis that Trump’s displays of policy ignorance, pettiness, and other clearly unpresidential behaviour are merely “for show”, and that behind this facade there is actually a competent and qualified presidential candidate; much like the emperor’s new clothes, this alleged competence is supposedly only visible to a select few. And so the charade continues.
I feel that it is time for the charade to end: Trump is unfit to be president, and everybody knows it. But more people need to say so, openly.
Important note: I anticipate there will be any number of “tu quoque” responses, asserting for instance that Hillary Clinton is also unfit to be the US president. I personally do not believe that to be the case (and certainly not to the extent that Trump exhibits), but in any event such an assertion has no logical bearing on the qualification of Trump for the presidency. As such, any comments that are purely of this “tu quoque” nature, and which do not directly address the validity or epistemological status of Proposition 1, will be deleted as off-topic. However, there is a legitimate case to be made that there is a fundamental weakness in the current mechanics of the US presidential election, particularly with the “first-past-the-post” voting system, in that (once the presidential primaries are concluded) a voter in the presidential election is effectively limited to choosing between just two viable choices, one from each of the two major parties, or else refusing to vote or making a largely symbolic protest vote. This weakness is particularly evident when at least one of these two major choices is demonstrably unfit for office, as per Proposition 1. I think there is a serious case for debating the possibility of major electoral reform in the US (I am particularly partial to the Instant Runoff Voting system, used for instance in my home country of Australia, which allows for meaningful votes to third parties), and I would consider such a debate to be on-topic for this post. But this is very much a longer term issue, as there is absolutely no chance that any such reform would be implemented by the time of the US elections in November (particularly given that any significant reform would almost certainly require, at minimum, a constitutional amendment).
It has been a little over two weeks now since the protest site at thecostofknowledge.com was set up to register declarations of non-cooperation with Reed Elsevier in protest of their research publishing practices, inspired by this blog post of Tim Gowers. Awareness of the protest has certainly grown in these two weeks; the number of signatories is now well over four thousand, across a broad array of academic disciplines, and the protest has been covered by many blogs and also the mainstream media (e.g. the Guardian, the Economist, Forbes, etc.), and even by Elsevier stock analysts. (Elsevier itself released an open letter responding to the protest here.) My interpretation of events is that there was a significant amount of latent or otherwise undisclosed dissatisfaction already with the publishing practices of Elsevier (and, to a lesser extent, some other commercial academic publishers), and a desire to support alternatives such as university or society publishers, and the more recent open access journals; and that this protest (and parallel protests, such as the movement to oppose the Research Works Act) served to drive these feelings out into the open.
The statement of the protest itself, though, is rather brief, reflecting the improvised manner in which the site was created. A group of mathematicians including myself therefore decided to write and sign a more detailed explanation of why we supported this protest, giving more background and references to support our position. The 34 signatories are Scott Aaronson, Douglas N. Arnold, Artur Avila, John Baez, Folkmar Bornemann, Danny Calegari, Henry Cohn, Ingrid Daubechies, Jordan Ellenberg, Matthew Emerton, Marie Farge, David Gabai, Timothy Gowers, Ben Green, Martin Grotschel, Michael Harris, Frederic Helein, Rob Kirby, Vincent Lafforgue, Gregory F. Lawler, Randall J. LeVeque, Laszlo Lovasz, Peter J. Olver, Olof Sisask, Richard Taylor, Bernard Teissier, Burt Totaro, Lloyd N. Trefethen, Takashi Tsuboi, Marie-France Vigneras, Wendelin Werner, Amie Wilkinson, Gunter M. Ziegler, and myself. (Note that while Daubechies is current president of the International Mathematical Union, Lovasz is a past president, and Grotschel is the current secretary, they are signing this letter as individuals and not as representatives of the IMU. Similarly for Trefethen and Arnold (current and past president of SIAM).)
Of course, the 34 of us do not presume to speak for the remaining four thousand signatories to the protest, but I hope that our statement is somewhat representative of the position of many of its supporters.
Further discussion of this statement can be found at this blog post of Tim Gowers.
EDIT: I think it is appropriate to quote the following excerpt from our statement:
All mathematicians must decide for themselves whether, or to what extent, they wish to participate in the boycott. Senior mathematicians who have signed the boycott bear some responsibility towards junior colleagues who are forgoing the option of publishing in Elsevier journals, and should do their best to help minimize any negative career consequences.
Whether or not you decide to join the boycott, there are some simple actions that everyone can take, which seem to us to be uncontroversial:
- Make sure that the final versions of all your papers, particularly new ones, are freely available online, ideally both on the arXiv and on your home page.
- If you are submitting a paper and there is a choice between an expensive journal and a cheap (or free) journal of the same standard, then always submit to the cheap one.
A few days ago, inspired by this recent post of Tim Gowers, a web page entitled “the cost of knowledge” has been set up as a location for mathematicians and other academics to declare a protest against the academic publishing practices of Reed Elsevier, in particular with regard to their exceptionally high journal prices, their policy of “bundling” journals together so that libraries are forced to purchase subscriptions to large numbers of low-quality journals in order to gain access to a handful of high-quality journals, and their opposition to the open access movement (as manifested, for instance, in their lobbying in support of legislation such as the Stop Online Piracy Act (SOPA) and the Research Works Act (RWA)). [These practices have been documented in a number of places; this wiki page, which was set up in response to Tim’s post, collects several relevant links for this purpose. Some of the other commercial publishers have exhibited similar behaviour, though usually not to the extent that Elsevier has, which is why this particular publisher is the focus of this protest.] At the protest site, one can publicly declare a refusal to either publish at an Elsevier journal, referee for an Elsevier journal, or join the board of an Elsevier journal.
(In the past, the editorial boards of several Elsevier journals have resigned over the pricing policies of the journal, most famously the board of Topology in 2006, but also the Journal of Algorithms in 2003, and a number of journals in other sciences as well. Several libraries, such as those of Harvard and Cornell, have also managed to negotiate an unbundling of Elsevier journals, but most libraries are still unable to subscribe to such journals individually.)
For a more thorough discussion as to why such a protest is warranted, please see Tim’s post on the matter (and the 100+ comments to that post). Many of the issues regarding Elsevier were already known to some extent to many mathematicians (particularly those who have served on departmental library committees), several of whom had already privately made the decision to boycott Elsevier; but nevertheless it is important to bring these issues out into the open, to make them commonly known as opposed to merely mutually known. (Amusingly, this distinction is also of crucial importance in my favorite logic puzzle, but that’s another story.) One can also see Elsevier’s side of the story in this response to Tim’s post by David Clark (the Senior Vice President for Physical Sciences at Elsevier).
For my own part, though I have sent about 9% of my papers in the past to Elsevier journals (with one or two still in press), I have now elected not to submit any further papers to these journals, nor to serve on their editorial boards, though I will continue refereeing some papers from these journals. As of this time of writing, over five hundred mathematicians and other academics have also signed on to the protest in the four days that the site has been active.
Admittedly, I am fortunate enough to be at a stage of career in which I am not pressured to publish in a very specific set of journals, and as such, I am not making a recommendation as to what anyone else should do or not do regarding this protest. However, I do feel that it is worth spreading awareness, at least, of the fact that such protests exist (and some additional petitions on related issues can be found at the previously mentioned wiki page).
This weekend I was in Washington, D.C., for the annual meeting of the National Academy of Sciences. Among the various events at this meeting was an address to the Academy by President Obama this morning on several major science and education policy initiatives, including some already announced in the economic stimulus package and draft federal budget, and some carried over from the previous administration. (I myself missed the address, though, as I had to return back to LA to teach.) Among the initiatives stated were the creation of an Advanced Research Projects Agency for Energy (ARPA-E), modeled on DARPA (and recommended by the NAS); a significant increase in funding to the NSF and related agencies (which was committed to by the Bush administration, but not yet implemented; this is distinct from the one-time funding from the stimulus package discussed in this previous post), leading in particular to a tripling in the number of NSF graduate research fellowships; and a “race to the top” fund administered by the Department of Education to provide incentives for states to improve their quality of maths and science education, among other goals. Some of these initiatives may not survive the budgetary process, of course, but it does seem that there is both symbolic and substantive support for science and education at the federal level.
Here are the video, audio, and transcript of the talk.
[Update, Apr 28: Another event at the meeting is the announcement of the new membership of the Academy for 2009. In mathematics, the new members include Alice Chang, Percy Deift, John Morgan, and Gilbert Strang; congratulations to all four, of course.]
I came across the following news item today which might be of interest to many of the readers of this blog: as part of a bipartisan effort (headed by Sen. Susan Collins (R-ME) and Sen. Ben Nelson (D-NE)) to reduce the size of the U.S. federal government stimulus package (currently at over $900 billion) by about $77 billion, the entire appropriation for the National Science Foundation (NSF) in the package ($1.4 billion – about 0.15% of the entire stimulus package) is being proposed to be eliminated, with significant cuts in related agencies (NASA, DOE office of science, NOAA, etc.). The $1.4 billion for the NSF in the Senate version of the package is already a reduction from the $2.5 billion allocated in the House version.
For comparison, the entire 2009FY budget for the NSF is $6.9 billion, or about 0.5% of the discretionary federal budget of $1.21 trillion.
[Full disclosure: a majority of my own research funding comes from the NSF.]
[Update, Feb 8: It now appears that $1.2 billion of the funding for the NSF has been restored in a Senate compromise.]
[Update, Feb 12: After the House/Senate reconciliation process, the amount allocated to the NSF has been increased to $3 billion. Thanks to Alex Iosevich for the link. See also this Sciencedebate update.]
The level and quality of discourse in this U.S. presidential campaign has not been particularly high, especially in recent weeks. So I found former Gen. Powell’s recent analysis of the current state of affairs, as part of his widely publicised endorsement of Sen. Obama, to be a welcome and refreshing improvement in this regard:
It’s a shame that much of the rhetoric and commentary surrounding this campaign – from all sides – was not more like this. [In keeping with this, I would like to remind commenters to keep the discussion constructive, polite, and on-topic.]
[Update, Oct 22: Unfortunately, some of the more recent comments have not been as constructive, polite, and on-topic as I would have hoped. I am therefore closing this post to further comments, though anyone who wishes to discuss these issues on their own blog is welcome to leave a pingback to this post here.]
I usually try to keep political issues out of this blog, and I certainly try to avoid asking friends and readers of this blog for favours, but there is an urgent situation developing in mathematics (and related disciplines) in my home country of Australia, and I need to ask all of you for assistance to prevent an impending disaster.
When I was an undergraduate at Flinders University in South Australia from 1989 to 1992, the level of mathematics education in Australia was comparable to that of world-class institutions overseas. Even in a small and little-known university such as Flinders, I received a first-rate honours undergraduate education in mathematics, computer science, and physics which I continue to use daily in my career. (Examples of topics I learned as an undergraduate include wavelets; information theory; Lie algebras; differential geometry; nonlinear PDE; quantum mechanics; statistical mechanics; and harmonic analysis. I rely on my knowledge of all of these topics today, for instance many of them are are helpful for me in teaching my current class on the Poincaré conjecture.) In addition, several of the faculty (including the chair and my undergraduate advisor, Garth Gaudry) had the time to spare an hour a week with me to discuss mathematics, as they were not overloaded with large teaching loads and other duties. I honestly think that I would not be where I am today without the high-quality undergraduate education that I received (in particular, I would definitely have floundered in graduate school at Princeton, if I were admitted at all).
The situation for mathematics education in Australia began however to deteriorate in later years, due to a combination of factors including government neglect (the federal government is the most significant source of funding for most universities in Australia) and the low priority of basic education in mathematics and sciences among university administrators. In particular, at Flinders University, the School of Mathematics suffered severe attrition due to lack of support and was eventually folded into the School of Informatics and Engineering. In fact the number of mathematicians on the faculty at Flinders has dwindled down to just three (in my day it was close to 20).
The decline of mathematics departments across the country, particularly in a time in which mathematics skills are desperately needed in the workforce, has been documented thoroughly in the 2006 national strategic review of the mathematical sciences. In response to that report, the federal government in 2007 announced an increase in the funding allocation to universities based on their student enrollments in key majors including mathematics and the sciences. The newly elected federal government is also likely to continue and extend this support in its upcoming budget in May of this year.
Unfortunately, it appears that at many universities, the additional funding was diverted away from the schools that it was intended to support, for the administrator’s own priorities. (See also the letter by the international authors of the above mentioned review, Jean-Pierre Bourguignon, Brenda Dietrich, and Iain Johnstone, condemning this diversion.) As a consequence, many mathematics departments are in fact in worse shape than before.
There is a particular crisis unfolding at the University of Southern Queensland. On March 17, the university announced a rationalisation and restructuring proposal that would cut the number of mathematics faculty from 14 to 6, eliminate the majors in mathematics, chemistry, physics, and statistics, and phase out all non-service courses (for instance, any of the types of courses I mentioned above at Flinders would be lost). Similar cuts were also proposed in statistics, computer science, and physics, although other schools retained their funding and some even obtained increases. This is despite the increases in funding from the federal government for mathematics and statistics students (enrollments in these areas at USQ has held steady so far, though of course with the proposed cuts this is unlikely to last). Already as a consequence of these proposals, initiatives of the department such as an education program for high school mathematics teachers have had to be scrapped. Somewhat ironically, the Dean of Sciences at USQ, Janet Verbyla, who has been heavily involved in proposing the cuts, had also presided over similar reductions in the school of mathematics at Flinders.
If the proposed cuts at USQ go ahead, it is likely that other small universities in Australia will be tempted to similarly ignore concerns about mathematics and science education and perform similar cuts, even while receiving government support for these disciplines. (The University of New England, which currently shares some statistics courses at USQ, would for instance be particularly vulnerable.) So the crisis here is not purely localised to USQ, but could be very damaging for mathematics and sciences in Australia as a whole.
The consultation period for these cuts ends very soon, on April 14, and the vice-chancellor of USQ, Bill Lovegrove, plans to announce the specific cuts on April 18 at an unspecified future date. While there has been some media attention in Australia given to this issue, it has not yet had much effect in reversing the decisions of these administrators. Because of this, I am reluctantly turning to my friends and readers of this blog to ask for your urgent assistance in saving the school of mathematics and computing at USQ. In collaboration with several good friends and colleagues in Australia, I have begun a web page on this blog,
https://terrytao.wordpress.com/support-usq-maths/
that is documenting the situation and outlining ways to help, including an online petition
https://terrytao.wordpress.com/about/petition-to-support-maths-statistics-and-computing-at-usq/
that you can sign to show support, and people to contact in the university administration and in the Australian government to express your concerns, or to express support for mathematics and its role in the sciences. Please also inform others, especially those in Australia and who may have influence in media, political, or administrative circles, of the current crisis. There is still time, especially in view of the expected increase in support for mathematics and sciences in the upcoming federal budget, to reverse the situation before the damage becomes permanent, and to show that the political support for mathematics education is not so negligible as to be easily ignored.
Thank you all in advance for any help you can give – and I promise that I will keep the remainder of my blog on topic and focus primarily on mathematics. :-)
[Update, April 9: See my editorial at the Funneled Web, “Mathematics in Today’s world“, for a more detailed discussion of the USQ crisis, and also the broader context of the importance of higher mathematics education, and the pivotal role universities have to play in providing it.]
[Update, April 12: The Toowoomba Chronicle has a two-page article by Merryl Miller focusing on the crisis, and in particular focusing on its impact on a 10-year old child prodigy, Adam Walsh, currently taking maths classes at USQ. (Reprinted with permission.)]
[Update, April 14: The petition has been formally sent to the USQ administration. Apparently, the previously planned announcement of the cuts on April
18 has been delayed to some unspecified later date, but no further details are currently available.]
[Update, April 17: In response to the concerns of constituents, Hon. Mike Horan MP, the state member for Toowoomba South, spoke in the Queensland parliament urging the University of Southern Queensland to reconsider its cutbacks to mathematics and statistics. (The full and official transcript of the day’s session in Parliament can be found here; the speech above is on page 1198.)]
[Update, April 29: The USQ administration released a revised draft proposal on April 22, but the details are largely unchanged (e.g. 11 staff cuts to the department of mathematics and computing instead of 12, and a “review” of the maths major and its courses rather than automatic elimination). The revised plan has already attracted criticism from the National Tertiary Education Union, and we are continuing to organise further opposition to the proposals. (For instance, László Lovász, President of the International Mathematical Union, wrote a letter of support on April 25.]
[Update, May 1. A second revised draft proposal has been released, which uses some new (but possibly non-permanent) sources of funding to add some specialised positions to partially offset the cuts (e.g. there will be 2-3 such positions in mathematics and statistics, although the 11 staff cuts are still in effect). The USQ administration has apparently also agreed to recheck the student load and financial data that is being used to underlie these proposals, as there appears to be some irregularities with this data in previous rationales.]
The newly elected Australian Prime Minister, Kevin Rudd, apologises to the “Stolen Generation” of indigenous Australians for past government policies.
This post will have only the most tangential connection to mathematics.
I am an Australian citizen (and permanent resident in the US), but I nevertheless take an interest in the upcoming US presidential election in 2008. I’ve recently learned of a grassroots campaign to have one of the presidential debates focused on policy issues in science, technology, health, and the environment. (See also this LA Times op-ed and Wall Street Journal op-ed.) Personally, I think this is an excellent idea, and hope that it succeeds; it seems that they are currently petitioning signatures towards this goal.
While on this topic, it is also interesting to see what the political prediction markets are currently forecasting as the outcome of the election…
[Via Bad Astronomy.]
[Update, Dec 20: Here is a table listing the major candidates and their positions on mostly science-related issues.]
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