Trigger warnings and stacks

After publishing my last post, I remembered that some colleagues actually used to issue what were effectively trigger warnings when they talked about stacks, especially to audiences of number theorists.  Here is a quotation from the book Degenerations of Abelian Varieties by Faltings and Chai [my emphasis]:

Because their definition [of stacks] is somewhat technical, many people seem to be afraid of and do not like them.  But speaking from experience, the difficulty is purely psychological and can be overcome with time.

I believe the theory of trigger warnings presupposes that one is never completely free of the anxiety provoked by the trigger.   This would not be good news for number theorists, because stacks are now popping up all over the field, from Ngô’s proof of the fundamental lemma to the Emerton-Gee paper that I covered in my graduate course last year.  Fortunately, there are now many articles and a few celebrated websites that specialize in stack-anxiety therapy, and it has been years since I heard a trigger warning about stacks in a seminar talk.


7 thoughts on “Trigger warnings and stacks

  1. John Sidles

    In any social hierarchy, anxiety is more prevalent in the lower ranks than the higher ranks. Here is an anxiety-provoking remark by Shafarevich in the Introduction to Volume 1 of his “Basic Algebraic Geometry” (3rd edition, 2007):

    The student who wants to get through the technical material of algebraic geometry quickly and at full strength should perhaps turn to Hartshorne’s book; however, my experience is that some graduate students (by no means all) can work hard for a year or two on Chapters 2-3 of Hartshorne, and still know more-or-less nothing at the end of it.

    Context  Institutions like the US Marines deliberately and carefully adjust stress levels — beginning in boot camp and continuing at every rank — with a view to producing a maximally large proportion of maximally competent Marines.

    Discussions of the moral injuries associated to this process form a historical, sociological, biological, and medical literature that is large, growing, widely read, unflinchingly objective, and rigorously prescribed (see “ALMARS Active Number 001/13” for example) … to the great benefit of individual Marines of every rank, and the great benefit of the service as a whole. Much the same can be said of the medical professions.

    Conclusion  At present the STEM processions lag far behind the military and medical professions in their institutional appreciation and mitigation of mechanisms of moral injury. Among the top ranks, many individual STEM professionals accept this unbenign neglect; perhaps the accepting proportion is not as great among lower-rank STEM professionals and students. MWA can be read (by me anyway) as a work that at least begins to redress this imbalance … which is why I personally value MWA so highly. 🙂


    1. John Sidles

      The thought-provoking merit of the (above-mentioned) USMC Commandant’s Professional Reading List is illuminated by the following essay extracted from Victor Krulak’s First to Fight (). The word “mathematicians” has been substituted for the word “Marines”.

      MWA readers may wish to reflect, too, upon the parallel sentiments of Bill Thurston’s highest-rated answer to the MathOverflow question “What’s a mathematician to do?.” It’s notable that Krulak’s essay was written in 1957, Thurston’s in 2010; how is it that the Marines got there decades earlier?

      Why does the world need mathematicians?

      Mathematics exists today — flourishes today — not because of what we know we are, or what we know we can do, but because of what the world believes we are and believes we can do.

      Essentially, because of the unblemished achievements of mathematics over centuries, the world believes three things about mathematicians.

      First, they believe that when trouble comes to the world, there will be mathematicians — somewhere — who through hard work have made themselves ready to do something about it, and do it at once. They picture mathematicians as mature individuals — dedicated members of a serious professional community.

      Second, they believe that when mathematicians bend their minds to a task, they invariably turn in a performance that is dramatically and decisively successful — not most of the time, but always. The world’s faith and convictions in this regard are almost mystical. The mere association of the word “mathematics” to a challenge is an automatic source of encouragement and confidence everywhere.

      The third thing that they believe is that training in mathematics is downright good for young people; that mathematicians are the masters of an unfailing alchemy that helps convert unoriented youths into proud, self-reliant stable citizens — citizens into whose hands the planet’s affairs may safely be entrusted.

      The people believe these three things. They believe them deeply and honestly, so much that they are willing to pay for mathematicians to solve problems, and to teach young people.

      Therefore, for reasons that completely transcend cold logic, the world wants mathematicians. These reasons are strong, they are honest, they are deep-rooted, and they are above question or criticism. So long as they exist — so long as people are convinced that mathematicians can really do the three things I have mentioned — we are going to have a mathematical profession.

      And likewise, should people ever lose that conviction — as the result of the mathematics community’s failure to meet their high — almost spiritual — standards, the profession of mathematics will swiftly disappear.

      Is there a chance that such a thing might happen? I think there is. I think that we ourselves can shake these convictions and the accompanying faith which really sustain us. By a lack of attention we can lose the inspirational personal relation that is shared between our senior members and our rank-and-file. Also, by carelessness or inordinate attention to less important things, we can lose the attributes of professional dedication and unfailing preparedness which, in centuries past, has deservedly made mathematics one of humanity’s treasures.

      How serious it is, I don’t profess to estimate to you, but it certainly worries me. It does, because if the world wanted to try, she could get along without a profession of mathematics.

      How many graduate students in mathematics hope to cultivate, in themselves and in their profession, these same three virtues, which in Krulak’s phrase “completely transcend cold logic”?

      Similarly, the antiwar sentiments of mathematicians like Alexander Grothendieck are mirrored and deepened in unflinching strategic analyses like H. R McMaster’s Dereliction of Duty: Lyndon Johnson, Robert McNamara, the Joint Chiefs of Staff, and the Lies that Led to Vietnam (1997), and in personal memoirs like Karl Marlantes’ Matterhorn: a Novel of the Vietnam War (2010); the latter is consciously constructed as a homomorphism and extension of the narrative Perceval, le Conte du Graal (circa 1135); that is, the Grail Myth.

      Nowadays the flooding tide of literature relating to moral injury is challenging the military professions, this literature can be read as our century’s extension of the Grail Myth. A very considerable virtue of MWA (as I read it), which is a virtue that the Commandant’s Reading List possesses too, is to prepare and inspire young people to meet this challenge.


  2. John Sidles

    Victor Krulak’s 1957 letter, from which the above passage directly derives, appears as the Preface to Krulak’s First to Fight: An Inside View of the U.S. Marine Corps.

    Several other books that embrace grail themes more-or-less explicitly are:

    • Hermann Melville’s Moby Dick
       (Ishmael finds the Grail of grace, Ahab doesn’t)
    • Mark Twain’s Huckleberry Finn
       (Huck and Jim find it, the King and Duke don’t)
    • Rudyard Kipling’s Kim
       (Kim and his lama find it; everyone else glimpses it)
    • Robert Heinlein’s Double Star
       (Lawrence Smith first fakes it, then finds it)
    • Isaac Singer’s A Piece of Advice
       (an unnamed scholar first fakes it, then finds it)
    • Annie Proulx’ That Old Ace in the Hole
       (young Bob Dollar is blind to it, then sees it)
    • Dominique Eddé’s Kamal Jann
       (young Kamal Jann’s family is destroyed for lack of it)
    • Karl Marlantes’ Matterhorn: a novel of the Vietnam War
       (young Waino Mellas finds it, under difficult circumstances)
    • Sheri Snively’s (nonfiction) Heaven in the Midst of Hell: A Quaker Chaplain’s View of the War in Iraq
        (various young people find it, under difficult circumstances)
    • Nina Strohminger’s and Shaun Nichols’ (nonfiction) “Neurodegeneration and identity” (2015) can be read as a scientific study of it.
    • Peter Sterling’s and Simon Laughlin’ (nonfiction, PROSE-winning) Principles of neural design (2015) surveys the scientific foundations for it.

    Other examples will occur to MWA readers; in fact, a great virtue of MWA (as I read it) is the assistance and encouragement that it provides in learning to recognize and appreciate grail themes.

    Liked by 1 person


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