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Prover’s Block

December 16, 2014


What to do when afraid to see if what you want is true

BerglerFace
Cropped from Canadian Bergler Society source

Edmund Bergler coined the term in 1947, the great writers Francis Fitzgerald—F. Scott to most—and Joseph Conrad among many others suffered from it, as did the great cartoonist Charles Schulz. The problem is writer’s block.

Today Ken and I want to write about something that I wonder if any of you have ever had.

I will call it prover’s block. It is related to, but different from, writer’s block. Of course writer’s block is the condition that makes one unable to write, unable to create new sentences, unable to produce. It is the fear of the blank sheet of paper, which today is more likely the fear of that blank laptop screen in front of you.

There are many suggestions on how to overcome writer’s block. One I like is from the poet William Stafford who offered this advice to poets:

There is no such thing as writer’s block for writers whose standards are low enough.

The point is not to write garbage. The point is to write something: get started and be prepared to throw away lots, but write. Start getting your ideas down and trust that later, with much re-writing and edits, the writing will be okay. Of all the advice I find this one very useful. I certainly use it for GLL. I hope we do enough re-writes and edits so that most of what gets out is not garbage.

Prover’s Block

Some what is prover’s block? Let me explain in a personal way, since am just about over a bad case. I actually hope that writing this piece will help me overcome my block.

I have been working for a long time—let’s not say how long right now—to prove a certain Lemma X. I have thought at least a hundred times I had found a proof of X, but alas each time I started to work out the details the proof failed. After a while I began to doubt that X was true, but I really want X to be true. If it is true I will have proved something quite nice. No not that—not a “breakthrough”—but something that is still quite important.

A few weeks ago I looked at the statement of X from a new angle. How I missed this angle before who knows; somehow I did miss it. A quick rough check showed that this new approach should yield a proof of X. So I ran right off to the computer to write up the LaTeX version of the full details of the proof. Right.

No. I did nothing. I am afraid. I want this new approach to work so very much. I think it will. But the fear is as with all the previous ones this approach will collapse when I start hashing out all the details. This is prover’s block. I am stuck right here.

I have a great new approach to X, but am afraid to work out all the details. Perhaps this is one of the advantages of working with co-authors. On this one, however, I am alone.

Some Observations by Ken

Sometimes I, Ken writing now, find it helps even just to define a few new LaTeX macros in a document header to get rolling. A similar idea definitely works for “programmer’s block”: define a few routines to make the problem smaller.

The “{T^3}” typesetting program which I introduced to Oxford in 1985, and which is still going strong today as “Scientific Word,” had the philosophy that nothing is ever started from scratch. There was no “New Document” menu item—every document had to begin as a modification of another document. I still do that with many LaTeX documents, including solo posts for this blog.

Personality-wise I work better in the mode of modifying and extending over creating ex nihilo. It may not be simplistic to ascribe this trait to the ‘P’ versus ‘J’ component of the Myers-Briggs typology. The ‘P’ stands for “perceiving” but may as well stand for “perfectionistic” or “procrastinating,” whereas those with high ‘J’ (for “judging”) may align with those able to generate content quickly from scratch with less concern over errors or polish.

Specifically with regard to proofs, one thing I’ve noticed is in trying to prove a “simple” lemma on-the-fly while typing. Often the details mill around and cause backtracking to the extent that I’m not even sure the lemma is true anymore. I still find I need to sit with a notebook or sheets of paper to nail it down.

Open Problems

Is Lemma X proved by this new method? I, Dick, am about to find out. This has energized me to delve in to seeing if it works or not. The worst that can happen is I will have a new angle on X and potentially new ideas will emerge. The best that can happen is that I will finally prove X.

I will let you know. Thanks for listening.

17 Comments leave one →
  1. December 16, 2014 7:12 pm

    On this one, however, I am alone.

    so dramatic! and why is that? apparently by your choice dude! you mention one of the biggest available antidotes in the world to this problem (both general, and maybe specific) of yours. the internet! your blog is amazing but in some ways its amazing how little senior scientists use cyberspace. it seems from anecdotal observation the younger generation has a different mindset and does not have this problem. anyway, try stackexchange questions and/or chat rooms sometime which yet seem to hold a lot of untapped potential/ promise.

    its kind of funky/ mysterious the way you dont even hint at all at the background of your particular math problem. one would guess that youve probably alluded to it in one of your hundreds of blog posts somewhere, or maybe the last one.

    it would seem from your approach/ thoughts on this that maybe you just dont want to share any credit….? maybe a topic for a whole other blog? quite funky given that your blog generally emphasizes/ celebrates collaboration. but hey its your choice!

    • December 16, 2014 8:03 pm

      VZN, I haven’t even heard yet what “Lemma X” is about.🙂

    • December 17, 2014 12:11 am

      Fan Chung has a page on advice for young researchers. During the section strongly encouraging collaboration, she adds:
      “Pick a problem that you really wish that you alone can solve and then enjoy/endure the frustration in secret.”
      It’s probably faster and more fun to solve problems with others, there’s something very special about doing it yourself.

      • December 17, 2014 12:13 am

        Tricked by HTML frames — the link is here.

  2. December 16, 2014 8:24 pm

    Good luck!

    I tend to have prover’s block in the evening, especially when a collaborator is in town. We use it as an opportunity to celebrate the possibility of a nice proof with dinner and drink. Then we sort out the details in the morning over coffee. The sleep helps to clear my mind and calm any emotions. Of course, sleep probably wouldn’t suffice if the desired result is my own Moby-Dick lemma.

  3. December 16, 2014 9:24 pm

    Freud wrote about work inhibitions, in particular, writing inhibitions, as early as 1926.

    Analysis shows that when activities like playing the piano, writing, or even walking are subjected to neurotic inhibitions it is because the physical organs brought into play — the fingers or the legs — have become too strongly eroticized. …

    Freud, S. (1926), Hemmung, Symptom, und Angst. English (1927), Inhibitions, Symptoms, and Anxiety. Alix Strachey (trans., 1936).

    Then again, sometimes a laptop is just the top of your lap.

    • December 16, 2014 9:35 pm

      errotum → erotized

    • Javaid Aslam permalink
      December 17, 2014 3:47 pm

      The inhibition quite often is because of the pain that we foresee in going through the details. Whether it is theorem proving or writing an algorithm details ( a constructive proof), the emotions are very similar.
      I suppose we all have such inhibitions.

  4. December 17, 2014 5:50 am

    Your post with very few changes, can describe efficiently what we could call the “Programmer’s block”. When it happens to me, it feels like I am in node n1 of a graph and I want to find the path to node n2 while I don’t even know if the graph is connected and how many nodes there are in the graph.
    It helps sometimes to stop working on the problem for a while. When later you start again working, you looking at it from some distance at this helps you see many missing spots.

  5. GASARCH permalink
    December 17, 2014 11:42 am

    A few thoughts

    1) Read papers or books about your problem. The good news is that even if you don’t solve it you have leaned stuff. The bad news is you may end up knowing a lot, even getting out some surveys, but not solving your problem. I recently ended up emailing an author about a paper he wrote in 1972. While it was enlightening, at that point maybe you need to come back to the present.

    2) The web is certainly a good place to go for info. But you can (similar to point one above) end up learning a lot, which is great, but not getting your problem solved. And you can start out (say) looking up if there is an exact easy formula for the change-problem, and end up
    finding out all about different currencies in difference countries. The web can suck you in.

    3) Asking other people or post a question on my blog. Sometimes it gets answered. A few times I got no response so I then thought “okay, this is not a known problem” and just knowing that helped me focus on solving it since I knew it would be an original result.

    4) The shower principle- you may do your best thinking away from pencil, paper, and especially your computer.

  6. December 18, 2014 12:33 am

    Alas, but what Schulz said was that “writer’s block is for amateurs” … and even if you don’t have an idea you like, you just have to charge ahead and go with the best you can have. (This may explain a lot of late-80s strips that amounted to Sally or Peppermint Patty mispronouncing a word, getting corrected, and then saying ‘Whatever’, although the strip quietly got its groove back in the 90s.)

  7. December 18, 2014 4:08 pm

    Another theory of blocks, inhibitions, and obstructions would chalk them up to the Sisyphus Syndrome —

  8. Serge permalink
    December 18, 2014 5:14 pm

    I’d like to draw connections between quantum mechanics and computer science, so as to show that algorithms and problems follow some uncertainty principle, along with other computational analogues to quantum phenomena such as a probabilistic notion of truth and process speed. It would be nice if such stuff could be derived from quantum mechanics… if only I was able to state the sought principles rigorously! I must be suffering from a conjecturer’s block…

  9. December 19, 2014 8:00 am

    What is the clinical word for “What to do when afraid to see if what you want is true” syndrome?

  10. January 29, 2015 3:51 am

    Reblogged this on Pathological Handwaving.

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