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Numbers by the numbers: one

[ by Charles Cameron — numbers as analytic categories, one, self-reference ]

Is that a self-eating watermelon?

Not exactly. It’s the ourobouros, the serpent in many mythologies which eats its own tail…


The thing about one is that it’s itself: as the song says, One is one and all alone, and ever more shall be so.

One is itself, it is self-contained, sufficient — it refers only to itself.

And so it is that all things self-referential have a special quality to them. Douglas Hofstadter recognized this specialness of the self-referential, and made it a feature of his book Godel Escher Bach. And my point in writing this post is simply to say that whenever I as an analyst recognize a self-reference, I pay special attention.

And I am almost always rewarded, either by an aha!, a sigh, or a laugh…


So for the last two months, I’ve been quietly noting down every self-referential structure in my twitter-stream. Insights, jokes, regrets, they’re all here:

@BryanAlexander, 120508: The trick is to have 3d printers printing 3d printers
@BryanAlexander, 120508: 3d printers all the way down

@tejucole, 120508: Perfectly sane except for persistent paranoia about being sent to an asylum, Miron, 20, of Elizabeth, N.J., was sent to an asylum.

@GEsfandiari, 120509: Kafkaesque Iran where Khamenei’s Fatwa on Antifiltering is Filtered http://www.rferl.org/content/iran_filters_khamenei_fatwa_on_antifiltering_internet/24575143.html

@emptywheel, 120514: MEK, about to be rewarded for its assassination of Iranian scientists, AKA terrorism, by being delisted as terrorists. http://goo.gl/4833u

@carlacasilli, 120515: “By default, Brackets shows its own source code (MIND BLOWN).” How’s that for recursive?

@imothanaYemen, 120529: Paradoxically, I can’t watch @frontlinepbs on Al-Qaeda in Yemen live because I am in Yemen :). Trying to do something about that!

@shephardm, 120612: Think someone has new chapter…Man hitchhiking across US writing “The Kindness of America” hurt in a drive-by shooting

@JimmySky, 120615: #ff @DaveedGR, one of the world’s foremost authorities on foremost authorities.

@DaveedGR, 120707: Ironically, the Brown Lloyd James firm is now in need of its own Brown Lloyd James firm.

@holysmoke, 120709: I wish sarcastic Tweeters would stay classy and STOP SAYING ‘STAY CLASSY’.

@rwhe, 120712: Attention, comedians! How’s “How’s that workin’ out for ya?” workin’ out for ya?


Each of those very bright fellows noticed a self-reference and thought it noteworthy, worth tweeting on to their various followers. It was the shape they noticed, the form, the way what they were tweeting about turned back on itself, like that proverbial serpent eating its own tail.

And the same shape crops up in scripture and poetry:

Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men. Ephesians 4:8, KJV — the Vulgate has captivam duxit captivitatem.

One short sleep past, we wake eternally,
And death shall be no more; Death, thou shalt die! — John Donne, Holy Sonnets, X.


Self-reference is an important analytic signal: pay special attention. It doesn’t tell you what kind of attention, or why it might be important, just that there’s something worth looking at. A data point, possibly an anomaly.

That’s the number one thing to note.


I am eager to know what sorts of insights you can derive from or find echoed in this series of posts.

12 Responses to “Numbers by the numbers: one”

  1. Charles Cameron Says:

    A few hours after writing the above, I was listening to a tape a friend of mine, Michael Mendizza, made of a recent conversation with Samdhong Rinpoche, an international Buddhist and Gandhi scholar, advisor to the Dalai Lama, long-serving member of the Krishnamurti Foundation of India, and first Kalon Tripa or Chairman of the Cabinet of the Tibetan government-in-exile.  
    Rinpoche was discussing what he terms “the misconception” — the false, “self-centered” notion of one’s own identity which in his Buddhist understanding is considered “the real barrier for recognizing oneself or recognizing the other” — and remarked:

    It is very, very difficult to see the misconception. The misconception itself prevents you to seeing that misconception.

    He’s presenting the very kernel of the Buddhist critique of our characteristic human way of thinking about ourselves, and he does it via self-reference.
    This reminds me of Meister Eckhart, the Dominican mystic, who said:

    The eye with which I see God is the eye with which God sees me.

  2. Derek Robinson Says:

    I have noticed that there’s a funny kind of circular reasoning loop which prevents narrowly linear cause-effect thinking from perceiving circular causation. As Albrecht von Haller said, “Nature connects her genera in nets, not in chains, but we humans can follow only chains, since we cannot in speaking expound several things at once.”

  3. Cheryl Rofer Says:

    I’ll sing you one, O!
    Green grow the rushes, O!
    What is you one, O?
    One is one and all alone and ever more shall be so!

  4. Charles Cameron Says:

    Today’s offering: 

    What’s the best word to describe a lecturer lecturing about the death of lectures?

  5. Charles Cameron Says:

    And today’s:

  6. Charles Cameron Says:

    More self-referential ugliness, it would seem:

    The Chief of the Sexual Assault Prevention and Response branch of the U.S. Air Force was arrested and charged with sexual battery in Arlington over the weekend.

    Humans are very prone to this — see for instance the concept in Matthew 7.3:

    And why beholdest thou the mote that is in thy brother’s eye, but considerest not the beam that is in thine own eye?

    All too often there’s a feedback loop of some kind involved — we get angry in others at what all too precisely reminds us of ourselves. That’s pure self-reference, but distanced in an attempt to protect our own self-image.

  7. Curtis Gale Weeks Says:

    Charles, that last link has this sentence:


     “The victim fought the suspect off as he attempted to touch her again and alerted police.” 


    So “as he attempted to touch her again and alerted the police” might be an unintentional self-reference! (Meaning he failed the assault prevention portion but succeeded on the response portion of his duties!)       

  8. Charles Cameron Says:

    Curtis, you’re being too clever by half, I fear.  The crime report just needs better grammar.

  9. Curtis Gale Weeks Says:

    Charles, some of the examples above are a result of either hypocrisy or unintentional (unintended) irony. The hypocrisy or irony in those cases is a result of fallacy related to identity (“identity fallacy”?) whether this fallacy is believed by the individuals involved or else by witnesses commenting upon it or by us who are reading the commentary.


    In other words, the examples are not really much example of self-reflexivity, nor of ourobouros.  In fact, those “instances” of ourobouros could be said to be mere illusion. Granted I’m one all for stretching metaphors as needed — great utility can be had in the stretching — but it is also for this reason that I’m “being too clever by half.”

  10. Charles Cameron Says:

    Aha — I guess I think the illusion is as interesting (revealing) as the reality. And I’d agree that as phrased, the phrasing invites a reflexive meaning.

  11. Charles Cameron Says:

  12. Charles Cameron Says:

    Here’s a neat instance of the Chinese avoiding a self-referential problem, from ZP-friend TGreer:


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