Numbers by the numbers: two

[ by Charles Cameron — numbers as analytic categories, two, the duel and the duet ]

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Charles Darwin once said of his fellow species biologists:

Those who make many species are the “splitters,” and those who make few are the “lumpers”.

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The diagram above represents a card-game I’ve played on occasion in my mind, asking myself the question: what is the opposite of one?

Two is the usual answer — and it’s interesting, you can get there from one two ways: by adding, or by dividing.

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The human mind very often thinks in binaries, we talk about us and them, friend and foe, the Allies and the Axis Powers, and even an eye for an eye and a tooth for a tooth – our ideas of warfare, contest and justice alike are predicated on the number two.

As I said in my intro post, one is a single data point, perhaps an anomaly: two is a duel or a duet, an opposition or a trend.

So we don’t always have to think of us and them — we could also think about me and mine, you and yours, two heads are better than one…

And what if you can “turn” your enemy? Then the duel turns into a duet.

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The duel is all about two competing, contending, fighting, agonizing to see who shall be the one. It is arguably the most basic form of combat, the simplest, and possibly the most profound. It can be close to symmetric — “they were perfectly matched” — or the very essence of asymmetric — David and Goliath.

The duet is about two collaborating, counterpointing, harmonizing — seeing how, together, they are one…

War-fighting and music-making, war and peace, regiment and free form, the march and the dance…

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

12 comments on this post.
  1. Scott:

    Curious how you will deal with numbers above three, since in some cultures there is no number above that, just many…

  2. J. Scott Shipman:

    Hi Charles, 
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    Love this line: “Then the duel turns into a duet.”

  3. Kurt:

    The “duel” can also be observed as a “unity of opposites.” This is where opposite entities unite in purpose or relationship. This was also taken up by Hegel, and I suspect that Clausewitz pondered this paradox with his center of gravity analogy. Also look to Rene Girard for his descriptions of “two” becoming one that leads to cycles of violence.

  4. Charles Cameron:

    Scott:
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    I think that above three, a few different thinks happen.  One that I can foresee is that even numbers reduce down to half values, and perhaps all non-primes do the same, so that for practical purposes, only the primes would continue in the series. Another is that somewhere above three and before eleven there’s a point — Miller’s “magical number seven, plus or minus two” where the human mind can’t hold any more detail, so that’s a cut-off of sorts.  Perhaps that’s somehow equivalent to calling for a new mode of cognizing.  And then I think there are other sorts of numbers we could consider, fuzzy numbers like umpteen, plenty-six and so forth.  But we’ll see…
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    J Scott:

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    Thanks!  And yes, I love the “duel duet” binary, it’s just so simple & elegant!
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    Kurt:
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    Terrific.  Yes.  I want to make a quick study one of these days of coincidentia oppositorum in Giordano Bruno and Vico, and Jung’s complexio oppositorum.  I’ll probably return to twoness in a later post, and hopefully get into more depth, and will certainly welcome your own insights.  Threeness, too, beckons, with Boole, Clausewitz again, and CS Peirce among the notables to be attended to.
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    You’ve probably seen the slomo videos of argumentative conversations, which make it pretty clear that there’s a sort of dance going on, each party showing by micro-gestures just when they’re ready to interrupt and be interrupted… and I tend to think a lot of victimizer / victim situations could be usefully analyzed in terms of the tango, with its extraordinary parallelism carrying through even to the moment at the end of a long, what should I call it, glide? when there’s that sudden dip, or that peeling apart to arm’s length with sudden close return?
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    For the general delectation:
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    http://www.youtube.com/watch?v=in5EPHVgcXg  

  5. Derek Robinson:

    For my money (of which there is none, or very close ;- ) the opposite of one is one, or if you like, 1/1. The number one is a mirror – every rational value above one is mirrored between zero and one, as its reciprocal. One is self-dual, it is the mirrorrim.

  6. Derek Robinson:

    (o yuck, the winking emoticon becomes a smiley-face cartoon, ewww!)

  7. Derek Robinson:

    Or one could say the opposite of one is another one…
     

  8. Charles Cameron:

    I’ve given you your winking emoticon back, Derek.
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    And with your reciprocal, 1/1, you’ve given us one as Janus, right? 
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    So I think we’re back at two!

  9. Cheryl Rofer:

    I’ll sing you two, O!
    Green grow the rushes, O!
    What is you, two, O?
    Two, two, lily-white boys, clothed all in green, O!
    One is one and all alone, and ever more shall be so!

  10. larrydunbar:

    For me this is a timely post. I have been doing a lot of thinking about the Higg’s Bosom discovery, and have assigned it a one and, in a binary fashion, have given Einstein’s equation E=mc^2 the number zero, and have said that it is the opposite of 1.

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    “While E=mc^2 (energy as an area at the speed of light with no mass [or at least mass is all-inclusive]), the field represented by the Higgs boson is expressed as 1 (Hb=1).”  http://larrydunbar.com/2012/07/14/higgs-bosom/ 

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    So when a nuclear bomb goes off at 100% efficiency (100% the speed of light), what you end up with is zero. This is just the opposite of a Higg’s Bosom field, which, in my estimation, is, for the lack of a better word, mass forming. 

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    So there is just as much force in a zero as there is in a one, which, directional wise, makes zero the opposite of one.

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    On the other hand, as mass only displaces itself, in the direction it is able, and not in the direction of force, the opposite of one is probably two–as the opposite of love is not hate, but, in the terms of Facebook, unsubscribe.

  11. Charles Cameron:

    Hi Cheryl:
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    I’ll sing you three, O! — but not yet, I have a couple of other posts in the works, and much other thinking to do.

  12. At the round earths imagin’d corners:

    […] I pointed out in a recent comment here, “somewhere above three and before eleven there’s a point — Miller’s […]