Replying to LO27720 --
Leo Minnigh offers:
> Smuts: (2 + 10) > 2 + 10
> (3 + 9) > 3 + 9
> (4 + 8) > 4 + 8
> (5 + 7) > 5 + 7
> (6 + 6) > 6 + 6
> Newton: 2 x 10 = 20
> 3 x 9 = 27
> 4 x 8 = 32
> 5 x 7 = 35
> 6 x 6 = 36
Judy Tal adds:
> Let me suggest another point of view (formula :o): suppose the ratio of
> the components to be constant - then by adding to one, you automatically
> change the other ... (this can be put nicely in a formula, making x times
> y to stay constant (C), and then looking at (x+t) and C/(x+t), but why
> bother?)
> now, this doesn't necessarily increase the sum, but still i would say that
> it makes the "whole" bigger than it's components' sum by "fraternity" -
> for good and worse.
Winfried Dressler introduces another "product":
> From this experience, the formula for wholeness is:
> (inside the circle + circle + outside the circle)
> (inside the square + square + outside the square)
> (inside the rectangle + rectangle + outside the rectangle)
> (plane + line)
> (plane + point)
> plane
Finally, Eric Sawyer chimes in:
> I think that this is the clue in fully understanding ( being able to
> describe) the whole. Heidegger describes things in terms of their
> relationships, and this seems to work. I.e. a hammer is an object used to
> drive nails. It is a a combination of head and handle, which when broken
> can still be defined as head and handle, but will not drive nails, so from
> this point of view is not a hammer...
What's especially interesting to me in all this, is to look for the
associative pattern (the "umlomo", introduced by At in LO17111 and
LO18276).
[Host's note: Those msgs are at...
http://www.learning-org.com/98.02/0327.html
http://www.learning-org.com/98.06/0040.html ..Rick]
I read Leo as saying (among other things) that the phrase "sum of its
parts" leads one to the wrong umlomo (addition), one that can't "deliver"
wholeness; he offers multiplication as an alternative. Judy suggests
"ratio" as an alternative.
Winfried changes the ground from arithmetic to planar geometry; here, it
seems, the line (thread) plays the part of the associator, demarcating the
inside (when there is one) from the outside and joining the two (sureness
and otherness). To me, this implies that the last element in his list,
the bare "plane", is much less whole for being undifferentiated. (It also
reminds me powerfully of the beginning of Spencer-Brown's Laws of Form:
"draw a distinction; call it the first distinction".)
Eric, then, brings us back to more practical wholes and not-wholes. (Is a
person who's not allowed to exercise his/her creativity still a person?)
At, now that we've done some associativity, how about some words on
monadicity: when is an organization a monad? when is a community of
practice a monad? I'd give it a try, but it's been 20+ years since I
studied Montague's logic, and even more since my brief brush with Leibniz.
Thanks to Leo, for brewing this storm, and to "all y'all" for making it
even more intense.
--Don Dwiggins "Solvitur Ambulando" d.l.dwiggins@computer.org
Learning-org -- Hosted by Rick Karash <Richard@Karash.com> Public Dialog on Learning Organizations -- <http://www.learning-org.com>
"Learning-org" and the format of our message identifiers (LO1234, etc.) are trademarks of Richard Karash.