[PREV - TRACTATUS]    [TOP]

IMPOSSIBLE_GEOMETRIES

                                             August  7, 2022


Of late I've been playing around with collage off-and-on,
and after culling my old collection of "Otaku USA" magazines
I decided to do something with the anime illustrations.

Pretty frequently an anime review includes a large splash
page display showing the entire cast, frequently posed in a
radially-oriented design.  I clipped a number of these, and
started following a proceedure-- not always as rigidily as,
say, John Cage would, but I would at least start out trying
to stick to this:

   Choose three splash page images.

   Pick a focal point in the image.

   Slice them up into a few dozen wedges,
   like skinny pie-piece shapes with points
   at the focus.  Preserve the order of the
   pieces.

   Going clockwise, take the next piece in
   sequence from each of the three images,
   and glue it down into the collage.

   The initial idea was to:

      (1) line up the edge of each piece against
          the edge of the last, without overlap

      (2) position each of the points of the wedges
          against each other.


   Following these rules, you automatically get a new
   radially oriented image with a single focal point,
   like the original three images.

   The funny part: I kept envisioning I would be able
   to follow these rules and get *something else*, for
   example a swooping arc of the stacks of pieces, with
   the points making an arc instead of being in one
   coincident location.  Given the above rules, this is
   a complete, geometric impossibility, and I realized
   this pretty quickly-- and yet it kept hovering
   around in my thinking, I kept trying to find little
   cheats and variations that would get nearer to this
   impossibility.


And you would probably have to say that I'm someone
with a decent sense of spatial relations-- I often find
it frustrating talking to people who aren't that good
with this: they often imagine things will fit in places
they can't possibly, or that something will line-up
with something else that isn't there, and so on.

And one of the well-known purposes of engineering
design drawings is to use them as a tool to act as a
check on your own thinking: it's really easy to forget
you were planning on using a region of space for one
component and to think that you're going to be able
to fit a different piece in there.


From Wittgenstein's "Tractatus":
                                                     TRACTATUS
   "3.02 ... What is thinkable is also possible."
   "3.03  We cannot think anything unlogical ..."

That would be a "Uh... No."


These kind of sweeping statements about Thought
can usually only be salvaged by inventing a new
category, any mental process that doesn't fit
your definition isn't really "thought".

If you use a conventional meaning for "thought",
then anything flowing through your head would
count as one, even if you can sub-categorize
it as "dream", "fantasy" or "misconception"...




--------
[NEXT - MATHISM]