<p>In the past you started out with points; points went to lines; lines swept a surface in two dimensional forms. When you went to three dimensional forms the first form was a sphere, because that's the simplest; then from a sphere [you can make a hole in a sphere and stretch the sphere out (as far as topology is concerned, you're allowed to stretch everything)] you went to a donut; a donut to be a donut had to have a hole in the middle, and you could stretch it as much as you wanted but it still had a hole in it.</p>
<p>The klein form is different. There's no inside; there's no outside. Instead you have a contained tube and an uncontained tube, a contained hole and an uncontained hole from which you can make interlocking klein forms in a chain ... Any part of the form can touch, contact, communicate with, flow with any other part, and the parts, the whole, in time flow through each other in a way the donut and sphere cannot. We have a quality of continuousness in the form and at the same time intracontainment or infolding; we have intrinsic to the form identifiable relationships that are not diadic (inside, outside) but are always at least triadic (context). There is no central governance or cooperative communication. There is enormous variation — the basic structure is so informationally rich that no two systems are sufficiently similar to value a same "thing" at the same time — indeed there are no "things" except as special cases.</p>
<p>The beauty about the klein form is that for the first time you are not captured by spheres or donuts, You can talk about a jet of air that goes up through the part of the klein form that is in contact with the external environment (where it is uncontained) and then becomes contained within itself and continues. For the first time you have a form which allows you to talk about something contained within itself ... if I put my hand on my knee it forms a kind of hole where the "outside" is in complete contact with the arm and where the energy from my hand goes back through my body and <em>alters</em> what happens "outside" again as it passes from within my body down through my shoulder ... I start to have a loop which is partly uncontained that is, really senses that which is outside itself, and partly contained, that is, it senses itself wilhin itself. It is a form that begins to have the capacity to know about its own behavior as it behaves "outside," that is, in simple connection with the environment, and as it behaves "inside," as informational representation to the environment within itself.</p>
<p>Paul spoke of how the klein worm has a capacity for anticipation and wc find that anticipation has meaning only if we are considering a time-form geometry, a
<p>Paul spoke of how the klein worm has a capacity for anticipation and we find that anticipation has meaning only if we are considering a time-form geometry, a
geometry of relations rather than things (no longer Newtonian geometry but an Einsteinian time-space form, a form that does not define time but is time that is
by definition) ... ("Taping something new with yourself is a part uncontained. To replay the tape for yourself is to contain it in your perceptual system ...")</p>
<p>When you model with a klein form you have to change your head around, because for the first time you can talk about time as influencing behavior. Consider the
Simon Browne
6 years ago