The INTEGRITY PAPERS Mathematics Group ceptualinstitute.com
Dimensions & Boundaries
Recognizing potentials , Opening horizons"You see what you want to see, and you hear what you want to hear. Y' dig?"
The RockMan to Oblio, in Harry Nilsson's film "The Point" © 1968
Jean Piaget formally enunciated what every parent thoughout history already "knew" -- that young offspring (which each of us have been at one time) encounter the world and learn by interaction. Mentally and physically we experience and coordinate/re-coordinate experience. Reinforcing mental pathways, increasing neurological interconnections, synchronizing ever improving muscle coordinations with events and processes internal and external with our being. We integrate and symbionize - symphonize -- our dynamics with the world at large.
Energies transduced shared modeled and remembered, over and over again. Mutual support of co-existence enacted via shared dynamics, shared relational qualities.
It is all quite simple. We can sentiently juggle brainloads of memories ideas and knowledge, but in the quiet moments of crystal clarity, we can also pause to think on the elegant simplicity which the massive entwoven universe rests upon.
We experience first -- and now we take a moment to look and appreciate what we know.
As simple as a few dots on a sheet of paper, as a dot in the midst of a circle, as a chess knight surrounded by friends and foes, poised to moved. Symbols and actors on small terrains with obvious limits. Or are they so obvious? Or are the assumed? Tacitly, conventionally -- accepted? The paper ends-where-it-ends. The computer screen holds just so much and no more. The chess board has physicality, has size limitations, and then the world takes over beyond that.
But in our minds we know another truth. That we encounter but pieces of planes, of forms or space, that extend off in incredible distance in all directions. Infinite directions to be exact. So where are the bounds, "really"? Form and shape define some of them. We hold, we grasp, we encounter - sit on them, ride in them, wear them, chew them, stub against them, breathe them, sense them, drink them, embrace and cherish them, pleasure in them and pain in them. But. Where are the bounds, "really"? They are pauses, you see. Temporary place holders in space and time. True, they have utility and purpose. They indeed define and create the specifics of existence and being. A cup is a cup, not a coat. We are each the physicalness of our bodies. But we are infinite also. And so is the structure of Universe. It tells us so, shows us so, if we but listen, if we but look.
This way for example.
Nine dots on a flat surface. Three rows of three. A box of nine. A diamond quite possibly. A parallelogram. Rectangle. Square. Just dots on a sheet of paper. For ease of example, we keep the symmetry square. Now, connect the dots if you will. With just one restriction: only four straight lines are allowed.
Or this.
A sheet of paper. With a circle. With a dot in the middle. With the task: draw the dot-circle picture, without having the pen or pencil point leave the paper, and without erasing any intermediate lines.
Or this way, for fun.
In chess the queen is the "most powerful" piece. Yet the knight can do something no other piece can, even the queen. What is that? How can that be? What wisdom does that teach us about the structure of Universe?
Stay here for a while. Think about them and try them. Get paper and pencil and work the solutions. Then think about the solutions and the relationships they expose and rely on.
Tried them? Really thought about them for a while? Good. Now let's go talk.
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