| The INTEGRITY PAPERS | Mathematics Group |
| Dimensions & Boundaries Recognizing unfenced potential |
"You see what you want to see, and you hear what you want to hear. Dig?"
The RockMan to Oblio, in Harry Nielsson's film "The Point" © 1968Nine 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.
The human mind is an extension and a tiered expression of the basic organizations of existence: wave functions. Patterns embellishing patterns. In neuro-science (the study of brain operations) one of those behavior patterns gets expressed as the phenomenon called "gestalt". Your visual architecture experiences and re-organizes floods of patterns in the world you see. Sometimes that energy intersperses and residual imagery arises out of nothingness. Sometimes the pulses of images and energies resonate inside and through brain cells and light which is no longer there interacts with new light and images. This is called "persistance of vision" . . . the phenomena by which we can see a stream of individual frames of movie film yet "experience" a smooth unbroken flow of activity.
Our minds smooth over and organize images, even pieces of images, into objects and forms that we co-experience with our other senses. The process helps us evaluate the world we are in, and even survive in it, drawing conclusions when only a smattering of information is available. In this case, that mental process is impacted by past experiences and "more often than not" conclusions. The nine orderly dots give the foremost impression of "square". We don't even 'think about it'. We just recognize it. An instantaneous 'gestalt' and 'most often the case' sense-of-it occurs. And, with it, the assumption that the virtual-square implies a limitation somehow.
So, when asked to connect the dots with only 4 straight lines, we can claim "impossible, you need 5 lines to connect them". Not so. You can do it by throwing off the shackles of implied limits -- limits not really there, just assumed, because it might once have been convenient to use them.
You stretch your mind and unleash your potential when you see beyond the norm. Time and Space literally open up for you and you recognize that there are new ways to link things together. Paths of connection. Opportunities. The structure of the universe is a blending of many infinities -- open spaces with alternative pathways to other open spaces. And if the number of locations is that open and infinite, how much greater are the alternative combinations of pathways that can link them?!
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.
Now, this one takes you a step further. To stretch your thinking in 3 rather than 2 dimensions of space. At some point in the future I'll have rendered diagrams or digital photos showing the process, but for now, grab pencil and paper and follow along with this description.
The key notion of the task is of course, 'without leaving the paper'. You comply with this by merely taking an edge of the paper and bring it curving over the front of the sheet until the edge rests down on the center of the pagefront. You draw a dot on the page front, just next to the edge of the folded paper , then immediately move the pencil point up onto the "back" of the page and out to where you want the circumference of the circle to be and come back down onto the front of the paper, completing the circle while unfolding the page. The scribing pen/pencil never leaves contact with the paper (or one of its six 'surfaces').
This quirky little problem - in all its gamey simplicity - has a lot to teach us about the universe and "dimensionality". Space has connectivity with all parts of itself, and we realize that there may always not be a rigid structure to it. There is "form", yes, but primarily there are multitudes of pathways for getting from one location to another. Convention and habit may keep us on familiar territory - like always writing on one surface of a sheet of paper - but other options and possibilities are available when we examine the total structure of something. Bending the sheet of paper is like finding an additional dimensional region through which we can travel from one place to another, no longer confined to a flat 2D surface. We see with a different perspective now. There are indeed other options for information or energy transcription.
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?
This is another version of the previous question. In chess the Knight cannot be hemmed in by surrounding it physically. It doesn't "slide" around the chess field. Instead it leaps into the third dimension to move around the board. The universe too uses all possible option-spaces in the transmission and transduction (coding/uncoding) of energy and information. All the geometry, trigonometry, integral calculus, vector/tensor mathematics, topology, quantum mechanical distribution probabilities, supersymmetry models, and everything else in that language of human comprehension, are merely ways of describing the relationships possible in all the dimensionality and time-spaces of existence.
And these are very real processes which we experience . . . light, heat, rooms and ladders,, word of mouth - the sharing and communicating of ideas,, information received by reading, by listening, by watching ,, transportation companies which get products to comsumers,, roadways and channels . . .
Paths and routes of Connectivity. Massive infinities intricately intimately convoluted with one another. Admittedly awe inspiring and a little overwhelming, but not incomprehensible. Information getting along with information. Systems built like holding-patterns, interacting with other systems, which, gather, have, hold, utilize, and transfer information and energy with each other all the time. Having capacities to encounter - and to successfully endure those encounters, no matter how infinitely variable.
What is "simple" can indeed have far reaching implications.
I throw this one in as a life-bonus for you. There was a creativity test given in some university psychology labs several years ago. It went like this. You are given a peg board with some metal posts, a battery, some wires, and a small light bulb in a socket, also, a screw driver and a pair of pliers. The task is to make the necessary connections and form a circuit that gets the light bulb to glow.
The problem was, there just wasn't enough wiring to complete the circuit. So, as predicted, a vast majority of testees did not complete the task. However. A small group of them did. How? By recognizing that an electrical circuit is completed by "metal", not just by metal "wiring". A few savvy thinkers picked up the pliers and spread them open so that the bottom tips of the handles were able to reach across the final span, completing the circuit. In other words, there may be options available to us in life that we just have to be open minded enough to recognize. Appreciate all the possibilities around us, not just typical ones. There are panoramas of alternative new connections - in time, in space, and in opportunity.
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