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Tuesday, 03 August 2010 16:56

Math Word Problems

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Years ago when first reading word problems in my math book I felt I was reading about things on another planet. They did not make any sense to me. Why on earth would anyone try to figure out answers to the questions that book was asking. I entertained my self by drawing pictures in the margins, pictures that had a relationship to where I was sitting. The wording of those questions was as strange as the thinking I was supposed to do to get the answers. They always seemed to have a number of different answers even though we were told there was only one right answer. That just didn’t fit my young life.

Now I know there are questions that are not questions at all; where there are no right answers other than the answers that make sense. Traditionally they are called parables. Why didn’t we have parables in my math book? Why aren’t there parables in math books today? Too many right answers I guess.

Here are two contributions for a math book, if anyone cares to use them. They are certainly something one can draw pictures to, even if you can’t come up with the right answers.

Problem #1

The square when resting had a dream of triangles, pentagons, hexagons, trapezoids, octagons, and circles. Upon awaking he was troubled finding this dream disturbing.

The triangle when resting had a dream of squares, pentagons, hexagons, rhomboids, octagons, and circles. Upon awaking the triangle was also troubled finding this dream disturbing, but not as much as the square.

The circle when resting had a dream of triangles and squares, pentagons, hexagons, and all manner of polygons. Upon awakening the circle had a slight bitterness at the delightful recollection of this dream.

The sphere dreaming of all those things, upon awaking did not know it, and so continued dreaming on.

Problem #2

A man comes from a sphere; he does not remember. He grows up on a sphere, surrounded by endless spheres of all different sizes. He looked around and it appeared to him flat. He holds a ball in his hands; bounces it on the “flat” to entertain himself, then for profit, and possibly for the enjoyment of others.

Another man comes from a sphere; he does not remember. He holds an imaginary sphere in his hands; no one can see it. He compressed the sphere into a circle and then sticking his head into the circle his mind was consumed knowing spherical reality.

Wednesday, 07 July 2010 16:33

Beyond Circle Is Circle

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Folding circles is not just about geometry, mathematics, education, patterns, information, transformation, beautiful forms, and interesting movement systems. These are simply what is generated by folding and joining circles. Beyond those benefits folding the circle provides a different way of thinking; to reevaluate what we think about the circle, and by extension everything else we think we know. There is no comfort here, growing pains are real. The choices we make are all we can claim to be our own.

With many thousands of years of accumulated knowledge all we can think to do is to destroy the planet to which we have been born, that sustains and nourishes us, and to destroy other life forms, and each other, by conscious design and willful acts of choosing selfishly to consume. From a cosmic perspective this is irrational, irresponsible and totally unacceptable human behavior. We consider ourselves the most intelligent creatures on the planet while collectively we appear to demonstrate the opposite. We have developed relatively high levels of technology without developing any moral responsibility in using it.

Every culture builds on experience of human needs in a local setting. We all access the same mind spirit filtered through local cultural habits. These habits of thinking distort and undermine individual experience. There is a great need to rethink those things we take for granted, that we accept without giving thought. Each culture defines life by its own boundaries for its own survival. Observable facts combined with multi-generational stories cause information fragmentation and global confusion with little understanding of where we are or for what purpose. Reading the genetic code is only a story about local events that stops just before now.

Changing how we think is similar to rearranging elements in an equation and keeping the two sides equal. Nothing changes except the arrangement of symbols. Many of us have e-mail but none of us have e-quality. E-mail is the easy way out of the hard issue of e-quality. If only one person is considered to be more, or less, than others, there is no equality. But equality is an imaginary issue; it only functions in virtual reality.

When holding a circle, it is the same for everyone, nothing more or less than a circle. No matter how many different reformations can be folded, the circle remains Whole. When ask to describe the circle, most people will talk about the image; it has a center, it is round, etc, etc. We are then confronted with reconciling what we have been taught and what we individually experience. So often we deny our experience to uphold the stories we have been told. The circle is our experience which far exceeds the simply stories we have been told about it.

We fight for cultural histories, stories that are in conflict with human values and moral development. We think our story is better just because we happened to be born locally, here or there. Well, we are all born locally, in the same way on the same planet in the same space that is so much larger now than it was when Buckminster Fuller called this planet “spaceship earth.” Years have passed and disorganized mutiny continues. We have not yet figured out who is in control or where we are going. Science does not know how to repair the ship. Too many religious maps get in the way of being able to agree on any one destination.

We seem to be lost in our own internal space, warring against each other for ownership without much thought of a cosmic navigator or moral mind that knows the territory. Maybe the fight is not so much about who gets control, but more about flight by those who do not want to participate as crew members to keep this “spaceship earth” in working order and in keeping to the course towards human potential with an eye towards spiritual birthright.

Within the circle every movement is different; there is no conflict. Everything is interrelated and works together in unity beyond the circle/sphere shape.

Animal fear response is no excuse for separation. Fear prevents us from finding value in differences, from learning math, from approaching the unknown; the “X” factor. Fear disturbs comfort, restricts interaction, reduces meaning and fails to accommodate progressive change. It prevents from and gives us opportunity to realize our better selves. Fear inhibits curiosity, diminishes the wonderment about the diversity of life. Overcoming fear does not happen in the abstract, it is the reality of our lives, the choices we make. To overcome limitations stimulates the mind, ennobles the heart, nourishes the soul, and delights and gives courage to the spirit.

We all come up against personal/collective origin. The biggest unknown is the idea of God. We understand the fact of our beginning, yet cannot explain it. We are a purposeful part of creation and there is no agreement as to why. The creator is always more; always embedded within creation. We all are created in the same way, nobody is special, but we are all a different and unique personality. What ever story we accept about origin gives meaning to our existence and has direct impact on the choices we make. The accumulation of facts weaves different cultural stories. It is insight to what happens between stories that tie the facts together making up the true reality of our lives.

Holding a paper circle is to experience unity. The triunity of the circle demonstrates an elegant truth in the simple beauty of absolute symmetry, where goodness of movement is reflected in human striving towards these eternal values. These are qualities reflected in the movement of the spherical creation and of “spaceship earth.” Busy with local self-interest and ownership we have paid little attention to where we are and where we are going.

Only unity can withstand endless differentiation of division and the appearance of separation. To take away is to pretend there is no unity. There is nothing to add to what is inclusively Whole. The circle is never less, it cannot be more. It should not be a surprise that within endless diversity of all things is unity, the foundational, structural connective. What we call God is the only a concept of absolute unity; larger than human mind, beyond human imagination, and personal context for both. Anything less than unity is not; anything more than unity never was. So here again we come up against origin and purpose.

There are no facts that give direction, no diagrams or numbered explanations. Where in our math education do we find what makes us a better person, giving us the experience to change the way we relate to the world; to think differently? What in the abstractions and constructed generalizations of the stories is there to change our thinking towards higher ideals, to ennoble individual growth, to support personal relationships and advance human civilization? The pursuit of mathematics has much value, but very little that nourishes the human soul or elevates understanding through recognition of living truth, responding to beauty, and doing good; bringing triunity to a higher level of experiential reality. The only choice we really have is giving to faith in finding that one story that individually only we can hear. And for some that story is mathematics, but that is not the Whole story.

Everybody folds the same circle, but creases a different diameter. In that first folding there is inherent value that provides opportunity to be mindful and to experience a different way to think about these things.