The Point of the Line Is Plane to See – What Geometry Teaches Us About Why We Cannot See the Abundance Right in Front of Us

If you have to choose between not having enough or having enough, of anything, you tend to choose having enough. And, yet, you often experience lack. If there is actually enough, as ecosynomics suggests, then why can’t we normally see it? Maybe geometry can give us a different angle on this question.

Let’s try a thought experiment, starting with a point. My world is completely contained within a point, like the period at the end of this sentence. Sometimes I experience a lack – I want more. What can I see? Since I cannot move anywhere, there is no dimension of space, and since I cannot move, I don’t experience change over time. No space and no time experienced. And I want more. From this perspective, what can I see? More points? Even if I could imagine another point, like the one I live in, I cannot see the line that connects the points, as I have never experienced movement from one point to another – there is only my point. That is the point.

Now, let’s assume that I live in the world of a line. There are many points to choose from, along the line. I experience moving along this line: I experience changes over space and time.   When I experience lack on the line, I can try different points. Sometimes that works. Sometimes I experience more at different points. And, sometimes I want more. What can I see from this perspective? More lines? While I might be able to imagine another line of points, I cannot see other lines on the planes that intersect to form my line. I cannot see to move to another line. I can only see the points on my line.

Finally, let’s assume that I live in the world of a plane. I can move in any direction along the plane. I can see different lines and different points, and I can choose which ones I want to visit. I can move through different possibilities of lines, and through time and space.

In the plane, I can see the lines and the points – I can move among possibilities, time, and space. In the line, I can only see the points on the line – I can move through time and space. In the point, I can only see my point – no time and no space.

A rough analogy from this thought experiment might shed some light on our question of seeing choices in enough. In a world focused solely on outcomes, I only look at what I have right here, right now. No movement in space or time. Like the world of the point. In a world focused on development and on outcomes, I look at what I am learning as I move through space and time, and at my outcomes. Movement in space and time, like the world of the line. In a world focused on possibility, development, and outcomes, I can see and choose to move among different possibilities of space and time. Movement in possibility, space, and time, like the world of the plane.

Following the analogy, if it seems useful to you, from the world focused solely on outcomes, I cannot see other points or lines. I am confined to the one point, and I would never see to think about development and possibility, as they are realities that exist in the worlds of lines and planes, not in my world of the point. Likewise, from the world of development and outcomes alone, I cannot see other possibilities, as they reside in the world of the plane, a world I would never imagine from the world of the line. And, from the world of possibility, development, and outcomes, I can see other lines and other points. I can choose the line of development and the point I want to achieve.

So, if the predominant “point” mentality of today keeps me from seeing the choices, then how do people ever see and make choices? Maybe it is because people experience the world of planes, the world of possibility, development, and outcomes, where choices are everywhere. The problem is in the thinking – they try to explain their experience of the world of planes through the description of the world of the point. While the potential creativity in the possibility realm of the plane is nice, it is not the point. It’s fluffy, not real, from the view of the point world. Likewise, while the capacity building, relationship building, and learning along the line can be beneficial and fun, it’s not the point. The real point is the outcome. How much you have in the point. Yet, from the point, you cannot see the line or plane. That is the point.

[A hat tip to Edwin A. Abbott whose Flatland: A Romance of Many Dimensions (Dover, 1992) looks at a similar perspective.]

Note: In Euclidean geometry, a point (0-dimensional) is the intersection of two (1-dimensional) lines.  A line (1-dimensional) is an infinite set of points, described by the intersection of two (2-dimensional) planes.

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One thought on “The Point of the Line Is Plane to See – What Geometry Teaches Us About Why We Cannot See the Abundance Right in Front of Us

  1. Pingback: Ecosynomics — The Study of Negative Deviance — An Alternate Framing « Jim Ritchie-Dunham

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