“I am often asked if I am optimistic or pessimistic about the future. If I was optimistic, I might grow complacent and stop doing the work. If I was pessimistic, I might fall into despair and stop doing the work. The best thing to do is ignore the question and keep doing the work.” (To the best of my recollection)

E. F. Schumacher (To the best of my recollection. I think it was in his A Guide for the Perplexed)

Imagine us sitting on a mountainside. In the valley a mile below, a road climbs towards a low pass to the right. We see a car on the road. Its position is the first thing we notice. But as we watch, its position changes over time. It approaches a truck, also heading in the same direction, climbing towards the pass. We watch the car draw closer and closer behind the truck which means the car is moving faster than the truck. It is covering more feet per second (or miles per hour). There comes a time when the car becomes stuck behind the truck, forced to go its velocity. Having watched the car over this longer period, we know that even though the car’s position is still moving towards the right, its velocity is less than when we were first watching it.

The truck and car round a curve and a long straight section lies ahead of them. We see the car pull into the other lane and pass the truck. The gap between truck and car lengthens by the second. We know from experience that, as soon as the car had rounded the curve and the driver had seen the clear stretch ahead, the driver had  pressed down on the gas pedal and accelerated ahead, leaving the truck far behind.

We immediately see position. Given some time, we can develop a sense of velocity. Given more time, we can watch whether the velocity is changing and get a sense of acceleration. Mathematically, these relationships look like this:

POSITION
           Change in POSITION / Change in TIME = VELOCITY
                        Change in VELOCITY / Change in TIME = ACCELERATION

It’s like we start with position and then, underneath that, is velocity, and then underneath that, is acceleration. I think of position as dropping through time into velocity and then velocity dropping through time into acceleration. This forms an image I call the Cascade of Change.

Newton developed the calculus to explore the relationships between the different levels of this cascade. In his Laws of Motion, change requires a force and force is initiated at the underlying level of acceleration. F=ma. (Force equals mass times acceleration.) This is the level at which change is created.


Before going further, the reason I bring up Cascades of Change is because a time lag exists between each of the levels. I came to understand this when I was pondering my paradox of how the equinoxes can be the time of equal day and night while also being the time of greatest change in daylength.

To introduce this idea with my Chrysalis eighth graders, I made the following set of two graphs. They both share the same horizontal axis of Time (the weeks through the school year). The top graph shows the Daylength of each week’s Friday. The bottom graph shows Change in Daylength. For example, if Friday’s daylength was 9h 22m and the next Friday’s daylength was 9h 17m, then the change in daylength over that week is -5 minutes. The daylength is five minutes less than the week before.

I added the red lines and black labels to show how the midpoint in one graph coincides with an extreme on the other graph. Notice the consistent offset of the two graphs, how the bottom graph, Change in Daylength, leads the top graph, Daylength, by a quarter of the year. For example, the Change in Daylength graph bottoms out on September 21st (Fall Equinox) while the Daylength graph is just reaching the midpoint of its descent. When the Daylength graph finally bottoms out on December 21st (Winter Solstice), the Change in Daylength has risen to the 0 minutes of change line in the middle of the graph. This has to happen this way. After all, when you reach the shortest day of the year, the next day can’t be even shorter. The daylength has to start growing longer. The Change in Daylength has to shift from negative numbers (days growing shorter) to positive numbers (days growing longer). Therefore, the Change in Daylength graph has to pass through the 0 point on the shortest day of the year.


Time lags within the Cascade of Change are important to understand in order to navigate change in our world. For example, how does a Downward Spiral shift into an Upward Spiral? How does this change actually happen? Analyzing that helps sustain my hope during discouraging times. Imagine we are in a situation that is heading Downward at a faster and faster rate.

Then imagine that we start applying a Turning Upwards Force. It’s not very strong at first. Eventually, however, with allies emerging, it will become strong enough to turn the entire system onto an Upward direction but we don’t know that yet. All we see is the current situation growing worse and worse.

(A) Our Towards Upward force, beginning at A, is so weak that all it can do is barely reduce the rate at which the Downward Velocity is accelerating downward. That means that the Thermodynamic Velocity is still accelerating Downward, still going Downward at an ever-increasing, faster and faster rate. The system is losing Possibilities at an ever-faster rate. Our work appears to not be changing anything.

(B) The Towards Upward force grows strong enough now to slow the rate of Downwards acceleration to zero. That means that the Downward Thermodynamic Velocity is no longer increasing its Downward speed. Unfortunately, by this time, the Thermodynamic Velocity has reached a very fast Downward speed. On the graph, the velocity is no longer curving downward. It is going in a straight line at a steep downward angle. Again, we can easily feel like all of our work has been in vain. The situation is still deteriorating despite all our accumulated efforts. Much has been lost; look at how much lower B is than A.

From this point on, the Upward force is strong enough that the very fast Downward velocity begins slowing. It’s still heading Downward but at a less fast rate. Thermodynamic Velocity becomes Less Downward. It is shifting towards Upward. Graphically, the line will start pulling out of the dive.

 (C) As the rate of Towards Upward acceleration increases, the Thermodynamic Velocity flat lines, for a moment, heading neither up nor down.

(D) Finally the Thermodynamic Velocity becomes positive. The line on our graph heads Upward. This is the moment we’ve been working towards, the shifting of the system out of a Downward Spiral into an Upward Spiral.

Notice that the system is declining in Possibilities all the way from (A) to (C). Possibilities don’t start to increase until then. This can be very discouraging for those working to change our direction and preserve Possibilities. We work hard and everything is still falling apart. It’s hopeless. Why even try?

Because the work grows upon itself. As allies appear, we can accomplish more, but this process takes time. It is very easy to give up hope within this long, deteriorating situation. But when we work our way backwards through the sequence, we can see how each of the previous steps from (A) to (C) is a necessary part of the path we are trying to create. It’s just that the “improvement” first lies in slowing Downward. If one understands “Towards Upward” (the direction of our force as distinct from the direction of the velocity), decreasing the rate of decrease can inspire just as much hope as increasing the rate of increase. Decreasing the rate of decrease can open one’s eyes to lovely plays one would not see if one was only focused on increasing the rate of increase. Awareness of these plays nourishes hope when one might otherwise fall into despair.

However, this hope requires that we must accept that one’s efforts won’t create an instantaneous change in the world. The work takes time to grow on itself. This leads to another important conclusion: Do not wait until the last moment to start doing the work. There is a time lag between when the Towards Upward work starts and when the system finally turns Upward – as Donella Meadows was pointing out in the climate change essay Daniel responded to concerning leading causes and trailing effects.

This book is about changing the direction of our force to be Toward Upwards. Because both force and acceleration are vectors, changing the direction of our force creates a change in acceleration, even if there is no “speeding up” or “slowing down.” A change in acceleration over time creates an even lower level in the Cascade of Change. “Jerk is what physics calls this change in acceleration divided by the change in time needed for that change. It is called this because a sudden change in force/acceleration will cause a jerk, different than the unchanging, steady force of a subway smoothly accelerating from the station.

Two things determine the strength of the jerk in this situation. The first is the amount of change in direction of our force. The second is how quickly this change happens. Donella Meadows wrote a much-circulated article, “Leverage Points: Places to Intervene in a System”, (worth reading in its entirety) in which she lists and discusses twelve levels of leverage points from least effective to most powerful in changing a system. Two of her three most powerful are:

“3. The goals of the system.
2. The mindset or paradigm out of which the system — its goals, structure, rules, delays, parameters — arises.”

She describes this second most powerful leverage point of paradigm this way:

“The shared idea in the minds of society, the great big unstated assumptions — unstated because unnecessary to state; everyone already knows them — constitute that society’s paradigm, or deepest set of beliefs about how the world works.
There is a difference between nouns and verbs.
Money measures something real and has real meaning (therefore people who are paid less are literally worth less).
Growth is good.
Nature is a stock of resources to be converted to human purposes.
Evolution stopped with the emergence of Homo sapiens.
One can “own” land.

“Those are just a few of the paradigmatic assumptions of our current culture, all of which have utterly dumfounded other cultures, who thought them not the least bit obvious.

“Paradigms are the sources of systems. From them, from shared social agreements about the nature of reality, come system goals and information flows, feedbacks, stocks, flows and everything else about systems. …

“You could say paradigms are harder to change than anything else about a system, and therefore this item should be lowest on the list, not second-to-highest. But there’s nothing physical or expensive or even slow in the process of paradigm change. In a single individual it can happen in a millisecond. All it takes is a click in the mind, a falling of scales from eyes, a new way of seeing.”

Because a new way of seeing can happen in a millisecond (as happened to me with the rolling dancer and the Kiet Siel check dam), a significant change in direction divided by a tiny millisecond can mathematically produce an enormous, life-changing jerk.

The word, jerk, however, doesn’t sound appropriate for the process by which we re-align our force in the direction of increasing Possibilities. Jerk has a negative association such as “being jerked around” or being “dumped by a jerk”.  In the Fifth Dimension, the term “Intent” sounds more appropriate for this level below acceleration because it is our intent to realign our force Towards Upward that creates the jerk. So in this situation I will substitute “Intent” for “Jerk.”



What follows is a simplistic mathematical model to show this power of Intent. Despite the model’s naïve simplicity, it still reveals something important about this dynamic. (The model begins with zero as the value our acceleration, velocity, and position within the Fifth Dimension. The unit for time is undefined but is represented by each successive row in a spreadsheet. The spreadsheet begins with an intent to realign our force to more closely align with Towards Upward. I model that with a .5 value for Intent. After that, I scale Intent back to .01 for each time interval. That represents that within each time interval, we will detect some opportunity to redirect our force in some new way Upwards we had never noticed before. It might be something small, hence the low value of .01. I assume all the intents and accelerations happen uniformly through each time period.)

These assumptions create this graph:

The intent to re-align one’s force appears as a seemingly flat (except for the jerk at the beginning) blue line that is hard to distinguish from the horizontal axis of the graph. The intent is not a flat rise but it has a very small, seemingly insignificant rise. The change in the acceleration line also seems negligible. However, the level of Intent at the bottom of the Cascade of Change is powerful if it leads to a consistent change in how we direct our force. Change wells upward from that source. The velocity is increasing with a very slight upward curve over time. But the change in position – it increases Upward dramatically. This graph of the power of a shift in Intent matches my experiences with the rosy finch, the rolling dancer, the water splitting around the check dam. A sudden change in Intent can gradually lead one onto a whole new direction.

The lesson is to honor one’s intent by paying attention to all the little opportunities that present a chance to direct our force in a Towards Upward way. Our power lies in sustaining the change at the lower level of Intent. Never give up hope.

The change in the change in the change recedes into the future when going down four levels through the Cascade of Change from Position to Intent but blossoms when rising in the other direction, emerging from Intent. Time lags of cause and effect confuse us going down the cascade but can empower us as we rise upon our intent.

Intent is an ongoing feedback spiral – like balancing a pole. We have an image of what we would like to bring about with our life force. We apply our force. We watch what happens in response. We modify our force based on what happens which creates another change in the situation. We dance our lives with the world.




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