Every entity/system/relationship, whether fleeting or enduring, vast or minuscule, is striving for two opposing achievements:
- Maintenance (Homeostasis: do not change.)
- Growth (Evolution: change for the better.)
Embodiment is the organization of physical energy, which, itself, can neither be created nor destroyed. Substance must be quantitatively maintained, even while growing in structural complexity. The system’s corporeal stability requires negative feedback.
Enmindedness is the organization of metaphysical constructs. By memorizing what is meaningful, the metaphysical consciousness grows, which, in turn, helps to maintain a substantial existence. The system’s expanding consciousness requires positive feedback.
According to John Briggs, author of The Patterns of Chaos:
Non-linear systems are so webbed with positive feedback that the slightest twitch anywhere may become amplified into an unexpected convulsion or transformation.
While chaotic systems amplify feedback [positive feedback] to transform themselves into new regimes, living systems use feedback to manage change and remain relatively stable [negative feedback].
The maintenance of the system’s corporeal OUTformation depends upon its consciousness and how it grows a memory for meaningful INformation, which can then insure its stability under increasingly broader circumstances.
Positive and Negative Feedback Systematically Combined
There is no quantitative limit on Objects of INformation; their number grows exponentially via positive feedback. Corporeality, however, derives from one Substance. Never can there be more or less of that one Substance; therefore, OUTformation of Objects is a multiplication by division, a process made obvious by fractals. Earth maintains homeostatic balance through negative feedback.
When combined, the positive and negative feedback systems do not cancel to neutrality, or to a null-effect, as would a +1 and a -1, if they were to be combined. Rather than negating one another, maintenance and growth complement each other.
Within the ‘golden’ rectangle below is a logarithmic spiral. The arc angle of the spiral never changes, even as the squares grow/change/open-outwardly.
The proportions of the entire horizontal rectangle above are equivalent to the smaller vertically oriented rectangle within it (to the right of the leftmost and largest square). Inside that vertical rectangle, there is a large square at the base and another even smaller rectangle above it. This even smaller rectangle shares the same proportion possessed by the larger ones. This process can be repeated a few more times: detecting the squares and rectangles within each rectangle as the areas shrink and the spiral tightens inwardly.
For this pattern to hold, the sides of the rectangles must be in a special or golden ratio: either .618 to 1 or 1 to 1.618. Only these numbers facilitate the efficiency of fractality. As we divide the largest, exterior rectangle, the number of interior rectangles is multiplied.
Truncating the values to three decimal places, 1.618… and .618… are actually irrational numbers whose digits go on forever without repeating a pattern. These two numbers are the only pair of values that satisfy the requirement that they be both inverse of each other AND differ by the unitary value of one.
Why this is so significant is thoroughly explored in the big chapter, Quadernity’s Nature-Based Numberline and its asides.
Multiplying the two inverse numbers produce 1. Check this multiplication on your calculator! For more accuracy we round off the numbers at nine digits.
1.618033989 x .618033989 = 1
The same numbers differ by 1. Subtract the smaller from the larger to find their difference. You can do this in your head. 🙂
1.618033989 – .618033989 = 1
Whereas exponential growth, driven by positive feedback, would eventually become unmanageable, the restrictive parameters of negative feedback effectively slow growth for the sake of sustainability and possible evolution.
The creature called nautilus wishes to retain its pattern even as it is growing. The cutaway of its shell in the set of illustrations below shows its close resemblance to a logarithmic spiral.
The pine cone is an example of efficient seed packing. The number of seeds that spiral clockwise and the number of seeds that spiral counter-clockwise are closely aligned to the golden proportion. Sunflowers are another familiar example of this kind of spiraling seed-packing.
Notice how the Romanesco broccoli depicted above grows while repeating the same pattern again and again.
As the final example given here, the following is an optional eleven-minute video excerpted from the Men’s Group Review, under Presentations, which discusses how negative feedback affects positive feedback. (The video does have a little blip where the recording stops briefly, but don’t give up on it as it will automatically resume in a couple seconds. Sorry that I have not yet learned how to fix this glitch. :-/ )
Balancing between growth (changing) and maintenance (not changing) is critically important to living organisms, as well as to organizations like businesses and cities and ecosystems.
When positive and negative feedback are in the perfect proportion there is a slow, steady and sustainable growth/evolution. Without the regulation of negative feedback, growth becomes unruly and the system eventually implodes.
In current day politics (early 2000s), there are those who wish to eliminate regulations that curtail growth, and those who believe that careful regulations are an imperative for sustaining life on planet Earth. Which side of the argument would you most likely support?