Let’s return to our elastic band, to our manual bifurcation. When we squeezed it and got a deflection, we can play with it further, for example, try to put pressure on the bulge.
Fig. 6. Longitudinal and transverse action on an elastic object
Our «antistress» with a certain effort will begin to flip in the opposite direction. If we draw a set of solutions to the equation in the parameter space: Deflection / Longitudinal pressure / Transverse pressure, then we will find a funny surface in it, similar to the assembly of a fabric. This surface is in a section of mathematics called Catastrophe Theory and is called Cusp catastrophe.
On this decision surface, we will see the buckling path under longitudinal pressure, which we have already seen in Fig. 5. To do this, it is enough to cut our Assembly with a vertical plane, for which the transverse pressure is equal to zero.
Fig. 7. Surface of the state of an elastic object. Buckling under longitudinal compression
The area of instability is represented by a triangular «tongue», indicated by a dotted line in the middle of the Cusp, where the system can get and stay in this state for some time, until any infinitely small impact throws it into one of the stability zones – a deflection in one direction or another.
We can also trace the trajectory of the state of the object under the influence of transverse pressure.
Fig. 8. Transverse route on the state surface. Memory effect
By itself, the understanding of a mathematical catastrophe, as a kind of map, a qualitative picture of the space of possible states, already allows us to understand a lot about the behavior of an object, to be prepared for surprises, and moreover, to use these properties. Despite the fact that our pictures of catastrophic behavior do not promise any quantitative accuracy, the operating point of the system, having fallen into the zone of instability, for example, does not know when and where it will leave it.
The transverse route – the transfer of such systems from one state to the opposite (the so-called hysteresis phenomenon) is used in many places, for example, in binary memory cells. And in order to use this memory, it turns out that it is necessary to control only one control parameter, which switches the cell.
Is a high-quality picture enough to expect and manage high-quality transitions in our systems, including business ones? We will see this below.
Beyond the boundaries
Beyond the boundaries of physics as an exact science, there are attempts to generalize the formation and self-organization of structures in open systems that are far from thermodynamic equilibrium. As conceived by its creator, Professor Hermann Haken, synergetics is an interdisciplinary direction that is called upon to play the role of a kind of metascience, noticing and studying the general nature of those patterns and dependencies that private sciences considered «their own».
«Synergetics (from other Greek prefixes «syn» with the meaning of compatibility and «ergon» – activity) – «together action».
«It should be emphasized that synergetics is by no means one of the frontier sciences such as physical chemistry or mathematical biology, emerging at the intersection of the two sciences.»
This is a fairly new area of science – there are still no clear boundaries, or even clear definitions of areas. The area of research in synergetics is not clearly defined and can hardly be limited, since its interests extend to all branches of natural science. A common feature is the consideration of the dynamics of any irreversible processes and the emergence of fundamental innovations.
Since there are no clear boundaries and definitions, there is an inevitable dispute in scientific and pseudo-scientific circles. Anyone is ready to declare himself a zealot of true metaknowledge, and to call everyone else pseudo-scientists, scholastics and charlatans.
I must say that this is a completely normal phenomenon for science. True Science differs from faith or ideology in that it itself calls into question all its achievements. Especially on the frontier of knowledge, that is, exactly where new knowledge about the self-organization of matter is being formed today.
Maybe our approach will be accused of being pseudo-scientific. Real academics are simply obliged to do this.
Truth, scientists say, is just the most appropriate concept to explain facts. I think this principle is good for business as well. Let’s test our theory with practice.
So, what do we get from the sciences at the start of the path? No strict laws, no numerical mathematical apparatus. The more complex and larger the system, the less numerical accuracy, the more qualitative considerations. Is this enough to put such knowledge into practice and apply it successfully?
Here we’ll see. What difference does it make whether it is physics or something else, as long as the conclusions work! That is, they would help us in business.
Chaos that creates
Progress
The evolution of matter today is already widely considered as part of a global synergetic process. And the emergence of life on the planet, and the origin of the mind, the evolution of conscious life – as part of the epic self-organization of matter.
The origin of life itself is still a big mystery. And we’re not going to solve it. But, since we live in this world, now we are concerned about another question – how to live? For us, it is only important that with the transition from inanimate nature to living nature, the essential feature of systems changes. Inanimate systems are passive systems. And self-organization arises only when the system is pumped with energy from outside. The water in the kettle starts to move (convection), and then boils just because we turned on the stove. Whirlwinds in the atmosphere – cyclones and tornadoes – are the result of its heating by the energy of the sun. If the energy supply is cut off, the systems will rush to an equilibrium state, any heterogeneity will sooner or later be resolved.
But living matter is a completely different matter, these are active systems. Which have their own behavior. And the behavior of living organisms is aimed at reaching the sources of energy necessary for life. Energies in a broad sense are both the heat of the sun for plants, and a nutrient medium, and other living beings that serve as food for a predator, and all kinds of resources necessary for a person to live.
With the transition of passive-to-active systems, the driving force of self-organization changes by 180 degrees. If for the passive it is an excess of energy, then for the active, the main reason is its lack, or, in other words, resource hunger. Indeed, living nature has the ability to reproduce, to produce its own kind. And, in combination with a purposeful movement towards the most favorable living conditions, this inevitably leads to the fact that living organisms, populations and societies always create redundancy. Which, in turn, causes intra- and interspecies struggle and, finally, competition. As a result, there is a resource hunger, which is characteristic of wildlife in all its manifestations. As the poet noted: «Sweet gingerbread is always not enough for everyone.»
This pressure of hunger forces any systems to undergo stages of self-organization, qualitative rebirth, it is hunger that constantly drives them to more and more complex